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

Lesson 6.66.6 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can show that two expressions are equivalent by simplifying and combining like terms — one step at a time, with support.

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 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target With my small group, I can show that two expressions are equivalent by simplifying and combining like terms — one step at a time, with support.

Part 1Understand the ideamodels and meaning
  1. 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

    Hint Find the terms that have x. Combine only those. The plain number stays alone.

    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    x4x + 2x + 56x + 5
    3??
    Substitute x = 3 into both expressions.

    Are 4x + 2x + 5 and 6x + 5 equivalent? Test x = 3.

    1. 1Substitute x = 3 into 4x + 2x + 5. What do you get?
    2. 2Substitute x = 3 into 6x + 5. What do you get?
    3. 3Combine the like terms 4x and 2x.
    Final answer:
  2. 3Complete each step, then write the final answer.
    x3x + 4 + 2x + 15x + 5
    2??
    Substitute x = 2 into both expressions.

    Are 3x + 4 + 2x + 1 and 5x + 5 equivalent? Test x = 2.

    1. 1Group the like terms: the x terms and the plain numbers.
    2. 2Combine the x terms: 3x + 2x = ☐x. What number goes in the box?
    3. 3Combine 4 + 1. What do you get?
    4. 4Test x = 2 in both expressions. What value do both give?
    Final answer:
  3. 4Complete each step, then write the final answer.

    Fill in the box so the expressions are equivalent: 5x + 4x + 3 and ☐x + 3. What number goes in the box?

    Show your work

    Hint Combine the like terms 5x and 4x. The 3 stays the same.

    Final answer:
  4. 5Complete each step, then write the final answer.

    Simplify 6x + 9 + 3x. Then find its value when x = 4.

    Show your work

    Hint Combine 6x and 3x first. Then put 4 in for x.

    Final answer:
  5. 6Complete each step, then write the final answer.

    Producer A charges 2x + 3x + 12 dollars for x beats. Producer B charges 5x + 12 dollars. How much does each producer charge for 6 beats?

    Show your work

    Hint Put 6 in for x in each expression. Do the products first.

    Final answer:

Explain your thinkingTim tests one value, and both expressions match. Is that enough? How else can you show two expressions are equivalent?

Sentence starter I can combine like terms to show ___. · When x = ___, both expressions give ___, so ___.

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