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

Lesson 6.5Write and Evaluate Algebraic Expressions

Set B · Version ASecond form · supported practice

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

Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.

Why This Matters Evelyn is helping to plan the sixth-grade field day. The committee will order the items shown for each student participating in field day. They do not yet know how many students will be participating. The shipping cost for all items is a one-time cost of $23.50. What expression can Evelyn use to determine how much the committee will need to purchase the items?

RememberWrite and Evaluate Algebraic Expressions

Writing & Evaluating Algebraic Expressions An algebraic expression uses numbers, a variable (a letter for an unknown number), and operations. We read a word phrase and write it with math symbols.

  1. Define the variable to represent the unknown quantity.
  2. Translate mathematical phrases into operations, coefficients, and constants.
  3. Evaluate by substituting given numerical values for the variable

Words: Variable (Variable)Algebraic Expression (Expresión algebraica)Coefficient (Coeficiente)Constant (Constante)Like terms (Términos semejantes)

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

    A square room has sides of 7 feet. Which expression gives its area, and what is the value?

    1. A2⁷ = 128
    2. B7² = 49
    3. C7 × 2 = 14
    4. D7 + 7 = 14
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A music studio charges a $25 setup fee plus $8 per hour of recording time. Let h represent the number of hours. Which expression models the total cost for h hours?

    1. A8 + 25h
    2. B25 + 8h
    3. C25h + 8h
    4. D33h
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    In the expression 4 + 6 ÷ 2, which operation do you do first?

    1. AAdd 4 and 6
    2. BDivide 6 by 2
    3. CEither order gives the same answer
    4. DSubtract
    26
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.
  2. 4Circle the letter of the best answer. Show how you know.

    Evaluate: 5 + 3 × 2²

    1. A17
    2. B26
    3. C32
    4. D64
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  3. 5Circle the letter of the best answer. Show how you know.

    Evaluate: (8 − 3)² ÷ 5

    1. A1
    2. B2.6
    3. C5
    4. D45
    Rewrite the whole expression each lineWhat I simplified
    1. 1GroupingInside ( ) first.
    2. 2ExponentsThen powers.
    3. 3× ÷Left to right.
    4. 4+ −Left to right.
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Phrasethe product of a number n and 4
    2. 2Student's expressionn + 4
    3. 3ReasoningI saw two numbers and a variable, so I added them together.

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

    Hint Which operation does the key word 'product' name?

    Correct work
    Correct answer:

Explain your thinkingWhat key words helped you decide which operation to use? How can the same phrase be written differently?

Sentence starter The phrase '___ ' tells me to use ___ because the key word ___ means ___.

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.6a

Lesson 6.5Write and Evaluate Algebraic Expressions

Set B · Version BSecond form · core practice

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

Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.

Why This Matters Evelyn is helping to plan the sixth-grade field day. The committee will order the items shown for each student participating in field day. They do not yet know how many students will be participating. The shipping cost for all items is a one-time cost of $23.50. What expression can Evelyn use to determine how much the committee will need to purchase the items?

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

    Line 1: A lyric says '7 more than a number of beats n.' Which expression matches?

    1. An + 7
    2. B7n
    3. Cn − 7
    4. D7 − n
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Line 2: The chorus says '5 less than a number of tracks x.' Which expression matches?

    1. Ax − 5
    2. B5 − x
    3. C5x
    4. Dx + 5
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    Line 3: A verse says 'twice a number of speakers' (use s). Which expression matches?

    1. A2s
    2. Bs + 2
    3. Cs − 2
    4. Ds ÷ 2
    Show your work
  4. 4Write the name of the correct group on each line.

    Sort each studio lyric by the operation its key word names.

    Groups: Addition Subtraction Multiplication Division
    • the sum of a number of mics m and 9
    • a number of riffs r increased by 6
    • 4 less than a number of solos j
    • a number of takes k decreased by 8
    • the product of 5 and a number of loops g
    • a number of verses v divided by 3
Part 2Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    A music studio charges a $25 setup fee plus $8 per hour of recording time. Let h represent the number of hours. What is the total cost for 6 hours?

    1. A$33
    2. B$48
    3. C$73
    4. D$198
    per 1
  2. 6Circle the letter of the best answer. Show how you know.

    A music studio charges a $25 setup fee plus $8 per hour of recording time. Let h represent the number of hours. In 25 + 8h, what is the coefficient?

    1. A25
    2. B8
    3. Ch
    4. D25h
    Show your work

Explain your thinkingWhat key words helped you decide which operation to use? How can the same phrase be written differently?

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