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Why do this problem?
This game is a good one to play with young children once they are familiar with the basic number operations. They will like the idea of their number being "secret", and of course being able to work out someone else's "secret" number! Looking for a ''secret'' number is the basis for algebra and solving unknowns in equations. So as well as enjoying what they are doing, your class will be engaging with some important mathematical ideas.
A good way to start might be for you either to enter your own secret number and invite the class to suggest what to add, or perhaps ask two children to come to the front to demonstrate. This activity will create a great opportunity for rich discussion amongst the class about how they can work out the secret number. You could ask the children to think for themselves first, then share their ideas with a partner and finally with the whole group. (Think-pair-share.)
The best extension for this is for children to play the game with a partner as they are invited to do in the original problem. For some, there need be no limit to the numbers or operations involved. However, it would be a good idea to get all "secret" numbers and working out recorded!
Use a calculator openly with the children so that they can see exactly what is happening. When they understand the mechanism of the game then start using a "secret" number with very simple numbers. Learners could also use a number line or multiplication square to help.
Find a great variety of ways of asking questions which make 8.
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?