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

Lesson 6.116.11 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can solve real-world problems by writing and solving fraction division equations — 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
ModelSpanish: Modelo A picture or math way to show a problem so you can solve it. A bar model showing 3/4 split into 1/8-size pieces, or the equation 3/4 ÷ 1/8 = 6
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. 3/4 ÷ 1/8 = 6 — the left side (division) equals the right side (answer)
SolutionSpanish: Solución A number that makes the equation or inequality true. In 3/4 ÷ 1/8 = 6, the solution is 6 portions
ReasonablenessSpanish: Razonabilidad Checking if your answer makes sense. 3 ÷ 1/4 = 12. Is 12 reasonable? Yes, because 1/4 is small so many pieces fit into 3.
Inverse operationsSpanish: Operaciones inversas Two math actions that undo each other, like × and ÷. If 3/4 ÷ 1/8 = 6, then 6 × 1/8 = 6/8 = 3/4. Multiplication checks division.

How it worksWorked example

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

Agent Torres has 2/3 gallon of dust. Each test uses 1/6 gallon. How many tests can she run?

  1. Find the total. It is the dividend: 2/3 gallon
  2. Find the size of one test. It is the divisor: 1/6 gallon
  3. Write the equation and solve it: 2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4
  4. Check by multiplying back: 4 × 1/6 = 4/6 = 2/3
  5. She can run 4 tests.

Now you trySame steps, your turn

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

A ribbon is 3/4 yard long. Each bow uses 1/4 yard. How many bows can you make?

Answer:

Say it and write itSentence starters

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

  • The total amount is the because it is being split into groups. The size of each group is the because we are dividing by that amount.

Word bank ModelEquationSolutionReasonablenessInverse operationsdividenddivisortotalgroupsplitequation

Watch outA common mistake

A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup — how many servings? The correct setup is total ÷ group size = 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 servings. A student who reverses the setup calculates 1/8 ÷ 3/4 = 1/8 × 4/3 = 4/24 = 1/6, an answer smaller than 1 that can't possibly be a serving count. Before you submit, check: does my answer make sense as a NUMBER OF GROUPS? If the setup gives a fraction less than 1 for a 'how many' question, you likely swapped the dividend and divisor.

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

Lesson 6.116.11 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 solve real-world problems by writing and solving fraction division equations — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    25110
    How many tenths fit in 25?

    Agent Torres has 2/5 pound of clay. Each footprint cast uses 1/10 pound. How many casts can she make?

    1. 1What is the total? Is it the dividend or the divisor?
    2. 2Write the division equation: total ÷ size of one cast.
    3. 3Keep, change, flip: 2/5 × 10/1. How many casts?
    4. 4Check: what is 4 × 1/10? Is it the total?
    Final answer:
  2. 2Complete each step, then write the final answer.
    56512
    One snack bag holds 512 pound.

    A bag has 5/6 pound of trail mix. Each snack bag holds 5/12 pound. How many snack bags can you fill?

    1. 1Name the dividend and the divisor.
    2. 2Keep, change, flip. Write the multiplication.
    3. 3Multiply and simplify. How many snack bags?
    4. 4Check: what is 2 × 5/12?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A rope is 5/8 yard long. Each piece is 1/8 yard. How many pieces can you cut?

    Show your work

    Hint Write total ÷ size of one piece. Then keep, change, flip.

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

    Agent Torres has 3 pounds of plaster. Each cast uses 3/4 pound. How many casts can she make?

    Show your work

    Hint The total is 3 pounds. Divide it by the size of one cast.

    Final answer:
  5. 5Complete each step, then write the final answer.

    One batch of granola uses 2/3 cup of oats. Ana has 3 1/3 cups of oats. How many batches can she make?

    Show your work

    Hint Write 3 1/3 as a fraction first. Then divide by 2/3.

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

    Leo has 1/2 pound of beads. Each bracelet uses 1/12 pound. He writes 1/12 ÷ 1/2 and gets 1/6. How many bracelets can he really make?

    Show your work

    Hint Which amount is the total? The total is the dividend, so it goes first.

    Final answer:

Explain your thinkingHow do you decide which amount goes first in the division? Use Leo's bracelet mistake to explain.

Sentence starter The total is ___, so it is the dividend. · I check my answer by multiplying ___ by ___.

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