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

Lesson 6.15Simplify Algebraic Expressions

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

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

WordWhat it meansExample
Like TermsSpanish: Términos semejantes Terms with the same variable raised to the same exponent, like 2x and 5x. 5x and 3x are like terms (both x); 5x and 5y are NOT (different variables); 2x and 2x² are NOT (different powers)
CombineSpanish: Combinar To add or subtract terms with the same variable and exponent into one. 8m + 3m = 11m — add the coefficients (8 + 3 = 11) and keep the variable (m)
SimplifySpanish: Simplificar To rewrite an expression in a shorter form that is still equal to the original. 2a + 5a + 3 simplifies to 7a + 3 — the two a-terms combine, the constant stays
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. In 9x, the coefficient is 9 — it tells you 'nine groups of x'; if x = 2, then 9x = 18
TermSpanish: Término A single number, variable, or product of them, separated by + or − signs. In 3x + 5 − 2x, the terms are 3x, 5, and 2x.
Distributive propertySpanish: Propiedad distributiva Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac. 3(x + 4) = 3·x + 3·4 = 3x + 12.

How it worksWorked example

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

The rooms need microphones and stands: (4 + 2 + 6) microphones and (3 + 5 + 1) stands.

  1. Microphones are like items, so I add: 4 + 2 + 6 = 12 microphones.
  2. Stands are like items, so I add: 3 + 5 + 1 = 9 stands.
  3. In algebra this is the same as 4m + 2m + 6m + 3s + 5s + 1s = 12m + 9s.

Now you trySame steps, your turn

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

Let's simplify 5x + 3x. Are these like terms?

Answer:

Say it and write itSentence starters

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

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

Word bank Like TermsCombineSimplifyCoefficientTermDistributive propertyvariablelike termscoefficientcombinesame variabledifferent

Watch outA common mistake

A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms — for example, simplifying 6x + 4 + 2x as 12x by adding all three numbers (6 + 4 + 2 = 12) instead of recognizing that 4 has no variable and cannot combine with 6x and 2x. The correct simplified expression is 8x + 4 (combine 6x + 2x = 8x, and let the 4 stay on its own). Before you submit, check that every term you combined has the exact same variable part.

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

Lesson 6.15Simplify Algebraic Expressions

Version ASupported practice

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

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

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

    Sort each pair of terms by whether they are like terms (can be combined) or not.

    Groups: Like Terms Not Like Terms
    • 4m and 7m
    • 3x and 3y
    • 5n and n
    • 8 and 2p
    • 6a and 9a
    • 2x² and 2x

    Hint Like terms match in BOTH the variable letter and its exponent. Plain numbers only pair with plain numbers.

Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Simplify 7x + 3x.

    1. A10x
    2. B10x²
    3. C21x
    4. D73x

    Hint 7x and 3x have the same variable x, so they're like terms and can combine.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Simplify 9n + 4 + 2n.

    1. A11n + 4
    2. B11n² + 4
    3. C15n
    4. D92n + 4

    Hint There are two n-terms (9n and 2n) and one lonely constant (4) with no partner.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Which pair are like terms?

    1. A6x and 2x
    2. B6x and 6y
    3. C6x and 6
    4. D6x and 2x²

    Hint Like terms need the exact same variable raised to the exact same power.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Simplify 5a + 3 + 2a.

    1. A7a + 3
    2. B7a² + 3
    3. C10a
    4. D52a + 3

    Hint Spot the like terms: 5a and 2a share the variable a. The 3 has no variable.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Mistake — Exponent Slip

    1. 1Expression4x + 3x
    2. 2CombineAdd the coefficients: 4 + 3 = 7
    3. 3Simplify7x²

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint When you add like terms, does the little exponent on x change?

    Correct work
    Correct answer:

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 ___.

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

Version BCore practice

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

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

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Simplify each expression by combining like terms.

    ExpressionLike Terms CombinedSimplified
    3a + 5a + 23a + 5a = 8a
    6x + 4 + 2x + 7
    10m − 3m + 5
    4y + 3 + y + 9
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each expression to its simplified form.

    1. 8x + 3x + 1
    2. 5a − 2a + 7
    3. 4n + n + 6
    4. 12y − 5y
    5. 3m + 8 + 4m + 2
    6. 9p + 1 − 3p
    • A11x + 1
    • B3a + 7
    • C5n + 6
    • D7y
    • E7m + 10
    • F6p + 1
  3. 3Write the name of the correct group on each line.

    Simplify each expression, then sort by whether the simplified coefficient of the variable is greater than 6 or not.

    Groups: Coefficient > 6 Coefficient ≤ 6
    • 4x + 5x
    • 8n − 3n
    • 3a + a + 4a
    • 10m − 7m
    • 2y + 5y
    • 6p − p
  4. 4Decide whether each pair balances. Check Yes or No, then explain.

    Both simplify to 7x + 2 — they are equivalent.

    Left sideRight sideBalanced?
    Explain your choice
Part 2Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Mistake — Swept-Up Constant

    1. 1Expression6x + 4 + 2x
    2. 2CombineAdd everything: 6 + 4 + 2 = 12
    3. 3Simplify12x

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

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

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

ChallengeExtension

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

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

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Simplify each multi-variable expression. Only combine like terms (same variable).

    ExpressionSimplified
    3x + 2y + 5x + y
    7a + 4b − 2a + b
    6m + 3 + 2m + n + 1
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Simplification Error

    1. 1Expression5x + 3 + 2y + 4x
    2. 2Combine5x + 2y + 4x + 3
    3. 3Simplify11xy + 3

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    Three students simplified 4x + 3 + 2x + 5 + x differently. Student A got 7x + 8. Student B got 7x² + 8. Student C got 6x + 9. Who is correct? Explain the mistakes the other two students made.

    Write your answer

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

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