Lesson 14

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).

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.

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.

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.

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.