1. February 19, 2009 “Arithmetic is where the answer is right and everything is nice and you can look out of the window and see the blue sky - or the answer is wrong and you have to start over and try again and see how it comes out this time.” Carl Sandburg Carl Sandburg

2. February 19, 2009 Section 3.3 – Properties of Multiplication Watch Videos & discuss Homework

3. 3.3 (cont’d) Properties of Multiplication: 1.Zero property: a · 0 = 0 · a = 0 Ex: 3 · 0 = 0 0 · 27 = 0 *Is there any other number that has this property?

4. 3.3 (cont’d) Properties of Multiplication: 2. Identity property: a · 1 = 1 · a = a Ex: 3 · 1 = 3 1 · 27 = 27

5. 3.3 (cont’d) Properties of Multiplication: 3.Commutative property: a · b = b · a Ex: 3 · 4 = 4 · 3 38 · 27 = 27 · 38

6. 3.3 (cont’d) Properties of Multiplication: 4. Associative property: a · (b · c) = (a · b) · c Ex: 3 · (4 · 5) = (3 · 4) · 5

7. 3.3 (cont’d) Properties of Multiplication: 4. Distributive property: a · (b + c) = (a · b) + (a · c) a · (b – c) = (a · b) – (a · c) Ex: 3 · (4 + 5) = (3 · 4) + (3 · 5) 3 · (4 – 5) = (3 · 4) – (3 · 5)

8. 3.3 (cont’d) Notice that the number 0 is special for both Multiplication and Addition, though in different ways. Multiplication: a · 0 = 0 Addition:a + 0 = a (0 is the “identity” for addition)

9. 3.3 (cont’d) Also, both Multiplication and Addition have identities, but they are different. Multiplication: a · 1 = a Addition:a + 0 = a

10. Videos: turn to Class Notes pg 5. Take notes that will help you remember each child’s strategy (you will apply the strategy in the Class Notes). 3.3 (cont’d)

11. Homework Due Tuesday, 2/24: Link to online homework list