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Measurement Session 10: Classroom Case Studies
 
Session 10 Session 10 6-8 Part A Part B Part C Homework
 
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Session 10, Part C:
Activities That Illustrate Measurement Reasoning (55 minutes)

In this part, you'll look at several short activities that are appropriate for students in grades K-2. As you read through the activities, answer the following questions:

 Questions to Answer:

a. 

What is the measurement content in the problem? What are the big ideas that you want students to consider and understand?

b. 

What prior knowledge is required? What later content does it prepare students for?

c. 

How does the content in this problem relate to the mathematical ideas in this course?

d. 

What other questions might extend students' thinking about the problem?

e. 

What other instructional activities or problems might you use in conjunction with this one to further your content goals?

Problem C1

Solution  

Exploring Capacity

Activity Summary
Students recognize situations that involve capacity and compare capacities of different containers.

Materials Needed:

 

Containers of different sizes and shapes (including measuring spoons)

 

Water, rice, or sand

 

Pictures that illustrate capacity situations

Show students a variety of containers and ask them what types of things we might use to fill the containers. What might we measure using these containers? Next, show students pictures that illustrate capacity situations, such as a bottle of milk, a box, a sack of rice, a fish tank, and a swimming pool. For each picture, ask the students to describe what they could fill the object with. Students will often mention that they could fill the object with a liquid, but encourage them to also consider filling objects with solids, such as sugar or sand. Be sure to show the students objects or pictures of objects that cannot be filled -- a square, a rock, a piece of string. You may want to start using the term capacity, which refers to the available space inside a container, in your discussion. But don't expect your students to become comfortable with this term following just one lesson.

Work with a small group of students at a time, either at the sink or at the sand table. Provide them with a number of containers (use more containers with older students). Then ask them to predict which container holds the most and which holds the least, but do not expect students to be able to determine the greatest capacity merely by looking at the containers. Most students will need to pour materials from one container to another before they can make any sort of prediction.

Following experimentation with many containers, choose three or four containers that are different in height and diameter of base. For example, try to find three or four cans: a short, squat can; a tall, skinny can; and cans that are somewhere in between. Or use three rectangular prisms that differ in height. Have students predict which container holds the most and which holds the least, and then have them use filling (rice, sand, etc.) to put the containers in order from largest to smallest.

After all the groups have had an opportunity to work on the task, conduct a discussion about the results. Ask students to share what they discovered. Which can held the most, and which held the least? Ask the students how they arrived at their conclusions. Did tall cans or prisms always hold the most? What types of containers hold a lot of a particular filling, and what types hold very little? Continue to use the word capacity, and encourage students to talk about the capacity of the cans.


 

Problem C2

Solution  

Comparing Distances

Activity Summary
Students indirectly compare distances traveled by toy cars. Older students use nonstandard and standard units to measure the distances.

Materials Needed:

 

Toy cars and ramp

 

Paper tape and scissors

 

Links, multilink cubes, or some other object to use as a nonstandard unit

 

Inch rulers and yardsticks Note 3

Explain that today the students are going to compare the distances different toy vehicles travel. Have students work with a partner, and have each pair choose a small toy car to use. Each pair of students will release their toy vehicle from the starting line at the top of a ramp and then use a piece of paper tape to measure the distance the car traveled.

If you are working with younger students, you may wish to have them write their names on the end of the lengths. These lengths can then be taped to a bulletin board to make a bar graph. Conduct a discussion about the graph. In particular, ask students to compare the distance their cars traveled. Whose cars went the farthest? Whose cars went the shortest distance? How can we tell which cars traveled farther than Anita's (pick a distance in the middle of the group) by looking at the graph? Can we tell how much farther one car went than another? Depending on the toy vehicles used, you may find that the heavier cars traveled the greatest distance.

Older students, or those who are ready to use numbers, can determine the distances the cars traveled by using nonstandard units, standard units, or both. Students write the number of units on the tape prior to making the bar graph. When discussing the graph, they can use either the lengths of the tapes and/or the number of units to determine which car went the farthest. Furthermore, if both nonstandard and standard units were used to measure the distances, this is a great time to discuss why the number of units is not the same (e.g., why the car went 65 inches but not 65 links) for both measures.

When students are measuring with units, notice how they approach the task. Do they place units end to end? Do they use iteration of one unit, or do they use rulers and yardsticks to measure? If using nonstandard units, it is easier to use units such as links or multilink cubes that can be connected together. During the measurement process is the perfect time to give students individualized instruction on how to measure accurately and precisely.


 

Activities in Problems C1 and C2 adapted from The University of Georgia Geometry and Measurement Project. © 1990 by the University of Georgia. NSF Grant #MDR-8651611.

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