Or search by topic
"What totals did you get?"
List some of their totals.
"What questions might a mathematician ask now?"
If few suggestions are forthcoming, suggest:
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?
Allow students to work together on a question of their choice.
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.
Members of the NRICH team have worked with students and teachers on making all the possible combinations that add to 200. As the students/teachers found new combinations, we displayed them on the wall/board in a very particular arrangement to help them identify missing solutions. The arrangement also facilitated discussions about the patterns down a column and across a row, and why these patterns occur. Here is an image of the final arrangement of all the combinations (including an interesting one on the far right!):
(Click on the above image to open a larger version.)
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
Having digit cards available for students to physically manipulate will help those who are reluctant to commit ideas to paper.