1. Teaching Multiplication Unit 3

2. Learning about Multiplication • The biggest challenge is understanding groups of things as single entities while also understanding that a group contains a certain number of objects. • How many apples in 4 baskets of 8 apples each? • Children can count out 4 sets of 8 counters and then count up all the counters • To think multiplicatively about this situation, as four sets of 8, they must conceptualize each group of 8 as a single item to be counted (8, 16, 24, 32) • Experiences with making and counting groups, especially in contextual situations, are extremely useful.

3. Teaching Multiplication • Use Contextual Problems • Build lessons around 1-3 meaningful problems • Allow students to come up with their own techniques to solve problems • It is important for them to explain (with words, pictures, and numbers) what they did and why it makes sense • When students first solve simple multiplication story problems, they will most likely write repeated-addition equations to represent what they they did. • This is a good opportunity to introduce the multiplication sign and what the two factors mean.

4. “Each Orange Had 8 Slices” • This book offers children experiences counting groups. • Sample page

5. “Each Orange Had 8 Slices” 3 3 x 6 = 18 3 x 6 x 2 = 36

6. “Each Orange Had 8 Slices” • This book offers children experiences counting groups. • Sample page • Children can practice writing multiplication statements that go with the pictures. • They can also make up similar situations of their own.

7. Teaching Multiplication • Use Models • E.g., Arrays using graph paper or counters • Activity 3.1 Finding Factors • Use models to help students understand important multiplication properties • Commutative property (3 x 6 = 6 x 3) • Use arrays (3 rows of 6 squares contains the same total number of squares as 6 rows of 3 squares) • Distributive property • The idea that one of the two factors in a product can be split into two or more parts, and each part multiplied separately and then added: 6 x 9 = (6 x 5) + (6 x 4) • Activity 3.2 Slice It Up

8. Strategies for Multiplication Facts • Multiplication facts can be mastered by relating new facts to existing knowledge. • 2 x 4 is related to the addition fact 4 + 4 • The same relationship also applies to 4 x 2, which many children think about as 2 + 2 + 2 + 2 • Students must understand the commutative property! • Most of the fact strategies are more obvious with the factors in one order than the other, but “turn-around facts” should always be learned together.

9. Strategies for Multiplication Facts • Doubles • 2 x __ and __ x 2 • These are equivalent to addition doubles and should already be known by children who know addition facts. • 2 x 7 is double 7, but so is 7 x 2! • Fives Facts • 5 x __ and __ x 5 • Activity 3.3 Clock Facts

10. Strategies for Multiplication Facts • Zeros and Ones • These facts tend to get confused with addition “rules” • The fact 6+0 stays the same, but 6x0 is always 0. • The 1+4 fact is a one-more idea, but 1x4 stays the same. • Concepts behind these facts are best developed through story problems • Try to avoid arbitrary-sounding rules like “Anything x 0 = 0” • Helping Facts • The remaining facts can be learned by relating each to an already known fact or helping fact. • 3 x 8 is connected to 2 x 8 (double 8 and 8 more) • 6 x 7 can be related to either 5 x 7 (5 sevens and 7 more) or to 3 x 7 (double 3x7)