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

Lesson 6.66.6 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
Equivalent ExpressionsSpanish: Expresiones equivalentes Expressions that look different but have the same value for every allowed variable value. 7c + 9 + 6c = 13c + 9
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. 7c + 9 + 6c → 13c + 9
Like TermsSpanish: Términos semejantes Terms with the same letter raised to the same power, like 2x and 5x. 7c and 6c
CombineSpanish: Combinar To add or subtract terms with the same letter into one. 7c + 6c = 13c
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. the 13 in 13c

How it worksWorked examplesimplifying to test equivalence

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

Are 7c + 9 + 6c and 13c + 9 equivalent? Simplify to decide.

  1. Find the like terms. 7c and 6c both have the letter c.
  2. Combine the like terms. 7c + 6c = 13c
  3. Keep the constant. The 9 has no letter, so it stays alone.
  4. Compare. 13c + 9 matches the second expression.

Answer: Yes. Both expressions simplify to 13c + 9, 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 4k + 11 + 4k and 8k + 11 equivalent? Simplify to decide.

  1. Find the like terms. and both have the letter k.
  2. Combine the like terms. + =
  3. Keep the constant.
  4. Compare with 8k + 11.
Answer:the simplified form, 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.

  • The like terms are and because .
  • I combined them to get .
  • The constant stays by itself because .
  • The two expressions equivalent because .

Word bank equivalentlike termscombinesimplifycoefficientconstanttermvariablesame valuegroupaddcompare

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 6.66.6 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Part 1Understand the ideamodels and meaning
  1. 1Complete each step, then write the final answer.

    Producer A charges 3x + 15 + 2x dollars for x songs. Producer B charges 5(x + 3) dollars. What does Producer B charge for 4 songs?

    Show your work
    Final answer:
  2. 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
  1. 3Complete each step, then write the final answer.
    x3x + 45x
    21010
    3??
    Lily tested x = 2. Now test x = 3.

    Lily tests x = 2. She gets 10 for 3x + 4 and 10 for 5x. She says they are equivalent. Is she right?

    1. 1Check Lily's test. What is 3x + 4 when x = 2?
    2. 2Test x = 3. What is 3x + 4?
    3. 3Test x = 3. What is 5x?
    4. 4Are the expressions equivalent?
    Final answer:
  2. 4Complete each step, then write the final answer.
    x4(x + 3)4x + 12
    1??
    Substitute x = 1 into both expressions.

    Are 4(x + 3) and 4x + 12 equivalent? Test x = 1. Then prove it for every x.

    1. 1Find 4(x + 3) when x = 1.
    2. 2Find 4x + 12 when x = 1.
    3. 3Use the Distributive Property on 4(x + 3).
    4. 4Why do they match for every x, not just 1?
    Final answer:
  3. 5Complete 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:
  4. 6Complete each step, then write the final answer.

    Kim says 6x + 2 and 8x are equivalent. They match at x = 1. Test x = 4. What is 6x + 2 when x = 4?

    Show your work
    Final answer:

Explain your thinkingBen tested three values and all of them matched. Is that a proof? What is the best way to prove two expressions are equivalent?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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