ks3 scheme of work - year 8 - sets 2 & 3: impact 2b · web viewv3 – ch. 1–5 v4...

MATHS DEPARTMENT

YEAR 8SCHEME OF WORK

SETS 2 & 3: IMPACT 2B

SEPT 2004

2B PLAN

AUTUMN TERM – FIRST HALFTopic 1 Understanding Number 2B Ch. 1Topic 2 Symmetry & Angles 2B Ch. 2Topic 3 Fractions, Decimals & Percentages Additional Transition UnitTopic 4 Multiplication & Division 2B Ch. 3Topic 5 Working with Algebra 2B Ch. 4

TEST 1

AUTUMN TERM – SECOND HALFTopic 6 Fractions 2B Ch. 6Topic 7 Probability 2B Ch. 7Topic 8 Decimals & Percentages 2B Ch. 8

TEST 2

SPRING TERM – FIRST HALFTopic 9 Number Patterns 2B Ch. 5Topic 10 Multiplicative Relationships Additional UnitTopic 11 Shape & Measure 2B Ch. 9

TEST 3

SPRING TERM – SECOND HALFTopic 12 Handling Data + unit 2B Ch. 12 + Additional

UnitTopic 13 Positive & Negative Numbers 2B Ch. 10Topic 14 Formulae & Equations 2B Ch. 13

TEST 4

SUMMER TERM – FIRST HALFTopic 15 Graphs 2B Ch. 11Topic 16 Averages 2B Ch. 15Topic 17 Problem Solving Additional Unit

TEST 5

SUMMER TERM – SECOND HALFTopic 18 Perimeter, Area & Volume 2B Ch. 14

“OPTIONAL TESTS”Topic 19 Thinking Proportionally Additional Transition UnitTopic 21

TRANSFORMATIONS???

AUTUMN TERM A TOPIC 1

Topic: Understanding Number NC Level: 3 - 5

NC Programme of Study:Ref2a: use previous understanding of integers and place value to deal with arbitrarily large positive numbers and round them to a given power of 10; order integers.Ref3agij: add, subtract integers and then any number. Recall all positive complements to 100 (e.g. 37+62=100). Develop a range of strategies for mental calculation. Use standard column methods for addition and subtraction of integers.Ref4c: use a variety of checking procedures, including working through the problem backwards, and considering whether the result is of the right order of magnitude.

Learning Objectives: understand place value, recognising HTU etc. add and subtract integers extend mental methods of computation for addition and subtraction consolidate standard column procedures for addition and subtraction mentally estimate and approximate solutions to numerical calculations; justify such estimates use the laws of arithmetic and inverse operations use checking procedures, including working through the problem backwards and considering

whether the answer is sensible round positive numbers to any given power of 10.

Key Vocabulary:PLACE VALUE ORDER ROUND NEAREST CHECK ESTIMATE MENTALImpact Reference:Book 2B – ch. 1

Other references:V3 – ch. 1–5 V4 – ch. 2–4 V5 – ch. 2 KM82 – ch. 2

Mental & Oral Starters:2B folder: pg. 4 – 5 101 Starters: pg. 11, 14-18, 22, 47, 58Discussion opportunities:Spend time allowing pupils to explain their methods for addition / subtraction.Discuss whether an answer is ‘sensible’.Pair / Group Work:Students can show each other their methods or check each others’ answers; compare estimations.ICT Links:SMILESpiritual/Moral/Citizenship Links:

Investigation:

Time: 5 lessons

AUTUMN TERM B TOPIC 2

Topic: Fractions, Decimals & Percentages

NC Level:

NC Programme of Study:

Learning Objectives: Begin to use the equivalence of fractions, decimals and percentages to compare proportions Recall known facts including fraction to decimal conversions Use known facts to derive unknown facts, including products such as 0.7 & 6, and 0.03 & 8 Consolidate and extend mental methods to include decimals, fractions and percentages Solve word problems mentallyKey Vocabulary:EQUIVALENT FRACTION DECIMAL PERCENTAGECONVERT NUMERATOR DENOMINATOR PROPORTION

Impact Reference: Other references: Transition Unit lessons N2.1 & N2.2

Mental & Oral Starters:See lesson plansDiscussion opportunities: Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links:

Investigation:

Time: 2 lessons


Topic: Symmetry & Angles NC Level: 4 & 5

NC Programme of Study:Ref 2abcdg: recall and use properties of angles at a point, angles on a straight line, perpendicular lines and opposite angles at a vertex. Distinguish between acute, obtuse, reflex and right angles; estimate the size of an angle in degrees. Use parallel lines; the angle sum of a triangle is 180 degrees. Use angle properties of equilateral, isosceles, and right-angled triangles; understand congruence, recognising when 2 triangles are congruent; explain why the angle sum of any quadrilateral is 360 degrees. Calculate and use the sums of interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons.Ref 3b: recognise and visualise rotations, reflections, including the reflection and rotation symmetry of 2D shapes; transform 2D shapes by rotation and reflection, recognising that these transformations preserve length and angle.Ref4bd: understand angle measure, using the associated language. Measure and draw lines to the nearest millimetre and angles to the nearest degree; draw triangles and other 2D shapes using a ruler and protractor, given information about their side lengths and angles.

Learning Objectives: Identify all symmetries of 2D shapes – reflective and rotational Transform 2D shapes by simple rotations about a given point and reflections in a given mirror line Use correct vocabulary, notation and labelling for lines, angles and shapes. Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles. Use a ruler and protractor to measure and draw lines to the nearest millimetre and angles, including

reflex angles, to the nearest degree Identify parallel and perpendicular lines; know the sum of right angles, angles at a point, on a straight

line and in a triangle. Recognise vertically opposite angles. Identify alternate angles and corresponding angles Understand the proof that the sum of the angles of a triangle is 180 and quadrilateral is 360 Find the interior and exterior angles of different polygons

Key Vocabulary:ROTATION REFLECTION ANGLE DEGREE TURN ACUTE OBTUSE REFLEX MEASURE PROTRACTOR CONSTRUCT DRAW ESTIMATE LINE AT A POINT TRIANGLE QUADRILATERAL POLYGON REGULAR Impact Reference:Book 2B – ch. 2

Other references:V3 – ch. 9 V4 – ch. 13, 18 V5 – ch. 15 V6 – ch. 12, 13 KM82 – ch. 5, 7

Mental & Oral Starters:2B folder: pg. 18 - 21 101 Starters: pg. 73, 79, 80Discussion opportunities:Categorise shapes: no. of lines of symmetry and order of rotational symmetry – poster?Pair / Group Work:

ICT Links:SMILE – Angle 360, Snooker. LOGO can be used to construct shapes; experiment with angles.Spiritual/Moral/Citizenship Links: Reflection on own characterInvestigation: Find a shape with 4, 5, 6 lines of symmetry etc.Time: 8 lessons


Topic: Multiplication & Division NC Level: 3 - 5

NC Programme of Study:Ref2ab: Use concepts and vocabulary of factor, multiple, common factor, highest common factor, least common multiple, prime number and prime number decomposition. Use the terms square, positive square root.Ref3agk: multiply and divide integers; multiply or divide any number by powers of 10; find the prime factor decomposition of positive integers. Recall all multiplication facts to 10 x 10, and use them to derive quickly the corresponding division facts. Use standard column procedures for multiplication of integers.Ref4b: Select appropriate operations, methods and strategies to solve number problems.

Learning Objectives: multiply and divide integers, including 3 digit numbers by 2 digit numbers use standard column procedures for multiplication and division of integers mentally estimate and approximate solutions to numerical calculations use the laws of inverse operations recognise and use multiples, factors and primes find the prime factor decomposition of a number use squares, positive and negative square roots, cubes, cube roots and index notation for small

integer powers consolidate rapid recall of number facts including positive integer complements to 100 and

multiplication facts to 10 x 10, and quickly derive associated division facts

Key Vocabulary:MULTIPLY DIVIDE MULTIPLE FACTOR PRIME SQUARE POWERSQUARE ROOT Impact Reference:Book 2B – ch. 3

Other references:V3 – ch. 2 V4 – ch. 3, 4, 8 V5 – ch. 2, 3 KM82 – ch. 2

Mental & Oral Starters:2B folder: pg. 32-34 101 Starters: pg. 7, 10, 13, 24-32, 39, 41-45, 48-51Discussion opportunities:Pupils can explain their methods of computation.Pair / Group Work:Check each others’ methods/ answers.Dice Bingo – multiply the 2 scores on 12 sided dice together.ICT Links:SMILESpiritual/Moral/Citizenship Links:Sharing equally – we are all entitled to the same. Does it always happen?Investigation:Find all numbers that sum to 13 – which give the largest product? etc.Time: 7 lessons


Topic: Working With Algebra NC Level: 4 & 5

NC Programme of Study: Ref5abc: distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite unknown numbers in equations. Understand that the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms; distinguish in meaning between the words ‘equation’, ‘formula’, ‘identity’ and ‘expression.’ Use index notation for simple integer powers, and simple instances of index laws.

Learning Objectives: use letter symbols to represent unknown numbers or variables distinguish the different roles played by letter symbols in equations, formulae and functions know the meaning of the words ‘formula’ and ‘function’ know that algebraic operations follow the same conventions and order as arithmetic

operations simplify or transform linear expressions by collecting like terms multiply a single term over a bracket use powers in algebraic expressions

Key Vocabulary:COLLECT LIKE TERMS MULTIPLY SIMPLIFY EXPRESSION BRACKETS POWER INDEXImpact Reference:Book 2B – ch. 4

Other references:V4 – ch. 9 V5 – ch. 8, 9 KM82 – ch. 4

Mental & Oral Starters:2B folder: pg. 50-51 101 Starters: pg. 65-68Discussion opportunities:Discuss what the expressions represent.Pair / Group Work:Pupils can make up their own word / algebraic equations and test each other.ICT Links:EXCEL – inputting formulae to get the desired output, rather than typing in numbers.Spiritual/Moral/Citizenship Links:

Investigation:

Time: 4 – 5 lessons


Topic: Fractions NC Level: 5 & 6

NC Programme of Study:Ref2c: Use fraction notation; understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting then with a common denominator. Ref3c: Calculate a given fraction of a given quantity, expressing the answer as a fraction; express a given number as a fraction of another; add and subtract fractions by writing them with a common denominator.

Learning Objectives: recognise proportions of a whole and use simple fractions to describe these recognise equivalent fractions find equivalent fractions by multiplying or dividing cancel fractions to their lowest terms order fractions by writing them with a common denominator or by converting them to

decimals understand & interpret ‘mixed numbers’ and ‘improper fractions’ understand addition and subtraction of fractions use the laws of arithmetic and inverse operations add & subtract fractions by writing them with a common denominator calculate fractions of quantities

Key Vocabulary:FRACTION QUANTITY EQUIVALENT ORDER NUMERATOR DENOMINATOR MIXED NUMBER IMPROPER SIMPLIFY CANCELImpact Reference:Book 2B – ch. 6

Other references:V4 – ch. 6 V5 – ch.5 V6 – ch. 2 KM82 – ch. 9

Mental & Oral Starters:2B folder: pg. 76 - 77 101 Starters: pg. 36-37Discussion opportunities:

Pair / Group Work:

ICT Links:


Investigation:

Time: 4 – 5 lessons


Topic: Probability NC Level: 4 - 6

NC Programme of Study:Ref4cdf: Understand and use the probability scale. Understand and use estimates or measures of probability from theoretical models, including equally likely outcomes, or from relative frequency. Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1.Ref5i: Compare experimental data and theoretical probabilities.

Learning Objectives: understand and use the probability scale from 0 to 1 – in words and numbers. find and justify probabilities based on equally likely outcomes in simple contexts. calculate probabilities with one or more successful outcomes use the vocabulary of probability when interpreting the results of an experiment appreciate that random processes are unpredictable understand that if the probability of an event occurring is p, then the probability of it not

occurring is 1 – p (numerically rather than algebraically at this level) find and record all possible outcomes for single events and 2 successive events in a systematic

way using diagrams or tables. estimate probabilities from experimental data, understand that:

- if an experiment is repeated there may be different outcomes- increasing the number of times an experiment is repeated generally

leads to better estimates of probability

Key Vocabulary:CERTAIN IMPOSSIBLE POSSIBLE SCALE EVENT OUTCOME THEORETICAL EXPERIMENTAL

Impact Reference:Book 2B – ch. 7

Other references:V4 – ch. 22 V5 – ch. 22-24 V6 – ch. 20 KM82 – ch. 8

Mental & Oral Starters:2B folder: pg. 92-93 101 Starters: pg. 99 - 101Discussion opportunities:Discuss the likelihood of things happening in everyday life.Pair / Group Work:Probability experiments can be done in pairs to ensure results are recorded carefully.‘Play your cards right’, human probability scale, Bingo with dice.ICT Links:SMILESpiritual/Moral/Citizenship Links:Morality of gamblingInvestigation:Investigate the probability of real events occurring – set up hypotheses etc.Time: 6 – 7 lessons – perhaps more depending on practical work


Topic: Decimals & Percentages NC Level: 4 - 6

NC Programme of Study:Ref2de: Use decimal notation and recognise that each terminating decimal is a fraction. Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions; interpret percentage as the operators ‘so many hundredths of’.Ref3acehjkm: Add, subtract, multiply and divide integers and then by any number; multiply or divide any number by powers of 10, and any positive number between 0 and 1. Perform short division to convert a simple fraction to a decimal. Convert simple fractions of a whole to percentages of the whole and vice versa, then understand the multiplicative nature of percentages as operators. Round to the nearest integer; estimate answers to problems involving decimals. Use standard column procedures for addition and subtraction of integers and decimals. Use standard column procedures for multiplication of integers and decimals, understanding where to position the decimal point by considering what happens if they multiply equivalent fractions; solve a problem involving division by an integer. Solve simple percentage problems, including increase and decrease.

Learning Objectives: order decimals use standard column procedures for addition and subtraction of decimals multiply and divide decimals by powers of 10 round decimals to the nearest whole number, or to one or two decimal places use standard column procedures for multiplication and division of decimals; understand where to

position the decimal point by considering equivalent calculations use division to convert a fraction to a decimal interpret percentage as the operator ‘so many hundredths of’ convert percentages to decimals and fractions express one given number as a percentage of another calculate simple percentages use the equivalence of fractions, decimals and percentages to compare proportions find approximate answers to calculations, checking a result by considering whether it is of the right

order of magnitude and by working the problem backwards

Key Vocabulary:PLACE VALUE ROUND NEAREST DECIMAL PERCENTAGE APPROXIMATE ORDER EQUIVALENT CONVERT FRACTION AMOUNT INCREASE DECREASEImpact Reference:Book 2B – ch. 8

Other references:V4 – ch. 6 V5 – ch. 4-5 V6 – ch. 2,3 KM82 – ch. 9

Mental & Oral Starters:2B folder: pg. 104 - 106 101 Starters: pg. 38Discussion opportunities:Pair / Group Work:Human number lineICT Links:EXCEL for interest rates, discounts etc; perhaps set up a shop.Spiritual/Moral/Citizenship Links:No matter how small, everything is significant. Tax – where does it go?Investigation:Time: 9 – 10 lessons

SPRING TERM A TOPIC 9

Topic: Number Patterns NC Level: 4 & 6

NC Programme of Study:Ref5d: set up simple equation; solve simple equations by using inverse operations.Ref6abc: generate common integer sequences (inc. odd or even integers, squared integers, powers of 2, powers of 10, triangular numbers). Find the first terms of a sequence given a rule arising naturally from a context; find the rule for the nth term of a sequence. Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence; use linear expressions to describe the nth term of an arithmetic sequence.

Learning Objectives: generate and describe simple integer sequences know the meaning of the words ‘term’, ‘expression’, ‘equation’ generate sequences from practical contexts and describe the general term in simple cases use number machines – including inverse operations use the laws of arithmetic and inverse operations when generating terms and describing the

sequence express simple function in symbols represent mappings expressed algebraically generate terms of a linear sequence using term-to-term and position-to-term definitions of the

sequence on paper and using a spreadsheet or graphical calculator begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying

its form by referring to the activity or practical context from which it was generated

Key Vocabulary:PATTERN SEQUENCE NUMBER MACHINE INVERSE OPERATION nth TERMImpact Reference:Book 2B – ch. 5

Other references:V4 – ch. 8 V6 – ch. 6 KM82 – ch. 4

Mental & Oral Starters:2B folder: pg. 62 Discussion opportunities:Pupils should be encouraged to verbally explain the rules of sequences, share ideas.Pair / Group Work:Find sequences that occur in real life – e.g. apples, pineapples, leaves, plantsICT Links:EXCEL can be used to produce number patterns.Spiritual/Moral/Citizenship Links:

Investigation:See group workTime: 4 lessons


Topic: Multiplicative Relationships

NC Level:


Learning Objectives: Understand multiplication and division of integers and decimals; use laws of arithmetic and

inverse operations Check a result by considering whether it is of the right order of magnitude Use division to convert a fraction to a decimal; calculate fractions of quanities; multiply and

divide an integer by a fraction Interpret percentage as the operator ‘so many hundredths of’ and express one given number as

a percentage of another Use equivalence of fractions, decimals and percentages to compare proportions; calculate

percentages and find the outcome of a given percentage increase or decrease Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to

its simplest form, including a ratio expressed in different units; recognise links with fraction notation

Divide a quantity into 2 or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion

Identify the necessary information to solve a problem, using the correct notation and appropriate diagrams

Solve more complex problems by breaking them into smaller steps, choosing and using efficient techniques for calculation

Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counter-examples

Key Vocabulary:SCALE FACTOR MULIPLIER OPERATOR INVERSE MULTIPLICATIVE RATIO FRACTION PERCENTAGE PROPORTION RATE UNITARYImpact Reference: Other references:

Phase 3 Problem BankSEE MULTIPLICATIVE RELATIONSHIPS MINI-PACK FOR FURTHER GUIDANCE

Time: 9 lessons


Topic: Shape & Measure NC Level: 4 - 6

NC Programme of Study:Ref 2bfik: distinguish between acute, obtuse, reflex and right angles; estimate the size of an angle in degree. Recall the essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric properties. Recall the definition of a circle and the meaning of related terms including centre, radius, chord, diameter, circumference, tangent, arc, sector, segment. Use “D representations of 3D shapes and analyse 3D shapes through 2D projections and cross sections including plans and elevation.Ref 4acd: Interpret scales on a range of measuring instruments, including those for time and mass; know that measurements using real numbers depend on the choice of unit; convert measurements from one unit to another; know rough metric equivalents of pounds, feet, miles, pints and gallons. Understand and use compound measures. Measure and draw lines to the nearest millimetre and angles tot he nearest degree; draw triangles and other 2D shapes using a ruler and protractor, given information about their side lengths and angles; construct cubes, regular tetrahedra, square based pyramids and other 3D shapes from given information.

Learning Objectives: solve geometrical problems using side and angle properties of equilateral, isosceles and right-

angles triangles and special quadrilaterals, explaining reasoning with diagrams and text classify quadrilaterals by their geometric properties recognise parts of a circle recognise and draw common 3D solids recognise and produce 2D representations of 3D shapes - nets use units of measurement to estimate, calculate and solve problems in everyday contexts –

involving length, area, volume, capacity, mass, time and angle convert one metric unit to another know rough equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons) read and interpret scales on a range of measuring instruments

Key Vocabulary:SHAPE QUADRILATERAL TRIANGLE CIRCLE SOLID CONSTRUCT NET PLAN ELEVATION UNITS CAPACITY METRIC IMPERIAL TIMEImpact Reference:Book 2B – ch. 9

Other references:V4 – ch. 14, 16 V5 – ch. 11-13, 16 V6 – ch. 14, 15

Mental & Oral Starters:2B folder: pg. 122-125 101 Starters: pg. 74-78, 80-86Discussion opportunities:

Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links:We need to look at 3D shapes from different angles – similar to confrontation / conflicts. We need to consider everyone’s opinion.Investigation:Time: 8 lessons

SPRING TERM B TOPIC 12

Topic: Handling Data NC Level: 3 – 6

NC Programme of Study:Ref3b: Gather data from secondary sources, including printed tables and lists from ICT based sources.Ref4a: Draw and produce, using paper and ICT, pie charts for categorical data and diagrams for continuous data, including line graphs for time series, scatter graphs, frequency diagrams.Ref5b: Interpret a wide range of graphs and diagrams and draw conclusions.

Learning Objectives: design and use 2-way tables for discrete data calculate statistics, including with a calculator construct on paper and using ICT:

- pie charts for categorical data- bar charts and frequency diagrams for discrete data- simple scatter graphs- simple line graphs for time series

construct frequency tables with given equal class intervals for sets of continuous data interpret tables, graphs and diagrams for discrete data, and draw inferences that relate to the

problem being discussed relate summarised data to the questions being exploredKey Vocabulary:DATA DISCRETE CONTINUOUS GROUPED DATA PIE CHART BAR CHART PICTOGRAM SCATTER DIAGRAM LINE GRAPH INTERPRETImpact Reference:Book 2B – ch. ????

Other references:V3 – ch. 14 V4 – ch. 21 V5 – ch. 20 V6 – ch. 18,19 KM82 – ch. 3, 13

Mental & Oral Starters:2B folder: pg. 172 - 175 Discussion opportunities:Discuss methods of collecting data. Discuss advantages of each method.Pair / Group Work:Collecting data.ICT Work.ICT Links:EXCEL for producing graphs / charts. Internet for sets data to analyse.Spiritual/Moral/Citizenship Links:

Investigation:

Time: 7 – 8 lessons – may vary depending on practical work

ADDITIONAL UNIT

Topic: Handling Data NC Level:


Learning Objectives: Discuss a problem that can be addressed by statistical methods and identify related questions

to explore Decide which data to collect to answer a question, and the degree of accuracy needed; identify

possible sources Plan how to collect the data, including sample size; design and use 2-way tables for discrete

data Collect data using a suitable method, such as observation, controlled experiment using ICT or

questionnaire Construct on paper and using ICT: pie charts, bar charts, frequency diagrams, simple scatter

diagrams; identify which are most useful in the context of the problem Interpret tables, graphs and diagrams for discrete data, and draw inferences that relate to the

problem being discussed; relate summarised data to the questions being explored Communicate orally and on paper the results of a statistical enquiry and the methods used,

using ICT as appropriate; justify the choice of what is presented Solve more complex problems by breaking then into smaller steps or tasks choosing and using

resources

Key Vocabulary:MODE MEAN MEDIAN RANGE BAR CHART PIE CHART DISTRIBUTIONSTEM-AND-LEAF DIAGRAM LINE GRAPH FREQUENCY TABLE PRIMARY SOURCE SECONDARY SOURCE RAW DATA HYPOTHESISImpact Reference: Other references:

Data Library CD-ROMInteracting with Data Handling Pack from LEA

SEE HANDLING DATA MINI-PACK FOR FURTHER GUIDANCE

Time: 6 lessons


Topic: Positive & Negative Numbers NC Level: 5

NC Programme of Study:Ref2a: Understand and use negative numbers, both as positions and translations on a number line; order integersRef3a: Add, subtract, multiply and divide integers

Learning Objectives: Understand negative numbers as temperatures Understand negative numbers as positions on a horizontal number line Order positive and negative integers in context Add and subtract positive and negative numbers

Key Vocabulary:ORDER NUMBER LINE ADD SUBTRACT POSITIVE NEGATIVEImpact Reference:Book 2B – ch. 10

Other references:V3 – ch. 6 V5 – ch. 6 KM82 – ch. 6

Mental & Oral Starters:2B folder: pg. 138 -139 101 Starters: pg. 19-21, 23.Discussion opportunities:Where do negative numbers occur in real life?Pair / Group Work:Human number lineICT Links:EXCELSpiritual/Moral/Citizenship Links:Positive qualities can balance out the negative. Debt – 3rd WorldInvestigation:

Time: 4 lessons


Topic: Formulae & Equations NC Level: 4 - 6

NC Programme of Study:Ref4b: Select appropriate operations, methods and strategies to solve number problems, including trial and improvement where a more efficient method to find the solution is not obvious.Ref5d: Set up simple equations; solve simple equations, by using inverse operations or by transforming both sides in the same way.

Learning Objectives: know the meaning of the words ‘formula’ and ‘function’ use formulae from maths and other subjects substitute integers into simple formulae, including examples that lead to an equation to solve derive simple formulae express simple functions in words use letter symbols to represent unknown numbers or variables know the meanings of the words ‘term’, ‘expression’ and ‘equation’ derive simple formulae use the order of operations including brackets, with more complex calculations construct and solve simple linear equations with integer coefficients (unknown on one side

only) using appropriate method (e.g. inverse operations) begin to use graphs and set up equations to solve simple problems involving direct proportion

Key Vocabulary:WORD FORMULAE LETTER OPERATION SOLVE EQUATION NUMBER MACHINE ALGEBRA BALANCEImpact Reference:Book 2B – ch. 13

Other references:V4 – ch. 9 V5 – ch. 8, 9 V6 – ch. 7 KM82 – ch.4, 15

Mental & Oral Starters:2B folder: pg. 202 -204 101 Starters: pg. 62-67Discussion opportunities:Using algebra to model real lifePair / Group Work:

ICT Links:


Investigation:

Time: 6 –7 lessons

SUMMER TERM A TOPIC 15

Topic: Graphs NC Level: 5 & 6

NC Programme of Study:Ref6ef: use the conventions for co-ordinates in the plane; plot points in al 4 quadrants; recognise that equations of the form y=mx+c correspond to straight line graphs; plot graphs of functions in which y is given explicitly in terms of x, or implicitly. Construct linear functions arising from real life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations

Learning Objectives: generate points in all 4 quadrants recognise straight line graphs parallel to the x and y axes plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and

using ICT recognise that equations of the form y=mx+c correspond to straight line graphs construct linear functions arising from real life problems and plot their corresponding graphs discuss and interpret graphs from real life situations

Key Vocabulary:COORDINATE AXES EQUATION LINE PLOT CONVERSION SCALEImpact Reference:Book 2B – ch. 11

Other references:V4 – ch. 10 V6 – ch. 8, 9 KM82 – ch. 1, 16

Mental & Oral Starters:2B folder: pg. 150 - 152 101 Starters: pg. 90-92Discussion opportunities:

Pair / Group Work:

ICT Links:Omnigraph, EXCEL. Outware: “Carpark” “ Defender”Spiritual/Moral/Citizenship Links:Currency conversions – difference between 1st and 3rd WorldInvestigation:

Time: 6 lessons


Topic: Averages NC Level: 4 - 5

NC Programme of Study:Ref4b: Calculate mean, range and median of small data sets with discrete then continuous data; identify the modal class for grouped data. Ref5d: Compare distributions and make inferences, using the shapes of distributions and measures of average and range.

Learning Objectives: calculate statistics, including with a calculator – mode, median, mean, range recognise when it is appropriate to use the range, mean, median and mode calculate a mean using an assumed mean find the mean from frequency tables know when it is appropriate to use the modal class for grouped data compare 2 distributions using the range and one or more of the mode, median and mean relate summarised data to the questions being explored

Key Vocabulary:MODE MEDIAN MEAN RANGE FREQUENCY TABLE COMPARE DATAImpact Reference:Book 2B – ch. 15

Other references:V5 – ch. 19 KM82 – ch. 13

Mental & Oral Starters:2B folder: pg. 101 Starters: pg. 96 Discussion opportunities:

Pair / Group Work:Collect data in groupsICT Links:Perhaps for larger samples - EXCELSpiritual/Moral/Citizenship Links:Is anyone really average?Investigation:Set a hypotheses – collect results etc.Time: 5 lessons – may vary depending on practical work


Topic: Problem Solving NC Level:


Learning Objectives: Identify the necessary information to solve a problem Solve more complex problems by breaking them down into smaller tasks/steps Interpret the numbers on a calculator display in different contexts Carry out more difficult calculations effectively and efficiently Solve problems and investigate in a range of contexts Explain and justify methods and conclusions Identify exceptional cases or counter-examples

Key Vocabulary:EXPLAIN REASONS JUSTIFYImpact Reference: Other references:

Mental & Oral Starters:101 Starters: pg.

SEE PROBLEM SOLVING PACK FROM LEA

Time: 5 lessons

SUMMER TERM B TOPIC 18

Topic: Perimeter, Area & Volume NC Level: 4 - 6

NC Programme of Study:Ref4fgh: Find areas of rectangles, recalling the formula, understanding the connection to counting squares and how it extends this approach; recall and use the formulae for the area of a parallelogram and a triangle; find the surface area of simple shapes using the area formulae for triangles and rectangles; calculate perimeters and areas of shapes made from triangles and rectangles. Find volumes of cuboids, recalling the formula and understanding the connection to counting cubes and how it extends this approach; calculate volumes of right prisms and of shapes made from cubes and cuboids. Find circumferences of circles and areas enclosed by circles, recalling relevant formulae.Ref5f: Use formulae from maths and other subjects.

Learning Objectives: find the perimeter of simple shapes know and use the formula for the area of a rectangle deduce and use formulae for the area of a triangle, parallelogram and trapezium calculate areas of compound shapes made from rectangles and triangles know and use the formula for the volume of a cuboid and prism calculate the surface area of cubes and cuboids find the circumference of a circle estimate and then calculate the area of a circle

Key Vocabulary:PERIMETER AREA FORMULAE COMPOSITE SHAPE CIRCUMFERENCE PI ESTIMATE VOLUME CUBOID PRISM BASE HEIGHT LENGTH WIDTHImpact Reference:Book 2B – ch. 14

Other references:V4 – ch. 13, 18 V6 – ch. 11 KM82 – ch. 12, 14

Mental & Oral Starters:2B folder: pg. 214 -217 101 Starters: pg. 93, 94Discussion opportunities:

Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links:Dimensions – finite and infiniteInvestigation:

Time: 8 lessons

SUMMER TERM B TOPIC 19

Topic: Thinking Proportionally NC Level:


Learning Objectives: Identify the necessary information to solve a problem Represent problems and interpret solution in algebraic, geometric or graphical form, using

correct notation Use logical argument to establish the truth of a statement Suggest extensions to problems; conjecture and generalise Consolidate understanding of the relationship between ratio and proportion Reduce a ratio to its simplest form, including a ratio expressed in different units, recognising

links with fraction notationKey Vocabulary:RATIO PROPORTION DIRECT RATE PER NOTATION EQUIVALENT FRACTION DECIMAL PERCENTAGE

Impact Reference: Other references: Transition Unit lesson P1.1 & P1.2

Mental & Oral Starters:See lesson plansDiscussion opportunities: Pair / Group Work:

ICT Links:


Investigation:

Time: 2 lessons

ks3 scheme of work - year 8 - sets 2 & 3: impact 2b · web viewv3 – ch. 1–5 v4...

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