Add to 200
Why do this problem?
Possible approach
Start with the grid drawn on the board and ask students to copy it into their books.
Ask them to fill their grid with four digits of their choice. Ask them to read the two 2-digit numbers across and the two 2-digit numbers down, and then add them altogether.
"What totals did you get?"
List some of their totals.
"What questions might a mathematician ask now?"
What totals can be made?
What is the smallest possible total?
What is the largest?
Are all the totals in between possible?
Can some totals be made in more than one way?
Is it possible to make a total of 200?
When are the totals even and when are they odd?
After some time, bring the group together 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.
Add to 200 could be used as an activity for students learning to program. They could write a program to find all possible solutions.
For example, this program was written by Nevil Hopley, Head of Mathematics at George Watson's College, for the TI-Nspire software.
If you have the appropriate software, you can download his .tns file here: Add to 200.tns
Key questions
How do the four digits you choose contribute to the tens digit in the total?
Possible support
Having digit cards available for students to physically manipulate will help those who are reluctant to commit ideas to paper.
Possible extension
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