1. EXPLORING PROPERTIES THE COMMUTATIVE AND ASSOCIATIVE PROPERTIES

2. CONSIDER THIS – (COPY AND ANSWER THIS IN THE TOP LEFT SECTION OF PAGE 3) JACK To get to school Jack travels 5 miles on Pitchkettle Road and 3 miles on Kings Fork Road. JILL To get to school Jill travels 3 miles on Godwin Blvd. and 5 miles on Kings Fork Road. Which student has a longer commute to school? Explain.

3. THE COMMUTATIVE PROPERTY OF ADDITION/MULTIPLICATION Important note – this property only works for addition and multiplication

4. WHAT DO YOU NOTICE ….. 3 2 For a total of: 5 2 3 For a total of: ____

5. Our definition -

6. Addition 7 + 3 = 3 + 7 a + b = b + a (4 + 5) + 6 = (5 + 4) + 6 Multiplication 9 x 10 = 10 x 9 a ● b = b ● a 2 x (8 x 6) = 2 x (6 x 8) EXAMPLES OF THE COMMUTATIVE PROPERTY

7. On Monday Jen and Matt sat beside each other at the lunch table while Aaron sat by himself. On Tuesday Jen sat by herself at the lunch table while Matt and Aaron sat beside each other. CONSIDER THIS – (COPY AND ANSWER THIS IN THE TOP LEFT SECTION OF PAGE 5) How many students were sitting at the lunch table on Monday? On Tuesday? Did the total number of students change after the students switched their seating groups on Tuesday?

8. THE ASSOCIATIVE PROPERTY OF ADDITION/MULTIPLICATION Important note – this property only works for addition and multiplication

9. WHAT DO YOU NOTICE ….. 3 2 2 For a total of: 7 3 2 2 For a total of: ____

10. Our definition -

11. Multiplication ( 2 x 3) x 9 = 2 x (3 x 9) a ● (b● c) = (a ●b ) ● c EXAMPLES OF THE ASSOCIATIVE PROPERTY