Lesson 3

Measuring with Different-Sized Units

3.1: Width of a Paper (5 minutes)

Warm-up

Students begin by thinking about length in terms of non-standard units—9-cm and 6-cm Cuisenaire rods—and consider how the size of units affects the number of units needed to express a length. If Cuisenaire rods are not available, modify the task to say: Does it take more large paper clips or small paper clips lined up end-to-end to measure the width of a piece of paper?

Some students may be able to reason that it takes more of the smaller unit than the larger unit to measure the same length; encourage them to articulate their reasoning. Others may need to visualize the situation by drawing or by measuring with actual rods (or paper clips).

Launch

This activity is written to use 9-cm and 6-cm Cuisenaire rods, which are often blue and dark green, respectively. If your set of Cuisenaire rods has different colors, or if using small and large paper clips as substitutes, instruct students to modify the task accordingly.

Hold up the two sizes of rods or paper clips for the students to see. Give them quiet think time but not the manipulatives. Later, allow students to use the rods or paper clips to measure the paper if they need or wish to do so.

Student Facing

Your teacher will show you two rods. Does it take more green rods or blue rods lined up end to end to measure the width of a piece of printer paper?

Student Response

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Anticipated Misconceptions

Some students may assume that it will take more of the longer rods because they are used to associating the idea of “more” with “larger.” Encourage them to use the manipulatives to see that it actually takes fewer of the longer rods to reach across the paper.

Activity Synthesis

Ask students to share their responses and reasoning. Highlight the fact that it takes more of a smaller unit and fewer of a larger unit to measure the same length.

3.2: Measurement Stations (35 minutes)

Activity

In groups, students rotate through five different stations, where they measure one or more quantities using different units, and answer a series of summary questions afterward. Here are the quantities being measured and the units used at each station:

  • Station 1: Volume of a box, in cubic inches and cubic centimeters.
  • Station 2: Length, in meters and feet.
  • Station 3: Volume of water, in gallons, quarts, and liters.
    (If desired, you can have students measure water with actual containers instead of watching the video https://vimeo.com/illustrativemathematics/water.)
  • Station 4: Weights and masses of 2–3 objects, in ounces, pounds, grams, and kilograms.
    (You can have students weigh actual objects, use the digital simulation http://ggbm.at/eQQVYB7D, or use the paper simulations from the blackline master. If using one of the simulations instead of a real scale, prepare some real objects labeled with their weight or mass for students to hold and feel the weight of.)
  • Station 5: Volume of salt, in milliliters and teaspoons.

You will need the blackline master for this activity. Page 1 is a net for the box needed for station 1. If you are using the paper scale simulation instead of a real scale or the applet, pages 2–13 are the parts needed to assemble Station 4.

Launch

Tell students they will further investigate the idea of using different units to measure the same set of items. Introduce the five stations, what students are expected to do at each, the protocol for rotating through them, and the questions to answer at the end. Then, demonstrate how to use the straightedge to measure a level teaspoon of salt. If students do not use a level teaspoons of salt, they will not be able to answer the last set of questions about volume.

Arrange students into 5 groups and assign a starting station for each group.

If students have devices, Stations 3 and 4 can be digital. 

Engagement: Develop Effort and Persistence. Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy. For example, “I noticed _____ so I think…”
Supports accessibility for: Language; Social-emotional skills
Speaking, Representing: MLR8 Discussion Supports. Use this routine to support small-group discussion. As students rotate through stations, encourage students to solidify their own understanding by pressing for details and questioning their peers' explanations. Provide sentence frames for students to use, such as "I agree/disagree because . . .”, "How do you know . . .”, and “Can you give an example?” This will help students clarify their reasoning about comparing different measurements for the same quantity using different units. 
Design Principle(s): Support sense-making; Cultivate conversation

Student Facing

Station 1

  • Each large cube is 1 cubic inch. Count how many cubic inches completely pack the box without gaps.
  • Each small cube is 1 cubic centimeter. Each rod is composed of 10 cubic centimeters. Count how many cubic centimeters completely fill the box.
  cubic inches cubic centimeters
volume of the box    

Station 2

Your teacher showed you a length.

  • Use the meter stick to measure the length to the nearest meter.
  • Use a ruler to measure the length to the nearest foot.
  meters feet
length of ________________    

Station 3

Watch the video.

  • Count how many times you can fill the quart bottle from the gallon jug.
  • Count how many times you can fill the liter bottle from the gallon jug.

  quarts liters
1 gallon of water    

Station 4

Use the applet to record the weights of different objects in different units.