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

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

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?

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

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

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

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)

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)

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

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)

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