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.

Why This Matters This is your challenge small group for Lesson 6.15. 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
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 out!A common mistake

A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms

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.

Why This Matters This is your challenge small group for Lesson 6.15. 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.

  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.

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