**"Algebraic expressions"**

## Blocks, Bricks and Boxes

*By toni On 25 November, 2023 · Leave a Comment*

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units.

Is there more than one?

It is quite easy to find a few solutions. The big challenge is to find all possible solutions.

Can you provide a convincing argument that you have found […]

## Intersections

*By toni On 13 February, 2021 · Leave a Comment*

(1) Plot the graphs of the straight lines y = x, y = 1.1x – 0.2

and y = 0.9x – 0.1

What do the graphs tell you about the solutions to the two pairs of simultaneous equations (1a) y = x y = 1.1x – 0.2 and (1b) y = x […]

## Matchless

*By toni On 10 February, 2021 · 3 Comments*

Find values of x and y for which these five expressions all have the same value.

Do you have exactly the right amount of information or more information than you need?

Click here to download the MATCHLESS worksheet.

Click here to download the MATCHLESS worksheet.

Click here to download the AIMSSEC […]

## Difference of Squares and Area

*By toni On 10 February, 2021 · Leave a Comment*

What do you see in this image?

What is the area of the bigger square edged by dotted line segments of length a?

What is left of that area if you take away a square with edges of length b?

What is the area of the rectangle formed by the yellow […]

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 […]

## Almost Total Inequality?

*By toni On 2 February, 2021 · 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 […]

## Couples Puzzle

*By toni On 28 January, 2021 · Leave a Comment*

In a small village two thirds of the adult men are married to three quarters of the adult women.

How big is the smallest village for which this is true?

Can you describe the population of other villages for which this is true?

Click here to download the […]

## 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.

## 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.

## 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?

[…]

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