Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.96.9 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can divide a whole number by a fraction by multiplying by the reciprocal — one step at a time, with support.

Start hereWords for this lesson

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

WordWhat it meansExample
Whole NumberSpanish: Número entero A counting number with no fraction or decimal, like 0, 1, 2, 3. 4 is a whole number; as a fraction it is 4/1
FractionSpanish: Fracción A number that shows part of a whole, like 3/4. 1/2 means 1 out of 2 equal parts — like cutting a sandwich in half and taking one piece
ReciprocalSpanish: Recíproco A fraction turned upside down. The reciprocal of 2/3 is 3/2. Flip the fraction to divide: 6 ÷ 2/3 = 6 × 3/2
Keep, Change, FlipSpanish: Mantener, cambiar, invertir A way to divide fractions: keep the first, change ÷ to ×, flip the second. 6 ÷ 1/3 → Keep 6, Change ÷ to ×, Flip 1/3 to 3/1 → 6 × 3 = 18
QuotientSpanish: Cociente The answer when you divide. In 4 ÷ 1/2 = 8, the quotient is 8

How it worksWorked example

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

Agent Park has 4 pounds of powder. Each bag holds 1/2 pound. How many bags can he fill?

  1. Write the division: 4 ÷ 1/2
  2. Keep 4, change ÷ to ×, and flip 1/2: 4 ÷ 1/2 = 4 × 2/1
  3. Multiply: 4 × 2 = 8
  4. 4 ÷ 1/2 = 8. He can fill 8 bags.

Now you trySame steps, your turn

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

Find 3 ÷ 1/4. How many fourths fit in 3?

Answer:

Say it and write itSentence starters

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

  • 3 ÷ 1/4 = 12 because it takes jumps of to get from 0 to .

Word bank Whole NumberFractionReciprocalKeep, Change, FlipQuotient12fourthjumps3four timeseach whole

Watch outA common mistake

A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip' — students multiply by the divisor as it is instead of by its reciprocal. For example, for 6 ÷ 3/4, a student might write 6 × 3/4 = 4 1/2 and stop there, but the divisor 3/4 must be flipped to 4/3 first: 6 × 4/3 = 24/3 = 8. Before you submit, check: did I flip the second fraction (the divisor) upside down before multiplying?

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.96.9 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can divide a whole number by a fraction by multiplying by the reciprocal — one step at a time, with support.

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

    Find 6 ÷ 1/2.

    Show your work

    Hint Keep the 6, change ÷ to ×, and flip 1/2.

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

    Find 9 ÷ 3/4.

    Show your work

    Hint The reciprocal of 3/4 is 4/3. Multiply 9 by it.

    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.
    012312
    How many jumps of 12 fit in 3?

    Find 3 ÷ 1/2. How many halves fit in 3?

    1. 1Keep the 3. Change ÷ to ×. What is the reciprocal of 1/2?
    2. 2Multiply. What is 3 × 2?
    3. 3Does 6 make sense? How many halves are in 1 whole?
    Final answer:
  2. 4Complete each step, then write the final answer.
    0123425
    How many jumps of 25 fit in 4?

    Find 4 ÷ 2/5. How many 2/5-size pieces fit in 4?

    1. 1Keep the 4. Change ÷ to ×. What is the reciprocal of 2/5?
    2. 2Multiply the tops and the bottoms: 4 × 5/2.
    3. 3Simplify. How many pieces fit?
    Final answer:
  3. 5Complete each step, then write the final answer.

    Detective Park has 10 cups of flour. Each batch of cookies uses 2/3 cup. How many batches can he make?

    Show your work

    Hint Find 10 ÷ 2/3. Multiply by the reciprocal of 2/3.

    Final answer:
  4. 6Complete each step, then write the final answer.

    Leo wants 4 ÷ 1/6. He multiplies 4 × 1/6 and gets 4/6. Find the correct value of 4 ÷ 1/6.

    Show your work

    Hint Leo forgot to flip. What is the reciprocal of 1/6?

    Final answer:

Explain your thinkingWhy is 3 ÷ 1/2 greater than 3? Use the number line to explain.

Sentence starter Each whole has ___ halves, so ___. · Dividing by a fraction less than 1 gives ___ because ___.

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