· web viewpupil book 1.1 (3-year scheme of work) the following scheme of work provides a...

PUPIL BOOK 1.1 (3-year scheme of work) The following scheme of work provides a suggestion for how Pupil Book 1.1 can be taught over the course of one year, as part of a 3-year Key Stage 3 course.Please note that you can recombine the test questions provided on Collins Connect to create new tests if your frequency of assessment differs from that below, or if you wish to combine content from different chapters in your own half-term tests.This scheme of work is provided in editable Word and Excel format on the CD-ROMaccompanying this Teacher Pack.

Chapter Lesson No.of hours

Learning objective Comments/ suggestions

Half-term / Term 11 Using numbers

1.1 The calendar

1 • To read and use calendars

Tables and charts appear all over in real life. It is important that pupils become confident in their ability to extract and use information from tables and charts in increasingly unfamiliar and complex situations.Money problems have to be dealt with daily in real life and pupils need to realise how important their ability to interpret these problemsand identify the mathematics involved is to their future financial wellbeing. This chapter provides plenty of financial skills (FS) questions for practice.Pupils often confuse the operation of addition and subtraction of negative numbers as numbers on a number line, especially as the sign is the same for both. Encourage pupils to visualise the number line when making calculations.

1.2 The 12-hour and 24-hour clocks

1 • To read and use 12- hour and 24-hour clocks

• To convert between the12-hour and 24-hour systems

1.3 Managing money

2 • To work out everyday money problems

1.4 Positive and negative numbers

1 • To use a number line to order positive and negative wholenumbers

• To solve problems involving negative temperatures

1.5 Adding negative numbers

1 • To carry out additions and subtractions involving negative numbers

• To use a number line to calculate with negative numbers

1.6 Subtracting negative numbers

1 • To carry out subtractions involving negative numbers

Problem solving– Where in theUK?

1 This activity is designed to use both the mathematical reasoning and problemsolving outcomes coveredin this chapter in a series of real-life problems.

2Sequences

2.1 Function machines

1 • To use function machines to generate inputs and outputs

The ability to generalise is crucial in a complex modern society. Being able to identify and generate number sequences is the first step towards progressing from the

2.2 Sequences and rules

2 • To recognise, describe and write down sequences that are based on a simple rule

Maths Frameworking 3rd edition 236 © HarperCollinsPublishers Ltd 2014Teacher Pack 1.1

2.3 Finding terms in patterns

1 • To find missing terms in a sequence

particular to the general inmathematics.

2.4 The square numbers

1 • To introduce the sequence of square numbers

2.5 The triangular numbers

1 • To introduce the sequence of triangular numbers

Mathematical reasoning – Valencia Planetarium

1 This is an opportunity to apply what pupils have learnt to a less familiar problem.

3 Perimeter and area

3.1 Length and perimeter

1 • To measure and draw lines

• To work out the perimeter of a shape

Measurement, perimeter and area are used widely in many jobs and professions, from farming to astronomy. Encourage pupils to talk to family and relatives to see if anyone uses these skills in their work or to explore specific jobs on the internet. A good example is the building industry, which is totally dependent onworkers being able to measure lengths and calculate areas.Pupils could also talk to family and relatives about how they might use area and perimeter in projects such as laying carpets and flooring, and decorating, to estimate how much carpet, flooring or wallpaper is needed.

3.2 Area 1 • To work out the area of a shape by counting squares

3.3 Perimeter and area of rectangles

1 • To work out the perimeter of a rectangle

• To work out the area of a rectangle

Problem solving– Design a bedroom

1 This activity is designed to show pupils an everyday situation that involves area and perimeter. Pupils are given practice in using their measuring, mathematical reasoning and problemsolving skills.

Chapter 1–3 assessment on Collins ConnectHalf-term

Half-term / Term 24 Decimal numbers

4.1 Multiplying and dividing by10, 100 and1000

1 • To multiply and divide decimal numbers by10, 100 and 1000

Pupils will be aware of decimals all around them, and should know that the decimal is used to separate: pounds from pence in prices; kilograms from grams in weights;

4.2 Ordering decimals

1 • To order decimal numbers according to size


4.3 Estimates 2 • To estimate calculations in order to spot possible errors

kilometres from metres indistances. Make sure they are aware of the impact of incorrect conversions. When solving money problems, pupils need to draw on their financial skills abilities.The zeros in decimals may cause confusion, for example, when comparing and ordering decimals. Provide pupils with plenty of practice in giving values to each digit.When asked to estimate an answer, pupils often think that the full calculation will be better. Pupils may also be unable to see how to simplify a calculation in order to complete it mentally. Provide plenty of practice.

4.4 Adding and subtracting decimals

1 • To add and subtract decimal numbers

4.5 Multiplying and dividing decimals

1 • To be able to multiply and divide decimal numbers by any whole number

Financial skills – Shopping for leisure

1 This activity is designed to apply the skills learnt in this chapter to a multi-step problem. The context may be familiar but pupils are unlikely to have engaged with it themselves.

5 Working with numbers

5.1 Square numbers

1 • To recognise and use square numbers up to225 (15 × 15)

The objectives in this chapter are probably some of the most widely-used objectives in terms of real- life application. It is important for pupils to build on their mental methods when developing written methods, so that they understand why they are doing this, and are not just applying a set of rules that they do not understand.Remind pupils that these objectives will be very useful in building confidence and fluency in applying their financial skills in the questions and in real life.

5.2 Rounding 1 • To round numbers to the nearest whole number, 10, 100 or1000

5.3 Order of operations

1 • To use the conventions of BIDMAS to carry out calculations

5.4 Long and short multiplication

2 • To choose a written method for multiplying two numbers together

• To use written methods to carry out multiplications accurately

5.5 Long and short division

2 • To choose a written method for dividing one number by another

• To use written methods to carry out divisions accurately


5.6 Calculations with measurements

1 • To convert between common metric units

• To use measurements in calculations

• To recognise and use appropriate metric units

Problem solving – Whatis your carbonfootprint?

2 This activity is designed to use theskills covered in this and earlier ‘number’ chapters to give a real-life context to mathematics.

6 Statistics 6.1 Mode, median and range

1 • To understand the meaning of mode, median and range

Pupils need to think about how we use statistics to model populations where it is difficult or in many cases impossible to gather all the population information.Pupils also need to consider how they could present this information.

6.2 Readingdata from tables and charts

1 • To read data from tables and charts

6.3 Using a tally chart

1 • To create and use a tally chart

6.Using data 1 • To understand how to use data

6.5 Grouped frequency

2 • To understand and use grouped frequency

6.6 Data collection

2 • To gain a greater understanding of data collection

Challenge – Trains in Europe

1 This activity is designed to use both the mathematical reasoning and problem solving outcomes covered in this chapter se in a situation that is familiar to pupils.Ask pupils to summarise what they have learnt in the chapter, as they will use much of this material to complete the activity.

Chapter 4–6 assessment on Collins ConnectHolidays

Half-term / Term 37 Algebra 7.1 Expressions

and substitution1 • To use algebra to write

simple expressions• To substitute numbers

into expressions to work out their value

In algebra, pupils often struggle to recognise that letters represent variables and that the answer can vary depending on the situation. Provide lots of opportunities for pupils to see this in action in familiar contexts such as ‘Think of a number’ word problems.

7.2 Simplifying expressions

2 • To learn the rules for simplifying expressions

7.3 Using formulae

2 • To use formulae


7.4 Writing formulae

1 • To write formulae To avoid serious confusion when multiplying brackets, make sure pupils understand that letter symbols used in algebra stand for unknown numbers or variables and not labels. For example, ‘5b cannot mean ‘5 bananas.

Problem solving–Winter sports

1 A common response to algebra is to ask how it can be used. This activity provides one of the everyday uses of algebra in terms of using a formula to work out costs.

8 Fractions 8.1 Equivalent fractions

1 • To find simple equivalent fractions

• To write fractions in their simplest form

Pupils are encouraged to think about and explore the fact that fractions as we know them did not exist in Europe until the 17th century. At first, fractions were not even thought of as numbers in their own right, simply as a means of comparing whole numbers with one another.When working with fractions, pupils are often aware of the role of the denominator when finding equivalent fractions but may fail to understand the role of the numerator. Working with visual images may help.

8.2 Comparing fractions

1 • To compare and order two fractions

8.3 Adding and subtracting fractions

2 • To add and subtract fractions with the same denominator

• To add and subtract fractions with different denominators

8.4 Mixed numbers and improper fractions

1 • To convert mixed numbers to improper fractions

• To convert improper fractions to mixed numbers

8.5 Calculations with mixed numbers

1 • To add and subtract simple mixed numbers with the same denominator

• To add and subtract simple mixed numbers with different denominators

Challenge – Fractional dissection

1 This activity explores partitioning in a familiar context, which is an important concept in understanding fractions. The tasks involve splittinga shape into unequal parts, which will help pupils’ understanding of the part– whole relationship between the numerator and denominator in fractions.


9 Angles 9.1 Using the compass to give directions

1 • To use a compass to give directions

In the real world, geometry is everywhere, for example, in buildings, planes, cars and maps, homes. Without an understanding of angles and their properties none of these structures would stay together. Show examples to the class.Another use of angles in real life is how we find our way around the world. Without a basic understanding of angles in terms of a measure of rotation we would not reach our destination.Pupils often do not appreciate the need for accuracy when measuring and drawing angles. Make sure that pupils are given plenty of practice in using a protractor accurately.

9.2 Measuring angles

1 • To know the different types of angles

• To use a protractor to measure an angle

9.3 Drawing angles

1 • To use a protractor to draw an angle

9.4 Calculating angles

1 • To calculate angles at a point

• To calculate angles on a line

• To calculate opposite angles

9.5 Properties of triangles and quadrilaterals

2 • To understand the properties of parallel, intersecting and perpendicular lines

• To understand and use the properties of triangles

• To understand and use the properties of quadrilaterals

Investigation – Snooker tables

1 This activity encourages pupils to think about how angles can affect a possibly familiar real-life situation – the way oneplays the game of snooker. Pupils may find it interesting to see how much mathematical calculation is involved in playing a good game.


Half-term / Term 410Coordinate s and graphs

10.1Coordinates and graphs

1 • To understand and use coordinates to locate points

The use of graphs to represent data is probably one of the most common uses of mathematics in the modern world. Pupils may be surrounded to such an extent by visual representations of data in the media, and become so used to it, that they no longer notice it. The

10.2 From mappings to graphs

1 • To work outcoordinates from a rule

• To draw a graph for a simple rule

10.3 Naming graphs

1 • To recognise and draw line graphs of fixed values


10.4 Graphs from the real world

1 • To learn how graphs can be used to represent real-life situations

• To draw and use real- life graphs

following website providessome interesting insights into the use of data in a modern society: http://www.gapminder.org

Challenge – Global warming

2 This activity is designed to apply pupils’ learning in a real-life topical situation.

11Percentage s

11.1 Fractions and percentages

1 • To understand what a percentage is

• To understand the equivalence between some simple fractions and percentages

Percentages are everywhere in real life. From bargains in the shops to taxes on payslips. It is important for pupils to becomfortable with calculating percentages if they are going to be functional in a modern society.

11.2 Fractions of a quantity

1 • To find a fraction of a quantity

11.3Percentages of a quantity

1 • To find a percentage of a quantity

11.4Percentages with a calculator

1 • To write a percentage as a decimal

• To use a calculator to find a percentage of a quantity

11.5Percentage increases and decreases

2 • To work out the result of a simple percentage change

Financial skills– Income tax

2 This activity is designed to use both the mathematical and transferable process skills covered in this chapter in a very important real-life context, which may be completely unfamiliar to pupils.

12Probability

12.1 Probability words

1 • To learn and use words about probability

Probability is an area of mathematics that pupils often find interesting but may be contrary to what seems right.

12.2 Probability scales

1 • To learn about and use probability scales from0 to 1

• To work out probabilities based on equally likely outcomes

12.3Experimental probability

2 • To learn about and understand experimental probability

• To understand the difference between theoretical probability and experimental probability


Financial skills– School EasterFayre

1 This activity combines pupils’ understanding of experimental and theoretical probability and applies it in a real-life context.


Half-term / Term 513Symmetry

13.1 Line symmetry

1 • To recognise shapes that have reflective symmetry

• To draw lines of symmetry on a shape

Symmetry is everywhere around us, both natural and human-made. Symmetry is probably one of the easier topics for pupils to see links to the real world, although some links may not be as obvious as others. This chapter provides many real- life examples, and each lesson has links to anumber of these.

13.2 Rotational symmetry

1 • To recognise shapes that have rotational symmetry

• To find the order of rotational symmetry for a shape

13.3 Reflections 1 • To understand how to reflect a shape

• To use a coordinate grid to reflect shapes

13. 4Tessellations

1 • To understand how to tessellate shapes

Activity – Landmark spotting

1 This activity is designed to show pupils some of the aspects of symmetry used in the real world, by examining the line symmetry of six famous landmarks.

14Equations

14.1 Finding unknown numbers

1 • To find missing numbers in simple calculations

The history of algebra goes back to ancient Egypt and Babylon. However, it is not just an ancient topic. Most of our modern society is dependent on the use of algebra. For more information search the internet for: ‘mathematician Andrew Wiles’ or ‘Fermat’s last theorem’.

14.2 Solving equations

1 • To understand what an equation is

• To solve equations involving one operation

14.3 Solving more complex equations

1 • To solve equations involving two operations

14.4 Setting up and solving equations

2 • To use algebra to set up and solve equations

Challenge – Number puzzles

1 In this activity pupils apply what they know to an abstract number problem. They need to identify and solve multi-step linear equations to solve the problem.


15Interpreting data

15.1 Pie charts 1 • To read data from pie charts, where the data is given in simple sectors

Statistical data is everywhere in a modern society and to function in this society it is important to be able to critically analyse the data being presented.

15.2 Comparing data by median and range

1 • To use the median and range to compare data

• To make sensible decisions by comparing the median and rangeof two sets of data

15.3 Statistical surveys

2 • To use charts and diagrams to interpret data

Challenge – Dancing competition

1 This activity is designed to use both the interpretation and communication skills covered in this chapter in a familiar scenario.


Half-term / Term 616 3Dshapes

16.1 3D shapes and nets

1 • To know how to count the faces, vertices and edges on a 3D shape

• To draw nets for 3Dshapes

There are only five regular3D shapes or (regular polyhedra) that can bemade using the sameregular polygon throughout. Problems can occur with the change of vocabulary between 2D and 3D, for example, sides become faces. Use visual images to support understanding and memory. The imprecise use of language in real life can also confuse pupils. Discuss examples of this.Also discuss the concept of subsets, for example, a cube is a regular cuboid. Identify this concept of subsets as beingapplicable across mathematics.

16.2 Using nets to construct 3D shapes

1 • To construct 3Dshapes from nets

16.3 3Dinvestigations

2 • To work out the rule connecting faces, edges and vertices of3D shapes

• To solve problems involving 3D shapes

Problem solving– Delivering packages

1 This is a common type of problem used at GCSE so it is important that pupils can identify this type of problem.

17 Ratio 17.1Introduction to ratios

1 • To introduce ratio notation

• To use ratios to compare quantities

Ratios are a very useful way to compare quantities without the distraction of the actual values. For example, saying that the diameter of Saturn is 1017.2 Simplifying

ratios1 • To write a ratio as

simply as possible


17.3 Ratios and sharing

1 • To use ratios to find missing quantities

times the diameter of theEarth (or the ratio is 10 : 1) provides an immediate mental image. This would not be as obvious just by quoting the diameters.

17.4 Ratios and fractions

1 • To understand the connection between fractions and ratios

Problem solving–Smoothie bar

1 This problem-solving activity is designed to reinforce the use of ratios by puttingratios in a realistic context.

Chapter 16–17 assessment on Collins Connect


PUPIL BOOK 1.2 (3-year scheme of work) The following scheme of work provides a suggestion for how Pupil Book 1.2 can be taught over the course of one year, as part of a 3-year Key Stage 3 course.Please note that you can recombine the test questions provided on Collins Connect to create new tests if your frequency of assessment differs from that below, or if you wish to combine content from different chapters in your own half-termly tests.This scheme of work is provided in editable Word and Excel format on the CD-ROMaccompanying this Teacher Pack.

Chapter Lesson No.of hours


Half-term / Term 11 Using numbers 1.1

Timetables, charts andmoney

1 To be familiar with everyday uses of tables and charts

To carry out calculations from information given in tables and charts

Tables and charts appeareverywhere in real life. It is important that pupils become confident in theirability to extract and use information from them in increasingly unfamiliarand complex situations.1.2 Positive

and negative numbers

1 To use a number line to order positive and negative numbers

To understand and use the symbols < (less than) and > (greater than)

1.3 Addingnegative numbers

2 To carry out additions and subtractions involving negative numbers

To use a number line to calculate with negative numbers

1.4Subtracting negative numbers

2 To carry out subtractions involving negative numbers

Travelling inAsia andEasternEurope

1 This activity is designed to use boththe mathematical and problem solving outcomes covered in thischapter in a very common real-life problem set in a slightly less familiarcontext.

2 Sequences 2.1 Functionmachines

1 To use function machines to generate inputs and outputs

The ability to generalise is crucial in acomplex modern society. Being able to identify and generate number sequences is the first step towards progressing from the particular to the general in mathematics.

2.2Sequences and rules

2 To recognise, describe and generate sequences that use a simple rule

2.3 Workingout missing terms

1 To find missing terms in a sequence

2.4 Othersequences

1 To know and understand the sequences of numbers known as the square numbers and thetriangular numbers

Mathematicalreasoning – Valencia Planetarium

1 This is an opportunity to apply whatpupils have learnt to a less familiar problem.

3 Perimeter,area and volume

3.1 Perimeterand area

1 To work out the perimeter of 2Dshapes.

To work out the area of 2Dshapes

3.2 Perimeterand area of rectangles

1 To use a simple formula to calculate the perimeter of arectangle

To use a simple formula to calculate the area of a rectangle


3.3 Perimeterand area of compoundshapes

1 To work out the perimeter and area of a compound shape

3.4 Volume ofcubes and cuboids

2 To work out the volume of a cube and cuboid, using a simple formula

To work out the capacity of a cube or cuboid

Problemsolving – Design a bedroom

1 To be able to multiply and divide decimal numbers by 10, 100and 1000

This activity is designed to showpupils an everyday situation that involves area and perimeter.

Chapter 1-3 assessment on Collins ConnectHalf-term

Half-term / Term 24 Decimalnumbers

4.1 Multiplyingand dividing by 10, 100and 1000

1 To be able to multiply and divide decimal numbers by 10, 100and 1000

Pupils often do not appreciate thereal purpose of estimation so when asked to estimate an answer theythink that if they give the full calculation that will be better. They also lack the ability to see how tosimplify a calculation so they can complete it mentally. Give pupils plenty of practice with mental calculation and opportunities toassess how best to approach different types of calculations.

4.2 Orderingdecimals

1 To be able to order decimal numbers according to size

4.3 Estimates 2 To estimate calculations in order to spot possible errors

4.4 Addingand subtractingdecimals

1 To be able to add and subtract with decimal numbers

4.5 Multiplyingand dividing decimals

1 To be able to multiply and divide decimal numbers by any wholenumber

Financial skills– Shopping for leisure

1 This activity is designed to apply theskills learnt in this chapter to a multi- step problem. The context may be familiar to learners but they are unlikely to have engaged with it themselves.

5 Working withnumbers

5.1 Squarenumbers and square roots

1 To recognise and use square numbers up to 225 (15 15)and the corresponding squareroots

5.2 Rounding 1 To round numbers to a given degree of accuracy

5.3 Order ofoperations

1 To use the conventions ofBIDMAS to carry out calculations

5.4 Long andshort multiplication

2 To choose a written method for multiplying two numberstogether

To use written methods to carry out multiplications accurately

5.5 Long andshort division

2 To choose a written method for dividing one number by another

To use written methods to carry out divisions accurately

5.6Calculations with measure-ments

1 To convert between common metric units

To use measurements in calculations

To recognise and use appropriate metric units

Problemsolving –

2 This activity is designed to use theskills covered in this and earlier


What is yourcarbon footprint?

‘number’ chapters to give a real-lifecontext to mathematics.

6 Statistics 6.1 Mode,median and range

1 To understand and calculate the mode, median and range ofdata

Pupils need to think about how weuse statistics to model populations where it is difficult or in many casesimpossible to gather all the population information.

6.2 The mean 1 To understand and calculate the mean average of data

6.3 Statisticaldiagrams

1 To be able to read and interpret different statistical diagrams

6.4 Collectingand using data

1 To create and use a tally chart

6.5 Groupedfrequency

2 To understand and use grouped frequencies

6.6 Datacollection

2 To develop greater understanding of data collection

Challenge –Schools sports day

1 This activity is designed to use boththe mathematical reasoning and problem solving outcomes covered in this chapter se in a situation that is familiar to pupils.

Chapter 4-6 assessment on Collins ConnectHolidays

Half-term / Term 37 Algebra 7.1

Expressions and substitution

1 To use algebra to write simple expressions

To substitute numbers into expressions to work out their value

7.2 Simplifyingexpressions

1 To learn the rules for simplifying expressions

7.3 Usingformulae

2 To use formulae

7.4 Writingformulae

2 To write formulae

Problemsolving – Winter sports

1 A common response to algebra is toask how it can be used. This activity provides one of the everyday uses of algebra in terms of using a formula to decide cost.

8 Fractions 8.1 Equivalentfractions

1 To find simple equivalent fractions

To write fractions in their simplest form

8.2Comparing fractions

1 To compare and order two fractions

8.3 Addingand subtractingfractions

2 To add and subtract fractions with the same denominator

To add and subtract fractions with different denominators

8.4 Mixednumbers and improperfractions

1 To convert mixed numbers to improper fractions

To convert improper fractions to mixed numbers

8.5 Addingand subtracting mixed numbers

1 To add and subtract simple mixed numbers with the same denominator

To add and subtract simple mixed numbers with different denominators


Fractionaldissection

1 This activity is designed to buildconfidence and fluency by allowing pupils to apply what they have learntto an interesting problem in an unfamiliar context.

9 Angles 9.1 Measuringand drawing angles

1 To use a protractor to measure an angle

To use a protractor to draw an angle

Pupils often do not appreciate theneed for accuracy when measuring and drawing angles. Relate this tothe contexts in the introduction to this chapter. Pupils need plenty ofpractice in using a protractor accurately.

9.2Calculating angles

1 To calculate angles at a point To calculate angles on a straight

line To calculate opposite angles

9.3 Angles ina triangle

1 To know that the sum of the angles in a triangle is 180°

9.4 Angles ina quadrilateral

1 To know that the sum of the angles in a quadrilateral is 360°

9.5 Properties of trianglesand quadrilaterals

2 To understand the properties of parallel, intersecting and perpendicular lines

To understand and use the properties of triangles

To understand and use the properties of quadrilaterals

Activity –Constructing triangles

1 This activity is designed to buildconfidence and fluency.


Half-term / Term 410 Coordinatesand graphs

10.1Coordinates

1 To understand and use coordinates to locate points in all four quadrants

10.2 Graphsfrom relationships

1 To draw a graph for a simple relationship

10.3 Graphsfor fixed values of x ory

1 To recognise and draw line graphs with fixed values of x and y

10.4 Graphsof the formy = ax

1 To recognise and draw lines of the form x = ax

10.5 Graphsof the formx + y = a

1 To recognise and draw graphs of the form x + y = a

10.6 Graphsfrom the real world

1 To learn how graphs can be used to represent real-life situations

To draw and use real-life graphsChallenge –Global warming

2 This activity is designed to applypupils learning in a real-life topical situation.

11 Percentages 11.1Fractions, decimals andpercentages

1 To understand the equivalence between a fraction, a decimal and a percentage

Percentages are everywhere in reallife. From bargains in the shops to taxes on payslips. It is important forpupils to be comfortable with calculating percentages if they are going to be functional in a modern society.

11.2 Fractionsof a quantity

1 To find a fraction of a quantity

11.3Percentages of a quantity

1 To find a percentage of a quantity


1 To use a calculator to find a percentage of a quantity

To know when it is appropriate to use a calculator


11.5Percentage increases anddecreases

2 To work out the result of a simple percentage change

Financial skills– Income tax

2 This activity is designed to use boththe mathematical and transferable process skills covered in this chapterin a very important real-life context that may be less familiar to them than might be expected.

12 Probability 12.1Probability words

1 To learn and use the correct words about probability

12.2Probability scales

1 To learn about and use probability scales from0 to 1

To work out probabilities based on equally likely outcomes


2 To understand experimental probability

To understand the difference between theoretical probability and experimental probability

Financial skills– SchoolEaster Fayre

1 This activity combines pupils’understanding of experimental and theoretical probability and applies it in a real-life context.

Chapter 10-12 assessment on Collins ConnectHolidays

Half-term / Term 513 Symmetry 13.1 Line

symmetry1 To recognise shapes with

reflective symmetry To draw lines of symmetry on a

shape13.2Rotational symmetry

1 To recognise shapes that have rotational symmetry

To find the order of rotational symmetry for a shape

13.3Reflections

1 To understand how to reflect a shape

To use coordinates to reflect shapes in all four quadrants

13. 4Tessellations

1 To understand how to tessellate shapes

Activity –Landmark spotting

1 This activity is designed to showpupils some of the aspects of symmetry used in the real world, by examining the line symmetry of sixfamous landmarks.

14 Equations 14.1 Findingunknown numbers

1 To find missing numbers in simple calculations

14.2 Solvingequations

1 To understand what an equation is

To solve equations involving one operation

14.3 Solvingmore complex equations

1 To solve equations involving two operations

14.4 Settingup and solving equations

2 To use algebra to set up and solve equations

Challenge –Number puzzles

1 In this activity pupils apply what theyknow to an abstract number problem. They need to identify and solve multi-step linear equations to solve the problem.

15 Interpretingdata

15.1 Piecharts

1 To read data from pie charts in which the data is given as percentages

Statistical data is everywhere in amodern society and to function in this society it is important to be able to


15.2Comparing mean andrange

1 To use the mean and range to compare data

To make sensible decisions by comparing the mean and range of two sets of data

critically analyse the data being presented.

15.3 Statisticalsurveys

2 To use charts and diagrams to interpret data

Challenge –Dancing competition

1 This activity is designed to use boththe interpretation and communication skills covered in this chapter in afamiliar scenario.


Half-term / Term 6

16 3D shapes 16.1 Namingand drawing3D shapes

1 To be familiar with the names of3D shapes and their properties

To use isometric paper to draw shapes made from cubes

16.2 Usingnets to construct 3D shapes

1 To draw nets of 3D shapes To construct 3D shapes from

nets


2 To make the connection between faces, edges andvertices of some 3D shapes

To solve problems involving 3Dshapes

Problemsolving – Packing boxes

1 This is a common type of problemused at GCSE so it is important that pupils can identify this type ofproblem.

17 Ratio 17.1Introduction to ratios

1 To use ratio notation To use ratio to compare

quantities17.2Simplifying ratios

1 To write a ratio as simply as possible

17.3 Ratiosand sharing

1 To use ratios to find totals or missing quantities

17.4 Solvingproblems

1 To understand the connections between fractions and ratios

To understand how ratios can be useful in everyday life

Problem solving –Smoothie bar

1 This problem-solving activity is designed to reinforce the use ofratios by putting ratios in a realistic context.

Chapter 16-17 assessment on Collins Connect

End of year assessment on Collins Connect


PUPIL BOOK 1.3 (3-year scheme of work) The following scheme of work provides a suggestion for how Pupil Book 1.3 can be taught over the course of one year, as part of a 3-year Key Stage 3 course.Please note that you can recombine the test questions provided on Collins Connect to create new tests if your frequency of assessment differs from that below, or if you wish to combine content from different chapters in your own half-termly tests.This scheme of work is provided in editable Word and Excel format on the CD-ROMaccompanying this Teacher Pack.

Chapter Lesson No. of hours


Half-term / Term 11 Using numbers

1.1 Charts and financial mathematics

1 To carry out calculations from information given in tables and charts

To understand and use financial language

Tables and charts appear everywhere in real life. It is important that pupils become confident in their ability to extract and use information from them in increasingly unfamiliar and complex situations.

1.2 Positive and negative numbers

1 To use a number line to order positive and negative numbers, including decimals

To understand and use the symbols < (less than) and > (greater than)

1.3 Simple arithmetic with negative numbers

2 To carry out additions and subtractions involving negative numbers

To use a number line to calculate with negative numbers

1.4 Subtracting negative numbers

1 To carry out subtractions involving negative numbers

1.5 Multiplying negative numbers

1 To carry out multiplications involving negative numbers

Travelling in Asia and Eastern Europe

1 This activity is designed to use both the mathematical and problemsolving outcomes covered in this chapter in a very common real-life problem set in a slightly less familiar context.

2 Sequences 2.1 Function machines

1 To use function machines to generate inputs and outputs

To use given inputs and outputs to work out a function

The ability to generalise is crucial in a complex modern society. Being able to identify and generate number sequences is the first step towards progressing from the particular to the general in mathematics.2.2 Sequences

and rules2 To recognise, describe and

generate sequences that follow a simple rule

2.3 Working out missing terms

1 To work out missing terms in a sequence

2.4 Working out the nth term

1 To work out the nth term To use the nth term to work

out any term in a sequence

2.5 Other sequences

1 To know and understand the square and triangular number sequences, the Fibonacci sequence and Pascal’s triangle

Mathematical reasoning – Valencia Planetarium

1 This is an opportunity for pupils to apply what they have learnt to a less familiar problem.


3 Perimeter, area and volume

3.1 Perimeter and area of rectangles

1 To use a simple formula to work out the perimeter of a rectangle

To use a simple formula to work out the area of a rectangle

3.2 Perimeter and area of compound shapes

1 To work out the perimeter and the area of a compoundshape

3.3 Area of some other 2D shapes

1 To work out the area of a triangle

To work out the area of a parallelogram

To work out the area of a trapezium

3.4 Surface area and volume of cubes and cuboids

2 To work out the surface area of cubes and cuboids

To work out the volume of cubes and cuboids

Problem solving– Design a bedroom

1 This activity is designed to show pupils an everyday situation that involves area and perimeter.


Half-term / Term 24 Decimal numbers

4.1 Multiplying and dividing by10, 100, 1000 and10 000

1 To be able to multiply and divide decimal numbers by 10,100, 1000 and 10 000

Pupils often do not appreciate the real purpose of estimation, so when asked to estimate an answer they think that if they give the full calculation that will be better. They also lack the ability to see how to simplify a calculation so they can complete it mentally. Give pupils plenty of practice with mental calculation and opportunities to assess how best to approach different types of calculations.

4.2 Ordering decimals

1 To be able to order decimal numbers according to size

4.3 Estimates 1 To estimate calculations in order to spot possible errors.

To round up or down, to one decimal place

4.4 Adding and subtracting decimals

1 To be able to add andsubtract with decimal numbers

4.5 Multiplying decimals

1 To be able to multiply decimal numbers

4.6 Dividing decimals

1 To be able to divide with decimals

Financial skills – Shopping for leisure

1 This activity is designed to apply the skills learnt in this chapter to a multi- step problem. The context may be familiar to learners but they are unlikely to have engaged with it themselves.

5 Working with numbers

5.1 Square numbers and square roots

1 To recognise and use square numbers up to 225 (15 15) and the corresponding square roots

5.2 Rounding 1 To round numbers to more than one decimal place (dp)

To round numbers to one or two significant figures (sf)

5.3 Order of operations

1 To use the conventions of BIDMAS to carry out calculations

5.4 Multiplication problems without a calculator

2 To use written methods to carry out multiplications involving decimals accurately

5.5 Division problems without a calculator

2 To use written methods to carry out divisions involving decimals accurately


5.6 Calculations with measurements

1 To convert between common metric units

To use measurements in calculations

To recognise and use appropriate metric units

Problem solving – What is yourcarbon footprint?

2 This activity is designed to use the skills covered in this and earlier‘number’ chapters to give a real-life context to mathematics.

6 Statistics 6.1 Mode, median and range

1 To understand and calculate the mode, median and range of data

Pupils need to think about how we use statistics to model populations where it is difficult or in many cases impossible to gather all the population information.

6.2 The mean 1 To understand and calculate the mean average of data

6.3 Statistical diagrams

1 To be able to read and interpret different statistical diagrams

6.4 Collecting and using discrete data

1 To create and use a tally chart

6.5 Collecting and using continuous data

2 To understand continuous data and use grouped frequency

6.6 Data collection

2 To develop greater understanding of data collection

Challenge – Schools sports day

1 This activity is designed to use both the mathematical reasoning and problem-solving outcomes that have been covered in this chapter, in a familiar situation.


Half-term / Term 37 Algebra 7.1 Expressions

and substitution1 To use algebra to write simple

expressions and recognise equivalent expressions

To substitute numbers into expressions to work out their value

7.2 Simplifying expressions

1 To learn how to simplify expressions

7.3 Using formulae

2 To use formulae

7.4 Writing formulae

2 To write formulae

Problem solving–Winter sports

1 A common response to algebra is to ask how it can be used. This activity provides one of the everyday uses of algebra in terms of using a formula to decide cost.

8 Fractions 8.1 Equivalent fractions

1 To find equivalent fractions To write fractions in their

simplest form8.2 Comparing fractions

1 To compare and order two fractions


2 To add and subtract fractions with different denominators

8.4 Mixed numbers and improper fractions

1 To convert mixed numbers to improper fractions

To convert improper fractions to mixed numbers


8.5 Calculations with mixed numbers

1 To add and subtract simple mixed numbers with different denominators

Challenge – Fractional dissection

1 This activity is designed to build confidence and fluency by allowing pupils to apply what they have learnt to an interesting problem in an unfamiliar context.

9 Angles 9.1 Measuring and drawing angles

1 To use a protractor to measure an angle

To use a protractor to draw an angle

Pupils often do not appreciate the need for accuracy when measuring and drawing angles. Relate this tothe contexts in the introduction to this chapter. Pupils need plenty ofpractice in using a protractoraccurately.

9.2 Calculating angles

1 To understand the properties of parallel, intersecting and perpendicular lines

To calculate angles around a point

To calculate angles on a straight line

To calculate opposite angles

9.3Corresponding and alternateangles

1 To calculate angles in parallel lines

9.4 Angles in a triangle

1 To know that the sum of the angles in a triangle is 180°

9.5 Angles in a quadrilateral

1 To know that the sum of the angles in a quadrilateral is360°

9.6 Properties of triangles and quadrilaterals

1 To understand and use the properties of triangles

To understand and use the properties of quadrilaterals

Activity – Constructing triangles

1 This activity is designed to build confidence and fluency.


Half-term / Term 410 Coordinates and graphs

10.1Coordinates in four quadrants

1 To understand and use coordinates to locate points in all four quadrants

10.2 Graphs from relationships

1 To draw a graph for a simple relationship

10.3 Predicting graphs from relationships

1 To understand the connection between pairs of coordinates and the relationship shown in an equation and a graph

10.4 Graphs of fixed values of x and y,y = x and y = –x

1 To recognise and draw line graphs with fixed values of x and y

To recognise and draw graphs of y = x and y = –x

10.5 Graphs of the formx + y = a

1 To recognise and draw graphs of the form x + y = a

10.6 Graphs from the real world

1 To learn how graphs can be used to represent real-life situations

To draw and use real-life graphs

Challenge – Global warming

2 This activity is designed to apply pupils learning in a real-life topical situation.


11Percentages

11.1 Fractions, decimals and percentages

1 To understand the equivalence between a fraction, a decimal and a percentage

To understand and use percentages greater than100%

Percentages are everywhere in real life. From bargains in the shops to taxes on payslips. It is important for pupils to be comfortable with calculating percentages to enable them to be functional in a modern society.

11.2 Fractions of a quantity

1 To work out a fraction of a quantity without using a calculator

11.3 Calculating simple percentages

1 To work out a percentage of a quantity without using a calculator


1 To use a calculator to workout a percentage of a quantity

To know when it isappropriate to use a calculator

11.5 Percentage increases and decreases

2 To work out the result of a percentage change

Financial skills – Income tax

2 This activity is designed to use both the mathematical and transferable process skills covered in this chapter in a very important real-life context that may be less familiar to them than might be expected.

12 Probability 12.1 Probability scales

1 To learn and use the correct words about probability

12.2 Combined events

1 To use sample space diagrams to work out the probability of a combined event


2 To understand experimental probability

To understand the difference between theoretical probability and experimental probability

Financial skills – School Easter Fayre

1 This activity combines pupils’ understanding of experimental and theoretical probability and applies it in a real-life context.


Half-term / Term 513 Symmetry 13.1 Line

symmetry and rotational symmetry

1 To recognise shapes that have reflective symmetry and draw their lines of symmetry

To recognise shapes that have rotational symmetry and find the order of rotational symmetry

13.2 Reflections 1 To understand how to reflect a shape

To use coordinates to reflect shapes in all four quadrants

13.3 Rotations 1 To understand how to rotate a shape

13.4Tessellations

1 To understand how to tessellate shapes

Activity – Landmark spotting

1 This activity is designed to show pupils some of the aspects of symmetry used in the real world, by examining the line symmetry of six famous landmarks.

14 Equations 14.1 Finding unknown numbers

1 To find missing numbers in simple calculations


14.2 Solving equations

1 To understand what an equation is

To solve equations involving one operation

14.3 Solving more complex equations

1 To solve equations involving two operations

14.4 Setting up and solving equations

2 To use algebra to set up and solve equations

Challenge – Number puzzles

1 In this activity pupils apply what they know to an abstract number problem. They need to identify and solve multi- step linear equations to solve the problem.

15 Interpreting data

15.1 Pie charts 1 To use a scaling method to draw a pie chart

To read and interpret data from pie charts

Statistical data is everywhere in a modern society and to function in this society it is important to be able to critically analyse the data being presented.

15.2 Comparing range and averages of data

1 To use averages and range to compare data

To make sensible decisions by comparing averages and ranges of two sets of data

15.3 Statistical surveys

2 To carry out a statistical survey

To use charts and diagrams to interpret data and then write a report

Challenge – Dancing competition

1 This activity is designed to use both the interpretation and communication skills covered in this chapter in a familiar scenario.


Half-term / Term 616 3D shapes 16.1 Naming

and drawing 3D shapes

1 To be familiar with the names of 3D shapes and their properties

To use isometric paper to draw shapes made from cubes

16.2 Using nets to construct 3D shapes

1 To draw nets of 3D shapes To construct 3D shapes from

nets including more complex shapes


2 To understand the relationship between faces, edges and vertices for 3D shapes

To solve problems involving3D shapes

Problem solving– Packing boxes

1 This is a common type of problem used at GCSE, so it is important that pupils can identify this type of problem.

17 Ratio 17.1 Introduction to ratios

1 To use ratio notation To use ratio to compare

quantities17.2 Simplifying ratios

1 To write a ratio as simply as possible with whole numbers

To write ratios in the form 1 : xwhere x could be a decimal.

17.3 Ratios and sharing

1 To use ratios to find totals or missing quantities

To write ratios to compare more than two items


17.4 Solving problems

1 To understand theconnections between fractions and ratios

To understand how ratios can be useful in everyday life

Problem solving–Smoothie bar

1 This problem-solving activity is designed to reinforce the use of ratios by putting ratios in a realistic context.

Chapter 16–17 assessment on Collins ConnectEnd of year assessment on Collins Connect


Chapter Lesson No. ofhours


Half-term / Term 11 Working with numbers

1.1 Adding and subtracting with negative numbers

1 • To carry out additions and subtractions involving negative numbers

Pupils often learn rules without really understanding the reasoning behind each rule. Pupils will benefit from visual images such as a number line and/or an understanding of the patterns that lead to the rules, in this case how we use the four operations with positive and negative numbers. Then, when pupils are in stressful situations such as examinations, they can fall back on these images to provide backup if they are uncertain.

1.2 Multiplying and dividingnegative numbers

1 • To carry out multiplications and divisions involving negativenumbers

One of the main misconceptions pupils have when multiplying twonegative numbers is giving a negative answer. Reinforce the fact that whenmultiplying two negative numbers, theanswer will always be positive. And, when multiplying two numbers, pupils often think that the sign of the answer is determined by the sign of the largest number. Remind pupils not to rush through their work, as they need to have a clear understanding of the rules.

1.3 Factorsand highest common factors (HCF)

1 • To understand and use highestcommon factors

Pupils sometimes confuse factors andmultiples. (Say that multiples come from multiplying.)

1.4 Multiplesand lowest common multiple (LCM)

1 • To understand and use lowestcommon multiples

1.5 Squares,cubes and roots

1 • To understand and use squaresand square roots

• To understand and use cubes and cube roots

Reinforce the fact that the square rootof a number can be both positive and negative. Another problem is that pupils often think that n2 is n × 2 or that n3 is n × 3. Explain clearly that this is not the case.

1.6 Primefactors

1 • To understand what primenumbers are

• To find the prime numbers of an integer

Remind pupils to include themultiplication signs when writing a number as a product of its prime factors. (These are often replaced incorrectly by addition signs or commas.)

Challenge –The EiffelTower

1 This activity encourages pupils tothink about a tourist attraction with different facilities and what is involved in running them. The topic could lead to class discussion about environmental issues such as electricity and water usage.

2 Geometry 2.1 Paralleland perpendicular lines

1 • To identify parallel lines• To identify perpendicular lines

Pupils often assume that whensomething seems to be correct, it is. However, pupils need to understand the importance of correct mathematical notation, for example, to identify parallel lines.


2.2 Angles intriangles and quadrilaterals

1 • To know that the sum of theangles in a triangle is 180°

• To know that the sum of the angles in a quadrilateral is 360°

Pupils often confuse rules becausethey don’t really understand them. Give them the opportunity to apply the rules in a range of contexts andmake the link between the angles in a triangle and the angles in a quadrilateral. This will serve as abasic introduction to proof. Provide lots of opportunity for discussion and encourage pupils to reflect on and extend the responses of other pupils.

2.3Translations

1 • To understand how to translate apoint or a shape

A sound understanding of coordinatesin all four quadrants will help pupils to understand translations. Physical demonstrations will also help pupils who may struggle with this.

2.4 Rotations 1 • To understand how to rotate ashape

Pupils struggle to visualise rotations.Provide plenty of practice and if possible use active geometry packages such as GeoGebra.

Challenge –Constructing triangles

1 This challenge gives pupils theopportunity to extend their learning to slightly more complex constructions. They need to be able to reproduce a set of instructions that build on what they have already done in the lesson.

Chapter 1–2 assessment on Collins Connect3 Probability 3.1 Probability

scales1 • To use a probability scale to

represent a chanceAsk the class: 'What is the probabilitythat you will ever travel in space?' Add that 100 years ago, the chance of this was nil because then it was impossible. However, the chance is increasing every decade. Scientists predict that many pupils who attendschools now will have a fair chance of travelling into space one day in their lifetime. Scientists calculate the probabilities by working out what is technically possible, and who mightbe able to afford it. We do not know if mass space travel will happen, but by studying probability, we can understand how likely it is to happen and how the scientists work it out.

3.2 Collecting data for afrequency table

1 • To collect data and use it to find probabilities

• To decide if an event is fair or biased

3.3 Mixedevents

1 • To recognise mixed eventswhere you can distinguish different probabilities

3.4 Using asample space to calculate probabilities

1 • To use sample spaces tocalculate probabilities


1 • To calculate probabilities from experiments

Pupils often struggle to relate experimental data results toprobabilities. Make sure pupils understand that experimentalprobabilities will be closer to thetheoretical probability values if they increase the number of times they perform the experiment.

Financial skills– Fun in the fairground

1 In this activity learners extend theirunderstanding of probability to a real- life application that may be new to them. Pupils also make a real-life link between probability and financial skills.

Half-termHalf-term / Term 24 Percentages 4.1 Calculating

percentages1 • To write one quantity as a

percentage of anotherPercentage increase and decrease is probably one of the most common uses of mathematics in real life. Everyone meets it in some form or other even if only in terms of financial capability. Fractions, decimals and percentages are everywhere and it is important for pupils’ confidence and accuracy to be able to move between these different representations. This chapter reinforces the links between fractions, decimals and percentages.

4.2 Calculatingthe result of a percentage change

2 • To calculate the result of apercentage increase or decrease

4.3 Calculatinga percentage change

2 • To work out a change of valueas a percentage increase or decrease

Challenge –Changes in population

1 This activity is designed to give pupilsthe opportunity to demonstrate their understanding of percentage change in a real-life situation.


5 Sequences 5.1 TheFibonacci sequence

2 • To know and understand theFibonacci sequence

Fibonacci numbers appeareverywhere in nature, and are applicable to the growth of everyliving thing. The ability to generalise is crucial in a complex modern society. Being able to identify and generatenumber sequences is the first steptowards progressing from the particular to the general in mathematics. Mathematics is all about the ability to see patterns, tohypothesise about these patterns and then seek to prove the hypothesis from first principles.

5.2 Algebra and functionmachines

2 • To use algebra with function machines

5.3 The nthterm of a sequence

2 • To use the nth term of asequence

Investigation –Pond borders

1 Pupils apply their understanding ofsequences to a real-life scenario. They will need to work methodically and be able to justify their solutions. Ask more able pupils to generalise their rules for an m × n pool.

Chapter 3–5 assessment on Collins Connect6 Area 6.1 Area of a

rectangle1 • To use a formula to work out the

area of a rectangleRemind pupils that perimeter, areaand volume are used widely in many jobs and professions, from farming to astronomy. Encourage pupils to ask family and friends if they use these units of measure in their work. Pupils could also explore specific jobs on the internet. A good example is the building industry, which is totally dependent on workers being able to measure lengths and calculate areas.

6.2 Areas ofcompound shapes

1 • To work out the area of acompound shape

6.3 Area of atriangle

1 • To use a formula to work out thearea of a triangle

6.4 Area of aparallelogram

2 • To work out the area of aparallelogram

Pupils should understand that theheight of a parallelogram is the vertical height, not the length of a side.

Investigation –Pick’s formula

2 In this investigation, pupils arerequired to apply their understanding of area to a more complex extended problem. Pupils need to work methodically and be able to explain their solutions. This is a good transferable skills objective to share with pupils when they work on this investigation. Ask pupils to share not only their solutions but also how they approached working on the problem.

HolidaysHalf-term / Term 37 Graphs 7.1 Rules with

coordinates1 • To recognise patterns with

coordinatesThis chapter builds on previous work on mapping diagrams and graphs covered in Year 7, where pupils identified functions from inputs and outputs (including the inverse function) and related these to coordinate pairs, which are used to draw graphs.

7.2 Graphsfrom rules

1 • To draw graphs of linear rules

7.3 Graphsfrom simple quadratic equations

2 • To recognise and draw thegraph from a simple quadratic equation

7.4 Distance–time graphs

2 • To read and draw distance–time graphs

Problemsolving – TheM60

1 This problem solving activityencourages pupils to think about the M60, one of the UK’s busiest orbital motorways. Read and then discuss the text in the Pupil Book. Ask pupils some questions relating to the text.

8 Simplifyingnumbers

8.1 Powers of10

1 • To multiply and divide by 100and 1000

• To round numbers to one decimal place

As with all use of powers, pupils tendto confuse 10n with 10 × n. Provide pupils with plenty of opportunity to compare the two and to grasp why they are different. Comparing the two graphically could also help pupils to reinforce the difference.

8.2 Largenumbers and rounding

1 • To round large numbers Pupils sometimes have problems withnumbers that end in 9, especially if there are several 9s. Pupils may also


struggle with numbers with trailingzeros. Provide plenty of opportunity to discuss examples. This applies to large numbers in the same way as it does to smaller numbers. Help pupils to see that in fact making thenumbers larger does not make the process of rounding any different.

8.3 Significantfigures

1 • To round to one significant figure Pupils tend to confuse rounding todecimal places and significant figures. Provide plenty of opportunity forpupils to compare the two. Pupils also struggle with the role of 0, and whenthis counts as a significant figure.Give pupils practice and answer any questions that arise.

8.4 Estimatinganswers

2 • To use rounding to estimaterough answers to calculations

Pupils often assume that giving anexact answer is better than an estimate. Make sure that pupils grasp that this is often impractical or impossible in the real world. Give them a range of examples and make sure they appreciate that a good estimation provides an appropriate degree of accuracy while still being easier to calculate than the original calculation.

8.5 Problemsolving with decimals

1 • To solve problems with decimalnumbers

Pupils are often confident whenapplying their understanding of place value to numbers greater than one, but may struggle with decimalfractions. Encourage pupils to seethat the patterns are the same either side of the decimal point.

Challenge – Space – to seewhere no one has seenbefore

1 This activity is designed to combine the skills covered across this chapterto explore an interesting real-life problem in a slightly more abstractcontext.

Chapter 6–8 assessment on Collins Connect9Interpreting data

9.1 Informationfrom charts

1 • To revise reading from chartsand tables

In this chapter, pupils will look atsome commonly used types of statistical diagrams – pie charts, line graphs and scatter graphs. Pupils will learn how to interpret them correctly and create them themselves.

9.2 Readingpie charts

1 • To interpret a pie chart

9.3 Creatingpie charts

1 • To use a scaling method to drawpie charts

9.4 Scattergraphs

2 • To read scatter graphs

Challenge –What should we eat?

2 This activity will challenge pupils tothink about a familiar topic. Pupils are required to discuss what constitutes a healthy diet – the elements and proportions.

Half-termHalf-term / Term 410 Algebra 10.1 Algebraic

notation1 • To simplify algebraic

expressions involving the four basic operations

Introduce algebra as a universal language with rules that are used all over the world. Mathematicians have been developing the rules of algebra for over 3000 years. The Babylonians used a form of algebra when they wrote on clay tablets, some of which have survived until today.Discuss a range of examples in which algebra is used. For example, the classic handshakes problem.

10.2 Liketerms

1 • To simplify algebraicexpressions by combining like terms

10.3Expanding brackets

1 • To remove brackets from an expression

10.4 Usingalgebra

2 • To use algebraic expressions indifferent contexts

10.5 Using powers

2 • To write algebraic expressions involving powers

Mathematicalreasoning – Strawberries

2 This activity develops confidence andfluency with algebraic notation. Pupils often struggle to decode everyday language into mathematics. This activity gives them the opportunity to practise this in a range of contexts.


11 Congruenceand scaling

11.1Congruent shapes

1 • To recognise congruent shapes Discuss the golden rectangle: its size(side lengths are in the ratio 1 : Φ; Φ is the Greek letter phi and is approximately equal to 1.618). Explain that this rectangle is special, because if you cut a square from oneend of it, you will be left with a smaller shape, which is another golden rectangle, with sides that are in thesame ratio as the rectangle youstarted with. The golden rectangle has been described as one of the most visually pleasing rectangular shapes, which many artists and architects have used in their work.

11.2 Shape and ratio

1 • To use ratio to compare lengths and areas of 2D shapes

11.3 Scale diagrams

2 • To understand and use scale diagrams

Financial skills– Carpeting a bungalow

2 Pupils will need to be familiar with using basic scales and calculatingareas and perimeters of rectangles and compound shapes involvingrectangles. Pupils may also need acalculator for the financial elements.


Half-term / Term 512 Fractions and decimals


2 • To add and subtract fractions and mixed numbers

You could introduce this chapter by telling pupils that fractions have been written in different ways throughout history. Nowadays we use two ways of writing fractional numbers – either as one whole number over another whole number, or using a decimal point. In this chapter, pupils will see how these two methods compare.

12.2Multiplying fractions and integers

2 • To multiply a fraction or a mixednumber by an integer

12.3 Dividingwith integers and fractions

2 • To divide a unit fraction by aninteger

• To divide an integer by a unit fraction

12.4Multiplication with powers of ten

1 • To multiply by a power of ten mentally

12.5Division with powers of ten

1 • To mentally divide by a power of10

Problem solving –Making estimates

1 This activity gives pupils the opportunity to practice their mentalstrategies in some real-life contexts. It also encourages pupils to make linksto the use of estimation as well as theneed to make assumptions when tackling real-life problems.

13 Proportion 13.1 Directproportion

1 • To understand the meaning ofdirect proportion

• To find missing values in problems involving proportion

This chapter introduces the conceptsof direct and inverse proportion as a means of solving practical questions. Pupils will also learn about graphs that show direct proportion.13.2 Graphs

and direct proportion

1 • To represent direct proportiongraphically and algebraically

13.3 Inverseproportion

1 • To understand what is meant byinverse proportion

• To solve problems using inverse proportion

13.4 Thedifference between direct and inverse proportion

1 • To recognise the differencebetween direct and inverse proportion in problems

• To work out missing values

Challenge – Coach trip

1 For this challenge pupils apply their understanding of proportion to atypical real-life context including speed, time and fuel consumption.The questions increase in complexityand pupils will need to use a range of graphical and algebraic skills to tackle them. Pupils also need to be able to interpret some quite complex language.


Chapter 12–13 assessment on Collins Connect14 Circles 14.1 The circle

and its parts1 • To know the definition of a circle

and the names of its partsTell pupils that the circle is probablythe most important shape in the universe. It is also the most mysterious. We use a fascinating number that pupils may have heard of, called pi, written as π, which is used to calculate the circumference (perimeter) of a circle. But π cannotbe written exactly as a number and its decimal places never end. Pupils could prepare for this chapter bydoing their own research on π. Encourage pupils to present their findings to the class.

14.2Circumference of a circle

1 • To work out the relationshipbetween the circumference and diameter of a circle

14.3 A formulato work out the approximate circumference of a circle

1 • To use a formula to work out thecircumference of a circle

Activity –Constructions

2 You may want to start this activity byrecapping how to construct triangles to remind pupils how they developed their ability to follow a set ofinstructions. Pupils working at thislevel often lack the motor skills required for construction activities. Give them time to practise, encouraging them not to rush.

Half-termHalf-term / Term 615 Equations and formulae

15.1 Equations 1 • To solve simple equations This chapter starts by reviewing the simple equations that pupils have solved previously. Pupils are then shown how to solve equations with brackets and fractions. Finally, pupils will learn how to substitute into a formula.

15.2 Equationswith brackets

1 • To solve equations whichinclude brackets

15.3 More complexequations

2 • To solve equations involving two operations

15.4Substituting into formulae

1 • To substitute values into avariety of formulae

Reasoning –Old trees

1 In this activity, pupils usemathematical reasoning to make links between formulae and the real world.

16 Comparingdata

16.1Frequency tables

1 • To create a grouped frequencytable from raw data

Encourage pupils to think about howstatistics are used. Pupils need to consider how to present information. Pupils also need to think about how we use statistics to model populations where it is difficult, or in many cases impossible, to gather all thepopulation information.

16.2 The mean 1 • To understand and calculate themean average of data

16.3 Drawingfrequency diagrams

1 • To be able to draw a diagramfrom a frequency table

16.4Comparing data

1 • To use the mean and range to compare data from two sources

16.5 Whichaverage to use?

1 • To understand when eachdifferent type of average is most useful

Problemsolving – Questionnaire

1 This activity is designed to combineall the lessons in this chapter by taking pupils sequentially through the steps of tabulating and displaying data for a very familiar real-life problem. All the data is given, but pupils will need to read and think carefully about how they display the data so that they can make valid comparisons.






Half-term / Term 11 Working with numbers

1.1 Multiplying and dividing negative numbers

1 • To carry out multiplications and divisions involving negative numbers.

One of the main misconceptions when multiplying two negative numbers together is consistently giving a negative answer. Another problem pupils have when multiplying two numbers together is that they often think the sign of the answer is determined by the sign of the largest number. Make sure that pupils do not rush through their work and that they have a clear understanding of the rules.

1.2 Factorsand highest common factors (HCF)

1 • To understand and use highest common factors

Students sometimes confuse factorsand multiples. (Tell them that multiples come from multiplying.)

1.3 Lowestcommon multiples (LCM)

1 • To understand and use lowest common multiples

1.4 Powersand roots

2 • To understand and use powers and roots

1.5 Primefactors

1 • To understand what prime numbers are

• To find the prime numbers of an integer

Challenge –BlackpoolTower

1 This activity is designed to give pupilsthe opportunity to apply their learning to a real-life multi-step problem.

2 Geometry 2.1 Angles inparallel lines

1 • To calculate angles in parallel lines

2.2 Thegeometric properties of quadrilaterals

1 • To know the geometric properties of quadrilaterals

2.3 Rotations 1 • To understand how to rotate a shape

Pupils struggle to visualisetransformations Give them plenty of practice and if possible use active geometry packages such as Geogebra to help them http://www.geogebra.org/cms/en/ You could also use readymade examples on Geogebra tubehttp://www.geogebratube.org/mater ial/show/id/2163

2.4Translations

1 • To understand how to translate a shape

2.5Constructions

1 • To construct the mid-point and the perpendicular bisector of a line

• To construct an angle bisector

Pupils are often not precise enoughwhen doing constructions in mathematics. Give them the opportunity to assess the errors inexemplars and explain how they canbe avoided. Use dynamic geometry software to support learners.

Challenge –More constructions

1 This challenge gives pupils theopportunity to extend their learning to more complex constructions. They need to be able to reproduce a set of instruction that extend what they have


already done in the lesson.Chapter 1–2 assessment on Collins Connect3 Probability 3.1 Probability

scales1 • To use a probability scale to

represent a chanceThis chapter builds on previousknowledge of probability and extends this first to see how probability is applied differently to theory and experiments, and then to being able to compare the two results critically.

3.2 Mutuallyexclusive events

1 • To recognise mutually exclusive events

3.3 Using a sample spaceto calculate probabilities

1 • To use sample spaces to calculate probabilities


2 • To calculate probabilities from experiments


1 In this activity learners extend theirunderstanding of probability to a common real-life application that they may not have previously considered. It also makes a real-life link between probability and financial skills.


percentages1 • To write one quantity as a

percentage of another• To use percentages to compare

quantities

Fractions, decimals and percentages are everywhere in real life and it is important for confidence andaccuracy to be able to move between these different representations. This chapter reinforces the links between fractions, decimals and percentages.

4.2 Calculatingpercentage increases and decreases

2 • To use a multiplier to calculate a percentage change

4.3 Calculatinga change as a percentage

2 • To work out a change in value as a percentage increase or decrease


1 This activity is designed to give pupilsthe opportunity to demonstrate their understanding of percentage change to a real-life situation. All the information they need is provided but they will need to read the questions carefully to decide which information they need and what mathematical skills to use.

5 Sequences 5.1 Using flowdiagrams to generate sequences

1 • To use flow diagrams to generate sequences

The ability to generalise is crucial in acomplex modern society. Being able to identify and generate number sequences is the first step towards progressing from the particular to the general in mathematics.

5.2 The nthterm of a sequence

2 • To use the nth term of a sequence

5.3 Workingout the nth term of a sequence

2 • To work out the nth term of a sequence

5.4 TheFibonacci sequence

1 • To know and understand theFibonacci sequence

Investigation –Pond borders

1 Pupils apply their understanding ofsequences to a real-life scenario. They will need to work methodically and be able to justify their solutions.Ask more able pupils to generalisetheir rules for an m × n pool.

Chapter 3–5 assessment on Collins Connect6 Area of 2Dand 3D shapes

6.1 Area of atriangle

1 • To work out the area of a triangle

Pupils should understand that theheight of a triangle, parallelogram and trapezium (except in some specific examples) is the vertical height, notthe length of a side.Encourage pupils to see how they can use what they already know, for example, the area of a triangle and a rectangle, to work out things they may not know or have forgotten.

6.2 Area of aparallelogram

1 • To work out the area of a parallelogram

6.3 Area of atrapezium

1 • To work out the area of a trapezium


6.4 Surfaceareas of cubes and cuboids

2 • To find the surface areas of cubes and cuboids

Pupils often confuse the concept ofsurface area and volume. Use concrete examples to help them understand the difference.

Investigation –A cube investigation

2 Pupils apply their understanding ofarea to a more complex problem. They will need to work methodically and be able to explain their solutions. Ask more able pupils to justify any rules by revisiting the structure of the problem.

HolidaysHalf-term / Term 37 Graphs 7.1 Graphs

from linear equations

1 • To recognise and draw the graph of a linear equation

This chapter builds on previous work on mapping diagrams and graphs covered in Year 7. The important concept of the gradient of a straight line is introduced in this chapter and the form y = mx + c for a straight line is explored.

7.2 Gradient(steepness) of a straight line

1 • To work out the gradient in a graph from a linear equation

• To work out an equation of the form y = mx + c from the graph

7.3 Graphsfrom simple quadratic equations

2 • To recognise and draw the graph from a simple quadratic equation

7.4 Real-lifegraphs

2 • To draw graphs from real-life situations to illustrate the relationship between twovariables

Challenge –The M25

1 A common response to algebra is toask how it can be used. This activity provides an everyday use of algebrain terms of graphical representation of algebraic relationships set in real life contexts. Encourage pupils tosuggest possible questions.

8 Simplifyingnumbers

8.1 Powers of10

1 • How to multiply and divide by powers of 10

This chapter builds on previouswork with decimals, introducing powers of 10 as a lead in to working with standard index form. Estimation is used as a means of teaching whether answers are realistic or sensible.Some of the work is specifically designed to reinforce skills in mental arithmetic, and there is also work on using calculators efficiently.

8.2 Largenumbers and rounding

1 • To round large numbers


1 • To round to one or more significant figures

8.4 Standard form with largenumbers

2 • To write a large number in standard form

You can introduce standard form as a powerful tool, which is widely used inscience.

8.5 Multiplyingwith numbers in standard form

1 • To multiply with numbers in standard form

Challenge -Space – to see where no one has seen before

1 This activity is designed to combinethe skills covered across this chapter to explore an interesting real-life problem in a slightly more abstract context.

Chapter 6–8 assessment on Collins Connect9Interpreting data

9.1 Pie charts 1 • To work out the sectors in pie charts by their angles at the centre

This chapter builds on previously learnt statistical principles. It extendspupils’ use of data and knowledge of how to interpret statistical diagramsand charts. This is vital if pupils are to understand and interrogate the databeing presented.

9.2 Creatingpie charts

1 • To use a scaling method to draw pie charts

9.3 Scattergraphs and correlation

1 • To read scatter graphs• To understand correlation

9.4 Creatingscatter graphs

2 • To create scatter graphs

Challenge -Football attendances

2 This activity consolidates the previouswork on statistics.

Half-term


Half-term / Term 410 Algebra 10.1 Algebraic

notation1 • To simplify algebraic


Introduce algebra as a universal language with rules that are used all over the world.Discuss a range of examples in which algebra is used.Pupils often struggle to appreciatethat letters represent variables and try to substitute particular values for the letters.Give pupils plenty of opportunity toreflect on the use of algebra as generalised number and to make clear links to the rules they have learnt for number.

10.2 Liketerms

1 • To simplify algebraic expressions by combining like terms


1 • To remove brackets from an expression

10.4 Usingalgebraic expressions

2 • To manipulate algebraic expressions

• To identify equivalent expressions

10.5 Usingindex notation

2 • To write algebraic expressions involving powers

Mathematical reasoning –Writing in algebra

2 This activity develops confidence and fluency with algebraic notation. Pupilsoften struggle to decode everyday language into mathematics. Thisactivity gives them the opportunity topractise this in a range of contexts.

11 Congruenceand scaling

11.1Congruent shapes

1 • To recognise congruent shapes Pupils often do not realise that youcan test for congruence by placing one shape on top of the other. Encourage the use of tracing paper todo this. Also reinforce the fact thatshapes can have different orientations and still be congruent. Pupils can often use an incorrect point as the centre of enlargement or often just enlarge the shape without reference to the given point.

11.2Enlargements

1 • To enlarge a 2D shape by a scale factor

11.3 Shapeand ratio

2 • To use ratio to compare lengths, areas and volumes of 2D and3D shapes

11.4 Scales 1 • To understand and use scale drawings

• To know how to use map ratiosProblemsolving – Photographs

2 This activity consolidates topicspreviously covered on extracting data, area and ratio.


Half-term / Term 512 Fractions and decimals


2 • To add and subtract fractions and mixed numbers

Help pupils to understand the relationship between decimals and fractions as being different representations of parts of a whole.


2 • To multiply a fraction and an integer

12.3 Dividing with integersand fractions

2 • To divide a fraction or a mixed number by an integer

• To divide an integer by a unit fraction

12.4Multiplication with large and small numbers

1 • To multiply with combinations of large and small numbers mentally

12.5Division with large and small numbers

1 • To divide combinations of large and small numbers mentally

Challenge –Guesstimates

1 This activity gives pupils theopportunity to practice their mental strategies in some real-life contexts. It also encourages pupils to make linksto the use of estimation as well as theneed to make assumptions when tackling real-life problems.

13 Proportion 13.1 Direct proportion

1 • To understand the meaning of direct proportion

• To find missing values in problems involving proportion

Pupils will often mix up direct and inverse proportion usually using directproportion to answer inverse proportion questions.

13.2 Graphsand direct proportion

1 • To represent direct proportion graphically and algebraically



1 • To understand what inverse proportion is

• To use graphical and algebraic representations of inverse proportion

13.4Comparing direct proportion andinverseproportion

1 • To recognise direct and inverse proportion and work out missing values

Challenge –Planning a trip

1 For this challenge pupils apply theirunderstanding of proportion to a typical real-life context including speed, time and fuel consumption. The questions increase in complexity and pupils can use a range of graphical and algebraic skills to tackle them. They also need to be able to interpret some quite complex language.

Chapter 12–13 assessment on Collins Connect14 Circles 14.1 The circle

and its parts1 • To know the definition of a circle

and the names of its partsPupil’s often confuse radius anddiameter. Give them plenty of opportunity to use both.Pupils often do not make the link between the work they have done previously on perimeter and area andthe work on the circumference andarea of a circle.

14.2Circumference of a circle

1 • To work out the relationship between the circumference and diameter of a circle

14.3 Formulafor the circumference of a circle

1 • To calculate the circumference of a circle

14.4 Formulafor the area of a circle

1 • To calculate the area of a circle

Financial skills– Athletics stadium

2 This activity is designed to give pupilsthe opportunity to apply their knowledge to a multi-step real-life problem. The context is common, but is presented in a slightly more complex way than pupils are used to.


15.1 Equations with brackets

1 • To solve equations involving brackets

A common problem often seen when expanding a bracket is to multiply the first term by the number outside the bracket and just write down the second term. Pupils will sometimes get confused with adding or subtracting from each side when dealing with equations with unknowns on both sides.

15.2 Equationswith the variable on both sides

1 • To solve equations with the variable on both sides

15.3 More complexquestions

2 • To solve equations with fractional coefficients.

• To solve equations with brackets and fractions

15.4Rearranging formulae

1 • To change the subject of a formula

Mathematicalreasoning – Using graphs to solveequations

1 In this activity pupils usemathematical reasoning to make links between equations and formula and their graphical representation. Bycomparing graphical and algebraicrepresentations pupils check their ability to solve equations. This ability to use different representations to check their understanding is a valuable generic skill.

16 Comparingdata

16.1 Groupedfrequency tables

1 • To create a grouped frequency table from raw data

Encourage pupils to think about howstatistics are used. Pupils need to consider how to present information.



1 • To interpret frequency diagrams• To draw a frequency diagram

from a grouped frequency table

Pupils also need to think about howwe use statistics to model populations where it is difficult, or in many cases impossible, to gather all thepopulation information.

16.3Comparing data

2 • To use mean and range to compare data from two sources

16.4 Which average touse?

• To understand when each different type of average is most useful

Problemsolving – Technology questionnaire

1 This activity is designed to combineall the lessons in this chapter by taking pupils sequentially through the steps of tabulating and displaying data for a very familiar real-life problem.All the data is given, but pupils will need to read and think carefully about how they display the data so that they can make valid comparisons.



PUPIL BOOK 2.3 (3-year scheme of work)The following scheme of work provides a suggestion for how Pupil Book 2.3 can be taught over the course of one year, as part of a 3-year Key Stage 3 course.Please note that you can recombine the test questions provided on Collins Connect to create new tests if your frequency of assessment differs from that below, or if you wish to combine content from different chapters in your own half-term tests.This scheme of work is provided in editable Word and Excel format on the CD-ROMaccompanying this Teacher Pack.



Half-term / Term 11 Working withnumbers

1.1 Multiplyingand dividing negative numbers

1 To carry out multiplications and divisions involving negativenumbers

One of the main misconceptionspupils have when multiplying two negative numbers is giving a negative answer. Reinforce the fact that when multiplying two negative numbers, the answer will always be positive. And, when multiplying two numbers, pupils often think that the sign of the answer is determined by the sign of thelargest number. Make sure that pupils do not rush through their work, asthey need to have a clear understanding of the rules.

1.2 Factorsand highest common factor(HCF)

1 To understand and use highest common factors

Pupils sometimes confuse factors andmultiples. Say that multiples come from multiplying. Pupils shouldunderstand that the multiples of a number are the times table for that number.

1.3 Multiplesand lowest common multiple (LCM)

1 To understand and use lowest common multiples

1.4 Powersand roots

2 To understand and use powers and roots

Reinforce the fact that the square rootof a number can be both positive and negative. Pupils often think that n2 is n× 2 or that n3 is n × 3. Explain clearly that this is not the case.

1.5 Primefactors

1 To find the prime numbers of an integer

Make sure that less able pupils arefamiliar with Venn diagrams before they start Exercise 1E in the PupilBook.

Challenge –BlackpoolTower

1 This challenge encourages pupils tothink about a tourist attraction with different facilities and what is involved in running them. The topic could leadto class discussion about environmental issues such as electricity and water usage.

2 Geometry 2.1 Parallellines

1 To calculate angles in parallel lines

Pupils often assume that becausesomething looks right, it is right. However, pupils need to understandthe importance of correct mathematical notation, for example,to identify parallel lines, and the need for rigorous mathematical proof.

2.2 Thegeometric properties ofquadrilaterals

1 To know the geometric properties of quadrilaterals

2.3Translations

1 • To understand how to translate a shape

A sound understanding of coordinatesin all four quadrants will help pupils to understand translations. Physical demonstrations will also help the pupils who may struggle with this.

2.4Enlargements

1 • To enlarge a 2D shape by a scale factor

Pupils often fail to consider whethertheir enlargement will fit on the sheet of paper they are using. Encourage pupils to ask themselves this question before starting any enlargement.


2.5Constructions

1 • To construct the mid-point and the perpendicular bisector of a line

• To construct an angle bisector• To construct a perpendicular to

a line from or at a given point• To construct a right-angled

triangle

Pupils are often not precise enoughwhen doing constructions in mathematics. Give them theopportunity to assess the errors in exemplars and explain how they can avoid these errors. Use dynamicgeometry software to support pupils (for example: www.geogebra.org). Make sure pupils understand eachstep, or they will fail to apply the steps in complex or less familiar contexts.

Challenge –More constructions

1 This challenge gives pupils theopportunity to extend their learning to more complex constructions. They need to be able to reproduce a set ofinstructions that extend what they have already done in the classroom.

Chapters 1–2 assessment on Collins Connect3 Probability 3.1 Mutually

exclusive outcomes and exhaustive outcomes

1 To recognise mutually exclusive and exhaustive events

To use a probability scale to represent a chance

Make sure that pupils understand thefact that mutually exclusive events cannot happen at the same time. This knowledge will help pupils to avoid confusion in later years with independent events. Pupils may also be confused by sentences with the words ‘or’ and ‘and’. Explain the meanings carefully.

3.2 Using asample space to calculateprobabilities

1 To use sample spaces to calculate probabilities

Remind pupils that they will need tobe very methodical when recording outcomes, otherwise pupils mightmiss some of the outcomes.

3.3 Estimatesof probability

1 To use relative frequency to estimate probabilities

Pupils often struggle to relateexperimental data results to probabilities. Make sure pupils understand that experimental probabilities will be closer to the theoretical probability values if they increase the number of times they perform the experiment.


1 Pupils extend their understanding ofprobability to a common real-life application that may be new to them.Pupils also make a real-life link between probability and financialskills.


percentages1 To write one quantity as a

percentage of anotherRather than simply learning a rule to calculate percentages of a quantity, pupils need to understand what theyare doing and why. Pupils often confuse fractions and percentages, for example, by calculating 27% asone-twenty-seventh instead of 27 of100. Make links to fractions and percentages so that pupils grasp theconnection. Make sure pupils know what a percentage is and how to find a percentage of a quantity in a rangeof contexts.

4.2 Calculatingpercentage increases and decreases

2 To use a multiplier to calculate a percentage change

Pupils are often confused when theycome across percentages greater than 100. Using a real-life example here could help, starting with percentages with which they can work comfortably. Pupils need a good understanding of 100% as a whole before tackling percentage increase and decrease successfully.

4.3 Calculatinga percentage change

2 To work out a change in value as a percentage increase or decrease

Pupils make the mistake of pairing anincrease with an equivalent decrease. For example, they think that a 50% increase followed by a decrease of50% will take them back to their starting value. This misconception stems from using additive instead of


multiplicative reasoning. Part 3 of thislesson tackles this misconception and pupils should draw on their work oninverse relationships during the lesson to explain their responses.


1 This activity is designed to give pupilsthe opportunity to demonstrate their understanding of percentage changein a real-life situation. All the information they need is provided but they will need to read the questionscarefully to decide which information they need and what mathematical skills to use.

5 Congruentshapes

5.1 Congruentshapes

1 To recognise congruent shapes Pupils often do not realise that theycan test for congruence by placing one shape on top of the other.Encourage the use of tracing paper to do this. Also reinforce the fact that shapes can have differentorientations and still be congruent.

5.2 Congruenttriangles

2 To know the conditions for recognising congruent triangles

The most common mistake pupilsmake when answering problems, and with proof, is to assume facts that are not actually given in the questions.

5.3 Usingcongruent triangles tosolve problems

2 To solve geometrical problems using congruent triangles

Problemsolving – Using scalediagrams to work outdistances

1 Pupils will need to be familiar withscale diagrams and ruler compass constructions before starting thequestions for this activity. You may need to model some examples.

Chapters 3–5 assessment on Collins Connect6 Surface areaand volume of prisms

6.1 Metricunits for area and volume

1 To convert metric units for area and volume

Pupils often learn rules without reallyunderstanding them, so they may not be sure whether to multiply or dividewhen converting between units. Encourage pupils to use estimationand real-life contexts to help them understand which operations to use. Less able pupils would benefit fromusing concrete objects to help them visualise given conversions.

6.2 Surfacearea of prisms

1 To calculate the surface area of a prism

Not understanding rules can cause confusion. Pupils also make mistakes with units. Pupils need to grasp thatarea is two-dimensional and volume is three-dimensional, and the effect this has on the formulae and units they will use.

6.3 Volume ofprisms

1 To calculate the volume of a prism

Investigation –A cube investigation

2 In this investigation, pupils apply theirunderstanding of area to a more complex problem. Pupils need towork methodically and be able to explain their solutions. This is a goodtransferable skills objective to share with pupils when doing this investigation. Ask pupils to share notonly their solutions but also how they approached working on the problem.

HolidaysHalf-term / Term 37 Graphs 7.1 Graphs

from linear equations

1 To extend the range of graphs of linear equations

Pupils often struggle to recognise thatletters represent variables and that the answer can vary depending onthe situation. Provide lots of opportunity for pupils to see this inaction in contexts with which they are familiar, for example, ‘Think of a number’ word problems. Pupils needto understand that letter symbols used in algebra stand for unknown numbers or variables and not labels. E.g. 5b cannot mean five bananas.


7.2 Gradient(steepness) of a straight line

1 To work out the gradient in a graph from a linear equation

To work out an equation of the form y = mx + c from its graph

Pupils often ignore the scales on theaxes and just count the squares when calculating the gradient or divide thechange in x over the change in y by mistake. Pupils will also occasionally give the x-intercept instead of the y-intercept. Make sure that you address these points and that pupils have a clear understanding of how to dothese questions correctly.

7.3 Graphsfrom quadratic equations

2 To recognise and draw the graph from a quadratic equation

To solve a quadratic equation from a graph

Pupils often misread the scales whenreading or drawing quadratic graphs. Another common problem relates to errors in calculations, which stem from an incorrect understanding of BIDMAS. Pupils sometimes draw the bottom of a quadratic graph flat if its minimum point lies between two plotted points.

7.4 Real-lifegraphs

2 To draw graphs from real-life situations to illustrate the relationship between two variables

Pupils can get confused by thedifferent ways that times are written. For example, they may assume that1.4 hours is the same as 1 hour and40 minutes or that 1 hour and 50 minutes is 1.5 hours. Make these points to pupils during the lesson.

Challenge –The M25

1 This challenge activity encouragespupils to think about the M25, one ofEurope’s busiest motorways.

8 Number 8.1 Powers of10

1 How to multiply and divide by negative powers of 10

As with all use of powers, pupils tend to confuse 10n with 10 × n. Provide opportunities for pupils to compare the two and understand why they are different. Comparing the two using visual images and making links toarea could also help to reinforce the difference.


1 To round a specific number of significant figures

Pupils sometimes confuse roundingto decimal places and significant figures. Provide opportunities for pupils to compare the two. Some pupils may struggle with the role of 0 and when this counts as a significant figure. Go over the text in the Pupil Book (at the beginning of the lesson) thoroughly.

8.3 Standardform with large numbers

1.5 To write a large number in standard form

Pupils need to be confident with thedefinition of standard form as being a number written as A × 10n. The most important thing is for pupils to appreciate that A is always between 1 and 10 no matter the size (large orsmall) of the number. Be careful how you explain this, as explanations involving moving the decimal point can be misleading and lead to misconceptions about place value ingeneral. Give pupils plenty of practice in converting numbers.

8.4 Multiplyingwith numbers in standardform

2 To multiply with numbers in standard form

Introduce standard form as a powerfultool that is widely used in science. Pupils need to be confident with theideas in the previous lessons before tackling this lesson. Encourage pupils to revisit these lessons if necessary.

Challenge –Space – to see where no onehas seen before

1.5 This activity is designed to combinethe skills covered across this chapter to explore an interesting real-lifeproblem set in a slightly less familiar context. The context is one of thebest examples of the use of very large numbers.

Chapters 6–8 assessment on Collins Connect9Interpreting data

9.1 Interpretinggraphs and diagrams

1 To interpret different charts seen in the media

Go through the key vocabulary thatpupils will use when working with real-life graphs.


9.2 Relativesized pie charts

1 To draw pie charts relative to data size

Demonstrate the correct method ofdrawing pie charts to the class, with emphasis on starting themeasurement of each angle at the end of the previous sector. The sumof the angles of the sectors of any piechart must always be 360°, so pupils should check that the angles add up to 360 (approximation can make the sum of the angles one degree higher or lower).

9.3 Scattergraphs and correlation

1 To read scatter graphs To understand correlation

Explain that correlation does notimply causality, or interconnection, as this is a common problem area in the interpretation of correlation.

9.4 Creatingscatter graphs

2 To create scatter graphs and use a line of best fit

Make sure pupils understand thatscatter diagrams are different to line graphs (some pupils may try to jointhe plots).

Challenge –Football attendances

2 In order to be able to do thischallenge, pupils will need to be able to read and interpret the table, drawpie charts relative to the data in the table, and draw on their knowledge of averages, means and scatterdiagrams. Pupils are given the opportunity to practise these skills in what is most likely a familiar context.

Half-termHalf-term / Term 410 Algebra 10.1 Algebraic

notation1 To simplify algebraic


Pupils may struggle to understandthat letters represent variables, and so try to substitute particular values for the letters. Provide pupils with plenty of opportunity to reflect on the use of algebra as generalised number, and to make clear links tothe rules they have learnt for number. Discuss the power of algebra or generalisation.

10.2 Liketerms

1 To simplify algebraic expressions by combining like terms

Pupils often struggle to identify whatconstitutes ‘like’ in this context. Provide opportunities for pupils tocompare and discuss what are and what are not like terms. Pupils often do not make the connection fromLesson 10.1 that when we write a letter with no number in front such as x, that there is in fact a 1 in front ofthe x and we have ‘one x’. Say that this is just one of the conventions of writing mathematics that hasdeveloped over the years.


1 To remove brackets from an expression

Pupils often forget to multiply all theterms in brackets. Pupils also struggle to interpret negative signs in brackets accurately. Making links to grid multiplication may be useful to help pupils make links and visualise whatis happening.

10.4 Usingalgebraic expressions

2 To manipulate algebraic expressions

To identify algebraic expressions

Difficulties with substitution intoformulae often come from a failure to grasp the fundamentals of BIDMASand negative numbers, along with an inability to recognise that letters represent variables. When this is thecase, pupils tend to want to substitute specific values. Provide lots of opportunity for pupils to see this inaction in familiar contexts, before moving on to more complex or abstract examples.

10.5 Usingindex notation

2 To write algebraic expressions involving powers

Pupils struggle to identify whatconstitutes ‘like’ when powers are included. Provide plenty ofopportunity for pupils to compare and


discuss what are and what are notlike terms.

Mathematicalreasoning – Writing inalgebra

2 This activity develops pupils’confidence and fluency with algebraic notation. Pupils may struggle todecode everyday language into mathematics, so this activity also gives pupils the opportunity topractise this in a range of contexts.

11 Shape andratio

11.1 Ratio oflengths, areas and volumes

1 To use ratio to compare lengths, areas and volumes of 2D and3D shapes

Pupils often make errors with units inquestions involving ratio. Remind them that the units must be the same before they form a relationship involving ratio.

11.2 Fractionalenlargement

1 To enlarge a 2D shape by a scale factor

Pupils often use an incorrect point asthe centre of enlargement, or they just enlarge the shape without referenceto the given point.Sometimes pupils do not enlarge all the lines, or they enlarge by anincorrect scale factor. Remind pupils that the shape produced after anenlargement will look similar to the original; it will just be a bigger or smaller version.

11.3 Mapscales

2 To understand how to use map scales

Pupils occasionally mix units whenworking with map scales. Make sure pupils understand that units must bethe same before writing a ratio.

Activity – Mapreading

2 This activity consolidates topicspreviously covered on extracting data, area and ratio.

Chapters 9–11 assessment on Collins ConnectHolidays

Half-term / Term 512 Fractions anddecimals

12.1 Addingand subtractingfractions

2 To add or subtract fractions and mixed numbers

Pupils often get taught rules withoutfully understanding them. As a result, pupils may struggle to apply the rulesin different contexts and often confuse the rules for adding andsubtracting fractions with those for multiplying and dividing fractions. Another common problem is that pupils add or subtract thedenominators as well as the numerators when adding and subtracting fractions.


2 To multiply a fraction or a mixed number and an integer

12.3 Dividingwith integers and fractions

2 To divide a fraction or a mixed number by an integer

To divide an integer or a mixed number by a fraction

12.4Multiplication with large and small numbers

1 To multiply with combinations of large and small numbers mentally

Pupils often find decimal fractionsdifficult to understand, though without realising it, they may have encountered decimals when solving money problems. Working with decimals is an extension of pupils’ understanding of place value. Most pupils have an understanding that each column to the left of another is10 times greater. Build on this so that pupils are aware that each column tothe right is 10 times smaller.

12.5Division with large and smallnumbers

1 To divide combinations of large or small numbers mentally

Challenge –Guesstimates

1 This activity gives pupils theopportunity to practise their mental strategies in some real-life contexts. It also encourages pupils to make linksto the use of estimation as well as the need to make assumptions when tackling real-life problems.

13 Proportion 13.1 Directproportion

1 To understand the meaning of direct proportion

To find missing values in problems involving proportion

Pupils often mix up direct and inverseproportion, usually by using direct proportion to answer inverseproportion questions. Pupils sometimes use an incorrect multiplier.

13.2 Graphsand direct proportion

1 To represent direct proportion graphically and algebraically

Some pupils may struggle to drawcorrectly scaled axes for questions in this exercise. Draw the scales forthese pupils and explain the reasoning behind the chosen values.



1 To understand what inverse proportion is

To use graphical and algebraic representations of inverse proportion

Pupils often use direct proportionrather than inverse proportion. Make sure pupils can point out key words ina question that indicate inverse proportion. Also make sure that pupils write the variables the correct wayaround in their formula.

13.4Comparing direct proportion and inverse proportion

1 To recognise direct and inverse proportion and work out missing values

Make sure that pupils are aware ofthe important words in a question,and the patterns of numbers in a table that indicate whether to use direct orinverse proportion.

Challenge –Planning a trip

1 For this challenge pupils apply theirunderstanding of proportion to a typical real-life context including speed, time and fuel consumption. The questions increase in complexity and pupils can use a range ofgraphical and algebraic skills to tackle them. They also need to be able tointerpret some complex language.

Chapters 12–13 assessment on Collins Connect14 Circles 14.1 The

circumference of a circle

1 To know the definition of a circle and the names of its parts

To work out the relationship between the circumference and diameter of a circle

Pupils often confuse radius anddiameter. Give them plenty of opportunity to use both. Collective memory activities would be useful to help pupils remember which is which.

14.2 Formulafor the circumferenceof a circle

1 To calculate the circumference of a circle

Pupils often do not make the linkbetween the work they have done previously on perimeter and area, andthe work on the circumference and area of a circle.

14.3 Formulafor the area of a circle

1 To calculate the area of a circle Pupils may confuse the definitions ofthe parts of circles. They may also confuse the formulae, particularly interms of the use of radius and diameter. This is because pupils cannot visualise what they are doing.Use activities like the one in Part 2 of Lesson 14.1 to help pupils overcome both of these problems.

Financial skills– Athletics stadium

2 This activity is designed to give pupilsthe opportunity to apply their knowledge to a multi-step real-lifeproblem. The context is common, but is presented in a slightly morecomplex way than pupils are used to.


15.1 Equations with brackets

1 To solve equations involving brackets

To solve equations where the answers are fractions ornegative numbers

A common problem often seen whenexpanding a bracket is to multiply the first term by the number outside thebracket and just write down the second term. Pupils will sometimes get confused with adding orsubtracting from each side when dealing with equations with unknowns on both sides.

15.2 Equationswith the variable onboth sides

1 To solve equations with the variable on both sides

Pupils are sometimes confused withadding or subtracting from each side when dealing with equations withunknowns on both sides. Make it clearer for less able pupils by explaining that to remove a negativevalue they must add to both sides; to remove a positive value they must subtract from both sides. Pupils whostruggle may benefit from following these steps:1. Remove the smallest x value by

adding or subtracting from both sides (explain, for example, that –5x is smaller than 2x).

2. Remove the number on the same side as the remaining x value by


adding or subtracting from bothsides.

3. Finally, divide both sides by the number in front of the x to obtainyour answer.

15.3 Morecomplex equations

2 To solve equations with brackets and fractional coefficients

To solve simple equations involving squares

A common problem that pupils havewhen expanding a bracket is to multiply the first term by the numberoutside the bracket and write down only the second term. Another problem is that sometimes pupils addinstead of multiplying. When solving equations that contain fractions, pupils will sometimes remove the fraction by multiplying, but they leavethe denominator next to the bracket.For example: 1 (x + 2) = 5 may be4written incorrectly as: 4(x + 2) = 20.

15.4Rearranging formulae

1 To change the subject of a formula

To change the subject of a formula involving squares

Pupils sometimes forget to applyBIDMAS correctly when rearranging formulae, so their answers areincorrect. Remind pupils that when rearranging a formula, they should follow the methods learned earlier inthe chapter for solving equations. Pupils who struggle with rearranging formulae may find the input-outputmethod easier to understand.

Mathematicalreasoning – Using graphs to solve equations

1 In this activity, pupils will usemathematical reasoning to make links between equations and formulae and their graphical representations. Comparing graphical and algebraic representations enables pupils to check their ability to solve equations. Tell pupils that the ability to use different representations to checktheir understanding is a valuable skill.

16 Comparingdata

16.1 Groupedfrequency tables

1 To create a grouped frequency table from raw data

Pupils often struggle to identifyappropriate groups. They want to follow a set of rules and often strugglewith making links between the data and the question that is being asked. They often fail to appreciate how thisshould inform their decisions. Give them lots of real life examples to discuss. This will help them see thereis not necessarily a correct answer but that some grouping is more efficient/informative than others.


1 To interpret frequency diagrams To draw a frequency diagram

from a grouped frequency table

Pupils often do not associate drawingfrequency diagrams with the analytical process of comparingoutcomes or gathering evidence to support a hypothesis. Give pupils arange of examples, some good and some less good, from real-life contexts. Ask pupils to discuss howuseful the representations are in terms of assessing the evidence and/or delivering a clear message.

16.3Comparing sets of data

2 To be able to compare data from two sources

Pupils may struggle with interpretingdata accurately. Provide many opportunities for pupils to comparedifferent representations. Encourage pupils to generate their own questions about the data and to assess theadvantages and disadvantages of different representations and statistical measures.

16.4Misleading charts

To recognise when a statistical chart may be misleading

In real life, people often accept datawithout being critical of where it has come from or how it is being used. Aspart of this critical appraisal, pupils need to consider how the data is


being represented. In preparation forthis lesson you could have a class discussion around some topicalexamples in the media.

Problemsolving – Why do we use so many devices to watch TV?

1 This activity is designed to combineall the lessons in this chapter by taking pupils through the steps of tabulating and displaying data for a familiar real-life problem. All the data is given, but pupils will need to read and think carefully about how they display the data so that they can make valid comparisons.

Chapters 14–16 assessment on Collins ConnectEnd of year assessment on Collins Connect





Half-term / Term 11Percentages

1.1 Simple interest

1 • To understand what simple interest is

• To solve problemsinvolving simple interest

Pupils often struggle when they start usingpercentages greater than 100. Using real- life examples will help them overcome this.Start with percentages that pupils are already comfortable working with.

1.2 Percentageincreases and decreases

1 • To calculate the result of apercentage increase or decrease

• To choose the most appropriate method to calculate a percentage change

Pupils need a good understanding of 100%as a whole before tackling percentage increases and decreases successfully.The concept of using percentage as an operator is an important step to ensure confidence and fluency, so make sure you take time over it.

1.3 Calculatingthe original value

2 • Given the result of apercentage change, to calculate the original value

This lesson looks at inverse operations tocalculate the percentage change or to calculate an initial value. This is anotherconcept with which pupils will need to be fluent, to ensure confidence in applyingtheir understanding of percentages to real- life problems.

1.4 Usingpercentages

1 • To revise the links withinfractions, decimals and percentages

• To choose the correct calculation to work out a percentage

Pupils often meet the different types ofquestions over a period of time, so they never have the opportunity to identify thetype of question and make independent decisions about which method to use. Give pupils lots of opportunity to check theirunderstanding by making choices and decisions over the approaches they use in a range of increasingly complex andunfamiliar situations.

Challenge – TheRoyal Albert Hall

2 This challenge activity starts with a literacyactivity and moves onto calculations involving time and percentages in a real-life situation. Pupils will need to have grasped the work on percentages from the chapter. Less able pupils may need a quick explanation of significant figures and daysin a year before starting the activity. This activity could be linked to other subjectssuch as History

2 Equationsand formulae

2.1 Multiplyingout brackets

1 • To multiply out brackets This chapter builds on previously learnedalgebraic techniques and moves on to more advanced methods of algebraicmanipulation. These include: expanding brackets, factorising algebraic expressions and solving linear equations involvingbrackets and fractions.

2.2 Factorisingalgebraic expressions

1 • To factorise expressions


1 • To solve equations withone or more sets of brackets

2.4 Equationswith fractions

1 • To solve equationsinvolving fractions

2.5 Formulae 1 • To practise using formulae

Maths Frameworking 3rd edition © HarperCollinsPublishers Ltd 2014Teacher Pack 3.1

Financial skills –Wedding day

1 This financial skills activity gives pupils theopportunity to apply the skills they have learned in the chapter to a practicalsituation that many will encounter in the future. The cost formula used is often encountered in GCSE exams and it isimportant that pupils have a good grasp of this.

Chapters 1–2 assessment on Collins Connect3 Polygons 3.1 Polygons 1 • To know the names of

polygons• To know the difference

between an irregular polygon and a regularpolygon

This chapter introduces the sums of theinterior and exterior angles of polygons, including regular polygons.

3.2 Angles inpolygons

1 • To work out the sum ofthe interior angles of a polygon

3.3 Interiorangles of regular polygons

1 • To work out the sizes ofthe interior angles in regular polygons

Activity – Regularpolygons and tessellations

2 For this activity, pupils learn abouttessellations and use their knowledge of angles and polygons to find out if regularpolygons will tessellate. Ask more able pupils to come up with solutions tocombine polygons that don’t tessellate with other polygons in order to make a tessellation pattern.

Half-termHalf-term / Term 24 Using data 4.1 Scatter

graphs and correlation

1 • To infer a correlation fromtwo related scatter graphs

This chapter picks up the ideas from previous years in statistics. It develops ways of illustrating distributions and howwe can use data to explore possibilities as well as to compare them. This chapter concludes with pupils conducting their owninvestigations, using the ideas from the first part of the chapter.

4.2 Interpretinggraphs and diagrams

1 • To use and interpret avariety of graphs and diagrams

4.3 Two-waytables

1 • To interpret a variety oftwo-way tables

4.4 Comparingtwo or more sets of data

1 • To compare two sets ofdata from statistical tables and diagrams

In order to make comparisons betweengraphs, pupils need to be able to understand what the graph represents,what the axes mean and how to read data from the graph.

4.5 Statisticalinvestigations

1 • To plan a statisticalinvestigation

Challenge –Rainforest deforestation

1 This challenge does not intend to makeany judgement values. Instead, this activity has been devised to allow pupils to find what the statistics may suggest – in other words, that economic growth can affect the amount of deforestation.

Chapters 3–4 assessment on Collins Connect5 Circles 5.1 The formula

for the circumference ofa circle

1 • To calculate thecircumference of a circle

Pupils are introduced to the number π andthen shown how to use it in order to calculate the area and circumference of acircle. Pupils can then show their understanding by applying their learning to a variety of practical problems involvingarea and circumference.Make sure pupils understand the difference between perimeter and circumference.

5.2 The formulafor the area of a circle

2 • To calculate the area of acircle

5.3 Mixedproblems

2 • To solve problemsinvolving the circumference and area ofa circle

Financial skills – Athleticsstadium

2 This financial skills activity is designed to give pupils the opportunity to apply theirknowledge to a multi-step real-life problem. Pupils will need to have a good understanding of the work covered in thechapter along with volumes of prisms.

6Enlargements

6.1 Scale factorsand enlargements

2 • To use a scale factor toshow an enlargement

This chapter builds on previous years’ workon scale and scale drawing and introduces pupils to the concept of enlarging a shape by a scale factor.6.2 The centre

of enlargement1 • To enlarge a shape about

a centre of enlargement


6.3Enlargements on grids

2 • To enlarge a shape on acoordinate grid

Problem solving– Photographs

2 This problem solving activity is designed togive pupils the opportunity to apply their knowledge of enlargements to a multi-stepreal-life problem.

HolidaysHalf-term / Term 37 Fractions 7.1 Adding and

subtracting fractions

1 • To add or subtract anytwo fractions

This chapter builds on the Year 8 work onfractions. Pupils often get taught rules without fully understanding them and oftenconfuse rules for adding and subtracting fractions with those for multiplying and dividing fractions. Take time to buildunderstanding; don’t just teach the process.

7.2 Multiplyingfractions

1 • To multiply two fractions

7.3 Dividingfractions

1 • To divide one fraction byanother

Problem solving– The 2016Olympic Games in Rio

2 In this problem solving activity pupils arerequired to apply their understanding of fractions to a more complex problem.Pupils need to work methodically and be able to explain their solutions.

Chapters 5–7 assessment on Collins Connect8 Algebra 8.1 Expanding

brackets1 • To multiply out brackets

with a variable outside them

This chapter recalls previous work onalgebra and revisits expansion of brackets and collection of like terms.Pupils are then shown how to completely factorise a linear expression.Finally the more complex technique ofexpanding a pair of brackets and simplifying into a quadratic expression is introduced to pupils. Using the FOIL method to expand two brackets is a technique that may be useful.



8.3 Expand andsimplify

2 • To expand expressionswith two brackets and simplify them

Challenge –California gold

1 This challenge activity requires pupils toapply their learning in an unfamiliar context. Introduce it with some recentexamples of treasure trove finds from the internet and get pupils to research the current price of gold per gram.

9 Decimalnumbers

9.1 Multiplicationof decimals

1 • To practise multiplyingdecimal numbers

The ability to understand place value isvery important for being able to use numbers effectively when doingcalculations in real life. The work in this chapter builds on pupils’ existingknowledge. If necessary, check earlier objectives involving an understanding of place value.

9.2 Powers of10

1 • To understand and workwith both positive and negative powers of ten

9.3 Roundingsuitably

1 • To round numbers, wherenecessary, to a suitable degree of accuracy

9.4 Dividingdecimals

1 • To confirm ability to dividewith decimals

9.5 Solvingproblems

1 • To solve real-life problemsinvolving multiplication or division

Pupils often struggle to decode wordproblems to identify the mathematics they need to use. Provide plenty of opportunity for pupils to discuss word problems to identify the mathematics required independently.

Mathematicalreasoning – Paper

2 All the information is provided in thismathematical reasoning activity, but it is quite complex. Pupils will need to read the questions very carefully to decide whichinformation they need and what mathematical skills to use in each case.

Half-termHalf-term / Term 410 Surfacearea and volume of 3Dshapes

10.1 Surfacearea of cubes and cuboids

2 • To work out the surfacearea of cubes and cuboids

Pupils often get confused when convertingbetween different units for area and volume, and simply multiply or divide bythe length conversion factor. Make sure that pupils know the difference whenconverting between area and volume.

10.2 Volume ofcubes and cuboids

2 • To use a simple formula towork out the volume of a cube and cuboid

• To work out the capacity of a cube or cuboid

10.3 Volume oftriangular prisms

2 • To work out the volume ofa triangular prism

Some pupils are confused by the differencebetween working out volume and surface area.


Investigation – Acube investigation

2 Pupils apply their understanding of area toa more complex problem in this investigation. They will need to workmethodically and be able to explain their solutions. Start by introducing them to the use of isometric paper. Ask more ablepupils to justify any rules they discover by revisiting the structure of the problem.

Chapters 8–10 assessment on Collins Connect11 Solvingequations graphically

11.1 Graphsfrom equations in the formy = mx + c

1 • To draw a linear graphfrom any linear equation

• To solve a linear equation from a graph

This chapter provides examples of the factthat many equations can arise from real-life situations, and it builds on straight-line graphs and quadratics with more complex examples. Pupils are introduced to the idea that while many equations that are used to model real life are difficult to solve by algebraic methods, they are more easily solved by drawing a graph.

11.2 Problemsinvolving straight-linegraphs

1 • To draw graphs to solvesome problems

11.3 Solvingsimple quadratic equations by drawing graphs

2 • To solve a simplequadratic equation by drawing a graph

11.4 Problemsinvolving quadratic graphs

2 • To solve problems thatuse quadratic graphs

Problem solving– Squirrels

2 This problem solving activity gives pupilsthe opportunity to involve themselves in the practical aspects of using data in real life contexts. Make sure pupils have a good understanding of correlation.

HolidaysHalf-term / Term 512 Distance, speed and time

12.1 Distance 2 • To work out the distance travelled in a certain time at a given speed

• To use and interpret distance–time graphs

This chapter teaches pupils how tocalculate with different measures. Pupils are introduced to the relationship betweenspeed, distance and time.

12.2 Speed 2 • To work out the speed ofan object, given the distance travelled and thetime taken

12.3 Time 2 • To work out the time anobject will take on a journey, given its speed and the distance travelled

Financial skills –Shopping at the market

1 This financial skills activity requires pupilsto apply their learning from this chapter in an everyday, practical context. You couldextend this activity by asking pupils to compare prices of the same product indifferent quantities from supermarket sites on the internet.

13 Similartriangles

13.1 Similartriangles

2 • To understand whatsimilar triangles are

This chapter introduces the importantproperties of why triangles can be classed as similar and demonstrates to pupils howthey can use these properties in real-life situations. Take your time with the introduction, making links with proportional reasoning. Otherwise pupils will struggle toretain what they have learnt in this lesson.

13.2 A summaryof similar triangles

1

13.3 Usingtriangles to solve problems

2 • To understand thattriangles can be used to solve some real problems

Investigation –Barnes Wallis and the bouncing bomb

2 This investigation is an interestingapplication of the learning in this unit. Pupils may be familiar with the idea from films but will probably be surprised at itsuse here. This is a good opportunity to demonstrate links to other subjects, in this case history.

Chapters 11–13 assessment on Collins Connect


14 Revisionand GCSEpreparation

• Practice• Revision• GCSE-type

questions

6 This chapter is going to:• Help pupils to practise and

revise topics covered intheir current course

• Get pupils started on theirGCSE course

The exercises in this chapter of the PupilBook cover the following mathematical strands:• Algebra• Geometry and measures• Statistics• NumberThe material will provide excellent practice so that pupils become mathematicallyfluent. Encourage pupils to work through this whole chapter before their End of Year9 tests.

Chapter 14 assessment on Collins ConnectEnd of year assessment on Collins Connect






1.1 Simple interest

1 • To understand what simple interest is

• To solve problems involving simple interest

Pupils often struggle when they start usingpercentages greater than 100. Using real- life example will help them overcome this.Start with percentages that pupils are already comfortable working with.


1 To calculate the result of a percentage increase or decrease

To choose the most appropriate method to calculate a percentage change

Pupils need a good understanding of 100%as a whole before tackling percentage increases and decreases successfully.The concept of using percentage as an operator is an important step to ensure confidence and fluency, so make sure you take time over it.

1.3 Calculatingthe original value.

2 Given the result of a percentage, to calculatethe original value

This lesson looks at inverse operations tocalculate the percentage change or to calculate an initial value. This is anotherconcept with which pupils will need to be fluent, to ensure confidence in applyingtheir understanding of percentages to real- life problems

1.4 Usingpercentages

1 To choose the correct calculation to work out a percentage

Pupils often meet the different types ofquestions over a period of time, so they never have the opportunity to identify thetype of question and make independent decisions about which method to use. Give pupils lots of opportunity to check theirunderstanding by making choices and decisions over the approaches they use in a range of increasingly complex andunfamiliar situations.

Challenge –Exponential growth

2 This challenge gives pupils the opportunityto extend their learning by making links to other areas of mathematics including the work in Chapter 5 (Applications of graphs).



1 • To multiply out brackets This chapter builds on previously learnedalgebraic techniques and moves on to more advanced methods of algebraicmanipulation. These include: expanding brackets with negative coefficients, factorising algebraic expressions, solving linear equations involving fractions andrearranging formulae.




1 • To solve equations with one or more sets of brackets


1 • To solve equations involving fractions

2.5 Rearrangingformulae

1 To change the subject of a formula

Investigation –Body mass index

1 This investigation will help to embed theconcepts and skills learned in this chapter.

Chapters 1–2 assessment on Collins Connect3 Polygons 3.1 Angles in

polygons1 To work out the sum of the

interior angles of apolygon

To work out exterior angles of polygons

This chapter introduces the sums of theinterior and exterior angles of polygons. It also includes more complex constructions.Pupils try to learn justifications such as those in Lesson 3.1 and Lesson 3.3 by


3.2Constructions

1 To make accurate geometric constructions

memory instead of understanding the logic. Discuss this with pupils so that they are clear on this. Give pupils the opportunity toidentify the steps in the process and to use similar logic in different contexts.

3.3 Angles inregular polygons

1 To work out the exterior angles of a regularpolygon

To work out the interior angles of a regular polygon

3.4 Regularpolygons and tessellations

1 To work out which regular polygons tessellate

Activity –Garden design

1 For this activity, pupils will need to applytheir knowledge of angles in polygons and more complex multi-step constructions.

Half-term / Term 24 Using data 4.1 Scatter


1 To infer a correlation from two related scatter graphs

This chapter picks up the ideas fromprevious years in statistics. It develops ways of illustrating distributions and howwe can use data to explore possibilities as well as to compare them. This chapter concludes with pupils conducting their owninvestigations, using the ideas from the first part of the chapter.

4.2 Time-seriesgraphs

1 To use and interpret a variety of time-series graphs

4.3 Two-waytables

1 To interpret a variety of two-way tables

4.4 Comparingtwo or more sets of data

1 To compare two sets of data from statistical tables and diagrams

In order to make comparisons betweengraphs, pupils need to be able to understand what the graph represents,what the axes mean and how to read data from the graph.


1 To plan a statistical investigation

Challenge –Rainforest deforestation

1 This challenge does not intend to makeany judgement values. Instead, this activity has been devised to allow pupils to findwhat the statistics may suggest; in other words, that economic growth can affect theamount of deforestation.

5 Applicationsof graphs

5.1 Step graphs 1 To interpret step graphs Graphs are common in everyday life but itis important that pupils understand what different graphs can and cannot tell them.

5.2 Time graphs 2 To interpret and draw time graphs

5.3 Exponentialgrowth graphs

2 To interpret and draw exponential growth graphs

Problem solving– Mobile phone tariffs

2 This activity uses the context of mobilephones, a topic that will be very familiar to pupils. However, pupils may not havethought of using graphs to make the best decisions about which tariff to buy.

Chapters 3–5 assessment on Collins Connect6 Pythagoras’theorem

6.1 IntroducingPythagoras’theorem

2 To understandPythagoras’ theorem

This chapter teaches pupils aboutPythagoras’ theorem as well as giving them the opportunity to apply it to morecomplex and real-life situations.6.2 Calculating

the length of the hypotenuse

1 To calculate the length of the hypotenuse in a right-angled triangle

6.3 Calculatingthe length of a shorter side

2 To calculate the length of a shorter side in a right- angled triangle

To show that a triangle is right-angled

6.4 UsingPythagoras’theorem to solve problems

1 To use Pythagoras’theorem to solve problems

Activity –PracticalPythagoras

1 This practical activity will help to deepenpupils’ understanding of Pythagoras’theorem.

Half-term / Term 37 Fractions 7.1 Adding and


1 To add or subtract any two mixed numbersconfidently

This chapter builds on the Year 8 work onfractions. Pupils often get taught rules without fully understanding them and often


confuse rules for adding and subtracting fractions with those for multiplying and dividing fractions. Take time to buildunderstanding, not just teaching the process.

7.2 Multiplyingfractions

1 To multiply two fractions

7.3 Multiplyingmixed numbers

1 To multiply one mixed number by another

7.4 Dividingfractions and mixed numbers

1 To divide one fraction or mixed number by another

Investigation –Fractions from one to six

1 In this investigation pupils are required toapply their understanding of fractions to a more complex problem. Pupils need to work methodically and be able to explain their solutions.

8 Algebra 8.1 More aboutbrackets

1 To expand a term with a variable or constantoutside brackets

This chapter recalls previous work onalgebra and revisits expansion of brackets and collection of like terms.

8.2 Factorisingexpressions containing powers

2 To take out a variable as a factor

8.3 Expandingthe product of two brackets

2 To multiply out two brackets

Challenge –Graphs from expressions

1 This challenge activity requires pupils toapply their learning from this chapter in a less familiar practical context.

Chapters 6–8 assessment on Collins Connect9 Decimalnumbers

9.1 Powers of10

1 To understand and work with both positive andnegative powers of ten

The ability to understand place value isvery important for being able to use numbers effectively when doing calculations in real life. The work in this chapter builds on pupils’ existing knowledge. If necessary, check earlier objectives involving an understanding of place value.

9.2 Standardform

1 To understand and work with standard form, using both positive and negativepowers of ten

9.3 Roundingappropriately

1 To round numbers, where necessary, to anappropriate or suitable degree of accuracy

9.4 Mentalcalculations

1 To learn and understand some routines that can help in mental arithmetic

9.5 Solvingproblems

1 To solve real-life problems involving multiplication ordivision

Pupils often struggle to decode wordproblems to identify the mathematics they need to use. Provide plenty of opportunityfor pupils to discuss word problems to identify the mathematics requiredindependently.

Mathematicalreasoning – Paper

2 All the information is provided but it is quitecomplex. Pupils will need to read the questions very carefully to decide which information they need and what mathematical skills to use in each case.

Half-term / Term 410 Prismsand cylinders

10.1 Metric unitsfor area and volume

1 To convert from one metric unit to another

Pupils often get confused when converting between different units for area and volume, and simply multiply or divide bythe length conversion factor. Make sure that pupils know the difference when converting between area and volume.

10.2 Volume ofa prism

1 To calculate the volume of a prism

10.3 Surfacearea of a prism

1 To calculate the surface area of a prism

Some pupils are confused by the difference between working out volumeand surface area.10.4 Volume of

a cylinder1 To calculate the volume of

a cylinder10.5 Surfacearea of a cylinder

2 To calculate the curved surface area of a cylinder

To calculate the total surface area of a cylinder

Problem solving– Packaging cartons of fruit juice

2 This problem-solving activity will helppupils to make their learning relevant, by applying it to a real-life situation.



11 Solvingequations graphically

11.1 Graphsfrom equations in the formay ± bx = c

1 To draw any linear graph from any linear equation

To solve a linear equation from a graph

This chapter provides examples of the factthat many equations can arise from real-life situations, and it builds on straight-linegraphs and quadratics with more complex examples. Pupils are introduced to the idea that while many equations that are used tomodel real life are difficult to solve by algebraic methods, they are more easily solved by drawing a graph.

11.2 Graphsfrom quadratic equations

1 To draw graphs from quadratic equations

11.3 Solvingquadratic equations by drawing graphs

2 To solve a quadratic equation by drawing a graph

11.4 Solvingsimultaneous equations bygraphs

2 To solve a pair of simultaneous equations

Challenge –Linear programming

2 Pupils often ask why they do mathematicswith which they are not familiar. Linear programming is a good example of howmathematics can be used for unexpected and exciting ways that are extremely valuable in a modern society.

Half-term / Term 512 Compoundunits

12.1 Speed 2 To understand and use measures of speed

This chapter teaches pupils how tocalculate with different measures. Pupils are introduced to the relationship betweenspeed, distance and time, followed by the relationship between mass, density and volume.

12.2 More aboutproportion

2 To understand and use density and other compound units

12.3 Unit costs 2 To understand and use unit pricing

Challenge –Population density


13 Right-angled triangles

13.1 Introducingtrigonometric ratios

2 To understand what trigonometric ratios are

This chapter introduces these importantproperties of right-angled triangles and demonstrates to pupils how they can use these properties in real-life situations. Take your time with the introduction, makinglinks with proportional reasoning, otherwise pupils will struggle to retain what they have learnt in this lesson.

13.2 How to findtrigonometric ratios of angles

1 To understand what the trigonometric ratios sine,cosine and tangent are

13.3 Usingtrigonometric ratios to findangles

1 To find the angle identified from a trigonometric ratio

13.4 Usingtrigonometric ratios to find lengths

1 • To find an unknown length of a right-angled triangle given one side and another angle

Investigation –Barnes Wallis and thebouncing bomb

2 This investigation is an interestingapplication of the learning in this unit. Pupils may be familiar with the idea fromfilms but will probably be surprised at its use here. This is a good opportunity to demonstrate links to other subjects, in thiscase history.

Chapters 11–13 assessment on Collins Connect14 Revisionand GCSEpreparation

Practice Revision GCSE-type

questions

6 This chapter is going to: Help pupils practise and

revise topics covered in their current course

Get pupils started on their GCSE course

The exercises in this chapter of the PupilBook cover the following mathematical strands: Algebra Geometry and measures Statistics NumberThe material will provide excellent practice so that pupils become mathematicallyfluent. Encourage pupils to work through this whole chapter before their End of Year9 tests.







1.1 Simpleinterest

1 • To understand what ismeant by simple interest

• To solve problems involving simple interest

Pupils often struggle when they start usingpercentages that are greater than 100. Use real-life examples to help pupils overcomethis. Start with percentages that pupils can work with comfortably.


1 • To use the multipliermethod to calculate the result of a percentageincrease or decrease

• To calculate the percentage change in avalue

Pupils need a good understanding of 100%as a whole before tackling percentage increases and decreases successfully. Usereal-life examples and start with percentages that pupils can work withcomfortably.

1.3 Calculatingthe original value

2 • Given the result of apercentage change, to calculate the original value

This lesson continues to develop theconcept of using percentage as an operator by looking at the inverse tocalculate the percentage change or to calculate an initial value. Pupils will need to be fluent with this concept so that they areconfident in applying their understanding of percentages to real-life problems. Encourage discussion to challenge anymisconceptions.

1.4 Repeatedpercentage changes

1 • To calculate the result ofrepeated percentage changes

Pupils often learn rules without reallyunderstanding them. This means that pupils may meet the different questions over time, and so may never have the opportunity to identify the type of question and make independent decisions about which method to use. Provide pupils with opportunities in a range of increasingly complex and unfamiliar situations

Challenge –Exponential growth

2 This challenge activity gives pupils theopportunity to extend their learning by exploring the connected but unfamiliar context of exponential growth that links this lesson with other areas of mathematics, including the work in Chapter 5 (Applications of graphs).



1 • To expand brackets andsimplify more complex expressions

This chapter builds on previous work onexpanding a term over brackets, and recalls expansion of two such terms andsimplification of the results by collecting like terms. This is an introduction tofactorisation of terms into a bracket with a numerical and/or algebraic coefficient outside. Pupils are then shown how tofactorise a quadratic expression. Finally, pupils will learn how to solve equations involving fractions.


1 • To factorise more complexexpressions

2.3 Expressionswith several variables

1 • To expand and factoriseexpressions with more than one variable


1 • To solve equations wherethe variable is in the denominator of a fraction

Investigation –Body mass index

1 This investigation will help to embed theconcepts and skills that pupils have learned in this chapter.



3 Polygons 3.1 Properties ofpolygons

1 • To work out the sum of theinterior angles of a polygon

• To work out exterior angles of polygons

This chapter introduces pupils to findingthe sums of the interior and exterior angles of polygons. Further work on regularpolygons is discussed by using tessellations. Pupils apply their existingknowledge to solve geometrical reasoning introducing them to simple ideas of proof.

3.2 Interior andexterior angles of regularpolygons

1 • To calculate the interiorand exterior angles of regular polygons

3.3Tessellations and regularpolygons

1 • To work out which regularpolygons tessellate

Mathematicalreasoning – Semi-regular tessellations

2 This activity is designed to give pupils theopportunity to apply what they have learnt about tessellation to a more complex problem. The activity combines work that pupils have done previously on angles, and in some cases algebra. Pupils will need to use this prior learning in ways with which they are familiar, but they will also need to extend what they know in order to support more detailed arguments.

Half-termHalf-term / Term 24 Using data 4.1 Scatter


1 • To infer a correlation fromtwo related scatter graphs

• To draw a line of best fit to show a correlation

This chapter picks up the ideas fromprevious years in statistics. It develops ways of illustrating distributions and howwe can use data to explore possibilities as well as compare them. Pupils are introduced to cumulative frequency graphsand shown how to calculate the interquartile range. Finally, pupils will learn how to conduct their own investigationsusing the ideas from the first part of the chapter.

4.2 Two-waytables

1 • To interpret a variety oftwo-way tables

4.3 Estimation ofa mean from grouped data

1 • To estimate a mean fromgrouped data

4.4 Cumulativefrequency diagrams

1 • To draw a cumulativefrequency diagram

• To find the interquartile range

Occasionally pupils forget to add thefrequencies or make mistakes when doing so. Remind pupils that the last cumulativefrequency value will be the same as the total frequency. Pupils may also forget toplot on the upper class width. Explain why we do this.


1 • To plan a statisticalinvestigation

Challenge –Census

1 In this challenge activity, pupils arerequired to apply their learning to a real-life situation. Ask pupils what they know aboutthe national census.

5 Applicationsof graphs

5.1 Step graphs 1 • To interpret step graphs Graphs are used in many real-lifesituations. The example given to introduce this chapter in the Pupil Book is to improvethe performance of racing-car drivers. Their speed, at various points on the race track, is plotted on a graph, which is thenanalysed by the driver’s team.

5.2 Time graphs 2 • To interpret and draw timegraphs

5.3 Exponentialgrowth graphs

2 • To draw exponentialgrowth graphs

Problem solving– Mobile phone tariffs

2 This activity uses the context of mobilephones, a topic that will be very familiar to pupils. However, pupils may not have thought of using graphs to make the best decisions about which tariff to buy.

Chapters 3–5 assessment on Collins Connect6 Pythagoras’theorem

6.1 IntroducingPythagoras’theorem

2 • To use Pythagoras’theorem in right-angled triangles

This chapter teaches pupils aboutPythagoras’ theorem. First, pupils are introduced to the concept and then shown how to use the theorem to calculate both the hypotenuse and one of the adjacent sides. Next, pupils are shown how to use Pythagoras’ theorem to solve problems. Finally, pupils are introduced to the converse of Pythagoras’ theorem

6.2 Using Pythagoras’ theoremto solve problems

2 • Using Pythagoras’theorem to solve problems


6.3 Theconverse ofPythagoras’theorem

2 • To use the converse ofPythagoras’ theorem

Activity –PracticalPythagoras

1 This practical activity will help to deepenpupils’ understanding of Pythagoras’theorem.

HolidaysHalf-term / Term 37 Fractions 7.1 Adding and


1 • To choose an appropriatemethod to add or subtract mixed numbers

The number system has evolved from itsinitial use, which was simply for counting in positive whole numbers. Later, the number system was extended to include zero, which is very important as a place holderand for negative numbers and fractions. By now, pupils should have an understandingof the ordinal value of fractions as well as their use as operators. This chapter builds on the Year 8 work on fractions, includingusing mixed numbers in a range of situations, and extends this to include algebraic fractions.

7.2 Multiplyingfractions and mixed numbers

1 • To multiply two fractionsor mixed numbers

7.3 Dividingfractions and mixed numbers

1 • To divide one fraction ormixed number by another fraction or mixed number

7.4 Algebraicfractions

1 • To add, subtract, multiplyor divide fractions containing a variable

Investigation – Fractions fromone to six

1 Pupils are required to apply their understanding of fractions to a morecomplex problem. They need to work methodically on the questions and be able to explain their solutions. This is a good transferable skills objective to share withpupils when doing this investigation. Ask pupils to share not only their solutions but also how they approached working on theproblems.

8 Algebra 8.1 Expandingthe product of two brackets

1 • To multiply out (or expand)two brackets

This chapter builds on previous work onexpanding a term over a bracket. Pupils are then shown how to expand two and then three linear brackets to form a quadratic, and cubic expressions. Next, pupils learn how to factorise quadratic expressions before learning how to find the difference of two squares.

8.2 Expandingexpressions with more than twobrackets

1 • To multiply out three ormore brackets

8.3 Factorisingquadratic expressions with positive coefficients

1 • To factorise quadraticexpressions with positive coefficients

8.4 Factorisingquadratic expressions with negative coefficients

1 • To factorise quadraticexpressions with negative coefficients

8.5 Thedifference of two squares

1 • To recognise and use thedifference of two squares

Challenge –Graphs from expressions


Chapters 6–8 assessment on Collins Connect9 Decimalnumbers

9.1 Powers of10

1 • To understand and workwith both positive and negative powers of ten

Place value is a key concept inmathematics. The ability to understand place value is central to the ability to use numbers effectively when doing calculations in real life. The work in this chapter builds on pupils’ existing knowledge. A good understanding of place value is also crucial to the extension to powers and significant figures. Thischapter uses very large and very small numbers to introduce standard form,although pupils have briefly met the idea of using a concise method for representingnumbers of this type. Pupils’ understanding of approximation is also developed through the introduction ofupper and lower bounds.

9.2 Standardform

1 • To understand and workwith standard form, using both positive and negativepowers of ten

9.3 Multiplyingwith numbers in standard form

1 • To multiply numbers instandard form, using both positive and negative powers of ten

9.4 Dividing withnumbers in standard form

1 • To divide numbers instandard form, using both positive and negativepowers of ten

9.5 Upper andlower bounds

1 • To understand the limits ofaccuracy when using rounded data


Mathematicalreasoning – To the stars andback

2 This activity uses the context of outerspace, with which pupils may be familiar. Outer space provides the opportunity forcomplex use of the mathematics that pupils have learnt. In order to do theactivity, pupils will need to draw on and combine learning across the chapter. All the information they need is provided inthe text. However, pupils will need to read each question very carefully so that they can decide on what information andmathematical skills they should use.

Half-termHalf-term / Term 410 Surface area and volume ofcylinders

10.1 Volume of a cylinder

1 • To calculate the volume of a cylinder

Pupils occasionally use mixed units whencalculating the volume of a cylinder. Some pupils are confused by volume and surfacearea. Pupils occasionally forget to check that all of the units are the same before calculating, so remind pupils to provideunits with their answer.

10.2 Surfacearea of a cylinder

2 • To calculate the curvedsurface area of a cylinder

• To calculate the total surface area of a cylinder

10.3 Compositeshapes

2 • To calculate the volumesand surface areas of composite shapes

Problem solving– Packaging soup

2 This activity will help pupils to make theirlearning from this chapter relevant by applying it to a real-life situation.

Chapters 9–10 assessment on Collins Connect11 Solvingequations graphically

11.1 Graphsfrom equations in the formay ± bx = c

1 • To draw any linear graphfrom any linear equation

• To solve a linear equation from a graph

There are all sorts of different equationsthat arise from real situations and pupils will meet some examples in this chapter. They will have met straight-line graphs andquadratics before but this chapter buildson this with more complex examples. It will introduce the idea that many equationsthat are used to model the real world are difficult to solve by algebraic methods and are more easily solved by drawing a graph.

11.2 Solvingsimultaneous equations by drawing graphs

2 • To solve a pair ofsimultaneous equations by drawing graphs

11.3 Solvingquadratic equations bydrawing graphs

2 • To solve quadraticequations by drawing graphs

11.4 Solvingcubic equations by drawinggraphs

2 • To solve a cubic equationby drawing a graph

Challenge –Maximum packages

2 This activity is designed to give pupils theopportunity to apply what they have learnt in a familiar context. However, pupils are unlikely to have considered using graphs in this context before.

HolidaysHalf-term / Term 512 Compound units

12.1 Speed 2 • To understand and use measures of speed

This chapter teaches pupils how tocalculate with different measures. Pupils are introduced to the relationship betweenspeed, distance and time, followed by the relationship between mass, density and volume. Pupils will learn how to solveproblems involving these measures. Pupils will also learn how to solve financial problems using unit costs

12.2 Morecompound units

2 • To understand and usedensity and other compound units

12.3 Unit costs 2 • To understand and useunit pricing

Challenge –Population density

1 This challenge activity requires pupils toapply their learning from this chapter in a less familiar practical context. Remindpupils about S.A.L.T. (scales, axes, labels, titles) when drawing graphs, along with the need for accuracy.

13 Right-angled triangles

13.1 Introductionto trigonometric ratios

2 • To understand whattrigonometric ratios are

Trigonometry is the branch of mathematicsthat studies the relationships between the sides and angles of triangles. This chapterintroduces these important properties of right-angled triangles and demonstrateshow this can be used in real life situations such as estimating the height of a tree.

13.2 How to findtrigonometric ratios of angles

1 • To understand what thetrigonometric ratios sine, cosine and tangent are


13.3 Usingtrigonometric ratios to findangles

1 • To find the angle identifiedfrom a trigonometric ratio

13.4 Usingtrigonometric ratios to findlengths

1 • To find an unknown lengthof a right-angled triangle given one side and anangle

Investigation –Barnes Wallis and the bouncing bomb

2 This investigation is an interestingapplication of the learning in this unit. Pupils may be familiar with the idea from films but will probably be surprised at its use here. This is a good opportunity to demonstrate links to other subjects, in this case history.

Chapters 11–13 assessment on Collins Connect14 Revisionand GCSEpreparation

• Practice• Revision• GCSE

preparation: solving quadratic equations

• GCSE-type questions

6 This chapter is going to:• Help pupils to practise and

revise topics covered intheir current course

• Get pupils started on theirGCSE course

The exercises in this chapter of the PupilBook cover the following mathematical strands:• Number• Algebra• Geometry and measures• StatisticsThe material will provide excellent practice so that pupils become mathematicallyfluent. Encourage pupils to work through this whole chapter before their End of Year9 tests.



· web viewpupil book 1.1 (3-year scheme of work) the following scheme of work provides a...

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