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

Lesson 6.116.11 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve real-world problems by writing and solving fraction division equations, explain what each part stands for, and build one for a situation I have not seen before.

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.

Mia used 3/4 cup of paint to cover 1/2 of a wall. How much paint does she need for the whole wall?

  1. Write the known ratio in the table: 1/2 wall → 3/4 cup
  2. Find the scale factor from 1/2 to 1: 1 ÷ 1/2 = 2
  3. Multiply the paint by 2 too: 3/4 × 2 = 6/4 = 11/2
  4. Check by multiplying back: 11/2 × 1/2 = 3/4
  5. She needs 11/2 cups of paint for the whole wall.

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 2

Group 2Challenge practice

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

Learning target I can solve real-world problems by writing and solving fraction division equations, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    Fence (part)131Paint (cups)23?× ?× ?
    13 of the fence uses 23 cup.

    Kim used 2/3 cup of paint to cover 1/3 of a fence. How much paint does she need for the whole fence?

    1. 1Write the known ratio. What part of the fence does 2/3 cup cover?
    2. 2What do you multiply 1/3 by to get 1 whole fence?
    3. 3Multiply the paint by 3 too. How many cups for the whole fence?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Tank (part)35151Water (gal)34??÷ ?÷ ?× ?× ?
    35 of the tank holds 34 gallon.

    3/4 gallon of water fills 3/5 of a fish tank. How many gallons fill the whole tank?

    1. 1Divide both by 3. How much water fills 1/5 of the tank?
    2. 2What do you multiply 1/5 by to get 1 whole tank?
    3. 3Multiply 1/4 gallon by 5 too. How many gallons fill the tank?
    4. 4Why is the answer greater than 3/4 gallon?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A jar holds 9/10 pound of dust. Each test uses 3/20 pound. How many tests can Agent Torres run?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Time (hr)141Distance (mi)58?× ?× ?
    She walks 58 mile in 14 hour.

    Agent Torres walks 5/8 mile in 1/4 hour. At this speed, how far does she walk in 1 hour?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Casts61Clay (lb)34?÷ ?÷ ?
    6 equal casts use 34 pound of clay.

    A 3/4-pound block of clay makes 6 equal casts. How much clay is in each cast?

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

    Max has 1 1/5 liters of juice. Each glass holds 2/5 liter. He multiplies and gets 12/25 glass. How many glasses can he really fill?

    Show your work
    Final answer:

Explain your thinkingKim's fence and Max's juice both use division. How do you decide which number is the dividend each time?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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