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E2.2 compare several everyday objects and order them according to length, area, mass, and capacity
Key Concepts
Objects can be compared and ordered according to whether they have more or less of an attribute. Comparing the same objects by different attributes may produce different ordering.
There are specific words and phrases that help describe and compare attributes:
more, less, smaller, and bigger often only describe general comparisons unless a specific attribute is included (bigger area; smaller capacity);
adding the suffix “-er” or “-est” typically creates a comparative term (e.g., heavier, lighter, heaviest, lightest).
Objects can be directly compared by matching, covering, or filling one object with the other to determine which has more length, mass, area, or capacity.
When a direct comparison cannot be easily made, a third object can serve as a “go-between” tool to make an indirect comparison. For example, a third container can be used to determine which of two containers holds more water. Indirect comparisons require using the transitivity principle and the conservation principle.
Capacity refers to the maximum amount that a container can hold. In the early primary grades, students develop an understanding of capacity by filling a variety of containers with pourable materials (e.g., water, rice, sand), and by comparing the amounts that the different containers hold. They measure capacity by counting the number of units (e.g., scoops) that a container holds.
Young students often assume that tall, narrow containers have a greater capacity than short, wide containers, because tall containers “look bigger”. Opportunities to estimate and measure the capacity of a variety of containers allow students to address their misconceptions about the relationships between the shapes and the capacities of containers.
As students develop an understanding of capacity, they develop language that allows them to compare containers by capacity. Initially, students make general comparisons (e.g., “The water jug is bigger than the baby food jar”). Later, they use more precise language – for example, “The juice bottle has a capacity of 15 scoops and the pop bottle has a capacity of 18 scoops. The pop bottle holds more than the juice bottle.
demonstrate an understanding of the use of non-standard units of the same size for measuring;
estimate, measure, and describe the capacity of an object, through investigations using non-standard units
compare two or three objects using measurable attributes and describe the objects using relative terms (e.g., taller, heavier, faster, bigger, etc.)
share their ideas using mathematical vocabulary and listen to others.
I can share my ideas and listen to others
I can ask questions if I don’t understand
I use math language to communicate clearly so that others will understand my ideas and my work
I can guess how many scoops different containers will hold and compare them.
Empty plastic containers (e.g., jars, cottage cheese containers, margarine tubs, juice bottles)
Materials for making Hungry Hounds: plastic googly eyes; pompoms for noses; ears, tongues, and legs cut from construction paper or foam core; pipe cleaners or pieces of yarn for tails; glue; tape (enough materials for each student to make his or her own Hungry Hound)
Small scoops (e.g., coffee scoops, small plastic cups, caps from liquid laundry detergent bottles)
Individual containers of pourable materials (e.g., water, rice, or sand)
Plastic funnels (e.g., the top part of a plastic bottle cut in half)
**Distance learning teachers can ask students to gather a variety of materials from the kitchen (with parental support) such as spoons, measuring cups, small plastic containers, cups, rice, water, ect.)
Estimation - Erasers
From “Steve Wyborney, Esti-mysteries (Sept. 2020)
Explore estimation situations that develop problem solving, reasoning, and proving skills. Students use their understanding of number, operation sense, measurement, and spatial sense to justify what they think is a reasonable estimate.
Explore some of these images with students, asking: “What would a ‘too high’ estimate be? What would a ‘too low estimate be? What is a reasonable estimate? What’s your reasoning? The emphasis is on building the ability to both determine a reasonable estimate and to justify their answer.
Click here to see Powerpoint of this Number Talk.
Show students a model of a Hungry Hound that you made ahead of time. Explain the following:
“Each of you will make a Hungry Hound. Once you have your own Hungry Hound, you will need to feed it. You will need to measure how many scoops of food your Hungry Hound can eat.”
Provide each student with a plastic container, ensuring that the students have containers of various sizes. Have students create their hounds by:
gluing plastic googly eyes, a pompom nose, paper or foam ears, and a paper or foam tongue to the front of the container.
gluing paper or foam legs to the container;
taping a tail (pipe cleaner or piece of yarn)
to the back of the container.
After students have created their Hungry Hounds, explain that they will determine how much their hounds eat by counting the scoops of food it takes to fill them.
Show students containers of pourable materials (e.g., rice, sand, beans), and explain that the materials represent dog food. Tell the students that each one’s task is to “feed” his or her Hungry Hound until it is full.
Provide each student with a small scoop and a copy of the Hungry Hounds recording sheet. Ask: “How many scoops of food do you think your Hungry Hound will eat?” Have the students record their estimates on their pages.
Observe the students as they fill their containers. (Provide plastic funnels for students who need them.) Emphasize the importance of filling the scoop to the same level each time. When the students have partially filled their containers, ask them to predict how many more scoops will be needed to fill the containers completely. Encourage the students to base their predictions on the numbers of scoops already poured into their containers. For example, knowing that 7 scoops filled half a container will help a student predict that 7 more scoops will be needed to fill the container. Students can also base their predictions on benchmark quantities (e.g., observing a quantity consisting of 2 scoops allows a student to predict the number of scoops that are needed to fill his or her container).
After the students have measured and recorded the capacities of their Hungry Hounds, ask them to compare their estimates with the actual measurements – for example, “My Hungry Hound has a smaller capacity than I thought. It took only 15 scoops to fill it, and I thought it would take 25 scoops.”
Next, have the students empty their Hungry Hounds and exchange them with a partner. (Ensure that each student receives a container that is different from the one that he or she measured previously.)
**Ensure students wash their hands before exchanging containers and after filling their partners containers.**
***Distance Learning students can choose a second container to measure.***
Have each student predict and record the number of scoops needed to fill the partner’s Hungry Hound, encouraging the students to base their estimates on the measurements of their own containers (e.g., if the partner’s container is smaller, fewer scoops will be needed to fill it). Have each student “feed” the partner’s Hungry Hound with the same material that he or she used previously and record the capacity of the container on his or her copy of the Hungry Hounds recording sheet.
After each student has recorded the capacity of the partner’s Hungry Hound, have the student compare the capacity of his or her own hound with the capacity of the partner’s by completing the bottom section of Cap1.BLM1: Hungry Hounds.
Gather the students together to review the activity. Ask a few students to show their Hungry Hounds and to tell the class their estimates and actual measurements of the capacities of their containers. Ask questions such as the following:
“How did you estimate the number of scoops needed to feed your Hungry Hound?”
“How did your estimate compare with your actual measurement?”
“Whose Hungry Hound has a greater capacity, yours or your partner’s? How do you know?”
“What did you learn about measuring capacity?”
Show two Hungry Hounds that have approximately the same capacity but different shapes. Ask students to estimate which container has the greater capacity, and have students explain their estimation strategies. For example, the students might compare the sizes of the containers by observing which container is taller or wider. Have the owners of the Hungry Hounds reveal the actual capacity measurements of the containers. Discuss how different-shaped containers can have capacities that are approximately the same.
Conclude the activity by having students explain what they learned about measuring capacity. Record their ideas on chart paper. For example, students might explain the following ideas:
Capacity is how much a container holds.
Capacity can be measured with scoops.
Containers can have different capacities.
Containers can look different but have the same capacity.
One way of comparing the capacities of containers is to count the number of scoops that each container holds, and then compare the numbers.
Extend the activity by having small groups of students order their Hungry Hounds from least to greatest capacity. Students might also investigate the use of different-size scoops (e.g., whether more small scoops than big scoops are needed to fill a container).
Observe students to assess how well they:
explain the meaning of capacity (i.e., how much a container holds);
make reasonable estimates about the capacity of a container (e.g., estimate the number of scoops a container will hold);
explain their estimation strategies;
measure accurately (e.g., by filling a measuring scoop to the same level each time
and carefully counting the number of scoops needed to fill a container);
compare the capacities of containers.
Possible Independent Tasks:
(From: https://www.kindergartenkindergarten.com/2012/07/math-problem-solving-measurement-capacity.html)