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

Lesson 6.156.15 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can simplify algebraic expressions by 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
Like TermsSpanish: Términos semejantes Terms with the same letter raised to the same power, 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 letter 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.

Simplify 9a + 6 − 4a + a − 2.

  1. Mark each term with the sign in front: +9a, +6, −4a, +a, −2
  2. Write the lone a as 1a: a → 1a
  3. Combine the a terms: 9 − 4 + 1 = 6 → 6a
  4. Combine the constants: 6 − 2 = 4
  5. The simplified expression is 6a + 4.

Now you trySame steps, your turn

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

Simplify 5x + 3x. Then explain a common mistake.

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 6.156.15 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can simplify algebraic expressions by combining like terms, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    m termsConstants
    ??
    ??
    Each term keeps the sign in front of it.

    Simplify 7m + 8 − 3m + m − 5.

    1. 1Write each term with the sign in front of it.
    2. 2Combine the m terms. Remember that m means 1m.
    3. 3Combine the constants.
    Final answer:
  2. 2Complete each step, then write the final answer.
    x termsConstants
    6x, −x9, −4
    ??
    This time a lone x is subtracted.

    Simplify 6x + 9 − x − 4.

    1. 1What is the coefficient of the term −x?
    2. 2Combine the x terms. Then combine the constants.
    3. 3Why is 6x − x equal to 5x, and not 6?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Simplify 8r − 3r + 2r. What is the coefficient of r in your answer?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Simplify 5h + 7 − 2h − 7. What is the constant in your answer?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Jen has 6 packs of x pencils. She gives away 2 packs, then buys 5 more packs: 6x − 2x + 5x. How many packs does she have now?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Kim simplifies 9p − 4 + 2p and gets 7p − 4. What is the correct coefficient of p?

    Show your work
    Final answer:

Explain your thinkingKim gave a minus sign to the wrong term. How do you decide which term a minus sign belongs to?

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