Mathematics / Year 7 / Number

Version 9
Curriculum content descriptions

use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies (AC9M7N06)

Elaborations
• solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
• choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as $$12.5$$%, $$\frac18$$, $$0.125$$ or $$\frac{125}{1000}$$
• developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate $$\frac23$$ of $$\frac12$$ giving $$\frac12$$ of $$\frac23$$=$$\frac13$$
• solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
• developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
• carry out calculations to solve problems using the representation that makes computations efficient such as $$12.5$$% of $$96$$ is more efficiently calculated as $$\frac18$$ of $$96$$, including contexts such as comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle
General capabilities
• Numeracy Numeracy
ScOT terms

Simple fractions,  Decimals,  Percentages,  Number operations

Refine by topic

Related topic

Moving out of home

This lesson explores costs and responsibilities associated with moving out of home and setting up living arrangements. The resource is part of a suite of lesson plans and activities from MoneySmart, designed to bring everyday financial topics into the classroom.

7N05A Percentages - Ochre Education

This unit of work focuses on percentages. Students represent percentages, including percentages greater than 100%; convert between decimals, fractions, and percentages; write one number as a percentage of another (including where the percentage is greater than 100%) and find a percentage of a number (including using percentages ...

7N03A Fractions - Ochre Education

This unit of work focuses on fractions. Students represent and convert between equivalent forms, such as improper and mixed numeral and equivalent and simplified fractions; compare and order positive and negative fractions; add, subtract, multiply, divide (including writing one number as a fraction of another and finding ...

7N04A Decimals - Ochre Education

This unit of work focuses on decimals. Students represent, compare, and order positive and negative decimals; convert between terminating decimals and fractions; add, subtract, multiply, divide (including writing one number as a decimal of another and finding a decimal of a number), square, cube, square root and cube root ...

The wide wide world of sports betting

This lesson explores the difference between perfectly predictable events (like the roll of a die) and less certain events (such as sports). Students investigate mathematically how sports bookmakers create odds to guarantee themselves a profit and pay gamblers less for a win than they deserve. The lesson is outlined in ...

Can you beat the system?

In this lesson, students calculate the average expected value of losses on a roulette wheel over time, and use these values to analyse the cost of gambling on these games. They also study the flaws inherent in betting systems to determine whether these systems are weighted in the favour of game operators making a profit. ...

Prediction vs. reality

This lesson explores how we perceive randomness. Students toss coins and record their observations while half of the class fake their results. They will then explore the differences between the random results and fake results sets and investigate theoretical probabilities for large numbers of coin flips. The lesson is outlined ...

Introduction to games of chance

This lesson explores how to predict outcomes of games of chance. Students investigate the concepts of luck, skill and fairness, using dice games. They calculate probabilities for one and two dice rolls and compare the odds for different combinations of dice in a variety of game scenarios. The lesson is outlined in detail ...

All operations: Year 7 – planning tool

This planning resource for Year 7 is for the topic of All operations. Students use all operations with positive rational numbers and to choose the most appropriate and efficient approach when solving a variety of problems.

Practical numbers: Part 2

In this lesson we use the context of an ancient bazaar to investigate measurement systems. Students select a name and base number for their system of measurement, using weights made from clay or similar material. They divide their clay into possible unit fractions to generate their set of weights. They assign a fictional ...

Estimating and rounding decimals

In this lesson, students draw on prior knowledge of rounding whole numbers to develop their understanding and fluency when rounding decimals and are encouraged to reason and problem-solve through a variety of contextual activities. Students will also develop an appreciation of the role of estimation in mathematics and science.

Practical numbers: Part 1

In this lesson, students explore standardised measuring systems. They encounter the challenge of a shopkeeper who must determine how to weigh different quantities of spices most efficiently. Working in a financial context, students model this scenario using fractions, percentages and ratios, and communicate their solution ...

Proportional reasoning video

Use this video as a springboard to explore scaling or proportional thinking, and to apply that thinking in a food context, drawing on reasoning and mathematical modelling.

How does income tax work?

Gen Fricker makes income tax interesting! Learn about income tax - what it is, how it works and when you have to pay it. Easy-peasy! Then test yourself with ASIC Moneysmart's "Things to think about" classroom exercises.

Expressing one quantity as a fraction of a second

This is a website designed for both teachers and students that addresses the expression of one quantity as a fraction of a second quantity from the Australian Curriculum for year 7 students. It contains material on using the unitary method to solve fraction problems. There are pages for both teachers and students. The student ...

Multiplication and division of decimals

This is a website designed for both teachers and students that addresses multiplication and division of decimals from the Australian Curriculum for year 7 students. It contains material on multiplication and division of decimals and helps students to understand multiplication and division as inverses of each other. There ...

This is a website designed for both teachers and students that addresses addition and subtraction of fractions. There are pages for both teachers and students. The student pages contain interactive questions for students to check their progress in the topics.

TIMES Module 17: Number and Algebra: the unitary method - teacher guide

This is an 18-page guide for teachers. This module introduces the idea of ratios and rates.

TIMES Module 20: Number and Algebra: percentages - teacher guide

This is a 15-page guide for teachers. This module introduces percentages and their many uses in science, commerce and measurement.

TIMES Module 14: Number and Algebra: fractions - teacher guide

This is a 16-page guide for teachers that provides an introduction to fractions. It covers ordering, the four basic arithmetic operations, cancelling, writing in simplest form, the use of the area model for multiplication and the use of the number line for ordering, adding and subtracting. A history of the development of ...