Math Delights

nrich.maths.org/991

Materials: sugar cubes, felt pens, and worksheets

Take 8 sugar cubes and arrange them into a 2x2 cube. Paint all 6 of the 2x2 sides. How many of the resulting of the resulting unit cubes are completely unpainted? How many are painted on just one side? How many are painted on two sides? How many are painted on three sides? There are 8 sugar cubes. Each face of each cube is to be painted either green or yellow. Work out how to paint the faces so that the cubes can be put together to make a 2 x 2 cube that is Green all over AND can be rearranged to make a 2 x 2 cube that is Yellow all over.

Note: The sugar cube activity was popular perhaps because the children liked the idea of playing with something sweet. We let them eat one sugar cube each at the end of the activity.

Note: The following book contains many more activities involving cubes.

Mathematics with Cubes: Problem Solving Activities for Older Children www.amazon.com/Mathematics-Cubes-Problem-Activities-Children/dp/1871098149

 What’s the difference between a two-digit number and its reverse?

Choose a two-digit number, e.g., 20. Make a new number by reversing the digits, e.g., 02. Subtract the smaller number from the larger number, e.g., 20 - 02 = 18. Check your subtraction by adding your result, e.g., 18 + 02 = 20. Do you notice a pattern? If not, choose another two-digit number and go back to step 1.

On the basis of your findings, see if you can predict the difference between a two-digit number and its reverse.

For more of a challenge, investigate three-digit numbers.