Lesson 3
Measuring with DifferentSized Units
3.1: Width of a Paper (5 minutes)
Warmup
Students begin by thinking about length in terms of nonstandard units—9cm and 6cm 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 endtoend 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 9cm and 6cm 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
Student responses to this activity are available at one of our IM Certified Partners
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.
Supports accessibility for: Language; Socialemotional skills
Design Principle(s): Support sensemaking; 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.