NSW Year 7 Program-topic 1

Topic 1 - Whole Numbers 1.01 Addition and subtraction Background 1.02 Multiplication Background 1.03 Division Background 1.04 Order of operations with whole numbers Background 1.05 Check reasonableness of calculations Background 1.06 Number calculations with technology Background 1.07 Write mathematical statements Background Topic 2 - Number Properties 2.01 Number operation properties MA4-ALG-C-01.3 2.02 Square Numbers MA4-IND-C-01.2 2.03 Square Roots MA4-IND-C-01.2 2.04 Powers of Whole Numbers MA4-ALG-C-01.1 MA4-IND-C-01.1 2.05 Powers of 10 MA4-IND-C-01.1 2.06 Factors and multiples Background

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2.07 Prime factorisations MA4-IND-C-01.1 2.08 Using factors and multiples MA4-FRC-C-01.1 MA4-IND-C-01.1 Topic 3 - Integers 3.01 Integers and the number line MA4-INT-C-01.1 MA4-INT-C-01.2 3.02 Compare Integers MA4-IND-C-01.1 3.03 Add and Subtract Integers MA4-IND-C-01.2 MA4-IND-C-01.4 Topic 4 - Fractions 4.01 Identify, order and compare fractions MA4-FRC-C-01.1 4.02 Negative fractions MA4-FRC-C-01.1 MA4-FRC-C-01.6 4.03 Equivalent and simplified fractions MA4-FRC-C-01.1 4.04 Add and subtract fractions MA4-FRC-C-01.7 4.05 Fractions of a quantity MA4-FRC-C-1.8 MA4-FRC-C-1.9 4.06 Multiply fractions MA4-FRC-C-01.8

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4.07 Divide fractions MA4-FRC-C-01.8 4.08 Order of operations with fractions MA4-FRC-C-01.7 MA4-FRC-C-01.8 Topic 5 - Decimals 5.01 Decimals and place value MA4-FRC-C-01.2 5.02 Add and subtract decimals Background 5.03 Convert between fractions and decimals MA4-FRC-C-01.4 5.04 Multiply decimals MA4-FRC-C-01.8 5.05 Divide decimals MA4-FRC-C-1.8 5.06 Round decimals MA4-FRC-C-01.2 Topic 6 - Percentages 6.01 Fractions, decimals and percentages MA4-FRC-C-01.4 MA4-FRC-C-01.6 MA4-FRC-C-01.10 6.02 Compare percentages MA4-FRC-C-01.6 MA4-FRC-C-01.10 6.03 Express a quantity as a percentage MA4-FRC-C-1.9 MA4-FRC-C-01.10

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6.04 Percentages of a quantity MA4-FRC-C-1.9 MA4-FRC-C-01.10 6.05 Percentages with technology MA4-FRC-C-1.9 MA4-FRC-C-01.10 Topic 7 - Ratios 7.01 Identify ratios MA4-RAT-C-01.1 MA4-RAT-C-01.2 7.02 Equivalent and simplified ratios MA4-RAT-C-01.1 MA4-RAT-C-01.2 7.03 Find part or whole measures MA4-RAT-C-01.1 MA4-RAT-C-01.2 Topic 8 - Algebra 8.01 Introduction to variables MA4-ALG-C-01.1 8.02 Build algebraic expressions MA4-ALG-C-01.1 MA4-ALG-C-01.2 MA4-ALG-C-01.3 8.03 Substitution MA4-ALG-C-01.2 MA4-EQU-C-01.2 8.04 Collect like terms MA4-ALG-C-01.3 Topic 9 - Equations

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9.01 Introduction to equations MA4-EQU-C-01.1 9.02 Write rules for relationships MA4-ALG-C-01.1 MA4-ALG-C-01.2 MA4-ALG-C-01.3 9.03 One-step equations MA4-EQU-C-01.1 MA4-EQU-C-01.2 9.04 Two-step equations MA4-EQU-C-01.1 MA4-EQU-C-01.2 Topic 10 - Number Plane 10.01 The number plane MA4-LIN-C-01.1 10.02 Directed numbers on the number plane MA4-LIN-C-01.1 10.03 Graphs of linear relationships MA4-LIN-C-01.2 Topic 11 - Angles, lines, and shapes 11.01 Geometry notation and language MA4-ANG-C-01.1 MA4-GEO-C-01.1 11.02 Measure angles MA4-ANG-C-01.2 11.03 Triangles MA4-GEO-C-01.1 Topic 12 - Length and Area 12.01 Units of length

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Background 12.02 Perimeter MA4-LEN-C-01.1 12.03 Perimeter of composite shapes MA4-LEN-C-01.1 12.04 Area of rectangles and squares MA4-ARE-C-01.1 12.05 Area of triangles MA4-ARE-C-01.1 12.06 Area of parallelograms MA4-ARE-C-01.1 12.07 Area of composite shapes MA4-ARE-C-01.1 12.08 Circumference of a circle MA4-LEN-C-01.2 Topic 13 - Solids and Volume 13.01 Nets of solids MA4-VOL-C-01.1 13.02 Visualise solids MA4-VOL-C-01.1 13.03 Volume using unit cube MA4-VOL-C-01.4 13.04 Units of volume MA4-VOL-C-01.4 13.05 Volume of right prisms MA4-VOL-C-01.2 13.06 Attributes in measurement formula Extension Opportunity Topic 14 - Statistics

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14.01 Types of data MA4-DAT-C-01.1 14.02 Frequency tables MA4-DAT-C-01.2 MA4-DAT-C-01.3 14.03 Summarise data MA4-DAT-C-02.1 14.04 Outliers MA4-DAT-C-02.2 14.05 Dot plots and column graphs MA4-DAT-C-01.2 MA4-DAT-C-01.3 MA4-DAT-C-02.1 14.06 Stem-and-leaf plots MA4-DAT-C-01.2 MA4-DAT-C-01.3 MA4-DAT-C-02.1

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Topic 1 - Whole Numbers Big idea Arithmetic skills, including order of operations, estimation, technology, and symbolic expressions, are essential tools for problem-solving and building a strong foundation for advanced mathematical concepts.

(1.01) Basic arithmetic operations such as addition and subtraction are essential to understanding more advanced mathematical concepts and can be visualised on a number line.

(1.02) Visualising multiplication can be accomplished through the use of rectangular grids and the area model, while the vertical algorithm is a way to multiply larger numbers efficiently by keeping place values aligned.

(1.03) Division is the inverse operation of multiplication and can be approached through strategies such as visual models and short division.

(1.04) It is essential to use the order of operations when evaluating expressions with multiple operations in order to perform accurate mathematical calculations.

(1.05) Estimation is a useful tool for checking the accuracy and reasonableness of calculations and involves rounding numbers.

(INVESTIGATION: How long does it take to count to a million?) Use estimation and rounding as a method to perform large calculations with more ease.

(1.06) Mastering the use of a hand-held calculator for whole number operations is a fundamental skill to efficiently solve problems, minimise errors, and verify the reasonableness of answers.

(1.07) Learning to express mathematical ideas using symbols and operations allows for clear communication and effective problem-solving in various math situations.

Syllabus Outcomes

Topic Expected Timing: ~1 week

Background

Key Vocabulary and Student supports included for each lesson outlined in detail below.

1.01 Addition and subtraction Essential understanding Basic arithmetic operations such as addition and subtraction are essential to understanding more advanced mathematical concepts and can be visualised on a number line.

Students will be able to: ● add multi-digit numbers. ● subtract multi-digit numbers.

Estimated Time: 1 lesson Lesson narrative In this lesson, students will review addition and subtraction, the fundamental skills that help them combine and separate quantities.

The lesson will cover the use of the + and − symbols and the strategy of adding or subtracting numbers using a place value table.

Students will practice single-digit and multi-digit addition and subtraction using both methods. They will also learn how to use regrouping, where they split each number up into convenient pieces such as thousands, hundreds, tens, and ones, to add or subtract large numbers. By the end of the lesson, students will be able to add and subtract numbers using a place value table and regrouping strategy, and have the confidence to tackle more complex problems.

Syllabus Outcomes: Background Key vocabulary

Tools

Regrouping

Place value chart Enlarged number lines

1.02 Multiplication Essential understanding Visualising multiplication can be accomplished through the use of rectangular grids and the area model, while the vertical algorithm is a way to multiply larger numbers efficiently by keeping place values aligned.

Students will be able to: ● multiply multi-digit numbers. ● use different methods to multiply small and large numbers.

Estimated Time: 1 Lesson Lesson narrative: In this lesson, students will review the concepts of multiplication and learn how to use both the area model and vertical algorithm to multiply larger numbers efficiently. The lesson will begin with exploring multiplication through visualising it with a rectangular grid of squares, and connecting it with place value. Students will also practice using an applet to model multiplication of single-digit numbers and answer questions based on it. Then, they will move on to using the area model to visualise multiplying larger numbers and see how a large rectangle can be divided into smaller rectangles based on place value to represent the multiplication.

Finally, students will learn to use the vertical algorithm to multiply larger numbers in a more efficient way by keeping the place values aligned. They will practice solving multiplication problems using both the area model and vertical algorithm. By the end of the lesson, students will be able to explain the reasoning behind each method and choose the most appropriate method for a given problem.

Syllabus Outcomes: Background Key vocabulary:

Tools

Commutative law Area model Vertical algorithm

Grid Paper Base ten blocks

Student Exploration (linked to student lesson)

Exploration Support (Linked to teacher guide)

1.03 Division Essential understanding Division is the inverse operation of multiplication and can be approached through strategies such as visual models and short division.

Students will be able to: ● divide multi-digit numbers. ● use different methods to divide small and large numbers.

Estimated Time: 1 Lesson Lesson narrative: In this lesson, students will review the concept of division. They will learn that division is the opposite of multiplication, using the ÷ symbol, and that it involves sharing or splitting quantities into equal parts. Students will explore how to use an area model to divide numbers up to 144 and learn how division is related to multiplication. They will then learn how to use short division to divide larger numbers, by considering each place value of the dividend separately. By the end of the lesson, students will be able to use short division to evaluate division problems involving larger numbers and understand the relationship between division and multiplication.

Syllabus Outcomes: Background Key vocabulary:

Tools

Short division Divisor Dividend Quotient

Handouts or visual aids

Student Exploration (Linked to student lesson)

Exploration Support (Linked to teacher guide)

1.04 Order of operations with whole numbers Essential understanding It is essential to use the order of operations when evaluating expressions with multiple operations in order to perform accurate mathematical calculations.

Students will be able to: ● perform arithmetic operations using the order of operations.

Estimated Time: 1 Lesson Lesson narrative: In this lesson, students will learn about the order of operations and how to use it to solve problems with multiple operations, like addition, subtraction, multiplication, and division. The order of operations provides a set of rules to follow that ensure we get the correct answer every time. Students will learn to evaluate expressions that contain brackets, indices, multiplication or division, and addition or subtraction. By the end of the lesson, students will have a solid understanding of the order of operations and be able to use it to solve problems accurately.

Syllabus Outcomes: Background Key Vocabulary

Tools

Order of Operations

Order of operations chart

1.05 Check reasonableness of calculations Essential understanding Estimation is a useful tool for checking the accuracy and reasonableness of calculations, and involves rounding numbers.

Students will be able to: ● estimate and check the reasonableness of an answer.

Estimated Time: 1 Lesson Lesson narrative: In this lesson, students will learn how to estimate and check the reasonableness of an answer. By rounding numbers to the nearest place value, students can get a rough idea of what the answer should be. They will also learn how to check the reasonableness of an answer by asking themselves if the answer makes sense in the context of the problem. This will ensure that the answer is correct and will help identify any calculation errors. By the end of the lesson, students will be able to confidently estimate and check the reasonableness of an answer.

Syllabus Outcomes: Background Key vocabulary Estimate

1.06 Number calculations with technology Essential understanding Mastering the use of a hand-held calculator for whole number operations is a fundamental skill to efficiently solve problems, minimise errors, and verify the reasonableness of answers.

Students will be able to: ● use technology to perform operations with whole numbers and check the reasonableness of their answer.

Estimated Time: 1 Lesson Lesson narrative: In this lesson, students will learn how to use a hand-held calculator to perform operations with whole numbers. They will learn the basic buttons to use and how to enter numbers and operations to get an answer. Students will also learn to check the reasonableness of their answer to ensure it is correct. They will understand the common calculator errors such as missing a digit from a number, swapping digits, using the wrong operation, and adding an extra digit. By the end of the lesson, students will be able to use a calculator to perform operations with whole numbers and check the reasonableness of their answer.

Syllabus Outcomes:

Background Key vocabulary

Tools

Order of operations

Scientific Calculator

1.07 Write mathematical statements Essential understanding Learning to express mathematical ideas using symbols and operations allows for clear communication and effective problem-solving in various math situations.

Students will be able to: ● translate written text into mathematical expressions using the four operations of addition, subtraction, multiplication, and division. ● describe the relationship between numbers using symbols such as greater than, less than, greater than or equal to, less than or equal to, equal to, and not equal to.

Estimated Time: 1 Lesson Lesson narrative: In this lesson, students will learn about the language of mathematics and how to translate between written text and mathematical expressions. They will be introduced to the four operations: addition, subtraction, multiplication, and division, and learn different ways to refer to them. Students will also learn about the symbols used to describe the relationship between numbers, including greater than, less than, greater than or equal to, less than or equal to, equal to, and not equal to. By the end of the lesson, students will be able to write and interpret mathematical expressions using numbers and symbols.

Syllabus Outcomes:

Background Key vocabulary

Tools

Equality Inequality

Cards with written mathematical phrases