Five-Minute Check (over Lesson 1–2)CCSSThen/NowNew VocabularyExample 1:Verbal to Algebraic ExpressionExample 2:Algebraic to Verbal SentenceKey Concept: Properties of EqualityExample 3:Identify Properties of EqualityKey Concept: Addition and Subtraction / Multiplication and Division Properties of EqualityExample 4:Solve One-Step EquationsExample 5:Solve a Multi-Step EquationExample 6:Solve for a VariableExample 7:Standardized Test Example

Over Lesson 1–2

Name the property illustrated by a + (7 + c) = (a + 7) + c.

Name the property illustrated by3(4 + 0.2) = 3(4) + 3(.02).

Simplify (2c)(3d) + c + 5cd + 3c2.

Over Lesson 1–2

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)

Over Lesson 1–2

A. naturals (N), wholes (W)

B. reals (R)

C. rationals (Q), reals (R)

D. integers (Z), reals (R)

Over Lesson 1–2

A. Associative Property of Addition

B. Distributive Property

C. Substitution Property

D. Commutative Property of Addition

Name the property illustrated by a + (7 + c) = (a + 7) + c.

Over Lesson 1–2

A. Associative Property of Addition

B. Identity Property

C. Distributive Property

D. Substitution Property

Name the property illustrated by3(4 + 0.2) = 3(4) + 3(.02).

Over Lesson 1–2

A. 3c2 + 5cd + c

B. 3c2 + 11cd + c

C. 3c2 + 10cd

D. 3c2 + c

Simplify (2c)(3d) + c + 5cd + 3c2.

Content Standards

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Mathematical Practices

3 Construct viable arguments and critiquethe reasoning of others.

8 Look for and express regularity in repeatedreasoning.

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.

• open sentence

• equation

• solution

Verbal to Algebraic Expression

A. Write an algebraic expression to represent the verbal expression 7 less than a number.

Answer: n – 7

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

A. 6x

B. x + 6

C. x6

D. x – 6

A. Write an algebraic expression to represent the verbal expression 6 more than a number.

A. x3 – 2

B. 2x3

C. x2 – 2

D. 2 + x3

B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.

Algebraic to Verbal Sentence

A. Write a verbal sentence to represent 6 = –5 + x.

Answer: Six is equal to –5 plus a number.

Algebraic to Verbal Sentence

B. Write a verbal sentence to represent 7y – 2 = 19.

Answer: Seven times a number minus 2 is 19.

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.

A. What is a verbal sentence that represents the equation n – 3 = 7?

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.

B. What is a verbal sentence that represents the equation 5 = 2 + x?

Identify Properties of Equality

A. Name the property illustrated by the statement.

a – 2.03 = a – 2.03

Answer: Reflexive 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

A. Reflexive Property of Equality

B. Symmetric Property of Equality

C. Transitive Property of Equality

D. Substitution 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

B. What property is illustrated by the statement?

If 3 = x and x = y, then 3 = y.

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

Answer: The solution is 5.5.

0.02 = 0.02 Simplify.

5.5 – 5.48 = 0.02 Substitute 5.5 for m.

?

Solve One-Step Equations

Original equation

Simplify.

Solve One-Step Equations

Answer: The solution is 36.

Substitute 36 for t.

Simplify.

Check Original equation

?

A. –8

B. –2

C. 2

D. 8

A. What is the solution to the equation x + 5 = 3?

B. What is the solution to the equation

A. 5

B.

C. 15

D. 30

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.

What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?

A. –6

B.

C.

D. 6

Solve for a Variable

Surface area formula

Subtract πr 2 from

each side.

Simplify.

Solve for a Variable

Divide each side by πr.

Simplify.

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.

A B

C D

Read the Test ItemYou 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.

Solve the Test Item

Answer: C

Original equation

Subtract 7 from each side.

Simplify.

A. 12

B. 6

C. –6

D. –12

If 2x + 6 = –3, what is the value of 2x – 3?