Mathematical Properties and Integers Simplification

1. Chapter 1 - Integers Century Middle School – Math 7 Ms. Burdick Ms. Swain Mr. Suits

2. Chapter 1 Overview • Global Context : Scientific and Technical Innovation • Statement of Inquiry : Equivalence and justification are closely related in the process of using rules of addition, subtraction, multiplication and division when working with rational numbers. Chapter 1 Opener 1.1 Activity1.1 Lesson 1.2 Activity1.2 Lesson 1.3 Activity1.3 Lesson 1.4 Activity1.4 Lesson 1.5 Activity1.5 Lesson

3. Chapter 1 Opener • Essential Question: How can you use mathematical properties to simplify an expression?

4. Chapter 1 – OpenerVocabulary • Commutative Property of Addition • Commutative Property of Multiplication • Associative Property of Addition • Associative Property of Multiplication • Multiplication Property of Zero • Multiplication Property of One

5. • Commutative Property To “commute” means to change or rearrange direction. The commutative property of addition or multiplication means to change the order. So 2 + 3 is the same as 3 + 2. Likewise 2 * 4 = 4 * 2

6. • Associative Property The associative property of addition or multiplication keeps the order exactly the same and changes the placement of the parenthesis. So (1 + 2) + 3 is the same as 1 + (2 + 3). Likewise (2 * 2) * 4 = 2 * (2 * 4)

7. • Multiplication Property Multiplication Property of zero – means to multiple a number or expression by 0 which results in a zero solution Multiplication Property of one – means to multiple a number or expression by 1 which does not change the solution

8. Example 1 • 4 + (c + 3) = 4 + (3 + c) Commutative Property of Addition = (4 + 3) + c Associative Property of Addition = 7 + c Add 4 + 3

9. Example 2 • 9 * y * 0 = 9 * 0 * y Commutative Property of Addition = (9 * 0) * y Associative Property of Addition = 0 * y Multiplication Property of Zero = 0

10. Global Context

11. THINK! How is football like solving a math problem?

16. Global Context

17. Do Now!

18. 1.1 Integers and Absolute Value • Essential Question: How can you use integers to represent the velocity and speed of an object?

19. 1.1 Vocabulary • Integers : positive and negative whole numbers on a number line. . . . , -4, -2, 0, 1, 2, 3, 4, . . . • Absolute Value : absolute value is the distance a number is from 0 on the number line. Mathematically absolute value is represented by | x |. So the | -3 | = 3 as -3 is 3 units from zero on the number line.

20. Example 1 Find the absolute value of 2 So, |2| = 2

21. Example 2 Find the absolute value of 6

22. Example 3 Find the absolute value of -3 So, |-3| = 3

23. Example 4 Find the absolute value of -11 Now complete the On Your Own

24. Example 5 Compare 1 and | -4 | 1 ? |- 4| Solving the |- 4| = 4 because -4 is 4 units from zero on the number line 1 ? 4 1 < 4 OR 1 < |- 4| Now complete the On Your Own

25. Example 6

26. Exit Ticket

27. Global Context

28. From 1.1Complete the following

36. Global Context

37. Do Now!

38. 1.2 Adding Integers • Essential Question: Is the sum of two integers positive, negative or zero? How can you tell?

39. 1.2 Vocabulary • Opposite : Two numbers that are exactly the same distance from zero but on either side of the number line • Additive Inverse Property : the sum of an integer and its opposite is zero

40. 1.2 Key Idea • Adding numbers with the same sign : add the numbers together and take the common sign • Adding numbers with different signs : subtract and take the sign of the number farthest from zero on the number line.

41. Example 1

42. Example 2 Find -3 + (-12)

43. Example 3

44. Example 4

45. Global Context

46. From 1.2Complete the following