1. How many of your students come to you with a good understanding of multiplication? Research shows that you should develop student understanding PRIOR TO teaching students an algorithm.

2. GOAL

3. 3X5 5+5+5 3+3+3+3+3 3 groups of 5 = 5 groups of 3

4. 5 x 23 Concrete: Build with tiles, use place value blocks Pictorial: Draw a representation  Use this to show how to use the distributive property to solve this problem Number: What does this strategy look like in number Algorithm

5. Concrete: 5 x 23

6. Using place value blocks for: 5 x 23

7. 5 X 105 X 10 5 x 3 5050 15

8. Pictorial: 5 x 23 Area model: 10103 5 10 X5 50 10 X5 50 5 X3 15

9. Connected to Number:5 x 23 5 x 23 23= 10+10+3 10 10 3 X5X5X5 5050 15

10. Partial Products

11. Traditional Algorithm H T O 1 2 1 4 x 3 7 9 8 seven times four is 28 ones which 2 0 can be regrouped as 2 tens and 8 ones seven times ten is 70, plus two more tens, is 9 tens or 90 30 times 4 is 120 which can be regrouped as 0 ones, 2 tens and 1 hundred, etc…

12. Final Thoughts Even though a focus of learning about multiplication in grades 3-5 is on developing computational proficiency, students also begin to see the usefulness of multiplication as a problem-solving instrument in many other situations. As students learn to recognize various situations as multiplicative, they begin to form an idea of multiplication as a powerful mechanism for representation and reasoning. This solidly rooted and growing understanding of multiplication and division in grades 3-5 lays the foundation for further understanding of these operations in other number domains, such as fractions and decimals.