1. Multiplying Integers with Tiles Student Expectation: 7 th Grade: 7.1.2C Use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms.

2. MULTIPLICATION Red and yellow tiles can be used to model multiplication. Remember that multiplication can be described as repeated addition. So 2 x 3 = ? The University of Texas at Dallas 2 groups of 3 tiles = 6 tiles

3. MULTIPLICATION 2 x - 3 means 2 groups of - 3 The University of Texas at Dallas x - 3 2 x - 3 = - 6

4. MULTIPLICATION Since 2 x 3 = 6 and 3 x 2 = 6, does it make sense that - 3 x 2 = - 6 ? - 3 x 2 = - 6 is true. - 3 x 2 = - 6 is true. + 2 x - 3 = - 6 and - 3 x + 2 = - 6 belong to a fact family: The University of Texas at Dallas + 2 x - 3 = - 6 - 3 x + 2 = - 6 - 6 ÷ + 2 = - 3 - 6 ÷ - 6 ÷ - 3 = + 2

5. MULTIPLICATION Use your tiles to model each multiplication problem. + 2 x + 4 = ? The University of Texas at Dallas ANSWER 2 groups of + 4 + 2 x + 4 = + 8

6. MULTIPLICATION + 3 x - 3 = ? The University of Texas at Dallas ANSWER 3 groups of - 3 + 3 x - 3 = - 9

7. MULTIPLICATION - 2 x + 4 = ? The University of Texas at Dallas ANSWER 4 groups of - 2 - 2 x + 4 = - 8 Use the fact family for - 2 x + 4 = ?  We can’t show - 2 groups of + 4 + 4 x - 2 = ?  we can show 4 groups of - 2

8. MULTIPLICATION + 1, - 1 are opposites the products are opposite Since + 2 and - 2 are opposites of each other, + 2 x - 3 and - 2 x - 3 have opposite products. + 2 x - 3 and - 2 x - 3 have opposite products. The University of Texas at Dallas + 1 x + 3 = + 3 - 1 x + 3 = - 3

9. MULTIPLICATION To model - 2 x - 3 use 2 groups of the opposite of - 3 The University of Texas at Dallas - 2 x - 3 = + 6

10. MULTIPLICATION Use tiles to illustrate - 3 x - 4 =? The University of Texas at Dallas ANSWER 3 groups of + 4 (the opposite of - 4) - 3 x - 4 = + 12