Use the tools to show each of these operations: This important question allows students to demonstrate the meaning of add, subtract, multiply and divide. In each case, the operation is shown by the student’s arm movements. "Add" is a pushing together of two amounts; "subtract" is a removing of one amount from another. Most students can show these easily; however, they have a harder time with multiply and divide.

"Multiply" can be shown by repeatedly adding an amount. 3 x 5, for example, can be shown in two ways, either by putting three blocks (or toothpicks) on the table five times, or by putting five blocks on the table three times. Often students will mistakenly get out three blocks and five blocks and add them together. The operation of multiply is in the arm movement—putting an amount on the table the required number of times.

Division is the trickier because of the arbitrary nature of writing the question; when we write 6 ÷ 2 we mean that six is to be divided up, not two. The operation of division is also in the arm movement; the second number controls the arm movement. 6 ÷ 2 can be shown in two ways:

two groups of three:

A squareA squareA squareA squareA squareA square

OR

three groups of two:

A squareA squareA squareA squareA squareA square

Here the question is, if I have six things and want to share them between two people, how many will each person get?

 

 

Here the question is, if I have six things, and give them out two at a time, how many people will get some?

Usually students will make the first demonstration; after they are easily able to talk about the operation of division in this form, I show them the other way, too. They will notice that the answer is the same, no matter which way you think of it.

Start with the first number, double it, double again, double at least five times: The purpose of this question is to encourage students to do some mental math, using tools as necessary to help them. The ability to double numbers easily is useful for teaching addition facts and the times tables. Nearly everyone can double numbers up to 10, and many people can double most of the numbers up to 15, and many common numbers upwards of there. I think it is worth spending a little time to teach them to double mentally starting from the left. So to double 125, for example, I think "Double 100 is 200, and double 25 is 50, which makes 250." Double 156 is double 100 (200) plus double 50 (300) plus double 6 (312).