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EMERGE LESSON: CUBES IN A DIXIE CUP
Suitable for grades 5-11
In this Emerge lesson, students compete in teams to uncover the relationship between the number of cubes in a cup and the mass of the cup. Game on!
LESSON GOALS
Elementary: Students will be able to use decimal operations to find the mass of the cup.
Middle School: Students will be able to use ratio reasoning and unit rate to find the mass of the cup.
High School: Students will be able to use linear functions to find the mass of the cup.
MATERIALS
Lightning Version (Phase 1 Only)
- 1 copy of the lesson handout
- 1 dry erase board and marker for each team
Medium Version (Phase 1 and 2)
- 1 copy of the lesson handout
- at least 1 scale that measures mass
- at least 1 cup
- at least 50 small cubes
- 1 dry erase board and marker for each team
Full Version (Phases 1, 2, 3, and 4)
- 1 copy of the lesson handout
- at least 1 scale that measures mass
- at least 2 paper cups
- at least 50 small cubes
- at least 30 other small objects, such as golf pencils or skittles
- 1 dry erase board and marker for each team
TIME REQUIRED
Lightning Version (Phase 1 Only): 10-20 Minutes
Medium Version (Phase 1 and 2): 30-45 Minutes
Full Version (Phases 1, 2, 3, and 4): 60-90 minutes or two 30-45 minute blocks
SET UP
Lightning Version
Arrange students into teams of 2-6. Find a place in the room to display team scores. Give each student a copy of the lesson handout. Project this web page.
Medium Version
Arrange students into teams of 2-6. Find a place in the room to display team scores. Give each student a copy of the lesson handout. Project this web page. If you have 1 scale, set it up in a place everyone can see and have the cubes and cup near it. If you have enough scales to give each team 1, set them up around the room near each team and put a cup and some cubes near each one. Save the other small objects for later.
Full Version
Arrange students into teams of 2-6. Find a place in the room to display team scores. Give each student a copy of the lesson handout. Project this web page. If you have 1 scale, set it up in a place everyone can see and have the cubes and cup near it. If you have enough scales to give each team one, set them up around the room near each team and put a cup and some cubes near each one. Save the other small objects for later.
THE LESSON
PHASE 1: INTRODUCTION (10-15 minutes)
- Play the video below and pause it when prompted.
3. Give each team a small amount of time (30 seconds to 2 minutes) to discuss and agree on a guess, write it on their team whiteboards, and hold it in the air so that it cannot be changed.
4. Play the video again, revealing the mass. Pause it when prompted again and announce the winner. Have students record the mass on their handout.
5. Ask students to discuss, in their groups, what they notice and wonder about the situation. Have a few students share.
6. Play two more rounds of the game, following the video’s prompts each time.
7. Ask students to complete the last video prompt, which asks them what their strategy would be if the game continued, on their handout.
PHASE 2: PHYSICAL EXPLORATION (10-15 minutes)
- Explain to students that the game will continue, but this time with real cubes and cups.
- Tell students that you will first be putting 10 cubes in the cup (this amount can be adjusted depending on the size of your cubes and cups).
- Give each team a small amount of time (30 seconds to 2 minutes) to discuss and agree on a guess for what they think the mass will be, write it on their team whiteboards, and hold it in the air so that it cannot be changed.
- Place the cubes in the cup (or have each team do it themselves if you’ve given each of them materials) and find the mass. Announce the winning team and have students record the data on their handout.
- Play two more rounds of the game, increasing the number of cubes in the cup each time.
- Play one final round, but this time
PHASE 3: STUDENT PRESENTATION (10-15 minutes)
- Play one last round, but this time, ask students to carefully record the method they are using on their whiteboards.
- After the final mass is revealed, have some of the student teams present their methods. Summarize and consolidate some key information that will connect with the Formal Learning Phase, which comes next.
PHASE 4: FORMAL LEARNING (30-45 minutes)
In this phase, the teacher introduces a specific, formal mathematical method for guessing the mass of the cup with cubes. The method that is taught will depend on the course and grade level. Each teacher will have to determine what the appropriate method is for their course. Here are the suggested methods based on general grade level ranges:
Elementary (Grades 5-6): Have students determine the mass of one cube using decimal subtraction and division (if 8 cubes added 16.8 grams, how much would 1 cube add?). Then have students determine the mass of the cup by itself using decimal multiplication and subtraction (If 5 cubes plus the cup had a mass of 11.8, how much does the cup weigh? We can find the mass of the 5 cubes by multiplying the mass of 1 cube by 5. How much is left for the cup?). Finally, have the students find the mass of the cup and cubes using decimal multiplication and addition (How much would 7 cubes plus the cup weigh? Well, since each cube weighs 2.1 grams, 7 cubes weighs 14.7 grams. Since the cup weighs 1.3, the total mass must be 14.7 + 1.3 = 16.0 grams).
Middle School (Grades 6-8): Have students determine the mass of the cup and cubes using proportional reasoning (if 8 cubes added 16.8 grams, then 6 cubes would add how many grams to the total?)
High School (Grades 8-11): Have students write a linear function that describes the data by calculating its slope and y-intercept. Then have students use the linear function to determine the mass of the cup and cubes.
Regardless of the method taught, the steps of this phase are the same:
Modeling and Guided Practice
- Using the Phase 4 section of the lesson handout, model the method you are teaching on the first set of data.
- Allow students to try to recreate the method on the second set of data. Guide them where needed.
- Allow students to try to use the method on the third set of data independently.
Independent Practice in Context
In this section, you will play a few more rounds of the game with students, but this time with slightly different objects in the cup, such as golf pencils or Skittles. Once you have the materials set up, play as many rounds as time allows, asking student teams to use the method that was taught.