Mathematical Practices Then/Now New Vocabulary Five-Minute Check Mathematical Practices Then/Now New Vocabulary Example 1: Verbal to Algebraic Expression Example 2: Algebraic to Verbal Sentence Key Concept: Properties of Equality Example 3: Identify Properties of Equality Example 4: Solve One-Step Equations Example 5: Solve a Multi-Step Equation Example 6: Solve for a Variable Example 7: Use Properties of Equality Lesson Menu

A. naturals (N), wholes (W), integers (Z) B. wholes (W), integers (Z), reals (R) C. naturals (N), wholes (W), rationals (Q), reals (R) D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R) 5-Minute Check 1

A. naturals (N), wholes (W), integers (Z) B. wholes (W), integers (Z), reals (R) C. naturals (N), wholes (W), rationals (Q), reals (R) D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R) 5-Minute Check 1

A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R) D. integers (Z), reals (R) 5-Minute Check 2

A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R) D. integers (Z), reals (R) 5-Minute Check 2

Name the property illustrated by a + (7 + c) = (a + 7) + c. A. Associative Property of Addition B. Distributive Property C. Substitution Property D. Commutative Property of Addition 5-Minute Check 3

Name the property illustrated by a + (7 + c) = (a + 7) + c. A. Associative Property of Addition B. Distributive Property C. Substitution Property D. Commutative Property of Addition 5-Minute Check 3

Name the property illustrated by 3(4 + 0.2) = 3(4) + 3(.02). A. Associative Property of Addition B. Identity Property C. Distributive Property D. Substitution Property 5-Minute Check 4

Name the property illustrated by 3(4 + 0.2) = 3(4) + 3(.02). A. Associative Property of Addition B. Identity Property C. Distributive Property D. Substitution Property 5-Minute Check 4

Simplify (2c)(3d) + c + 5cd + 3c2. A. 3c2 + 5cd + c B. 3c2 + 11cd + c C. 3c2 + 10cd D. 3c2 + c 5-Minute Check 5

Simplify (2c)(3d) + c + 5cd + 3c2. A. 3c2 + 5cd + c B. 3c2 + 11cd + c C. 3c2 + 10cd D. 3c2 + c 5-Minute Check 5

Which equation illustrates the Additive Identity Property? B. 5(1) = 5 C. 5 + (–5) = 0 D. 5-Minute Check 6

Which equation illustrates the Additive Identity Property? B. 5(1) = 5 C. 5 + (–5) = 0 D. 5-Minute Check 6

Mathematical Processes A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 8 Look for and express regularity in repeated reasoning. MP

You used properties of real numbers to evaluate expressions. Translate verbal expressions into algebraic expressions and equations, and vice versa. Solve equations using the properties of equality. Then/Now

open sentence equation solution Vocabulary

Verbal to Algebraic Expression A. Write an algebraic expression to represent the verbal expression 7 less than a number. Answer: Example 1

Verbal to Algebraic Expression A. Write an algebraic expression to represent the verbal expression 7 less than a number. Answer: n – 7 Example 1

Verbal to Algebraic Expression B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number. Answer: Example 1

Verbal to Algebraic Expression B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number. Answer: x2 – 5x Example 1

A. Write an algebraic expression to represent the verbal expression 6 more than a number. A. 6x B. x + 6 C. x6 D. x – 6 Example 1a

A. Write an algebraic expression to represent the verbal expression 6 more than a number. A. 6x B. x + 6 C. x6 D. x – 6 Example 1a

B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number. A. x3 – 2 B. 2x3 C. x2 – 2 D. 2 + x3 Example 1b

B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number. A. x3 – 2 B. 2x3 C. x2 – 2 D. 2 + x3 Example 1b

A. Write a verbal sentence to represent 6 = –5 + x. Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer: Example 2

A. Write a verbal sentence to represent 6 = –5 + x. Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer: Six is equal to –5 plus a number. Example 2

B. Write a verbal sentence to represent 7y – 2 = 19. Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer: Example 2

B. Write a verbal sentence to represent 7y – 2 = 19. Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer: Seven times a number minus 2 is 19. Example 2

A. What is a verbal sentence that represents the equation n – 3 = 7? A. The difference of a number and 3 is 7. B. The sum of a number and 3 is 7. C. The difference of 3 and a number is 7. D. The difference of a number and 7 is 3. Example 2a

A. What is a verbal sentence that represents the equation n – 3 = 7? A. The difference of a number and 3 is 7. B. The sum of a number and 3 is 7. C. The difference of 3 and a number is 7. D. The difference of a number and 7 is 3. Example 2a

B. What is a verbal sentence that represents the equation 5 = 2 + x? A. Five is equal to the difference of 2 and a number. B. Five is equal to twice a number. C. Five is equal to the quotient of 2 and a number. D. Five is equal to the sum of 2 and a number. Example 2b

B. What is a verbal sentence that represents the equation 5 = 2 + x? A. Five is equal to the difference of 2 and a number. B. Five is equal to twice a number. C. Five is equal to the quotient of 2 and a number. D. Five is equal to the sum of 2 and a number. Example 2b

Key concept

A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Identify Properties of Equality A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Answer: Example 3

A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Identify Properties of Equality A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Answer: Reflexive Property of Equality Example 3

Identify Properties of Equality B. Name the property illustrated by the statement. If 9 = x, then x = 9. Answer: Example 3

Answer: Symmetric Property of Equality Identify Properties of Equality B. Name the property illustrated by the statement. If 9 = x, then x = 9. Answer: Symmetric Property of Equality Example 3

A. Reflexive Property of Equality B. Symmetric Property of Equality A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3a

A. Reflexive Property of Equality B. Symmetric Property of Equality A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3a

A. Reflexive Property of Equality B. Symmetric Property of Equality B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3b

A. Reflexive Property of Equality B. Symmetric Property of Equality B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3b

Key Concept

A. Solve m – 5.48 = 0.02. Check your solution. Solve One-Step Equations A. Solve m – 5.48 = 0.02. Check your solution. m – 5.48 = 0.02 Original equation m – 5.48 + 5.48 = 0.02 + 5.48 Add 5.48 to each side. m = 5.5 Simplify. Check m – 5.48 = 0.02 Original equation 5.5 – 5.48 = 0.02 Substitute 5.5 for m. ? 0.02 = 0.02 Simplify.  Answer: Example 4

A. Solve m – 5.48 = 0.02. Check your solution. Solve One-Step Equations A. Solve m – 5.48 = 0.02. Check your solution. m – 5.48 = 0.02 Original equation m – 5.48 + 5.48 = 0.02 + 5.48 Add 5.48 to each side. m = 5.5 Simplify. Check m – 5.48 = 0.02 Original equation 5.5 – 5.48 = 0.02 Substitute 5.5 for m. ? 0.02 = 0.02 Simplify.  Answer: The solution is 5.5. Example 4

Solve One-Step Equations Original equation Simplify. Example 4

Check Original equation Solve One-Step Equations Check Original equation ? Substitute 36 for t.  Simplify. Answer: Example 4

Check Original equation Solve One-Step Equations Check Original equation ? Substitute 36 for t.  Simplify. Answer: The solution is 36. Example 4

A. What is the solution to the equation x + 5 = 3? B. –2 C. 2 D. 8 Example 4a

A. What is the solution to the equation x + 5 = 3? B. –2 C. 2 D. 8 Example 4a

B. What is the solution to the equation C. 15 D. 30 Example 4b

B. What is the solution to the equation C. 15 D. 30 Example 4b

53 = 3(y – 2) – 2(3y – 1) Original equation Solve a Multi-Step Equation Solve 53 = 3(y – 2) – 2(3y – 1). 53 = 3(y – 2) – 2(3y – 1) Original equation 53 = 3y – 6 – 6y + 2 Apply the Distributive Property. 53 = –3y – 4 Simplify the right side. 57 = –3y Add 4 to each side. –19 = y Divide each side by –3. Answer: Example 5

53 = 3(y – 2) – 2(3y – 1) Original equation Solve a Multi-Step Equation Solve 53 = 3(y – 2) – 2(3y – 1). 53 = 3(y – 2) – 2(3y – 1) Original equation 53 = 3y – 6 – 6y + 2 Apply the Distributive Property. 53 = –3y – 4 Simplify the right side. 57 = –3y Add 4 to each side. –19 = y Divide each side by –3. Answer: The solution is –19. Example 5

What is the solution to 25 = 3(2x + 2) – 5(2x + 1)? B. C. D. 6 Example 5

What is the solution to 25 = 3(2x + 2) – 5(2x + 1)? B. C. D. 6 Example 5

Subtract πr 2 from each side. Solve for a Variable Surface area formula Subtract πr 2 from each side. Simplify. Example 6

Divide each side by πr. Simplify. Answer: Solve for a Variable Example 6

Solve for a Variable Divide each side by πr. Simplify. Example 6

GEOMETRY The formula for the perimeter of a rectangle is where P is the perimeter, and w is the width of the rectangle. What is this formula solved for w? A. B. C. D. Example 6a

GEOMETRY The formula for the perimeter of a rectangle is where P is the perimeter, and w is the width of the rectangle. What is this formula solved for w? A. B. C. D. Example 6a

Use Properties of Equality A B C D Read the Test Item You are asked to find the value of the expression 4g – 2. Your first thought might be to find the value of g and then evaluate the expression using this value. Notice that you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality. Example 7

Subtract 7 from each side. Use Properties of Equality Solve the Test Item Original equation Subtract 7 from each side. Simplify. Answer: Example 7

Subtract 7 from each side. Use Properties of Equality Solve the Test Item Original equation Subtract 7 from each side. Simplify. Answer: C Example 7

If 2x + 6 = –3, what is the value of 2x – 3? B. 6 C. –6 D. –12 Example 7

If 2x + 6 = –3, what is the value of 2x – 3? B. 6 C. –6 D. –12 Example 7