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

Lesson 6.15Simplify Algebraic Expressions

Set B · Version ASecond form · supported practice

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

Learning target I can simplify algebraic expressions by combining like terms.

Why This Matters The music studio is placing supply orders for three rehearsal rooms. Room A needs 4 microphones and 3 stands. Room B needs 2 microphones and 5 stands. Room C needs 6 microphones and 1 stand. Instead of ordering separately, you can combine: (4 + 2 + 6) microphones and (3 + 5 + 1) stands = 12 microphones and 9 stands. That's simplifying by combining like items!

RememberSimplify Algebraic Expressions

Combining Like Terms Like terms are terms with the same variable raised to the same exponent, like 2x and 5x. To simplify an expression, you add or subtract the like terms to make it shorter.

  1. Like Terms: Terms that share the exact same variable part and exponent (e.g. 4x and 2x).
  2. Add or subtract the coefficients of like terms; keep the variable unchanged.
  3. Constants (numbers without variables) combine together separately

Words: Like Terms (Términos semejantes)Combine (Combinar)Simplify (Simplificar)Coefficient (Coeficiente)Term (Término)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    A music festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2). What does the 15m tell the festival?

    1. A15 cables are needed for every microphone
    2. BThere are 15 microphones
    3. C15 stages need cables
    4. DThe cables cost $15
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Expand 5(x + 3).

    1. A5x + 15
    2. B5x + 3
    3. C8x
    4. Dx + 15
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Which shows 6n + 18 factored using its GREATEST common factor?

    1. A2(3n + 9)
    2. B3(2n + 6)
    3. C6(n + 3)
    4. D6(n + 18)
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Expand 4(2y − 5).

    1. A2y − 20
    2. B6y − 20
    3. C8y − 20
    4. D8y − 5
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Use the distributive property to compute 7 × 62 mentally: 7 × (60 + 2) = ?

    1. A62
    2. B420
    3. C427
    4. D434
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  5. 6Circle the letter of the best answer. Show how you know.

    A music festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2). Simplify (8m + 5) + (3m + 7) + (4m + 2).

    1. A12m + 17
    2. B15m + 14
    3. C15m + 15
    4. D29m
    Show your work

Explain your thinkingWhat rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?

Sentence starter Two terms are like terms when they have the same ___. You cannot combine ___ and ___ because they represent different ___.

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

Lesson 6.15Simplify Algebraic Expressions

Set B · Version BSecond form · core practice

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

Learning target I can simplify algebraic expressions by combining like terms.

Why This Matters The music studio is placing supply orders for three rehearsal rooms. Room A needs 4 microphones and 3 stands. Room B needs 2 microphones and 5 stands. Room C needs 6 microphones and 1 stand. Instead of ordering separately, you can combine: (4 + 2 + 6) microphones and (3 + 5 + 1) stands = 12 microphones and 9 stands. That's simplifying by combining like items!

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    The terms are scattered across the mixing board. Sort each term into its like-term group so you know what can be combined.

    Groups: x-terms (have the variable x) Constants (just numbers)
    • 3x
    • 5x
    • 2x
    • 7
    • 4
    • 9
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A music festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2). If each stage has 4 microphones (m = 4), how many cables in total?

    1. A29
    2. B60
    3. C64
    4. D74
    per 1
  2. 3Circle the letter of the best answer. Show how you know.

    The board shows 3x + 5x on one channel. Simplify it.

    1. A8x
    2. B8x²
    3. C15x
    4. D35x
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Simplify the track: 4a + 2 + a.

    1. A5a + 2
    2. B5a²+ 2
    3. C6a
    4. D7a
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Clean up this channel: 7y − 3y.

    1. A4y
    2. B4
    3. C10y
    4. D21y
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    Simplify the mix: 6m + 4 + 3m.

    1. A9m + 4
    2. B9m + 4m
    3. C10m
    4. D13m
    Show your work

Explain your thinkingWhat rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?

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