Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.36.1–6.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 6.1–6.3 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 6.1–6.3: 6.1 Division Expressions with Fractions and Whole Numbers, 6.2 Division Expressions with Fractions and Mixed Numbers, 6.3 Explore Numerical Expressions with Exponents. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 3 ÷ 1/4 = 12, the dividend is 3 — it is the total being split
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 3 ÷ 1/4 = 12, the divisor is 1/4 — it is the size of each piece
QuotientSpanish: Cociente The answer when you divide. In 3 ÷ 1/4 = 12, the quotient is 12 — there are 12 quarter-size pieces in 3
ReciprocalSpanish: Recíproco A fraction turned upside down. The reciprocal of 1/4 is 4/1 = 4. Multiplying by the reciprocal gives the same result as dividing.
Unit fractionSpanish: Fracción unitaria A fraction with 1 on top, like 1/4. 1/2, 1/3, 1/4, 1/5 — each represents one equal part of a whole
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 8/12 → GCF is 4 → 8÷4 / 12÷4 = 2/3

How it worksWorked example

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

Write 9 × 9 × 9 × 9 as a power.

  1. The repeated factor is 9, so the base is 9.
  2. Count the 9s: there are four, so the exponent is 4.
  3. Check: the exponent counts factors, not × signs (there are only 3 × signs).

Answer: 9⁴; base 9, exponent 4

Now you trySame steps, your turn

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

Find 5 ÷ 1/2.

Answer:

Say it and write itSentence starters

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

  • In this power, the base is and the exponent is .
  • The exponent tells me to use the base as a factor times.
  • I read this power as to the power.
  • A power shows repeated , not repeated .

Word bank powerbaseexponentfactorrepeated multiplicationexpanded formsquaredcubedevaluateproductreadtimes

Watch out!A common mistake

A common mistake in Powers and Exponents is multiplying the base by the exponent instead of using the base as a repeated factor

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.36.1–6.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 6.1–6.3 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 6.1–6.3: 6.1 Division Expressions with Fractions and Whole Numbers, 6.2 Division Expressions with Fractions and Mixed Numbers, 6.3 Explore Numerical Expressions with Exponents. Work one example from each lesson, then prove you're caught up in the mixed practice.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 3 ÷ 1/5.

    Show your work

    Hint Put a 1 under the 3. Then keep, change, flip.

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

    Find 4/7 ÷ 3.

    Show your work

    Hint Write 3 as 3/1. Flip only the 3/1.

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

    Find 2/5 ÷ 1/10.

    Show your work

    Hint Keep 2/5. Change ÷ to ×. Flip 1/10.

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

    Find 1 1/2 ÷ 1/4.

    Show your work

    Hint Change 1 1/2 to an improper fraction first.

    Final answer:
Part 2Apply itreal-world problems
  1. 5Complete each step, then write the final answer.

    Find the value of 3².

    Show your work

    Hint Use 3 as a factor 2 times.

    Final answer:
  2. 6Complete each step, then write the final answer.

    Write 2 × 2 × 2 × 2 as a power. What is its value?

    Show your work

    Hint Count the factors of 2. That is the exponent. Then multiply.

    Final answer:

Explain your thinkingHow does the value change when you increase the exponent by 1? Why?

Sentence starter When the exponent increases by 1, the value is multiplied by ___ because the base is used as a factor ___ more time.

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