Sums and differences 1
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Age
7 to 11
Challenge level
Problem
This challenge is about adding and subtracting two-digit numbers.
Image
Find the sum of the numbers.
Find the difference between the numbers.
Can you find other numbers with the same sum and difference?
Getting Started
Begin by finding the sum and difference of the numbers you have chosen.
Then think carefully about other pairs of numbers with the same sum. Can you find a pair which also has the same difference?
It might be helpful to record your findings in a table like this:
Then think carefully about other pairs of numbers with the same sum. Can you find a pair which also has the same difference?
It might be helpful to record your findings in a table like this:
| 1st number | 2nd number | Sum | Same? | Difference | Same? |
| 24 | 31 | 55 | 7 | ||
| 15 | 40 | 55 | Yes | 25 | No, too high |
Teachers' Resources
Sums and Differences 1
This challenge is about adding and subtracting two-digit numbers.
Image
Find the sum of the numbers.
Find the difference between the numbers.
Can you find other numbers with the same sum and difference?
Why do this activity?
This activity provides a context for practising summing two two-digit numbers, and finding the difference between two two-digit numbers. It encourages working systematically as children attempt to try all possibilities to find two solutions with the same sums and differences.Possible approach
It would be good to start the lesson by practising strategies for summing numbers and finding the difference between numbers.The class could then work through a version of the challenge all together. You could model the following example and invite pairs/groups to find other pairs of numbers with the same sum:
| 1st number | 2nd number | Sum | Same? | Difference | Same? |
| 24 | 31 | 55 | 7 | ||
| 15 | 40 | 55 | Yes | 25 | No, too high |
As you gather their ideas, you could present them in the table in a systematic way:
| 1st number | 2nd number | Sum | Same? | Difference | Same? |
| 24 | 31 | 55 | 7 | ||
| 25 | 30 | 55 | Yes | 5 | No, too low |
| 26 | 29 | 55 | Yes | 3 | No, too low |
Children may notice a pattern. Will we ever find numbers with both the same sum and the same difference? Why?
Some children may move onto the extension task (below).
Key questions
What is the sum of the numbers? What is the difference between the numbers?Have you tried all of the combinations? Do you need to try them all?
Can you spot a pattern?
Can you explain the pattern?
Possible extensions
Extension 1: Can you find pairs of numbers where the sum and difference are both odd? Can you find pairs of numbers where the sum is odd and the difference is even? Why?Extension 2: Have a go at Sums and Differences 2. In this challenge you find the sum and difference of a pair of numbers and then find the sum and difference of the sum and difference!!