unit 4, lesson 9: how much in each group? (part...

Unit 4, Lesson 9: How Much in Each Group? (Part 2)

9.1: Number Talk: Greater Than 1 or Less Than 1? (5 minutes)

Setup: Display one problem at a time. 30 seconds of quiet think time, followed by a whole-group discussion.

Lesson GoalsReason about the amount in one group in various division contexts.

Required Materialstools for creating a visual displaygeometry toolkits

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GRADE 6 MATHEMATICS

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Unit 4: Dividing Fractions, Lesson 9: How Much in Each Group? (Part 2) 1

Student task statementDecide whether each of the following is greater than 1 or less than 1.

1.

2.

3.

4.

Possible responses

1. Greater than 1

2. Greater than 1

3. Less than 1

4. Greater than 1

Anticipated misconceptions

If students have trouble getting started,remind them that, in a previous lesson,one way they interpreted was

as “how many s are in 4?” Ask them if

that interpretation could apply here.Also encourage students to recall howthe size of the divisor affects thequotient.

Some students may struggle with thelast expression because they don’teasily see the relationship betweenfifths and eighths. Ask if they can thinkof a fraction, in eighths, that is close to

, or a fraction in fifths that is close to

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. If not, ask them how they would

reason about the expression if it wasinstead of .

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9.2: Two Water Containers (15 minutes)

Setup:

Students in groups of 3–4. Show the short video and discuss students' questions. 4–5 minutes of quiet work time, followed by 2 minutesof group discussion.

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Student task statement

1. After looking at these pictures, Lin says, “I see the fraction .” Jada says, “I see the fraction .” What

quantities are Lin and Jada referring to?

2. How many liters of water fit in the water dispenser?

Write a multiplication equation and a division equation for the question, then find the answer. Draw adiagram, if needed. Check your answer using the multiplication equation.

Possible responses

1. Lin is seeing that of the water

dispenser is filled. Jada is seeingthat the amount of water is liters.

2. Multiplication: (or

). Division: (or

).

3. (or ) liters. Check:

Anticipated misconceptions

For the second question, students maynot immediately see that, to answer thequestion “how many liters of water fit inthe dispenser?” they need to relate theamount in liter (as shown in themeasuring cup) to the fraction of thedispenser that is filled with water.Suggest that they think about theproblem in terms of equal-sized groupsand try to identify the groups, numberof groups, etc.

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9.3: Amount in One Group (15 minutes)

Setup:

Students in groups of 2. Each group chooses an even-numbered problem and an odd-numbered one. Access to geometry toolkits andtools for creating a visual display. 7–8 minutes of quiet time, a few minutes of partner discussion and collaboration on creating a visualdisplay.

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Student task statementWrite a multiplication equation and a division equation and draw a diagram to represent each situation andquestion. Then find the answer. Explain your reasoning.

1. Jada bought yards of fabric for $21. How much did each yard cost?

2. kilogram of baking soda costs $2. How much does 1 kilogram of baking soda cost?

3. Diego can fill bottles with 3 liters of water. How many liters of water fill 1 bottle?

4. gallons of water fill of a bucket. How many gallons of water fill the entire bucket?

Possible responses

1. Multiplication equation:, division

equation: (or

). Each yard costs $6.

2. Multiplication equation: ,

division equation: (or

). Each kilogram of baking

soda costs $4.50.



). (or ) liters fill 1

bottle.



). gallons fill the entire

bucket.

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Are you ready for more?The largest sandwich ever made weighed 5,440 pounds. If everyone on Earth shares the sandwich equally, howmuch would you get? What fraction of a regular sandwich does this represent?

Possible Responses

Answers vary. Sample response: Eachperson would get pound. This

amount is of a regular

sandwich. There are approximately7,347,000,000 people on Earth, so oneserving of the sandwich would be thetotal weight of 5,440 pounds divided bythe number of servings:

. If a regular

sandwich weighs approximately a halfpound, then one serving of the largestsandwich would be (or

) of a regular sandwich.

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9.4: Inventing a Situation (Optional, 15 minutes)

Setup:

Students in groups of 4. Access to tools for creating a visual display. 4–5 minutes of quiet think time, a few minutes to exchange feedback,and then time to complete the rest of the task.

Lesson Synthesis (5 minutes)How can we represent and reason questions such as: How long is a whole trip if of a trip is mile? How might we set up a tape

diagram to find the answer? Sometimes it is not always obvious whether a division situation involves finding the number of groups or thesize of 1 group, so we need to analyze the situation carefully to reason correctly.

Student task statement1. Think of a situation that involves a question that can be represented by Write a description of

that situation and the question.

2. Trade descriptions with a member of your group.

Review each other’s description and discuss whether each invented question is an appropriatematch for the equation.

Revise your description or question based on feedback from your partner.

3. Find the answer to your question. Explain or show your reasoning. If you get stuck, draw a diagram.

Possible responses

1. Answers vary. Possible answer: Linpoured liters of water into a

bottle and it filled of the bottle.

2. No answer is required.

3. , so liters. See lesson

plan for diagram.

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9.5: Refilling a Soap Dispenser (Cool-down, 5 minutes)

Setup: None.

Student task statementNoah fills a soap dispenser from a big bottle that contains liters of liquid soap. That amount of soap will fill

dispensers. How many liters of soap fit into one dispenser?

Use the diagram below to answer the question. Label all relevant parts of the diagram.

Possible responses

He can refill the dispenser or

times. See lesson plan for diagram.

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unit 4, lesson 9: how much in each group? (part...

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