How Much Will Fit?
5 min
Teacher Prep
Setup
Narrative
Previously, students studied the relationship between volume and height of liquid when poured into a cylindrical container. The purpose of this Warm-up is to shift students’ attention toward other types of containers and to consider how the volume of two containers differs. This Warm-up is direct preparation for the following activity in which students reason about volumes of several container types and refamiliarize themselves with the language of three-dimensional objects.
Launch
Tell students to close their books or devices. Arrange students in groups of 2. Display the image of the two containers filled with beans for all to see.
Give partners 1 minute to estimate how many beans are in each container. Poll the class for their estimates, and display them for all to see, in particular, the range of values expressed.
Tell students that the smaller container holds 200 beans. Ask students to open their books or devices and reconsider their estimate for the large container now that they have more information. Give 1–2 minutes for students to write down a new estimate. Follow with a whole-class discussion.
Student Task
Your teacher will show you some containers. The small container holds 200 beans. Estimate how many beans the large jar holds.
Sample Response
Sample response: approximately 1,000 beans
Activity Synthesis (Teacher Notes)
Poll the class for their new estimates for the number of beans in the larger container, and display these next to the original estimates for all to see. Tell the class that the large container actually holds about 1,000 beans.
Discuss:
- “How did you and your partner calculate your estimate for the large jar?” (We estimated the large jar holds 900 beans since the large jar is about 3 times taller than the smaller jar, and it’s about 1.5 times wider, and 200⋅3⋅1.5=900.)
- “Is there a more accurate way to measure the difference in volume between the two containers than ‘number of beans.’” (Yes, we could use something smaller than beans, such as rice or water, so there is less air.)
- “What are some examples of units used to measure volume? Where have you seen them used in your life?” (Cups, tablespoons, gallons, liters, cubic centimeters, etc. Drinks often have fluid ounces, gallons, or liters written on them. Recipes may use cups or tablespoons.)
Anticipated Misconceptions
If students are not sure how to start estimating the amount of beans in the larger jar once the number of beans in the smaller jar is known, consider asking:
- “Tell me what you notice is similar or different between the two jars.”
- “How could estimating some dimensions (for example, height and width) help you?”
Standards
- 8.G.C·Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- 8.G.C·Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
15 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
How Much Will Fit?
5 min
Teacher Prep
Setup
Narrative
Previously, students studied the relationship between volume and height of liquid when poured into a cylindrical container. The purpose of this Warm-up is to shift students’ attention toward other types of containers and to consider how the volume of two containers differs. This Warm-up is direct preparation for the following activity in which students reason about volumes of several container types and refamiliarize themselves with the language of three-dimensional objects.
Launch
Tell students to close their books or devices. Arrange students in groups of 2. Display the image of the two containers filled with beans for all to see.
Give partners 1 minute to estimate how many beans are in each container. Poll the class for their estimates, and display them for all to see, in particular, the range of values expressed.
Tell students that the smaller container holds 200 beans. Ask students to open their books or devices and reconsider their estimate for the large container now that they have more information. Give 1–2 minutes for students to write down a new estimate. Follow with a whole-class discussion.
Student Task
Your teacher will show you some containers. The small container holds 200 beans. Estimate how many beans the large jar holds.
Sample Response
Sample response: approximately 1,000 beans
Activity Synthesis (Teacher Notes)
Poll the class for their new estimates for the number of beans in the larger container, and display these next to the original estimates for all to see. Tell the class that the large container actually holds about 1,000 beans.
Discuss:
- “How did you and your partner calculate your estimate for the large jar?” (We estimated the large jar holds 900 beans since the large jar is about 3 times taller than the smaller jar, and it’s about 1.5 times wider, and 200⋅3⋅1.5=900.)
- “Is there a more accurate way to measure the difference in volume between the two containers than ‘number of beans.’” (Yes, we could use something smaller than beans, such as rice or water, so there is less air.)
- “What are some examples of units used to measure volume? Where have you seen them used in your life?” (Cups, tablespoons, gallons, liters, cubic centimeters, etc. Drinks often have fluid ounces, gallons, or liters written on them. Recipes may use cups or tablespoons.)
Anticipated Misconceptions
If students are not sure how to start estimating the amount of beans in the larger jar once the number of beans in the smaller jar is known, consider asking:
- “Tell me what you notice is similar or different between the two jars.”
- “How could estimating some dimensions (for example, height and width) help you?”
Standards
- 8.G.C·Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- 8.G.C·Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.