Encouraging our children to “go deep” in math can increase motivation, help them learn how to think and reason, and yes, even make math fun!  Many incorrectly believe that being good at mathematics means being fast at mathematics.  Supporting our children to think slowly and deeply about complex problems,  builds skills important to mathematical competence.  We need them to think deeply, connect methods, reason, and justify their answers.

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ICE CREAM SCOOPS

In this shop there are ten different ice cream flavors.  AND…. there are many different flavor combinations, even with only a 2-scoop cone.

For younger children…
How many kinds of 2-scoop cones are there with 5 different flavors?

For older children…
How many kinds of 2-scoop cones are there with 10 different flavors?

NOTE – Finding and understanding patterns is crucial to mathematical thinking and problem solving, and it is easier for our children to understand patterns if they know how to organize their information.  Creating an organized list, table, chart, or other graphic organizer are important problem-solving strategies.  

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This challenge is quite tricky, but it is a motivating context in which children can develop a logical, systematic approach.

Seven Flipped

You have seven hexagonal-shaped pieces – each with one red side and one blue.  Starting with all your pieces blue side up, they all need to be turned over to the red side.   You can only turn over  three at a time.  A piece may be turned over on one move and turned back over again on another.

What is the smallest number of moves it will take you to turn them all over to the red side?

NOTE:  Remember that you can try this not only on paper but using coins or other 2-sided objects. As long as you can tell the sides from each other, you can use them!

Recording your moves will help you keep track.  In the move box, you can write things like, flipped: 3 blue (3B) or flipped 2 blue (2B) and 1 red (1R)

NOW……You might like to  try with another number of pieces.
Do you notice any patterns?
Can you explain why these patterns occur?