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

Lesson 6.156.15 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can simplify algebraic expressions by 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
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.

Three rooms need microphones and stands. They need (4 + 2 + 6) microphones and (3 + 5 + 1) stands. How many of each do they need?

  1. Add the microphones: 4 + 2 + 6 = 12
  2. Add the stands: 3 + 5 + 1 = 9
  3. They need 12 microphones and 9 stands.
  4. Let m stand for microphones and s stand for stands. Simplify 4m + 2m + 6m + 3s + 5s + 1s.
  5. Group the like terms: (4m + 2m + 6m) + (3s + 5s + 1s)
  6. Add the coefficients of the m terms: 4 + 2 + 6 = 12 → 12m
  7. Add the coefficients of the s terms: 3 + 5 + 1 = 9 → 9s
  8. The simplified expression is 12m + 9s.

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.

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 1

Group 1Supported practice

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

Learning target With my small group, I can simplify algebraic expressions by combining like terms — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    p termsn terms
    ??
    ??
    Sort the terms by variable. Then add each column.

    A class orders pens (p) and notebooks (n). The order is 3p + 2n + 4p + 6n. Simplify the expression.

    1. 1Sort the terms. Which terms are like terms?
    2. 2Add the coefficients of the p terms. How many p's?
    3. 3Add the coefficients of the n terms. How many n's?
    Final answer:
  2. 2Complete each step, then write the final answer.
    y termsConstants
    ??
    ??
    Constants have no variable. They go in their own column.

    Simplify 4y + 7 + 3y + 1. This time there are constants.

    1. 1Which terms are like terms? Which are constants?
    2. 2Combine the y terms.
    3. 3Combine the constants.
    Final answer:
  3. 3Complete each step, then write the final answer.

    Simplify 6n + 3n. How many n's do you have?

    Show your work

    Hint Both terms have n, so add the coefficients.

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

    Simplify 5x + 4 + 2x + 6. What is the coefficient of x in your answer?

    Show your work

    Hint Add only the x terms: 5x + 2x. The constants make their own total.

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

    Three rooms need drums (d) and chairs (c). The order is 3d + 4c + 5d + 2c + 2d + 7c. Simplify. How many chairs do the rooms need?

    Show your work

    Hint Add only the c terms. Chairs are not like drums.

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

    Zoe says 3x + 4 + 5x = 12x. Is she right? Simplify 3x + 4 + 5x. What is the coefficient of x?

    Show your work

    Hint Is 4 a like term with 3x and 5x? A constant has no variable.

    Final answer:

Explain your thinkingZoe added the 4 to the x terms. Why can 4 not combine with 3x or 5x?

Sentence starter 4 is a ___, so it ___. · 3x and 5x are like terms because ___.

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