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Listed under:  Distributivity

### TIMES Module 10: Number and Algebra: division of whole numbers - teacher guide

This is a 26-page guide for teachers. This module contains a description of suitable models for division, a discussion of the types of problems that require division for their solution, and mental and written strategies for division.

### TIMES Module 7: Number and Algebra: addition of whole numbers - teacher guide

This is a 16-page guide for teachers. This module introduces addition of whole numbers.

### TIMES Module 19: Number and Algebra: whole number arithmetic - teacher guide

This is a 17-page guide for teachers, a module that introduces addition of whole numbers.

### Starting Smart: is it the same?

This curriculum resource package is a ten-week middle years teaching plan and set of supporting resources to extend students' understanding of algebraic expressions and equations. Students explore equivalences in arithmetic and algebraic expressions, evaluate algebraic expressions, and construct and learn to solve equations ...

### Order of operations

This is a set of interactive questions relating to the laws of arithmetic, their usefulness in calculations, and their importance and relevance in order of operations calculations. The questions challenge and extend students' thinking about generalisations of the laws and make a link between arithmetic and algebra. The ...

### Solving equations with the distributive property

This is a video demonstration of solving a linear equation by algebraic means. In the commentary, the presenter carefully explains the step-by-step method used to solve this example, which includes use of the distributive law and collecting like terms to simplify the equation. Having found the solution, the presenter verifies ...

### Algebra four

This is an interactive game for two students in which they solve algebraic equations, similar to 'Connect four'. The players can choose from problems that are one- or two-step, quadratic, have distributive properties or have variables on both sides, and more than one problem type can be chosen. The length of time each player ...

### Mental computation

This is a website designed for both teachers and students that discusses methods of mental computation. In particular, applying the associative, commutative and distributive laws to aid mental and written computation is discussed. These are important ideas for the introduction of algebra. There are pages for both teachers ...

### Algebraic expressions

This is a website designed for both teachers and students that addresses algebraic expressions from the Australian Curriculum for year 8 students. It contains material on using simple positive and negative fractions, substitution, collecting like terms, taking products, and expanding brackets using the distributive law ...

### Top drawer teachers: mental computation

This is a web page that comprehensively covers the teaching of strategies for mental computation through links to six sections. The first section covers the ‘Big ideas’ behind mental computation, and the second section uses research findings to identify some common learning issues when becoming fluent in mental computation. ...

### The laws of arithmetic and their use in algebra

This is a website designed for both teachers and students that refers to algebraic notation, the laws of arithmetic and the use of these laws in algebra from the Australian Curriculum for year 7 students. It contains material on algebraic notation, the commutative and associative laws, the use of brackets and the orders ...

### Brackets

A short, animated tutorial about expanding brackets, followed by an interactive quiz.

### reSolve: Working with algebra

This sequence of two lessons gives students opportunities to explore and share strategies for solving algebraic problems. The lessons focus on open-ended problem solving and developing multiple approaches to solving problems algebraically such as using like terms and substitution. Students work individually and in small ...

This sequence of lessons explores making algebraic generalisations of sequences. Students use spreadsheets to investigate potential arithmetic relationships and then use algebra to identify and justify which relationships are generally true. The task can be used as a springboard for an in-depth exploration of the Fibonacci ...

### reSolve: Algebra: Think of a number - Linear Equations

This lesson explores algebra by generalising results from arithmetic used in 'think of a number' games. Students connect arithmetic operations with algebraic notation and visualisations. The lesson begins with an observation made using arithmetic that students then justify and extend using algebra. The lesson is outlined ...

### reSolve: Algebra: Tens and Units

This sequence of lessons aims to develop understanding of algebra as generalised arithmetic. Students learn to express 2- and 3-digit numbers in a general form and use this to explain results of arithmetic operations involving numbers with their digits reversed. The task links the ideas of place value with algebraic reasoning. ...

### reSolve: Algebra: Think of a number- Binomial Equations

This lesson engages students in investigating a 'think of a number' game and then model it visually and algebraically. This develops skills in algebraic operations including expanding, factorising and collecting like terms. Students investigate whether the game will work for any number and are challenged to generate the ...

### reSolve: Algebra: Sums & Differences of Squares

This sequence of three lessons explores sums and differences of two squares. Students are introduced to the historical context of using lookup tables for multiplications and challenged to investigate and generalise the underlying process using algebraic means. In subsequent lessons students use visual and algebraic methods ...

### reSolve: Pythagoras' Theorem

This lesson challenges students to use Pythagoras' Theorem to solve a problem from an ancient Chinese text. They make physical models of the problem and use this to construct a graph. They use algebra skills associated with binomial expansions and simplification of fractions to show that the general solution given in the ...

### The array: go figure

This tutorial is suitable for use with a screen reader. It explains strategies for solving simple multiplications in your head such as 6x4. Work through sample questions and instructions explaining how to break up numbers into their factors. Solve multiplications by using arrays to break them up into rows and columns, then ...