7th Grade Math Expressions & Equations

1. 7th Grade Math Expressions & Equations

2. Setting the PowerPoint View • Use Normal View for the Interactive Elements • To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: • On the View menu, select Normal. • Close the Slides tab on the left. • In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen.  • On the View menu, confirm that Ruler is deselected. • On the View tab, click Fit to Window. • On the View tab, click Slide Master | Page Setup. Select On-screen Show (4:3) under Slide sized for and click Close Master View. • On the Slide Show menu, confirm that Resolution is set to 1024x768. • Use Slide Show View to Administer Assessment Items • To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 10 for an example.)

3. Table of Contents Commutative and Associative Properties Combining Like Terms The Distributive Property and Factoring Simplifying Algebraic Expressions Inverse Operations One Step Equations Two Step Equations Multi-Step Equations Distributing Fractions in Equations Translating Between Words and Equations Using Numerical and Algebraic Expressions and Equations Graphing & Writing Inequalities with One Variable Simple Inequalities involving Addition & Subtraction Simple Inequalities involving Multiplication & Division CommonCoreStandards: 7.EE.1, 7.EE.3, 7.EE.4

4. Day 1 Commutative and Associative Properties

5. Commutative Property of Addition: The order in which the terms of a sum are added does not change the sum. a + b = b + a 5 + 7 = 7 + 5 12= 12 Commutative Property of Multiplication: The order in which the terms of a product are multiplied does not change the product. ab = ba 4(5) = 5(4)

6. Associative Property of Addition: The order in which the terms of a sum are grouped does not change the sum. (a + b) + c = a + (b + c) (2 + 3) + 4 = 2 + (3 + 4) 5 + 4 = 2 + 7 9 = 9

7. The Associative Property is particularly useful when you are combining integers. Example: -15 + 9 + (-4)= -15 + (-4) + 9= Changing it this way allows for the -19 + 9 = negatives to be added together first. -10

8. Associative Property of Multiplication: The order in which the terms of a product are grouped does not change the product.

9. 1 Identify the property of -5 + 3 = 3 + (-5) A Commutative Property of Addition Commutative Property of Multiplication B C Associative Property of Addition D Associative Property of Multiplication

10. 2 Identify the property of a + (b + c) = (a + c) + b A Commutative Property of Addition Commutative Property of Multiplication B C Associative Property of Addition D Associative Property of Multiplication

11. 3 Identify the property of (3 x -4) x 8 = 3 x (-4 x 8) A Commutative Property of Addition B Commutative Property of Multiplication C Associative Property of Addition D Asociative Property of Multiplication

12. Discuss why using the associative property would be useful with the following problems: 1. 4 + 3 + (-4) 2. -9 x 3 x 0 3. -5 x 7 x -2 4. -8 + 1 + (-6)

13. Combining Like Terms

14. Term – can be a number, a variable, or a product of numbers and variables Coefficient – a number that is Multiplied by a variable in an algebriac expression

15. Exponent 2x2 2x2 Coefficient Variable

16. An Expression - contains numbers, variables and at least one operation.

17. Like terms: terms in an expression that have the same variable raised to the same power Examples: LIKE TERMS NOT LIKE TERMS 6x and 2x 6x2 and 2x 5y and 8y 5x and 8y 4x2 and 7x2 4x2yand 7xy2

18. Group the Like Terms 2t 3y2 7t k 4z x2 5a 4.5y2

19. 4 Identify all of the terms like 2x A 5x B 3x2 C 5y D 12y E 2

20. 5 Identify all of the terms like 8y A 9y B 4y2 C 7y D 8 E -18x

21. 6 Identify all of the terms like 8xy A 8x B 3x2y C 39xy D 4y E -8xy

22. 7 Identify all of the terms like 2y A 51w B 2x C 3y D 2w E -10y

23. 8 Identify all of the terms like 14x2 A -5x B 8x2 C 13y2 D x E -x2

24. If two or more like terms are being added or subtracted, they can be combined. To combine like terms add/subtract the coefficient but leave the variable alone. 7x +8x =15x 9v-2v = 7v

25. Sometimes there are constant terms that can be combined. 9 + 2f + 6 = 9 + 2f + 6 = 2f + 15 Sometimes there will be both coeffients and constants to be combined. 3g+ 7+ 8g - 2 11g + 5 Notice that the sign before a given term goes with the number.

26. It helps if you circle each term first including the operation sign before the numbers, variables, and constants. -5x3 + 3y + 7x3 - 2y – 4x2 -5x3 +3y +7x3 -2y -4x2 2x3+ y – 4x2

27. Try These: 1.) 2b +6g(3) + 4f + 9f 2.) 9j + 3 + 24h + 6 + 7h + 3 3.) 7a + 4 + 2a -1 9 + 8c -12 + 5c 4.) 8x + 56xy + 5y

28. 9 8x + 3x = 11x A True B False

29. 10 7x + 7y = 14xy A True B False

30. 11 2x + 3x = 5x A True B False

31. 12 9x + 5y = 14xy A True B False

32. 13 6x + 2x = 8x2 A True B False

33. 14 -15y + 7y = -8y A True B False

34. 15 -6 + y + 8 = 2y A True B False

35. 16 -7y + 9y = 2y A True B False

36. 17 9x + 4 + 2x = A 15x B 11x + 4 C 13x + 2x D 9x + 6x

37. 18 12x + 3x + 7 - 5 A 15x + 7 - 5 B 13x C 17x D 15x + 2

38. 19 -4x - 6 + 2x - 14 A -22x B -2x - 20 C -6x +20 D 22x