In many math classes children do not begin multiplying numbers until third grade, but in CGI classes children are solving problems involving multiplication early in the primary grades. Even though children are working with multiplication problems it is important to recognize that young children's understanding of multiplication is different than that of older children and adults, just like their understanding of addition and subtraction is different.

Situations involving multiplication often include groups of things, like 3 bags of 5 candies. This group structure helps children reason about multiplication problems using many of the same strategies employed for addition and subtraction problems. For example, children can use counters to represent 3 groups of 5, and then count all to find a total of 15 M&M's (direct model strategy).

Some children may try counting "5, 6, 7, 8, 9, 10-(pause) and 11, 12, 13, 14,
15, while others may use derived facts: 5 + 5 = 10 and 5 more is 15 (derived
fact/recall strategy).

Multiplication is used in many different problem situations.

Here are a few:

** Measurement-Scale **

When we use maps, we often measure on a scale. For example, if 1 inch = 5 miles on the map below, how far is it between Madison and Mount Horeb?

Measurement of area is a good way to expand your child's ideas about multiplication. For example, in one of the previous newsletters, you may have worked with your child to measure the area of your kitchen floor. In the figure at right, a kitchen is 9 tiles wide and 17 tiles long.

For this problem, some children may think about 17 groups of 9 while others may think of 9 groups of 17. This is an important point since most children do not think of these as the same when they start working with multiplication problems. Some children will use counters (like toothpicks) to directly model their solution, others may use numbers, like 9 + 9 + 9 ....(17 times). These strategies are good ways to solve this multiplication problem. Area problems like this also provides some opportunities to find out how your child thinks about groups of 10 -- counting by 10 is easier than counting by 9 or 17, so , for example, your child might try counting 17 groups of 10 to make 170, and 17 less (because the difference between 10 and 9 is 1 and there are 17 groups) is 153. You might want to try this problem out with your child (you can change the problem to make it easier by using smaller numbers.)