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

Lesson 6.4Write and Evaluate Numerical Expressions with Exponents

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Numerical expressionSpanish: Expresión numérica A math phrase built from numbers and operations, with no equal sign and no variable. 4 × 9 + 3 × 6
EvaluateSpanish: Evaluar To find the single value an expression is worth by carrying out its operations in order. 3 × 6 = 18
Order of operationsSpanish: Orden de las operaciones The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right. 3 + 4 × 2² → 3 + 4 × 4 → 3 + 16 = 19
PowerSpanish: Potencia A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2. 8 × 8 = 8^2
BaseSpanish: Base In a power, the number being multiplied by itself. In 2³ the base is 2. In 8^2, the base is 8.
ExponentSpanish: Exponente In a power, the small raised number that says how many times the base is used as a factor. In 8^2, the exponent is 2.

How it worksWorked examplewriting an expression from a situation

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A group buys 4 tickets at $9 each and 3 programs at $6 each. Write an expression for the total cost, then find it.

  1. Name the parts. tickets: 4 at $9 programs: 3 at $6
  2. Write a product for each part. 4 × 9 and 3 × 6
  3. Join them with the operation the story needs. 4 × 9 + 3 × 6
  4. Evaluate. 36 + 18 = 54

Answer: The expression is 4 × 9 + 3 × 6, and the total cost is $54.

Now you trySame steps, your turn

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

A team buys 7 shirts at $11 each and 2 hats at $8 each. Write an expression for the total cost, then find it.

  1. Name the parts. shirts: at $ hats: at $
  2. Write a product for each part. × and ×
  3. Join them with the right operation.
  4. Evaluate. + =
Answer:expression and total cost in dollars

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The word tells me to multiply by .
  • The expression for this situation is .
  • I used a power because the same factor repeats times.
  • An expression has no equal sign, so I only it.

Word bank numerical expressionevaluatepowerbaseexponentproductsumdifferenceeachin alloperationvalue

Watch outA common mistake

A common mistake with powers is multiplying the base by the exponent: reading 3² as 3 × 2 = 6 instead of 3 × 3 = 9. A second is evaluating strictly left to right, so 3 + 4 × 2 becomes 14 instead of 11. The order of operations exists so one expression has exactly one value: grouping symbols, then powers, then × and ÷ left to right, then + and − left to right.

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

Lesson 6.4Write and Evaluate Numerical Expressions with Exponents

Version ASupported 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.

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

    What does 2³ mean?

    1. A2 × 2 × 2
    2. B2 × 3
    3. C2 + 2 + 2
    4. D3 × 3

    Hint Which number is the base, and which is the exponent?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Sofia buys 4 tickets at $20 each and 2 tickets at $15 each. Which expression shows the total?

    1. A4 × 20 + 2 × 15
    2. B4 + 20 + 2 + 15
    3. C(4 + 2) × (20 + 15)
    4. D4 × 2 + 20 × 15

    Hint What does "each" tell you to do?

    Show your work
  3. 3Complete the table. Show how you found each value.

    Evaluate each expression, following the order of operations.

    ExpressionValue
    2 + 3 × 414
    10 − 2²
    (2 + 3) × 4

    Hint For 10 − 2²: evaluate 2² = 4 first.

    Show your work
Part 2Practice the skillshow every step
  1. 4Circle the letter of the best answer. Show how you know.

    Evaluate 3 + 4 × 2.

    1. A9
    2. B11
    3. C14
    4. D24

    Hint Which operation comes first in the order of operations?

    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
Part 3Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    Evaluate 5² + 3.

    1. A13
    2. B16
    3. C28
    4. D64

    Hint What must you evaluate first?

    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 4Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1ExpressionEvaluate 3 + 4 × 2²
    2. 2Step 13 + 4 = 7
    3. 3Step 27 × 2² = 7 × 4 = 28

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

    Hint Which stage comes first: adding or the power?

    Correct work
    Correct answer:

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.

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

Version BCore 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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Sofia buys 2 member tickets ($15), 4 non-member tickets ($20), and 8 student tickets (2³ dollars). Build the total.

    Ticket typeExpressionCost
    Member2 × 1530
    Non-member4 × 20
    Student8 × 2³
    Show your work
  2. 2Write the name of the correct group on each line.

    Sort each item into the stage of the order of operations where it is handled.

    Groups: Grouping symbols Exponents Multiply / divide Add / subtract
    • ( )
    • 2³
    • × and ÷ left to right
    • + and − left to right
    • [ ]
    • 5²
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    What is the total of 2 × 15 + 4 × 20 + 8 × 2³?

    1. A126
    2. B174
    3. C210
    4. D1,392
    Show each partial product, then add them
  2. 4Circle the letter of the best answer. Show how you know.

    Miguel evaluates 12 − 2 × 3 and gets 30. Margaret gets 6. Who is right?

    1. AMiguel, because he worked left to right
    2. BBoth are right
    3. CNeither is right
    4. DMargaret, because multiplication comes before subtraction
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1ExpressionEvaluate 20 − 3²
    2. 2Step 13² = 6
    3. 3Step 220 − 6 = 14

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

    Correct work
    Correct answer:

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?

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

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Evaluate each expression. Watch the stage each one tests.

    ExpressionValue
    (4 + 6) ÷ 25
    4 + 6 ÷ 2
    2 × 3²
    (2 × 3)²
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1ExpressionEvaluate 4 + 2 × (3 + 5)²
    2. 2Step 13 + 5 = 8
    3. 3Step 22 × 8 = 16
    4. 4Step 316² = 256, so 4 + 256 = 260

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

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    Seven friends split the bill for a pizza party. They order 4 pizzas at 3² dollars each, plus a one-time $6 delivery fee. Write ONE numerical expression for what each friend owes, evaluate it, and explain why the grouping symbols matter.

    Write your answer

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?

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