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

Lesson 6.4Write and Evaluate Numerical Expressions with Exponents

Set B · Version ASecond form · supported practice

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

Learning target I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.

Why This Matters The studio's booking sheet lists a price for each kind of seat. Writing one numerical expression for the whole order — and evaluating it in the right order — is faster and easier to check than adding costs one at a time. Some counts are written as powers, so the exponent has to be handled before any multiplying. The booking sheet lists a $150 base fee plus $12 for each speaker rented. Write one expression for the cost of renting 5 speakers.

RememberWrite and Evaluate Numerical Expressions with Exponents

Order of Operations (PEMDAS) A numerical expression is a math phrase made of numbers and operations, with no equal sign. Writing one for a whole situation keeps every part visible; evaluating it means finding its single value, following the order of operations.

  1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer.
  2. Exponents: Evaluate all powers.
  3. Multiply & Divide left to right; Add & Subtract left to right

Words: Numerical expression (Expresión numérica)Evaluate (Evaluar)Order of operations (Orden de las operaciones)Power (Potencia)Base (Base)

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

    Which expression shows 5³ as repeated multiplication?

    1. A3 × 3 × 3 × 3 × 3
    2. B5 × 5 × 5
    3. C5 × 3
    4. D5 + 5 + 5
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A rideshare app charges $2.50 plus $1.75 per mile. The expression for the fare is 2.50 + 1.75m, where m is miles traveled. Your friend lives 8 miles away. What does the 2.50 represent?

    1. AThe cost of one mile
    2. BA flat base fee charged no matter how far you go
    3. CThe number of miles
    4. DThe tip
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    What is the value of 6²?

    1. A8
    2. B12
    3. C36
    4. D62
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    What is the value of 4³?

    1. A7
    2. B12
    3. C43
    4. D64
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    In 2⁵, which number is the base and which is the exponent?

    1. ABase 2, exponent 5
    2. BBase 2, exponent 2
    3. CBase 5, exponent 2
    4. DBase 5, exponent 5
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A rideshare app charges $2.50 plus $1.75 per mile. The expression for the fare is 2.50 + 1.75m, where m is miles traveled. Your friend lives 8 miles away. What is 2.50 + 1.75(8)?

    1. A4.25
    2. B14.00
    3. C16.50
    4. D34.00
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?

Explain your thinkingTwo students evaluate 3 + 4 × 2 and get 14 and 11. Which one followed the order of operations, and why does the order have to be agreed on at all?

Sentence starter The correct value is ___ because ___ comes before ___. Without an agreed order, the same expression would have ___ values.

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.6c

Lesson 6.4Write and Evaluate Numerical Expressions with Exponents

Set B · Version BSecond form · core practice

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

Learning target I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.

Why This Matters The studio's booking sheet lists a price for each kind of seat. Writing one numerical expression for the whole order — and evaluating it in the right order — is faster and easier to check than adding costs one at a time. Some counts are written as powers, so the exponent has to be handled before any multiplying. The booking sheet lists a $150 base fee plus $12 for each speaker rented. Write one expression for the cost of renting 5 speakers.

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

    A rideshare app charges $2.50 plus $1.75 per mile. The expression for the fare is 2.50 + 1.75m, where m is miles traveled. Your friend lives 8 miles away. What does the 1.75 represent?

    1. AThe base fee
    2. BThe total cost
    3. CThe number of miles
    4. DThe cost per mile, multiplied by the number of miles
    Show your work
  2. 2Write the name of the correct group on each line.

    Sort each expression by which operation you do FIRST.

    Groups: Do the power first Do the parentheses first Do the multiplication first
    • 5 + 2³
    • (5 + 2) × 3
    • 5 + 2 × 3
    • 10 − 3²
    • (10 − 3) × 2
    • 10 − 3 × 2
  3. 3Write the letter of the matching item on each line.

    Match each power to its value.

    1. 2³
    2. 3²
    3. 5²
    4. 10³
    • A8
    • B9
    • C25
    • D1,000
Part 2Practice the skillshow every step
  1. 4Circle the letter of the best answer. Show how you know.

    Evaluate 6 + 2 × 5.

    1. A13
    2. B16
    3. C30
    4. D40
    Show each partial product, then add them
Part 3Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    Evaluate 4².

    1. A6
    2. B8
    3. C16
    4. D44
    Rewrite the whole expression each lineWhat I simplified
  2. 6Circle the letter of the best answer. Show how you know.

    Which numerical expression includes an operation and has no variable or equal sign?

    1. Ax + 5
    2. B8 × 3 + 2
    3. C8 × 3 = 24
    4. D24
    Show your work

Explain your thinkingTwo students evaluate 3 + 4 × 2 and get 14 and 11. Which one followed the order of operations, and why does the order have to be agreed on at all?

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