1. Multiplication How do we develop this concept with our students?

2. Basic Representations

3. Array 3 X 5 or 3 5 or three by five 3 5 X 555555 3 + 3 + 3 + 3 + 3 = 15

4. Area Model 3 X 5 You will want to move away from drawing an array quickly. The area model is a more efficient way to draw a representation of an array. Filling in each square is time consuming.

5. Sets

6. The Properties  Discover  Investigate  Understand  Communicate

7. Identity Property n 1 = n

8. Zero Property n0=0  This can cause conceptual challenges for students.  This property can not be demonstrated as an array or with the area model. Try it!  Show n0 in sets. Place it in context.  5 hops of 0 on a number line  Water has 0 grams of fat. How many grams of fat does 5 glasses of water have?

9. Commutative Property The Order Property of Multiplication Changing the order of the factors does not change the product. a b = b a The product of a times b will have the same value as b times a.

10. Commutative Property of Multiplication Representations

12. Associative Property  The Grouping Property of Multiplication  Changing the way you group the factors does not change the product.  (a b) c = a (b c)  The product of a times b then multiplied by c will have the same value as b times c and then multiplied by a.

13. Associative Property of Multiplication 3 sets of 4 is 12. 12 times 2 is 24. There are 24 bags of chips. (34) = 12 12 2 = 24

14. Associative Property of Multiplication 4 sets of 2 is 8. 8 times 3 is 24. There are 24 bags of chips. (42) = 8 8 3 = 24

15. Multiplying by a power of 10 This pattern is essential to understand as students move to multiplying larger values. Students can discover why I have a certain number of zeros in my product when I multiply by a power of 10. Discover what happens to the decimal point.

16. You DO NOT want to tell them, “Just count the zeros and add them to your product.” Look at 5 40 5 4 = 20 The zero is already there. Many students do not see the difference between adding one zero and a factor that has a zero in the ones place. Thinking 5 times 4 tens is 20 tens is much more precise.

17. Build It First. Many, many times. 3 1 3 1 ten = 3 tens 3 2 ten = 6 tens

18. 3 4 hundreds Explore Number Strings 3 4 = 12 3 4 tens = 12 tens= 120 3 4 hundreds = 12 hundreds=1200

19. Finally, look for patterns in number form. N 10N 100 3 1 = 3 3 1ten = 3 tens= 303 10 = 30 3 1 hundred = 3 hundreds= 300 3 2 = 6 3 2 tens = 6 tens = 603 2 0= 60 3 2 hundreds = 6 hundreds = 600 Now you can discover the math generalization or rule.

20. Put it all together. Represent 8 X 7 1.Build it with color tiles. 2.Represent it with pictures. 3.Represent it with numbers 4.Solve it with an algorithm.

21. 32 X 5 Build It

22. Let’s solve 32X28 with partial products. 30 2 208 30X2030X8 2X208X2