Nancy Anderson, EdD

Mathematics Teacher ~ Author ~ Consultant

- Multiplication can be thought of in terms of putting equal groups together (e.g., we can interpret the expression 3 x 7 as 3 groups of 7. When we interpret a multiplication in terms of equal groups, the first factor tells us the number of groups and the second factor tells us the size of each group.
- We can use an arrangement of equal rows of dots (i.e., an array) to model a multiplication expression. The first factor tells us the number of rows in the array and the second tells us the number of dots in each row.
- We can find the total number of dots in an array by multiplying the two factors in the related expression.We can use fluency with doubles to multiply 3 by another factor (3 x n). We can interpret the expression as 3 groups of a number and draw an array of 3 rows with n dots in each row. We can see the related array of 2 rows of n inside this array. We can find the total number of dots in the larger array by adding the product of 2 x n to the number of dots in the additional row.
- Knowing about the commutative property and putting that property to work can cut students' work in half!
- Students can develop fluency by working on subsets of facts at a time. They should progress through the facts by using known facts to derive unknown products.