Allow your child to see how 0 and 1 can be the child’s very good “friends” when there are math problems to be done—because they save time! Children enjoy seeing little time-saving devices and there are several that concern 0 and 1. To start, help your child count out several stacks of pennies, buttons, or other small objects into sets of 10. Pull one set of 10 in front of you (you can call this work area “the learning pad” and encourage your child to write 10 (for the number in the stack) X 1 (the number of stacks). Count how many objects there are (10) and complete the equation: 10 x 1 = 10. Now, pull one more stack of 10 to the Learning Pad and write the new equation: 10 x 2=20 right below the first. Do this two more times so that the equations are stacked one below the other, and ask your child if he/she sees a pattern. The pattern will probably be obvious: When multiplying by 10, the answer is the number you are multiplying by in the 10s column, with a 0 in the ones column. Ask your child to predict if this will work for a really big number—maybe 542 x 10. What would you imagine that the answer is? Help your child use a calculator to see that the answer is indeed 5420; the number to be multiplied by 10, with a 0 at the end. What you are really doing, you can point out, using your Place Value Pad, is moving each of the numbers (the 5, the 4 and the 2 over to the number column place to the left, and placing a 0 in the ones spot, and your child has just proved to himself that this time-saver works, and why.
Similarly, you can start at the beginning again, substituting “1” for the 0 so that the rule your child creates is that any number multiplied by 1 is still the same number.
To test your child’s understanding, ask if the “rules” that you created in the two learning tips above work if you want to subtract 1. (It does not work, but if you want to subtract 0, you still have the number you started with.) If you want to divide by one? (A set of objects divided into one set of objects still have that same number of objects in it.) Can you divide a group of objects by 0? No, this is a problem with no solution possible because we do not have any way to divide up a group of objects by nothing. The smallest whole number group we can divide by is a group of 1, and that simply tells us that we have the same set we started with. It was in one group to begin with, and it is still in that one group.