1. MODEL 1 Drag the shapes from the right to represent the situation. Write the algebraic expression (make your best guess) Show 3 groups of 1 apple and 2 banana = Total 1.) How are 3 groups of 1 apple and 2 banana represented? 4.) How is the picture related to the total? 2.) How many apples are there in your picture? 3.) How many bananas are there in your picture?

2. MODEL 1: Answer Key This is what your model should have looked like. Did you get it correct? Write the algebraic expression Show 3 groups of 1 apple and 2 banana 3(1a + 2b) 3a + 6b = Total The 3 means there are 3 groups. The ( ) show what is in the group. There is a total of 3 apples and 6 bananas. Can you see it in the picture?

3. MODEL 2 Look at the algebraic model 3(1a + 2b) 3a + 6b = Total There are 3 groups of (1a + 2b). Repeated addition is the same as multiplication. (1a + 2b) + (3a + 6b) You can use repeated addition. (1a + 2b) x 3 3·1a + 3·2b 3a +6b When multiply each part, you get the total.

4. MODEL 3 Drag the shapes from the right to represent the situation. Write the algebraic expression Show 2 groups of 3 apple and 2 banana = How do you show “groups”? Total

5. MODEL 3: Answer Key This is what your model should have looked like. Did you get it correct? Write the algebraic expression 2(3a + 2b)6a + 4b = How do you show “groups”? Total Show 2 groups of 3 apple and 2 banana 5.) What math symbol do you use to represent “groups” ? You should be able to see the total in the picture.

6. Write the algebraic expression Show 3 groups of 2 apples and 3 bananas = MODEL 4: Practice on your own How do you show “groups”? Total

7. Write the algebraic expression Show 2 groups of 3 apples and 2 bad bananas = MODEL 5: What do you think? Drag the shapes from the right to model the situation. How do you show “groups”? Total 6.) What do the “bad bananas” represent mathematically?

8. Write the algebraic expression Show 2 groups of 3 apples and 2 bad bananas 2(3a + -2b)6a + -4b = MODEL 5: Answer Key How do you show “groups”? Total 6.) What do the “bad bananas” represent mathematically? They represent negative numbers. The total is what you see in the picture.

9. Show 2 groups of 3 apples and 2 bad bananas MODEL 5: Algebraic Model 2(3a + -2b) 6a + -4b = Total Repeated addition is the same as multiplication. (3a + -2b) + (6a + -4b) (3a +- 2b) x 2 2·3a + 2·-2b 6a + -4b When multiply each part, you get the total. There are 2 groups of (3a + -2b). You can use repeated addition.

10. Write the algebraic expression Show 4 groups of 2 bad apples and 1 bad bananas = How do you show “groups”? Total 7.) How could you represent 100 groups of 3 apples and 2 bad bananas? MODEL 6: What do you think? Drag the shapes from the right to model the situation.

11. Distributive Property: 3 groups of 5a + 7 3 (5a + 7) is the same as (5a + 7) 15a + 21 OR3 (5a + 7) (5a + 7) x 3 15a + 21 OR3 (5a + 7) 3 ·5a + 3 · 7 15a + 21

12. Distributive Property: Fill this out on your notes (Look back to the previous slide for help) 8 groups of 3a + 20 is the same as OR x Too many to write in a list!!