Stage 3 Opportunity Class: Mathematics Program 2017Teacher: Mitchell Welham Year: 2017 School: Dubbo West Public School Compiled using: Mathletics, NSW K-10 Mathematics Syllabus, BOSTES website, obwm.weebly.com

Curriculum

Objectives

Knowledge, Skills and Understanding

Working Mathematically

· develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning

Number and Algebra

· develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation

Measurement and Geometry

· identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems

Statistics and Probability

· collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements.

Values and Attitudes

Students:

· appreciate mathematics as an essential and relevant part of life, recognising that its cross-cultural development has been largely in response to human needs

· demonstrate interest, enjoyment and confidence in the pursuit and application of mathematical knowledge, skills and understanding to solve everyday problems

· develop and demonstrate perseverance in undertaking mathematical challenges.

Stage Statement

By the end of Stage 3, students ask questions and undertake investigations, selecting appropriate technological applications and problem-solving strategies to demonstrate fluency in mathematical techniques. They use mathematical terminology and some conventions, and they give valid reasons when comparing and selecting from possible solutions, making connections with existing knowledge and understanding.

Students select and apply appropriate mental, written or calculator strategies for the four operations and check the reasonableness of answers using estimation. They solve word problems and apply the order of operations to number sentences where required. Students identify factors and multiples and recognise the properties of prime, composite, square and triangular numbers. They connect fractions, decimals and percentages as different representations of the same value. Students compare, order and perform calculations with simple fractions, decimals and percentages and apply the four operations to money in real-life situations. Students record, describe and continue geometric and number patterns, and they find missing numbers in number sentences. They locate an ordered pair in any one of the four quadrants on the Cartesian plane.

Students select and use the appropriate unit to estimate, measure and calculate length, area, volume, capacity and mass. They make connections between capacity and volume, and solve problems involving length and area. Students use 24-hour time in real-life situations, construct and interpret timelines and use timetables. They convert between units of length, units of capacity and units of mass. They construct and classify three-dimensional objects and two-dimensional shapes, and compare and describe their features, including line and rotational symmetries. Students measure and construct angles, and find unknown angles in diagrams using known angle results. They use a grid-reference system to locate landmarks and describe routes using landmarks and directional language.

Students use appropriate data collection methods to interpret and analyse sets of data and construct a range of data displays. They assign probabilities as fractions, decimals or percentages in simple chance experiments.

Source: NSW Syllabuses for the Australian curriculum – Mathematics http://syllabus.bos.nsw.edu.au/mathematics/mathematics-k10/stage-statements/

Teaching and learning

Aboriginal and Torres Strait Islander perspectives

Mathematics provides opportunities for students to strengthen their appreciation and understanding of Aboriginal peoples and Torres Strait Islander peoples and their living cultures. Specific content and skills within relevant sections of the curriculum can be drawn upon to encourage engagement with:

Aboriginal and Torres Strait Islander frameworks of knowing and ways of learning

Social, historical and cultural contexts associated with different uses of mathematical concepts in Australian Indigenous societies

Aboriginal peoples’ and Torres Strait Islander peoples’ contributions to Australian society and cultures.

Mathematics provides opportunities to explore aspects of Australian Indigenous knowing in connection to, and with guidance from, the communities who own them. Using a respectful inquiry approach students have the opportunity to explore mathematical concepts in Aboriginal and Torres Strait Islander lifestyles including knowledge of number, space, measurement and time. Through these experiences, students have opportunities to learn that Aboriginal peoples and Torres Strait Islander peoples have sophisticated applications of mathematical concepts which may be applied in other peoples’ ways of knowing.

General capabilities and crosscurriculum priorities

Opportunities to engage with:

Opportunities to engage with:

Opportunities to engage with:

Opportunities to engage with:

Key to general capabilities and cross-curriculum priorities

Literacy  Numeracy ICT capability Critical and creative thinking Ethical behaviour Personal and social capability Intercultural understanding

Aboriginal and Torres Strait Islander histories and cultures   Asia and Australia’s engagement with Asia   Sustainability

Dubbo West Public School Stage 3 Mathematics Scope and Sequence

1

2

3

4

5

6

7

8

9

10

Term 1

Whole Number

Addition & Subtraction

Multiplication & Division

Chance

2D Space

Angles

Fractions & Decimals

Fractions & Decimals

3D Space

Term 2

Whole Number

Revision / NAPLAN preparation

Revision / NAPLAN preparation

NAPLAN

Data

Length

Area

Time

Position

Mass

Term 3

Whole Number

Addition & Subtraction

Multiplication & Division

2D Space

Angles

Mass

Volume & Capacity

3D Space

Patterns & Algebra

Patterns & Algebra

Term 4

Whole Number

Area

Length

Time

Volume & Capacity

Fractions & Decimals

Chance

Volume & Capacity

Revision

Revision

Numeracy – Lesson ModelConstructivist Classroom (using Bruner’s theory)

Preparation:

· Before commencing the lesson, the classroom teacher works out questions prior to the lesson.

· Think about the Golden Circle: Why are my students learning this – How will they learn this – What will they learn?

1. Prior Knowledge

· Talking about and reflecting on prior learning that links to the upcoming lesson which involves the whole class.

· In ES1/S1, Maths groups can include activities that allow students at all levels of the Learning Framework in Number (eg., within the Early Arithmetical strategies) to be able to participate.

2. Evolving Student Learning (Main Focus - Whole Class or Most of Class)

· Model the required behaviour/strategy using explicit teaching. Ask students ‘What do you think we will be learning about today?’.

· Expose students to the language of the lesson and keep referring to it throughout the lesson cycle.

· Teaching and learning activities should allow students at all levels of the Learning Framework in Number to be able to participate.

· Use higher order thinking which links to prior knowledge.

· Encourage students to explain their solution strategies and discuss which methods are the most suitable.

· Students should be encouraged to explain their solution as this provides you with information about the solution strategies students’ use.

3. Inquiry Based

ES1 and Stage 1

Small groups (no more than 4) working on the core concept of the lesson.

· Guided/supported practice of the skill or knowledge

· Teaching and activities should target students of different levels. For example, Emergent, Perceptual, etc.

· Try to move between groups at times to keep students focused.

· You may wish to spend more time with students using less advanced strategies.

· Provide explicit feedback on the student’s performance e.g ‘Well done, you found all the numbers 1-10 by looking closely at the shapes of the numbers.’

· This is a good opportunity to make anecdotal observations and for students to undertake ongoing assessment tasks.

Stage 2 and Stage 3

Individual and paired work working on the core concept of the lesson.

· Guided/supported practice of the skill or knowledge

· Teaching and activities can be differentiated to accommodate the varying levels of learners in the classroom.

· Provide students opportunity to discuss their findings and share with the class.

· Provide explicit feedback on the student’s performance as well as opportunities for students to explore peer assessment.

· Students use technology to explore and apply learning.

· This is a good opportunity to make anecdotal observations and for students to undertake ongoing assessment tasks.

4. Reflection and Making Connections

· Reflect on the language of the

· Give students the opportunity to share and talk about their learning.

· Draw together the learning activities used during the lesson and the strategy that is being examined.

· Use the following questions to build the concept of ‘Making Connections’ to the real world.

1. What did you have to do? 2. What did you do?

3. What did you find out? 4. What did it add to what you already know?

Developed by Mitchell Welham, Dean Morrison (2014)

Stage 3 Checklist of Outcomes and Content Descriptors

Stage 3 Numbers and Algebra

T1

T2

T3

T4

Whole Numbers

Orders, reads and represents integers of any size and describes properties of whole numbers (MA3-4NA)

Recognise, represent and order numbers to at least tens of millions

Identify and describe properties of prime, composite, square and triangular numbers  (ACMNA122)

Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

Addition and Subtraction

Selects and applies appropriate strategies for addition and subtraction with counting numbers of any size (MA3-5NA)

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

Create simple financial plans (ACMNA106)

Multiplication and Division

Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation (MA3-6NA)

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)

Solve problems involving division by a one-digit number, including those that result in a remainder (ACMNA101)

Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

Explore the use of brackets and the order of operations to write number sentences (ACMNA134)

Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)

Fractions and Decimals

Compares, orders and calculates with fractions, decimals and percentages (MA3-7NA)

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

Recognise that the place value system can be extended beyond hundredths (ACMNA104)

Compare, order and represent decimals (ACMNA105)

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

Solve problems involving addition and subtraction of fractions with the same or  related denominators (ACMNA126)

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129)

Multiply and divide decimals by powers of 10 (ACMNA130)

Make connections between equivalent fractions, decimals and percentages  (ACMNA131)

Investigate and calculate  percentage  discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

Patterns and Algebra

Analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane (MA3-8NA)

Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)

Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

Stage 3 Measurement and Geometry

T1

T2

T3

T4

Length

Selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length (MA3-9MG)

Choose appropriate units of measurement for length (ACMMG108)

Calculate the perimeters of rectangles using familiar metric units (ACMMG109)

Connect decimal representations to the metric system (ACMMG135)

Convert between common metric units of length, mass and capacity (ACMMG136)

Solve problems involving the comparison of lengths and areas using appropriate units  (ACMMG137)

Area

Selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles (MA3-10MG)

Choose appropriate units of measurement for area (ACMMG108)

Calculate the areas of rectangles using familiar metric units (ACMMG109)

Solve problems involving the comparison of areas using appropriate units (ACMMG137)

Volume and Capacity

Selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity (MA3-11MG)

Choose appropriate units of measurement for volume and capacity (ACMMG108)

Connect volume and capacity and their units of measurement (ACMMG138)

Connect decimal representations to the metric system (ACMMG135)

Convert between common metric units of capacity (ACMMG136)

Calculate the volumes of rectangular prisms (ACMMG160)

Mass

Selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass (MA3-12MG)

Choose appropriate units of measurement for mass (ACMMG108)

Connect decimal representations to the metric system (ACMMG135)

Convert between common metric units of mass (ACMMG136)

Time

Uses 24-hour time and am and pm notation in real-life situations, and constructs timelines (MA3-13MG)

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

Interpret and use timetables (ACMMG139)

Determine and compare the duration of events

Draw and interpret timelines using a given scale

3D Space

Identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views. (MA3-14MG)

Compare, describe and name prisms and pyramids

Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)

Construct simple prisms and pyramids (ACMMG140)

2D Space

Manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties(MA3-15MG)

Classify two-dimensional shapes and describe their features

Describe translations, reflections and rotations of two-dimensional shapes (ACMMG114)

Identify line and rotational symmetries (ACMMG114)

Apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)

Investigate the diagonals of two-dimensional shapes.

Identify and name parts of circles.

Angles

Measures and constructs angles, and applies angle relationships to find unknown angles (MA3-16MG)

Estimate, measure and compare angles using degrees (ACMMG112)

Construct angles using a protractor (ACMMG112)

Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)

Position

Locates and describes position on maps using a grid-reference system (MA3-17MG)

Use a grid-reference system to describe locations (ACMMG113)

Describe routes using landmarks and directional language (ACMMG113)

Stage 3 Statistics and Probability

T1

T2

T3

T4

Data

Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables (MA3-18MG)

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

Describe and interpret different data sets in context (ACMSP120)

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

Interpret secondary data presented in digital media and elsewhere (ACMSP148)

Chance

Conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes (MAS-319MG)

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Recognise that probabilities range from 0 to 1 (ACMSP117)

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Describe probabilities using fractions, decimals and percentages (ACMSP144)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

Stage 3 Working Mathematically

T1

T2

T3

T4

Describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions (MA3-1WM)

Selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations (MA3-2WM)

Gives a valid reason for supporting one possible solution over another (MA3-3WM)

Mathematics

Term 1

2017

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 2

Looking at Whole Numbers

MA3-4NA Whole Number

Read and write numbers to 999 999

We read and write numbers in the order that we say them.

We read and write large numbers in groups of three.

We work from right to left and we put a gap between each group of numbers.

Place value to millions

The place of a digit in a number tells us its value.

Sometimes it is easier to express the number using exponents or powers. Powers tell us how many times to use a number in a multiplication process.

Can you see a connection between the power and the amount of zeros in the number?

Order numbers to 999 999

When ordering numbers, we need to pay close attention to the position and value of each digit.

Insert > (greater than) or < (less than) to make each statement true.

Look at each set of numbers and list some that come in between. Write them in order.

Expanded notation

When we write numbers using expanded notation, we identify and name the value of each digit.

How do we write 5 325 in expanded notation using powers?

Create and compare numbers

Use a random collection of numbers to make various larger numbers.

Compare population of cities from different time periods.

Order large Numbers

Order large numbers on a number line and using a table.

Assessment Task (It’s Holiday time)

Your family has just won the dream trip of a lifetime! You have won an all-expenses paid trip to 5 towns or cities of your choice. That’s right, anywhere in the world with everything paid for.

Assessment Task (The millionaires’ club)

Congratulations! You and a friend have just inherited a lot of money and can join the Millionaires’ Club. Your task is to order the members in the club, and then work out why there seem to be some cliques within the group.

Stage 3

Assessment Task (The new place is right!)

The aim of this game is to order as many numbers on a game board as possible. You’ll play the game in a group of 3 or 4. You’ll need a pencil and the game show boards below.

Assessment Task (Zero the hero)

In this activity, you are going to make different numbers by performing operations (not the medical kind) to remove zeros from a number. You will work with a partner. You’ll need a calculator to share.

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 3

Addition mental strategies

MA3-5NA Addition and Subtraction

Jump strategy

When we add we can use the jump strategy to help us. Look at 257 + 32:

1 First we jump up by the tens2 Then we jump up by the units

Jump strategy with decimals

The jump strategy is also useful when adding decimals. Look at how we do this with 38.6 + 2.6:

1 First we jump up by the whole numbers.2 Then we jump up by the tenths.

Split strategy

When adding large numbers in our heads it can be easier to split one of the numbers into parts and add each part separately.

Split strategy with decimals

Sometimes it is easier to split both numbers. Look at how we do this with 21.2 + 3.8

1 We split the numbers into whole numbers and decimals.2 We then rearrange the problem, adding the whole numbers and decimals separately.3 We add the 2 answers.

Compensation strategy

Sometimes we round one number in the problem to make it easier to do in our heads. Then we adjust our answer to compensate:

Compensation strategy with decimals

Follow these steps for the compensation strategy when adding decimals:

1 Round the number closest to a whole number.2 Compensate for rounding:

Assessment Task (Checkerboard race)

This is a game for 2 players. You will need a counter each, a die and some paper to keep score.

Bump strategy

The bump strategy is when the number closest to ten gets impatient to start the addition process. The other number must adjust to compensate.

Stage 3

Assessment Task (Crack the city code)

Work out the answers to these sums in your head. Each answer matches a letter in the list on the right. Write the letters next to your answers, then unjumble the letters to find the name of a city.

Bump strategy

1 Bump the number closest to a multiple of ten. This makes the problem easier to do in our heads.2 Adjust the other number so the difference between the 2 numbers stays the same. This keeps the problem the same.3 Solve this easier problem. This then gives us the answer to our original problem.

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 4

Subtraction mental strategies

MA3-5NA Addition and Subtraction

Jump strategy

When we subtract we can use the jump strategy to help us. Look at 189 – 35:

1 First we jump back by the tens.2 Then we jump back by the units.

Choosing when to add or subtract

Sometimes we come across problems that require us to both add and subtract or to make a choice between which one to use. Understanding key language terms can help with this decision.

Terms:

Split strategy

When subtracting large numbers in our heads it can be easier to split the number to be subtracted into parts and work with each part separately.

Addition and subtraction

In the previous topic we practised addition using specific mental strategies. In real life, we can choose the mental strategy that suits us. We may have one preferred strategy or we may choose a different one depending on the numbers involved in the problem. There is no one right way to solve a problem.

Compensation strategy

Sometimes we round one number in the problem to make it easier to do in our heads. Then we adjust our answer to compensate:

Assessment Task (First to 1 000)

Player 1 picks 2 cards from the deck and uses them to make a 2 digit number. You can use the 2 cards in any order. For example, if you pick a 5 and a 6 you could make 56 or 65. When the cards are the same colour, the 2 digit number is added to the player’s score. When the cards are different colours, the number is subtracted. Start the game with 100 points each. The first player to 1 000 wins.

Assessment Task (Snakes but no ladders)

Start at 200. Throw the dice and add the numbers. The answer is the number of spaces you can move. Follow the numbers. If you land on a square with a snake you must work out the answer to the subtraction and move back to that square! The winner is the first to finish … alive!

Assessment Task (Connect 3)

This is a game for 2 players. You will need 2 dice, 3 counters for each player in different colours and this game board.

Stage 3

Assessment Task (Darts)

A game of darts is usually scored by subtracting the number that you throw from 301. Throwing darts can be dangerous in a classroom so you will be throwing dice instead! You can play with 1 to 4 people. You will take turns. You will need a copy of this page, two dice, a pencil and paper to keep score.

Assessment Task (Totally challenging)

Arrange the cards into six piles.

The challenge is to make each pile add to the same total.

Use trial and error to work out what the total is.

Show what you discover in the space below:

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 5

Mental multiplication strategies

MA3-6NA Multiplication and Division

Doubling strategy

Doubling is a useful strategy to use when multiplying.

Doubling and halving

We can use the double and halve strategy to get to an easy multiplication fact.

Multiply by 10s, 100s and 1 000s

When we multiply by 10 we move the number one place value to the left.When we multiply by 100 we move the number two place values to the left.When we multiply by 1 000 we move the number three place values to the left.Look at how this works with the number 45:

Multiplying by multiples of 10

It is also handy to know how to multiply multiples of 10 such as 20 or 200 in our heads.

Multiplying by multiples of ten

Split strategy

Sometimes it’s easier to split a number into parts and work with the parts separately.

Split strategy

Compensation Strategy

When multiplying we can round to an easier number and then adjust.Look how we do this with 4 × 29

Compensation Strategy

When multiplying we can round to an easier number and then adjust or compensate.

Stage 3

Factors and Multiples

Factors are the numbers we multiply together to get to another number:

How many factors does the number 12 have? 4 × 3 = 12, 6 × 2 = 12, 1 × 12 = 12

4, 3, 6, 2, 1 and 12 are all factors of 12.

Multiples and multiplication facts

Multiples are the answers you get when you multiply 2 factors:

Think about your 12 times tables where 12 is always a factor.

What are the multiples of 12? 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 …

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 6

Chance and Probability

MA3-19SP Chance

Ordering events

Probability measures how likely something is to happen.An event that is certain to happen has a probability of 1.An event that is impossible has a probability of 0.An event that has an even or equal chance of occurring has a probability of ½ or 50%.

Probability scale

Probability measures how likely something is to happen.

Relating fractions to likelihood

So far we have looked at the language of chance and outcomes either being at 0 (impossible), ½ (even) or 1 (certain). But what is the likelihood of outcomes in the unlikely range or the likely range? Outcomes in these ranges can be expressed as either fractions, decimals or %. Remember that when finding the chance or likelihood of an event occurring, we must look at all possible outcomes.

Using samples to predict probability

Surveys are used to collect data about certain topics or questions. Once the data is collected, it is presented in a table so it is easy to understand. Surveys can be conducted to ask all kinds of questions. We can use probability to see an even bigger picture than the survey tells us. This table shows the data collected when 50 people were surveyed to find their favourite milkshake flavour.

Chance experiments

Before we conduct a chance experiment, we need to work out what all the possible outcomes are. This helps us to look at how likely a particular outcome is and if the results are surprising or not. To do this, we can use a tree diagram. We count the boxes at the end of the diagram to find the total number of options.

Tree diagrams

Tree diagrams are used to display all possible outcomes in a simple chance experiment. Here is an example: Matilda’s father is making her lunch and has given her the following choice: white or brown bread, lettuce or sprouts, tuna or egg. We can then follow each branch along to see the different options.

Fair or unfair

When everyone has the same chance of winning a game or competition, it is fair. It is unfair when everyone does not have the same chance of winning.

Using tables

When we work out all the possible outcomes of an event that could happen, we are finding out the theoretical probability. When we do the experiment and look at the probability of what actually happened, we call it experimental probability.

Stage 3

Assessment Task (Greedy Pig)

This is a famous game. It’s played with the whole class. Your teacher will need a die and you will need your own tally board set up like this:

Assessment Task (Location, location)

Play this game with a friend. You will need one copy of this game board, a counter each and two dice.

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 7

2D shapes

MA3-15MG 2D Shapes

Polygons

A polygon is a 2D (flat) shape with 3 or more straight sides. The word comes from the Greek words, poly and gonia, meaning many angles. All polygons are closed – they have no break in their boundaries. They have no curved sides.

Polygons

This is a regular pentagon. The 5 sides and angles are equal.

Irregular polygons have the same number of sides as regular polygons but their sides are not of an equal length and their angles are not equal.

This is an irregular pentagon.

Quadrilaterals

A quadrilateral is a kind of polygon. It’s a closed, flat shape with 4 straight sides and 4 angles. The name comes from the Latin, quad and latus, meaning 4 sides.

One of the things that can be confusing about quadrilaterals is that there are a number of classifications, and shapes can be called different names. This is how they all fit together:

Quadrilaterals

A quadrilateral is a kind of polygon. It is a closed, flat shape with 4 straight sides and 4 angles. The name comes from the Latin words, quad and latus, meaning ‘4 sides’. We know that squares, rhombuses, rectangles and trapeziums are all examples of quadrilaterals. We also know the interior angles of quadrilaterals always add to 360°.

Triangles

A triangle is a type of polygon. It has three sides and three angles. The three interior angles always add to 180°. Here are the 3 main types of triangles:

Triangles

There are 4 main types of triangles:

Circles

A circle is also a 2D shape. It’s a closed curve that has all of its points a fixed distance from the centre. Later on, you will learn about the formal maths of circles – they’re more complex than they look! Right now, it’s important to recognise the different parts and to explore the relationships between the parts.

Circles

A circle is also a 2D shape. It is a curve with its points a fixed distance from the centre.

Stage 3

Assessment Task (Circle sense)

You’ll play this game with a partner. You’ll each need a copy of this page and it may pay to study the information on the previous page. The aim is to score the highest number of points you can by answering 10 questions. The harder questions score more points but of course, there is a greater risk of getting them wrong!

Assessment Task (The shapes within)

We can construct regular shapes inside circles. You will use what you know about angles and degrees to help you. You’ll also need a protractor and a compass.

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 8

Lines and angles

MA3-16MG Angles

Lines

When we classify lines we use terms such as parallel, perpendicular, vertical and horizontal. Knowing these terms makes it easier for us to understand and work with shapes.

Lines

These terms are commonly used when we work with lines and angles:• parallel – these lines are always the same distance apart at every point, they never meet• perpendicular – these lines intersect at right angles• diagonal – these are lines within a shape that join a vertex (corner) to another vertex• intersection – the place where 2 or more lines cross over each other

Introducing angles

When an angle is less than a quarter turn of 90° we say it’s acute.When it’s exactly 90° we say it’s a right angle.When it’s between 90° and 180° we say it’s obtuse.When it’s exactly 180° we say it’s a straight angle.When it’s more than 180° we say it’s a reflex angle.

We use an arc to show where we’re measuring.

With right angles, we use a square symbol like this

Classifying angles

An angle is the amount of turn between the intersections of two rays (lines). Angles are conventionally measured in degrees on a protractor. 360° is a full turn, 180˚ is a half turn, and 90˚ is a quarter turn.

Measuring angles

Sometimes we need to be more precise when naming angles, instead of just using terms such as acute or obtuse. This is where a protractor comes in handy.

To measure an angle using a protractor we:

Fit the baseline of the protractor to one line of the angle, lining up the centre point of the protractor with the vertex of the angle

Look where the other line intersects the numbers, making sure we read round from 0°.

Measuring angles

Measure angles within large, irregular shapes.

Stage 3

Assessment Task (Time passes)

In this activity you will measure the passing of time not in minutes and hours, but in degrees. You can work with a partner and you may like to use a clock face with movable hands to help you work out the answers.

Assessment Task (It’s all in the timing)

You can work with a partner on this activity. You may like to use a clock with movable hands or to use copies of the clock faces below.

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 9

Fractions

MA3-7NA Fractions and Decimals

Fractions of shapes

A fraction is a part of a whole. This shape has 12 equal parts. 5 of these have been shaded.

Equivalent fractions

To find equivalent fractions without drawing diagrams we use the numerators and denominators to guide us.

Imagine your share of a cake is half. It is too big to pick up so you cut your half into halves. You now have 2 quarters of the cake.

You have doubled the number of parts (the denominator) and by doing this you have doubled the number of parts (the numerator).

This method can be used to find all equivalent fractions.

Fractions of a collection

Mixed numerals and improper fractions

Comparing and ordering fractions

We can use number lines or fraction strips to help us compare and order fractions.

Simplifying fractions

To find the simplest fraction, we divide both the numerator and the denominator by the same number. It makes sense for this to be the biggest number we can find so we don’t have to keep dividing. This number is called the Highest Common Factor (HCF).

Assessment Task (Find the fraction)

Your job is to work out what fraction of each shape is shaded. Some of them are simple to work out, others will take a little more thinking.

Comparing and ordering fractions

Comparing and ordering fractions with like denominators is a simple process: When there are different denominators we need to rename the fractions so they have the same denominators. This lets us compare apples with apples.

Stage 3

Assessment Task (Mmmmm, chocolate)

In this activity you will use your knowledge of fractions to share chocolates amongst a family.

Renaming and ordering fractions

Term 1

Learning Intention

Content

Extension Intention

Extension content

Registration

Week 10

3D Shapes

MA3-14MG

3D Shapes

Introduction

2D shapes have 2 dimensions – width and height. They’re flat.

3D shapes have 3 dimensions – height, width and depth.

Sometimes we call them solids. When we draw them, we often show them as transparent or as skeletons so we can ‘see’ all their sides.

3D shapes can have all flat sides, all curved sides, or a mixture of both.

Types and properties

Remember the surfaces of a 3D shape are 2D shapes. Where 2 surfaces meet is called the edge. The point where 2 or more surfaces meet is called the vertex. If we are talking about more than one vertex we call them vertices.

A Swiss mathematician called Leonhard Euler, found a mathematical rule that was so important, it was named after him. He wasn’t just a pretty face …

He discovered a connection between the number of faces (F), number of edges (E) and number of vertices (V) of polyhedrons. Here is part of Euler’s rule: F + V – E = ?

Polyhedrons

Some 3D shapes are polyhedrons. This means each surface is a polygon. The polyhedrons we most commonly come across are pyramids and prisms.

There are other kinds of polyhedrons. They’re also made up of polygons and have straight sides, but they don’t fit the rules for pyramids and prisms. Here are some examples:

Assessment Task (2 halves make a whole)

The nets of 5 solids are below – the problem is that they’ve been separated into two parts. Your job is to match the parts correctly. See if you can do it in your head.

If this proves too difficult, you can cut the nets out and physically join them to form the solid.

Spheres, cones and cylinders

Another group of 3D shapes has one or more curved surfaces. Examples include spheres, cones and cylinders.

Assessment Task (Tomb Raider)

You’re trapped in a tomb far underground. There are 6 key zones in the tomb. To escape, you must find 10 different ways to get from the ledge to the gold.

Drawing 3D shapes

When we draw 3D shapes, we can draw dotted lines to show the surfaces, edges and vertices we can’t see.

We can also use dot paper or hexagonal grids to guide us when we draw 3D shapes.

Drawing 3D shapes

When we draw 3D shapes, we can draw dotted lines to indicate the surfaces, edges and vertices we can’t see.

Stage 3

Nets

A net is the pattern of a 3D shape, unfolded and laid flat. It also helps if you can fold and unfold them in your head.

Nets

A net is the pattern of a 3D shape, unfolded and laid flat. It helps to visualise how nets fold up to create a 3D shape.

Maths

problem in

word

Solving a

2. Underline the question.

Tom had 15 stickers. Jim had 19 stickers. How many stickers are there altogether?

1. Read the problem.

Tom had 15 stickers. Jim had 19 stickers. How many stickers are there altogether?

3. Write the name of the answer.

Stickers

5. Write the algorithm (open number sentence).

15 + 19 =

6. Show your working out to solve the problem.

15 +

1934

7. Write your answer as a statement (in words).

There are 34 stickers altogether.

4. What is the operation (sign/signs)

+

Stage 3 Mathletics Break Down of Strands

MA3-4NA Whole Number

Year 5

Year 6

Topic 1 – Looking at Whole Numbers

· Read and write numbers to 999 999

· Order numbers to 999 999

· Create and compare numbers

· Assessment Task (It’s holiday time)

· Assessment Task (The new place is right)

Topic 1 – Read and understand numbers

· Place value to millions

· Expanded notation

· Order large Numbers

· Assessment Task (The millionaires’ club)

· Assessment Task (Zero the hero)

Topic 2 – Place Value of Whole Numbers

· Expanded notation

· Place value to 4 digits

· Place value to 6 digits

· Assessment Task (Place value mastermind)

· Assessment Task (Who am I)

Topic 2 – Types of numbers

· Negative numbers

· Prime and composite numbers

· Mixed Practice

· Roman Numerals

· Assessment Task (New system and Goldbach)

Topic 3 – Round and Estimate

· Round to a power of Ten

· Estimate

· Calculations

· Assessment Task (Round and estimate)

· Assessment Task (Shop till you drop)

Topic 3 – Round and estimate

· Round to the nearest power of ten

· Round and estimate

· Assessment Task (Butler fill my bath)

· Assessment Task (Word problems)

MA3-5NA Addition and Subtraction

Year 5

Year 6

Topic 1 - Addition mental strategies

· Jump strategy

· Split strategy

· Compensation strategy

· Assessment Task (Checkerboard race)

· Assessment Task (Crack the city code)

Topic 1 - Mental strategies

· Jump strategy review

· Jump strategy with decimals

· Split strategy review

· Split strategy with decimals

· Compensation strategy review

· Compensation strategy with decimals

· Bump strategy

Topic 2 – Subtraction mental strategies

· Jump strategy

· Split strategy

· Compensation strategy

· Assessment Task (Snakes but no ladders)

· Assessment Task (Darts)

Topic 2 – Applying strategies

· Addition

· Subtraction

· Choosing when to add or subtract

· Addition and subtraction

· Assessment Task x4

Topic 3 – Written methods

· Addition

· Subtraction

· Adding and subtracting decimals

· Assessment Task (Slippery dip race)

· Assessment Task (Subtraction puzzles)

Topic 3 – Written methods

· Addition

· Subtraction

· Adding and subtracting decimals

· Adding and subtracting

· Assessment Task (You can bank on it)

· Assessment Task (By jingo)

MA3-6NA Multiplication and Division

Year 5

Year 6

Topic 1 – Mental multiplication strategies

· Doubling strategy

· Multiply by 10s, 100s and 1 000s

· Split strategy

· Compensation Strategy

· Factors and Multiples

Topic 1 – Mental multiplication strategies

· Multiples and multiplication facts

· Doubling and halving

· Multiplying by multiples of 10

· Split strategy

· Compensation Strategy

Topic 2 – Mental division strategies

· Use multiplication facts

· Divide by 10s, 100s and 1 000s

· Halving strategy

· Split Strategy

· Test of divisibility

Topic 2 – Mental division strategies

· Inverse operations

· Split strategy

· Using factors

· Rules of divisibility

· Dividing by multiples of ten

Topic 3 – Written methods

· Contracted multiplication

· Extended multiplication

· Short division

· Short division with remainders

· Solving problems

Topic 3 – Written methods

· Contracted multiplication

· Extended multiplication

· Contracted division

· Remainders in division

· Solving problems

Topic 4 – Puzzles and investigations

· Assessment Task (Crack the code)

· Assessment Task (Smart buttons)

· Assessment Task (Bugs)

· Assessment Task (Puzzles)

Topic 4 – Puzzles and investigations

· Assessment Task (It’s graduation time)

· Assessment Task (Finish it)

· Assessment Task (Midnight Market)

· Assessment Task (Too big, too small)

· Assessment Task (Around the world)

MA3-7NA Fractions and Decimals

Year 5

Year 6

Topic 1 – Fractions

· Fractions of shapes

· Fractions of a collection

· Comparing and ordering fractions

· Assessment Task (Find the fraction)

· Assessment Task (Mmmmm, chocolate)

Topic 1 – Fractions

· Equivalent fractions

· Mixed numerals and improper fractions

· Simplifying fractions

· Comparing and ordering fractions

· Renaming and ordering fractions

· Assessment Task (Spend and save)

· Assessment Task (Trick or treat!)

Topic 2 – Types of fractions

· Equivalent Fractions

· Mixed numerals and improper fractions

· Assessment Task (Equivalent fraction snap)

· Assessment Task (Feeding Time)

Topic 2 – Decimal fractions

· Tenths, hundredths and thousandths

· Reading and writing decimals

· Comparing and ordering decimals

· Renaming decimals

· Rounding

· Percentages

· Assessment Task (Ask Around)

· Assessment Task (Percentage Problems)

Topic 3 – Fractions, decimals and percentages

· Tenths

· Tenths and hundredths

· Place value to thousandths

· Percentages

· Assessment Task (Match n’ Snap)

Topic 4 – Calculating

· Adding and subtracting fractions with like denominators

· Adding and subtracting fractions to and from a whole

· Adding and subtracting fractions

· Adding decimal fractions

· Subtracting decimal fractions

· Assessment task (you cut, i choose)

MA3-8NA Patterns and Algebra

Year 5

Year 6

Topic 1 – Patterns and functions

· Recursive number pattern

· Function number patterns

· Matchstick patterns

· Function machines

· Function tables with addition and subtraction

· Function tables with multiplication

· Assessment Task (Rows and columns)

· Assessment Task (Pizza pizzazz)

Topic 1 – Patterns and functions

· Recursive number sequences

· Function number sequences

· Function shape patterns

· Function machines and function tables

· Real life functions

· Assessment Task (Fabulous Fibonacci)

· Assessment Task (Triangular Numbers)

· Assessment Task (Pascal’s triangle)

Topic 2 – Equations and equivalence

· Understanding equivalence

· Using symbols

· Keeping balance

· Assessment Task (Magician’s hat trick)

· Assessment Task (Dhiffushi Island Currency)

Topic 2 – Algebraic thinking

· Making connections between unknown values

· Assessment Task (Present puzzle)

· Assessment Task (The Lolly Box)

Topic 3 – Using equations

· Balance strategy using inverse operations

· Word problems

· Think of a number

· Assessment Task (Number tricks 1)

· Assessment Task (Number tricks 2)

Topic 3 – Solving equations

· Introducing pronumerals

· Using pronumerals in an equation

· Simplifying algebraic statements

· Assessment Task (Happy Birthday)

· Assessment Task (Squelch Juiceteria)

Topic 4 – Properties of arithmetic

· Order of operations

· Commutative rule

· Distributive rule

· Assessment Task (Equation pairs)

MA3-9MG Length

Year 5

Year 6

Topic 1 – Units of length

· m, cm, mm

· Find and order length

· Metres to kilometres

· Assessment Task (Spot the distance)

· Assessment Task (Word problems)

Topic 1 – Units of length

· Choose units of measurement

· Convert measurements

· Estimate and measure

· Assessment Task (Size me up)

· Assessment Task (How long?)

Topic 2 – Travelling far

· Measure distance

· Maps and scale

· Speed and distance

· Assessment Task (Flag it!)

· Assessment Task (The city to school)

Topic 4 – Scale and distance

· Scale drawings

· Maps

· Speed, time and distance

· Assessment Task (All roads lead to Rome)

· Assessment Task (Where will it take you?)

Topic 3 – Perimeter

· Perimeter of shapes

· Calculate perimeter

· Construct shapes

· Assessment Task (Perimeter problems)

· Assessment Task (More perimeter problems)

Topic 2 – Perimeter

· Measure perimeters

· Perimeters of composite shapes

· Circumference

· Assessment Task (Circle work)

· Assessment Task (Perimeter puzzles)

MA3-10MG Area

Year 5

Year 6

Topic 4 – Area

· Introducing area

· Area of triangles

· Hectares and square kilometres

· Area and perimeter

· Assessment Task (Area puzzles)

· Assessment Task (Composite calculations)

Topic 3 – Area

· Square Units

· Find area using formulae

· Find area of irregular and composite shapes

· Area and perimeter

· Assessment Task (Area & perimeter puzzles)

· Assessment Task (Animal rescue)

MA3-11MG Volume and Capacity

Year 5

Year 6

Topic 1 – Volume and capacity

· Millilitres and litres

· Cubic centimetres and cubic metres

· Displacement

· Assessment Task (Milk it Maisie)

· Assessment Task (Think outside the box)

Topic 1 – Volume and capacity

· Millilitres and litres

· Cubic centimetres and cubic metres

· Displacement

· Linking mass, capacity and volume

· Assessment Task (Measuring mud)

· Assessment Task (Water, water, everywhere)

MA3-12MG Mass

Year 5

Year 6

Topic 2 – Mass

· Grams

· Kilograms

· Tonnes

· Assessment Task (Spuds and carrots)

· Assessment Task (Weighing it up)

Topic 2 – Mass

· Grams

· Grams and kilograms

· Tonnes

· Mass and capacity

· Assessment Task (The chocolate challenge)

· Assessment Task (Cupcake creation)

MA3-13MG Time

Year 5

Year 6

Topic 1 – Measuring time

· Time relationships

· Reading analogue clocks

· am and pm notation

· 24 hour time

· Time relationship challenges

· Assessment Task (Camping trip)

· Assessment Task (24 hour time dominos)

Topic 1 – Telling time

· Analogue and digital

· 24 hour time

· Timetables

· Assessment Task (L.A. here we come!)

· Assessment Task (Race against time)

Topic 2 – Calculating time

· Elapsed time

· Using a stopwatch

· Assessment Task (Lucky numbers)

· Assessment Task (Mayhem at max madness)

Topic 2 – Calculating time

· Time trails

· Word problems

· Using a stopwatch

· Assessment Task (Whodunit)

· Assessment Task (Connect clocks)

Topic 3 – Timetables

· Reading timetables

· Working out travel time

· Assessment Task (What’s on the box?)

· Assessment Task (Circus school)

Topic 3 – Time applications

· Calendars

· Australian time zones

· World time zones

· Assessment Task (Don’t forget to call home)

· Assessment Task (Timelines)

· Assessment Task (Time of your life)

MA3-14MG 3D Shapes

Year 5

Year 6

Topic 4 – 3D shapes

· Introduction

· Polyhedrons

· Spheres, cones and cylinders

· Drawing 3D shapes

· Nets

· Assessment Task (2 halves make a whole)

· Assessment Task (Tomb Raider)

Topic 4 – 3D shapes

· Types and properties

· Nets

· Drawing 3D shapes

· Assessment Task (To cube or not to cube)

· Assessment Task (Form an orderly queue)

MA3-15MG 2D Shapes

Year 5

Year 6

Topic 2 – 2D shapes

· Polygons

· Quadrilaterals

· Triangles

· Circles

· Assessment Task (Circle sense)

· Assessment Task (How many triangles?)

Topic 2 – 2D shapes

· Polygons

· Quadrilaterals

· Triangles

· Circles

· Assessment Task (The shapes within)

· Assessment Task (Rip it up)

Topic 3 – Transformation, tessellation and symmetry

· Symmetry

· Transformation

· Tessellation

· Assessment Task (Tessellate and create)

· Assessment Task (Dig it, Dr Jones)

Topic 3 – Transformation, tessellation and symmetry

· Line symmetry

· Rotational symmetry

· Transformation

· Tessellation

· Enlargement and reduction

· Assessment Task (Picture perfect)

· Assessment Task (Design Diva)

MA3-16MG Angles

Year 5

Year 6

Topic 1 – Lines and angles

· Lines

· Introducing angles

· Measuring angles

· Assessment Task (Time passes)

Topic 1 – Lines and angles

· Lines

· Classifying angles

· Measuring angles

· Assessment Task (Hand it over)

· Assessment Task (It’s all in the timing)

MA3-17MG Position

Year 5

Year 6

Topic 1 – Spatial orientation

· Point of view

· Directions

· Assessment Task (A picture tells a thousand words)

· Assessment Task (Tell me where to go)

Topic 1 – Spatial orientation

· Point of view

· Directions

· Assessment Task (Treasure trail)

Topic 2 – Coordinates

· Plotting coordinates

· Mapping using coordinates

· Assessment Task (Coordinate line up)

· Assessment Task (Coordinate design)

Topic 2 – Coordinates

· Plotting coordinates

· Street directions

· Assessment Task (Take me to the movies)

· Assessment Task (Connections)

Topic 3 – Directions

· Using a compass

· Maps

· Assessment Task (north, south, east and west)

Topic 3 – Maps and scale

· Scale drawings

· Assessment Task (Map it out)

· Assessment Task (Border or bust)

MA3-18SP Data

Year 5

Year 6

Topic 1 – Types of graphs 1

· Picture graphs

· Column graphs

Topic 2 – Types of graphs 2

· Pie charts

· Divided bar graphs

Topic 1 – Types of graphs 1

· Picture graphs

· Double column graphs

Topic 2 – Types of graphs 2

· Pie charts

· Divided bar graphs

Topic 3 – Types of graphs 3

· Reading line graphs

· Constructing line graphs

· Travel graphs

· Assessment Task (Whodunit?)

Topic 3 – Types of graphs 3

· Reading line graphs

· Constructing line graphs

· Double line graphs

· Travel graphs

Topic 4 – Collecting and analysing data

· Frequency tables

· Mean

· Collecting data

· Assessment Task (Data disaster)

Topic 4 – Collecting and analysing data

· Grouped data

· Range

· Mean

· Median

· Mode

· Surveys

· Misleading graphs

MA3-19SP Chance

Year 5

Year 6

Topic 1 – Chance and Probability

· Ordering events

· Relating fractions to likelihood

· Chance experiments

· Fair or unfair

· Assessment Task (The Mathletics Cup)

· Assessment Task (Greedy Pig)

Topic 1 – Chance and probability

· Probability scale

· Using samples to predict probability

· Tree diagrams

· Chance experiments

· Using tables

· Assessment Task (Location, location)

· Assessment Task (Lucky throw)