**"Algebraic expressions"**

## Years 9 – 12 Differences of Squares Investigation

*By toni On 15 November, 2019 · Leave a Comment*

1. What do you see in this picture?

Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .

2. What do you notice about the difference between squares of consecutive numbers?

Compare the differences between squares of numbers that differ by 1 […]

## Years 7 – 9 Use area to find x

*By Elizabeth Turok On 11 November, 2019 · Leave a Comment*

Three quarters of the area of the rectangle has been shaded.

What is the value of x?

Click here to download the USE AREA TO FIND x worksheet.

Click here for the Notes for Teachers.

## Years 6 – 8 Bananas Clock Hexagon

*By Tejumade Ogundipe On 12 August, 2019 · Leave a Comment*

Note: The symbols may be slightly different. Use the subtle differences in the images in working out your answer.

Click here to download the BANANAS CLOCK HEXAGON worksheet.

Click here to download the Notes for Teachers.

This puzzle is adapted from puzzlebrain.com.

## Years 5 – 9 Equipattern

*By toni On 12 November, 2017 · Leave a Comment*

Copy this pattern. You could use toothpicks or paper sticks or draw the pattern on isometric paper (download here).

Make or draw the next 3 patterns in the sequence. How would you explain to someone else on the telephone how to do this when you could not point to the diagram?

[…]

## Year 12 GP Algebraically

*By toni On 26 May, 2017 · Leave a Comment*

Multiply out these expressions:

What do you notice?

Does this pattern continue?

Can you prove it?

What does this tell you about the sum to n terms of the geometric series with first term 1 and common ratio r?

Why do we get a formula for all values of r except r = 1?

Explain […]

## Years 9-12 Distance-time graphs

*By Ben Walker On 9 January, 2017 · Leave a Comment*

This lesson is about moving between different representations of distance-time functions, namely between graphs, stories and tables. This activity should be given to the class as a formative assessment activity: it is designed to provide the teacher with information about the learners’ current levels of understanding.

During a short introduction the teacher displays a […]

## Grades 8-10 Interpreting Equations

*By Ben Walker On 9 January, 2017 · Leave a Comment*

This lesson is about moving between algebraic equations and the statements that they represent. This activity should be given to the class as a formative assessment activity: it is designed to provide the teacher with information about the learners’ current levels of understanding.

During a short introduction the teacher emphasises the importance of defining […]

## Grades 10-12 Multiple representations of algebraic relationships

*By Ben Walker On 8 December, 2016 · Leave a Comment*

This lesson is about

different representations of algebraic relationships, namely equations, graphs, tables and words. This activity should be given to the class as a formative assessment activity: it is designed to provide the teacher with information about the learners’ current levels of understanding.

After a short introduction, during which the teacher models […]

## Years 11 – 12 Almost Total Inequality?

*By toni On 27 November, 2016 · Leave a Comment*

When x is zero, A is greater than both B and C

For what other values of x is A the greatest?

For what values of x is B the greatest ?

For what values of x is C the greatest?

Is there a value of x when neither A nor B […]

## Grades 7 to 10 Painted Cube

*By toni On 5 November, 2016 · 22 Comments*

Imagine a large cube made up from 27 small red cubes each measuring 1 cm by 1 cm by 1 cm. What is its volume?

Imagine dipping the large cube into a pot of yellow paint so the whole outer surface is covered. What is its surface area?

Now imagine breaking the […]

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