Diagonal Differences

Introduction

Use the following worksheet (PRINT ME) for today's lesson.

Part 1 - 2 by 2 Squares

Look at the 2 by 2 square shaded on the right.  The numbers in the opposite corners of the shaded square are: 54 with 65 and 55 with 64.

1. Multiply these corner pairs.

2. Then work out the difference between the two answers.  What answer do you get?

3. Now try putting the ‘2 by 2’ square somewhere else on the grid and repeat the process: 

   • Multiply the numbers in diagonally opposite corners, 

   • Then work out the difference between your answers.

   • Try three examples, recording all your calculations,  what do you notice about your answers?

Part 2 - Other Size Squares

Look at the 3 by 3 square shaded on the right.  The numbers in the opposite corners of the shaded square are: 26 with 48 and 28 with 46.

1. Multiply these corner pairs.

2. Then work out the difference between the two answers.  What answer do you get?

3. Now try putting the ‘3 by 3’ square somewhere else on the grid and repeat the process for three other examples.  Recording all your calculations.  What do you notice about your answers?

4. Repeat the process for ‘4 by 4’ squares and for ‘5 by 5’ squares, each time doing four examples in total.  Summarise your results in the table below:

Further Questions and Challenges

Part 3 - Rectangles with Two Rows

Look at the 2 by 3 rectangle shaded on the right.  The numbers in the "opposite corners" of the shaded square are: 12 with 24 and 14 with 22.

1. Multiply these corner pairs.

2. Then work out the difference between the two answers.  What answer do you get?

3. Now try putting the ‘2 by 3’ rectangle somewhere else on the grid and repeat the process for three other examples.  Recording all your calculations.  What do you notice about your answers?

4. Repeat the process for other size rectangles shown in the table below.  Record your results in the table, and comment on what you notice about the results.