Sums and Differences 1
This challenge is about adding and subtracting twodigit numbers.
Pick two twodigit numbers.
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 twodigit numbers, and finding the difference between two twodigit 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!!
Possible support
A 100 square or number line/track might be useful.