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.

Why This Matters This is your challenge small group for Lesson 6.6. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 example

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

Simplify 7c + 9 + 6c. Is it equivalent to 13c + 9?

  1. Like terms: 7c and 6c.
  2. Combine: 7c + 6c = 13c. The 9 stays alone.
  3. 7c + 9 + 6c = 13c + 9.

Answer: 13c + 9; yes, equivalent

Now you trySame steps, your turn

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

Are 2x + 3x and 5x equivalent? Test x = 2. Then explain why they always match.

Answer:

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 out!A common mistake

A common mistake in Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms

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.

Why This Matters This is your challenge small group for Lesson 6.6. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help