Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Testing Equivalence by Substituting

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show that two expressions are equivalent by simplifying and combining like terms.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
Equivalent ExpressionsSpanish: Expresiones equivalentes	Expressions that look different but have the same value for every allowed variable value.	2(y + 7) and 2y + 14
EquivalentSpanish: Equivalente	Expressions that always have the same value.	2x + 4 and 2(x + 2): when x = 3, both = 10; when x = 7, both = 18 — always the same
SimplifySpanish: Simplificar	To rewrite an expression in a shorter form that is still equal to the original.	3x + 2x + 5 simplifies to 5x + 5 — fewer terms, same value
Like TermsSpanish: Términos semejantes	Terms with the same letter raised to the same power, like 2x and 5x.	3x and 7x are like terms (both x); 3x and 3y are NOT (x vs y); 3x and 3x² are NOT (x vs x²)
CombineSpanish: Combinar	To add or subtract terms with the same letter into one.	4n + 3n = 7n — add the coefficients (4 + 3 = 7) and keep the variable (n)
CoefficientSpanish: Coeficiente	The number in front of a letter, like the 3 in 3x.	In 5x + 3, the coefficient of x is 5 — when x = 2, the 5x part equals 10

How it worksWorked exampletesting equivalence with a value

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Are 2(y + 7) and 2y + 14 equivalent? Test them using y = 9.

Pick the test value. y = 9
Substitute into the first expression. 2(9 + 7) = 2 × 16 = 32
Substitute into the second expression. 2 × 9 + 14 = 18 + 14 = 32
Compare the two values. 32 and 32 match.

Answer: Both expressions give 32, so they are equivalent.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Are 4(n + 3) and 4n + 3 equivalent? Test them using n = 20.

Pick the test value. n = 20
Substitute into the first expression. 4( + 3) = 4 × =
Substitute into the second expression. 4 × + 3 = + 3 =
Compare the two values. and

Answer:the two values, and whether they are equivalent

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

I substituted into both expressions.
The first expression gave and the second gave .
The expressions are equivalent because .
The Property lets me change the without changing the value.

Word bank equivalentsubstitutetest valueCommutativeAssociativegroupingordervaluecomparecounterexamplepropertyevaluate

Watch outA common mistake

A common mistake in Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms — writing 3x + 2x as 5x² instead of 5x. Remember: 3x means 3 groups of x and 2x means 2 more groups of x, so you add the coefficients (3 + 2 = 5) and keep the variable's power the same (x¹, not x²).

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Testing Equivalence by Substituting

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can show that two expressions are equivalent by simplifying and combining like terms.

1Complete each step, then write the final answer.

Fill in the box: 3x + 5x + 4 is equivalent to ☐x + 4. What number goes in the box?
Show your work
Hint Combine 3x and 5x. The 4 stays the same.
Final answer:
2Complete each step, then write the final answer.

Are 4x + 2x and 6x equivalent? Find the value of each when x = 5.
Show your work
Hint Put 5 in for x in both expressions.
Final answer:
3Complete each step, then write the final answer.

Fill in the box: 7x + 2x + 1 is equivalent to ☐x + 1. What number goes in the box?
Show your work
Hint 7 x's plus 2 x's is how many x's?
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Testing Equivalence by Substituting

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can show that two expressions are equivalent by simplifying and combining like terms.

Part 1Understand the ideamodels and meaning

1Circle the letter of the best answer. Show how you know.
Which expression is equivalent to 3x + 5 + 4x?
1. A7x + 5
2. B12x
3. C7x + 9
4. D8x + 4
Show your work

Part 2Apply itreal-world problems

2Complete each step, then write the final answer.

Fill in the box so the expressions are equivalent: 5(x + 2) and 5x + ☐. What number goes in the box?
Show your work
Final answer:
3Complete each step, then write the final answer.

Fill in the box so the expressions are equivalent: 8x + 3x + 4 and ☐x + 4. What number goes in the box?
Show your work
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Testing Equivalence by Substituting

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can show that two expressions are equivalent by simplifying and combining like terms.

Part 1Understand the ideamodels and meaning

1Circle the letter of the best answer. Show how you know.
Which expression is equivalent to 4(x + 3)?
1. A4x + 12
2. B4x + 3
3. C7x
4. Dx + 12
Show your work
2Circle the letter of the best answer. Show how you know.
Which expression is NOT equivalent to 6x + 9?
1. A3(2x + 3)
2. B9 + 6x
3. C4x + 9 + 2x
4. D6(x + 9)
Show your work

Part 2Apply itreal-world problems

3Complete each step, then write the final answer.

Lee says 5x + 3 and 8x are equivalent because both equal 8 when x = 1. Test x = 2. What is 5x + 3 when x = 2?
Show your work
Final answer:

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help