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Here is a grid of four boxes:




You must choose four different digits from 1  9 and put one in each box. For example:
5 
2 
1 
9 
This gives four twodigit numbers:
52 (reading along the first row)
19 (reading along the first row)
51 (reading down the lefthand column)
29 (reading down the righthand column)
In this case their sum is 151.
Try a few examples of your own.
Is there a quick way to tell if the total is going to be even or odd?
Your challenge is to find four different digits that give four twodigit numbers which add to a total of 100.
How many ways can you find of doing it?
You may be interested in the other problems in our Mastering Mathematics: Developing Generalising and Proof Feature.
This problem is adapted from Make 200 from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES.
This low threshold high ceiling problem challenges pupils' understanding of place value and is a good way to practise a particular method of written addition.
It would be good to start with the grid drawn on the board and for you to explain the challenge orally to the group. You could use the example in the problem itself so that the task is clear.
Ask for suggestions as to how they might start and give learners a few minutes to think on their own, then share their ideas with a partner. Open this out to the whole class so that a few pairs share their thoughts with everyone. The suggestions are likely to be quite general at this stage.
Allow children to work together on the problem in their pairs. They will find miniwhiteboards or paper useful for keeping track of their calculations. After some time, bring the group together again and discuss any insights they have gained. Some pairs may have thought about the cells in the grid which make up the units digits of the four numbers, others may have concentrated on the cells which contribute to the tens digits. In either case, encourage them to explain the restrictions they have noticed, and look out for those pairs who are working systematically through the options.
What is the smallest total you can make? What is the largest? Can you make all the totals in between?
Add to 200 is a very similar task to this one, so offers opportunities to think in similar ways, but with the added challenge of there being many more possible solutions.
Two and Two also requires similar systematic thinking and could be a good problem for some children to try next.
Having digit cards available for learners to physically manipulate will help those who are reluctant to commit ideas to paper.