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

Lesson 6.4Order of Operations with Powers

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 × 20 is an expression; 4 × 20 = 80 is an equation
EvaluateSpanish: Evaluar To find the single value an expression is worth by carrying out its operations in order. 3 × 4 = 12
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. grouping, powers, × ÷, + −
PowerSpanish: Potencia A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2. 2^2 = 2 × 2
BaseSpanish: Base In a power, the number being multiplied by itself. In 2³ the base is 2. 2³ — the 2 is the base
ExponentSpanish: Exponente In a power, the small raised number that says how many times the base is used as a factor. 2³ — the 3 is the exponent

How it worksWorked exampleevaluating with grouping and a power

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

Find the value of 4 + 3 × (9 − 7)^2.

  1. Grouping first. (9 − 7) = 2, so now 4 + 3 × 2^2
  2. Powers next. 2^2 = 4, so now 4 + 3 × 4
  3. Multiply and divide, left to right. 3 × 4 = 12, so now 4 + 12
  4. Add and subtract, left to right. 4 + 12 = 16

Answer: The value of the expression is 16.

Now you trySame steps, your turn

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

Find the value of 30 ÷ (11 − 6) + 2^3.

  1. Grouping first. (11 − 6) = Rewrite: 30 ÷ + 2^3
  2. Powers next. 2^3 = Rewrite: ÷ +
  3. Multiply and divide, left to right. ÷ =
  4. Add and subtract, left to right. + =
Answer:value of the expression

Say it and write itSentence starters

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

  • I did first because .
  • After evaluating the power, the expression became .
  • Multiply and divide happen , not multiplication first.
  • The value of the whole expression is .

Word bank order of operationsgrouping symbolsparenthesesexponentpowerevaluatemultiplydivideleft to rightvaluefirststep

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 6.4Order of Operations with Powers

Apply Day · 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.

  1. 1Complete each step, then write the final answer.

    Evaluate 3 + 2 × 4².

    Show your work

    Hint Find 4² first. Then multiply. Add last.

    Final answer:
  2. 2Complete each step, then write the final answer.

    There are 5 boxes with 2³ apples in each box. 6 apples are bad. Evaluate 5 × 2³ − 6 to find the good apples.

    Show your work

    Hint Find 2³ first. Then multiply by 5. Subtract last.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Evaluate 20 − 3² + 4 × 2.

    Show your work

    Hint Power first, then multiply. Then add and subtract from left to right.

    Final answer:
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 6.4Order of Operations with Powers

Apply Day · 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.

  1. 1Complete each step, then write the final answer.

    Kim evaluates 3 + 4 × 5². She adds 3 + 4 first and gets 175. Is she right? Find the correct value.

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Evaluate 50 − 2 × 3³ ÷ 6.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Evaluate 10 + 3 × 4².

    Show your work
    Final answer:
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 6.4Order of Operations with Powers

Apply Day · 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.

  1. 1Circle the letter of the best answer. Show how you know.

    Evaluate the numerical expression 3 × 4² − 8.

    1. A16
    2. B24
    3. C40
    4. D136
    Show each partial product, then add them
  2. 2Complete each step, then write the final answer.

    Jay says 4 × 3² is 144, because 4 × 3 = 12 and 12² = 144. Find the correct value of 4 × 3².

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Evaluate (18 − 2³) × 3 + 4².

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help