C2C adapted with permission by NT DoE © The State of Queensland 1 of 17 www.det.nt.gov.au

C2C Multilevel Year Level Plan

Mathematics

Year 5/Year 6/Year 7

Year level description

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Year 5

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral

part of mathematics content across the three content strands: Number and Algebra, Measurement

and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of

working mathematically within the content and describe how the content is explored or developed.

They provide the language to build in the developmental aspects of the learning of mathematics.

At this level:

Understanding includes making connections between representations of numbers, using fractions to

represent probabilities, comparing and ordering fractions and decimals and representing them in

various ways, describing transformations and identifying line and rotational symmetry

Fluency includes choosing appropriate units of measurement for calculation of perimeter and area,

using estimation to check the reasonableness of answers to calculations and using instruments to

measure angles

Problem Solving includes formulating and solving authentic problems using whole numbers and

measurements and creating financial plans

Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns

involving fractions and decimals, interpreting results of chance experiments, posing appropriate

questions for data investigations and interpreting data sets

Year 6

At this year level:

Understanding includes describing properties of different sets of numbers, using fractions and

decimals to describe probabilities, representing fractions and decimals in various ways and describing

connections between them, and making reasonable estimations

Fluency includes representing integers on a number line, calculating simple percentages, using

brackets appropriately, converting between fractions and decimals, using operations with fractions,

decimals and percentages, measuring using metric units, and interpreting timetables

Problem Solving includes formulating and solving authentic problems using fractions, decimals,

percentages and measurements, interpreting secondary data displays, and finding the size of

unknown angles

Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chance experiments may differ from expected results

DEPARTMENT OF EDUCATION

C2C adapted with permission by NT DoE © The State of Queensland 2 of 17 www.det.nt.gov.au

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Year 7

At this year level:

Understanding includes describing patterns in uses of indices with whole numbers, recognising

equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian

plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and

properties of numbers to algebraic terms and expressions

Fluency includes calculating accurately with integers, representing fractions and decimals in various

ways, investigating best buys, finding measures of central tendency and calculating areas of shapes

and volumes of prisms

Problem Solving includes formulating and solving authentic problems using numbers and

measurements, working with transformations and identifying symmetry, calculating angles and

interpreting sets of data collected through chance experiments

Reasoning includes applying the number laws to calculations, applying known geometric facts to

draw conclusions about shapes, applying an understanding of ratio and interpreting data displays.

Achievement standard

Year 5

By the end of Year 5, students solve simple problems involving the four operations using a range of

strategies. They check the reasonableness of answers using estimation and rounding. Students

identify and describe factors and multiples. They explain plans for simple budgets. Students connect

three-dimensional objects with their two-dimensional representations. They describe transformations

of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret

different data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract

fractions with the same denominator. Students continue patterns by adding and subtracting fractions

and decimals. They find unknown quantities in number sentences. They use appropriate units of

measurement for length, area, volume, capacity and mass, and calculate perimeter and area of

rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to

locate landmarks. They measure and construct different angles. Students list outcomes of chance

experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose

questions to gather data, and construct data displays appropriate for the data.

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Year 6

By the end of Year 6, students recognise the properties of prime, composite, square and triangular

numbers. They describe the use of integers in everyday contexts. They solve problems involving all

four operations with whole numbers. Students connect fractions, decimals and percentages as

different representations of the same number. They solve problems involving the addition and

subtraction of related fractions. Students make connections between the powers of 10 and the

multiplication and division of decimals. They describe rules used in sequences involving whole

numbers, fractions and decimals. Students connect decimal representations to the metric system and

choose appropriate units of measurement to perform a calculation. They make connections between

capacity and volume. They solve problems involving length and area. They interpret timetables.

Students describe combinations of transformations. They solve problems using the properties of

angles. Students compare observed and expected frequencies. They interpret and compare a variety

of data displays including those displays for two categorical variables. They evaluate secondary data

displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity.

They add, subtract and multiply decimals and divide decimals where the result is rational. Students

calculate common percentage discounts on sale items. They write correct number sentences using

brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on

the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate

probabilities using simple fractions, decimals and percentages.

Year 7

By the end of Year 7, students solve problems involving the comparison, addition and subtraction of

integers. They make the connections between whole numbers and index notation and the relationship

between perfect squares and square roots.

They solve problems involving percentages and all four operations with fractions and decimals. They

compare the cost of items to make financial decisions. Students represent numbers using variables.

They connect the laws and properties for numbers to algebra. They interpret simple linear

representations and model authentic information. Students describe different views of three-

dimensional objects. They represent transformations in the Cartesian plane. They solve simple

numerical problems involving angles formed by a transversal crossing two parallel lines. Students

identify issues involving the collection of continuous data. They describe the relationship between the

median and mean in data displays.

Students use fractions, decimals and percentages, and their equivalences. They express one quantity

as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic

expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian

plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of

rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles

formed by a transversal crossing parallel line. Students determine the sample space for simple

experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate

mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.

C2C adapted with permission by NT DoE © The State of Queensland 4 of 17 www.det.nt.gov.au

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Unit outline Semester 1

Term 1 Term 2

Unit 1 Students have opportunities to develop mathematical understandings through the sub-strands Number and place value, Fractions and decimals (Years 5 and 6), Real numbers (Year 7), Patterns and algebra, Linear and non-linear relationships (Year 7 only), Using units of measurement (Years 5 and 6) and Location and transformation.

Unit 2 Students have the opportunity to develop mathematical understandings through the sub-strands — Number and place value, Real numbers, Fractions and decimals, Money and financial mathematics, Chance and Data interpretation and representation.

Unit 3 Students apply a variety of mathematical concepts in real-life, life-like and purely mathematical situations through the sub-strands — Number and place value, Fractions and decimals (Years 5 and 6), Real numbers (Year 7), Patterns and algebra, Using units of measurement and Shape.

Unit 4 Students have opportunities to develop mathematical understandings through the sub-strands — Number and place value, Using units of measurement, Fractions and decimals (Years 5 and 6), Real numbers (Year 7) and Data representation and interpretation.

General capabilities and Cross-curriculum priorities

Opportunities to engage with: Opportunities to engage with:

C2C adapted with permission by NT DoE © The State of Queensland 5 of 17 www.det.nt.gov.au

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Unit outline Semester 2

Term 3 Term 4

Unit 5

Students have opportunities to develop mathematical understandings through the sub-strands — Number and place value, Using units of measurement, Fractions and decimals (Years 5 and 6), Real numbers (Year 7), Location and transformation, and Patterns and algebra.

Unit 6

Students have opportunities to develop mathematical understandings through the sub-strands — Number and place value, Fractions and decimals (Years 5 and 6), Real numbers (Year 7), Chance, Data representation and interpretation, and Money and financial mathematics.

Unit 7

Students have opportunities to develop mathematical understandings through the sub-strands — Fractions and decimals (Years 5 and 6); Real numbers and Linear and non-linear relationships (Year 7); and Number and place value, Using units of measurement and Geometric reasoning.

Unit 8

Students have opportunities to develop understandings through the sub-strands — Number and place value (Years 5 and 6), Linear and non-linear relationships (Year 7), Units of measurement, Fractions and decimals, Real numbers, Shape, Geometric reasoning, Patterns and algebra, and Data representation and interpretation.

General capabilities and Cross-curriculum priorities

Opportunities to engage with: Opportunities to engage with:

Key to General capabilities and Cross-curriculum priorities

Literacy Numeracy ICT competence Critical and creative thinking Ethical behaviour

Personal and social

competence

Intercultural understanding

Aboriginal and Torres Strait

Islander histories and cultures

Asia and Australia’s

engagement with Asia

Sustainability

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Assessment Semester 1

Teachers and children organise evidence of learning in individual folios. The individual folio is constructed jointly by a teacher, a child, parents/carers and other partners.

It becomes a dynamic record of examples of a child’s learning and development.

Term 1 Term 2

Unit 1 Year 5, 6 and 7: Monitor student learning and progress throughout the unit and use feedback to inform teaching and learning. Unit 2 Year 5, 6 and 7: Chance Short answer questions Year 5 students list the outcomes of chance experiments as fractions. Year 6 students communicate probabilities using simple fractions, decimals and percentages. Year 7 students assign probabilities to the outcome of events and determine probabilities for events. Unit 2 Year 5: Division and fractions Short answer questions Students solve problems involving fractions and dividing by a single digit with no remainder.

Unit 2 Year 6: Positive and negative numbers and fractions Short answer questions

Students add and subtract positive and negative fractions. Unit 2 Year 7: Fractions and ratios Short answer questions Students solve problems involving fractions, percentages and ratios.

Unit 3 Year 5, 6 and 7: Monitor student learning and progress throughout the unit and use feedback to inform teaching and learning. Unit 4 Year 5, 6 and 7: Swimming pool blankets Short answer questions Year 5 students choose appropriate units to find length and area. Year 6 students solve problems involving the comparison of perimeter and area. Year 7 students use formulas to calculate perimeter and area of shapes involving rectangles. Unit 4 Year 5: Thinking multiplication and

equivalence Exam/Test Students solve problems involving multiplication of large numbers using a range of strategies and to represent problems using equivalent number sentences.

Unit 4 Year 6: Order of operations and properties of numbers Exam/Test

Students identify, describe and sequence whole numbers according to their properties and to apply the order of operations. Unit 4 Year 7: Linear equations and square

roots Exam/Test Students use index notation and square roots and to express problems using algebraic expressions.

Making consistent judgments / Feedback

Teachers will moderate to identify A-E samples before marking practical demonstration tasks. They will participate in on-going moderation conversations to achieve consensus and consistency of judgments.

C2C adapted with permission by NT DoE © The State of Queensland 7 of 17 www.det.nt.gov.au

Assessment Semester 2

Teachers and children organise evidence of learning in individual folios. The individual folio is constructed jointly by a teacher, a child, parents/carers and other partners. It becomes a dynamic record of examples of a child’s learning and development.

Term 3 Term 4

Unit 5 Year 5: Number Patterns Short answer questions Students describe, continue and create number patterns. Year 6: 2012 Year 6 Mathematics QCAT Written Students multiply decimals, and continue and create number sequences. Year 7: Expressions and variables Short answer questions Students create expressions and substitute values for variables to solve problems. Year 5: Changing shapes Short answer questions Students identify and describe the effects of transformations and identify line and rotational symmetry.

Year 6: Transformations

and tessellations Assignment/Project Students use a combination of transformations to create a shape that can be used in a tessellating pattern. Year 7: Plotting points and

transformations Exam/Test Students demonstrate their ability to number, name and plot points on a Cartesian plane and describe translations, reflections in an axis, and rotations of multiples of 90° using coordinates. Unit 6 Year 5: Data Explorer Short answer questions Students pose a question to gather data and construct, describe and interpret the data collected.

Year 6: Data decoder Short answer questions Students interpret and compare a range of data displays. Year 7: Basketball scores Short answer questions Students calculate mean, median, mode and range for sets of data. Year 5: Can you afford a pet? Exam/Test Student create a financial plan. Year 6: Percentage discounts Exam/Test Students create a simple budget. Year 7: Best value drink Exam/Test Students calculate unit price to compare products to decide best value.

Unit 7 Year 5, 6 and 7: Maths and me

Short answer questions Year 5 students solve problems involving multiplication by one- and two-digit multipliers, and compare and order decimals. Year 6 students solve problems involving all four operations with whole numbers and decimals. Year 7 students express one quantity as a fraction or percentage of another and find percentages of quantities. Year 5: What’s that angle? Short answer questions Student estimate, measure, compare and construct angles. Year 6: Investigating angles Short answer questions Students investigate angles on a straight line, vertically opposite angles and angles at a point.

Year 7: Triangles and Quadrilaterals

Short answer questions Students classify triangles, describe quadrilaterals and find missing angles. Unit 8 Year 5, 6 and 7: Monitor student learning and progress throughout the unit and use feedback to inform teaching and learning.

Making consistent judgments / Feedback

Teachers will moderate to identify A-E samples before marking practical demonstration tasks. They will participate in on-going moderation conversations to achieve consensus and consistency of judgments.

C2C adapted with permission by NT DoE © The State of Queensland 8 of 17 www.det.nt.gov.au

Balance and coverage of content descriptions

Year 5

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Number and place value 1 2 3 4 Using units of measurement 1 2 3 4 Chance 1 2 3 4

Identify and describe factors and multiples of whole numbers and use them to solve problems.

1 Choose appropriate units of measurement for length, area, volume, capacity and mass.

3 4

7 List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions.

2 6

Use estimation and rounding to check the reasonableness of answers to calculations.

1 Calculate the perimeter and area of rectangles using familiar metric units.

3 4

8 Recognise that probabilities range from 0 to 1.

2 6

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

3 4

6 7 Compare 12- and 24-hour time systems and convert between them.

1 5

Solve problems involving division by a one digit number, including those that result in a remainder.

2 5

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems.

1 4 6 7

Fractions and decimals Shape Data representation and interpretation

Compare and order common unit fractions and locate and represent them on a number line.

2 4 5

6

Connect three-dimensional objects with their nets and other two-dimensional representations.

3 Pose questions and collect categorical or numerical data by observation or survey.

2 6 8

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Balance and coverage of content descriptions

Year 5

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Fractions and decimals cont. 1 2 3 4 Data representation and interpretation cont.

1 2 3 4

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator.

1 2

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

2 4 6 8

Recognise that the number system can be extended beyond hundredths.

1 3 7 8

Describe and interpret different data sets in context.

4 6 8

Compare, order and represent decimals.

1 3 7 8

Money and financial mathematics

Location and transformation 1 2 3 4

Create simple financial plans. 2 6 8 Use a grid reference system to describe locations. Describe routes using landmarks and directional language.

1 8

Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries.

5

Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original.

5

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Balance and coverage of content descriptions

Year 5

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Patterns and algebra 1 2 3 4 Geometric reasoning 1 2 3 4

Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction.

1 5 Estimate, measure and compare angles using degrees. Construct angles using a protractor.

7

Use equivalent number sentences involving multiplication and division to find unknown quantities.

3 7

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Balance and coverage of content descriptions

Year 6

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Number and place value 1 2 3 4 Using units of measurement 1 2 3 4 Chance 1 2 3 4

Identify and describe properties of prime, composite, square and triangular numbers.

1 4 5 Connect decimal representations to the metric system.

3 Describe probabilities using fractions, decimals and percentages.

2 6

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers.

4 6 7 Convert between common metric units of length, mass and capacity.

7 Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies.

2 6

Investigate everyday situations that use positive and negative whole numbers and zero. Locate and represent these numbers on a number line.

2 3 Solve problems involving the comparison of lengths and areas using appropriate units.

4 8 Compare observed frequencies across experiments with expected frequencies.

6

Connect volume and capacity and their units of measurement.

7

Interpret and use timetables. 1 5

Fractions and decimals Shape Data representation and interpretation

Compare fractions with related denominators and locate and represent them on a number line.

2 Construct simple prisms and pyramids.

3 Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables.

2 4 6

Solve problems involving addition and subtraction of fractions with the same or related denominators.

1

2

Interpret secondary data presented in digital media and elsewhere.

8

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Balance and coverage of content descriptions

Year 6

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Fractions and decimals cont. 1 2 3 4

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

6

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

1 3 7

Multiply decimals by whole numbers and perform divisions that result in terminating decimals, with and without digital technologies.

5 7

8

Multiply and divide decimals by powers of 10.

5

Make connections between equivalent fractions, decimals and percentages.

4

Money and financial mathematics

Location and transformation 1 2 3 4

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

2 6 8 Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies.

5

Introduce the Cartesian coordinate system using all four quadrants.

1 5 8

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Balance and coverage of content descriptions

Year 6

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Patterns and algebra 1 2 3 4 Geometric reasoning 1 2 3 4

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

1 5 Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles.

7

Explore the use of brackets and order of operations to write number sentences.

3 7

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Balance and coverage of content descriptions

Year 7

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Number and place value 1 2 3 4 Using units of measurement 1 2 3 4 Chance 1 2 3 4

Investigate index notation and represent whole numbers as products of powers of prime numbers.

4 Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving.

3 4

Construct sample spaces for single-step experiments with equally likely outcomes.

6

Investigate and use square roots of perfect square numbers.

4 Calculate volumes of rectangular prisms.

7 Assign probabilities to the outcomes of events and determine probabilities for events.

6

Apply the associative, commutative and distributive laws to aid mental and written computation.

5

Compare, order, add and subtract integers.

1 5

Fractions and decimals Shape Data representation and interpretation

Compare fractions using equivalence. Locate and represent fractions and mixed numbers on a number line.

1 Draw different views of prisms and solids formed from combinations of prisms.

3 Identify and investigate issues involving continuous or large count data collected from primary and secondary sources.

4 8

Solve problems involving addition and subtraction of fractions including those with unrelated denominators.

2 Construct and compare a range of data displays including stem-and-leaf plots and dot plots.

4 8

Multiply and divide fractions and decimals using efficient written strategies and digital technologies.

3 5

6

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data.

6

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Balance and coverage of content descriptions

Year 7

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Fractions and decimals cont. 1 2 3 4 Data representation and interpretation cont.

1 2 3 4

Express one quantity as a fraction of another with and without the use of digital technologies.

6 7 Describe and interpret data displays and the relationship between the median and mean.

6

Round decimals to a specified number of decimal places.

3

Connect fractions, decimals and percentages and carry out simple conversions.

1 4

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies.

4 7 8

Recognise and solve problems involving simple ratios.

2

Money and financial mathematics

Location and transformation 1 2 3 4

Investigate and calculate 'best buys', with and without digital technologies.

2 6 8 Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries.

1 5

Pattern and algebra Geometric reasoning

Introduce the concept of variables as a way of representing numbers using letters.

3 Identify corresponding, alternate and co-interior angles when two parallel straight lines are crossed by a transversal.

8

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Balance and coverage of content descriptions

Year 7

Number and Algebra Term Measurement and Geometry Term Statistics and Probability Term

Pattern and algebra cont. 1 2 3 4 Geometric reasoning cont. 1 2 3 4

Create algebraic expressions and evaluate them by substituting a given value for each variable.

1 3 5 Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning.

8

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions.

Classify triangles according to their side and angle properties and describe quadrilaterals.

7

Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral. Measurement and Geometry

7

Linear and non-linear relationships

Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point.

1

Solve simple linear equations. 8

Investigate, interpret and analyse graphs from authentic data.

7 8

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References

http://www.australiancurriculum.edu.au/ Australian Curriculum Version 3.0 dated 23 January 2012

Copyright © The State of Queensland (represented by the Department of Education and Training)

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4002 Australia and is reproduced with its permission. No part may be further reproduced in hardcopy form by anyone outside the Northern Territory Department of

Education without the express permission of the Queensland Department of Education and Training.