7th grade math expressions & equations

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7th Grade Math Expressions & Equations

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7th Grade Math Expressions & Equations. 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: - PowerPoint PPT Presentation

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Page 1: 7th Grade Math Expressions & Equations

7th Grade Math

Expressions & Equations

Page 2: 7th Grade Math Expressions & Equations

Setting the PowerPoint ViewUse Normal View for the Interactive ElementsTo 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 ItemsTo administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 10 for an example.)

Page 3: 7th Grade Math Expressions & Equations

Table of Contents

Inverse OperationsOne Step EquationsTwo Step EquationsMulti-Step EquationsDistributing Fractions in Equations

Graphing & Writing Inequalities with One Variable

The Distributive Property and FactoringCombining Like Terms

Simple Inequalities involving Addition & SubtractionSimple Inequalities involving Multiplication & Division

Common Core Standards: 7.EE.1, 7.EE.3, 7.EE.4

Simplifying Algebraic Expressions

Translating Between Words and Equations

Commutative and Associative Properties

Using Numerical and Algebraic Expressions and Equations

Page 4: 7th Grade Math Expressions & Equations

Commutative and Associative Properties

Day 1

Page 5: 7th Grade Math Expressions & Equations

Commutative Property of Addition: The order in which the terms of a sum are added does not change the sum.a + b = b + a5 + 7 = 7 + 5 12= 12Commutative Property of Multiplication: The order in which the terms of a product are multiplied does not change the product.ab = ba4(5) = 5(4)

Page 6: 7th Grade Math Expressions & Equations

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

Page 7: 7th Grade Math Expressions & Equations

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

Page 8: 7th Grade Math Expressions & Equations

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

Page 9: 7th Grade Math Expressions & Equations

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

Page 10: 7th Grade Math Expressions & Equations

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

Page 11: 7th Grade Math Expressions & Equations

3 Identify the property of (3 x -4) x 8 = 3 x (-4 x 8)A Commutative Property of AdditionB Commutative Property of MultiplicationC Associative Property of AdditionD Asociative Property of Multiplication

Page 12: 7th Grade Math Expressions & Equations

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)

Page 13: 7th Grade Math Expressions & Equations

Combining Like Terms

Page 14: 7th Grade Math Expressions & Equations

Term – can be a number, a variable,or a product of numbers and variables

Coefficient – a number that isMultiplied by a variable in an algebriacexpression

Page 15: 7th Grade Math Expressions & Equations

2x2

2x2Coefficient

Exponent

Variable

Page 16: 7th Grade Math Expressions & Equations

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

Page 17: 7th Grade Math Expressions & Equations

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 4x2y and 7xy2

Page 18: 7th Grade Math Expressions & Equations

Group the Like Terms

2t 3y2 7t k

4z x2

5a 4.5y2

Page 19: 7th Grade Math Expressions & Equations

4 Identify all of the terms like 2x

A 5xB 3x2

C 5yD 12yE 2

Page 20: 7th Grade Math Expressions & Equations

5 Identify all of the terms like 8y

A 9yB 4y2

C 7yD 8E -18x

Page 21: 7th Grade Math Expressions & Equations

6 Identify all of the terms like 8xy

A 8xB 3x2yC 39xyD 4yE -8xy

Page 22: 7th Grade Math Expressions & Equations

7 Identify all of the terms like 2y

A 51wB 2xC 3yD 2wE -10y

Page 23: 7th Grade Math Expressions & Equations

8 Identify all of the terms like 14x2

A -5xB 8x2

C 13y2

D xE -x2

Page 24: 7th Grade Math Expressions & Equations

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 =15x9v-2v = 7v

Page 25: 7th Grade Math Expressions & Equations

Sometimes there are constant terms that can be combined.9 + 2f + 6 =9 + 2f + 6 =

2f + 15Sometimes there will be both coeffients and constants to

be combined.3g + 7 + 8g - 2

11g + 5Notice that the sign before a given term goes with the

number.

Page 26: 7th Grade Math Expressions & Equations

It helps if you circle each term firstincluding the operation sign beforethe numbers, variables, and constants.

-5x3 + 3y + 7x3 - 2y – 4x2

-5x3 +3y +7x3 -2y -4x2

2x3 + y – 4x2

Page 27: 7th Grade Math Expressions & Equations

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

Page 28: 7th Grade Math Expressions & Equations

9 8x + 3x = 11xA TrueB False

Page 29: 7th Grade Math Expressions & Equations

10 7x + 7y = 14xy

A TrueB False

Page 30: 7th Grade Math Expressions & Equations

11 2x + 3x = 5xA TrueB False

Page 31: 7th Grade Math Expressions & Equations

12 9x + 5y = 14xyA TrueB False

Page 32: 7th Grade Math Expressions & Equations

13 6x + 2x = 8x2

A TrueB False

Page 33: 7th Grade Math Expressions & Equations

14 -15y + 7y = -8yA TrueB False

Page 34: 7th Grade Math Expressions & Equations

15 -6 + y + 8 = 2yA TrueB False

Page 35: 7th Grade Math Expressions & Equations

16 -7y + 9y = 2yA TrueB False

Page 36: 7th Grade Math Expressions & Equations

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

Page 37: 7th Grade Math Expressions & Equations

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

Page 38: 7th Grade Math Expressions & Equations

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