How Many in the Jar?

Goal: Estimate how many things are ia a jar

Grades: K, 1, 2, 3, 4, 5, 6, 7

Group size: Any

Time: 10 to 20 minutes (in a single session or spread out over several days)

Spotlight: Estimating number of objects

Materials:

Empty, clear gallon or half-gallon jar

Same-size objects to fill the jar (e.g., cotton balls, beans, shells)

Paper and pencils

Box for estimates (optional)

Prerequisites:

None

Preparation

Fill the jar with cotton balls, pennies, or something related to an upcoming project.

Easy: Fill the jar with up to 50 objects.

Medium: Use 50 to 100 objects.

Hard: Use 100, 500, or more objects that come in packages labeled by quantity (e.g., two bags of 100 cotton balls each).

1. Estimate

Children look carefully and estimate the number of objects in the jar. They may not count each one.

They write their names and estimates on paper and put them in a special box, or they call out their estimates while you record.

2. How did you make your estimate?

Children explain their thinking.

3. Compare estimates and actual amounts

If time permits, pour out some of the objects for each child or pair to count. Then, ask for a volunteer to use a calculator or mental math to find the total. Otherwise, tell children how many are in the jar.

Ask children to look over the estimates and find the closest.

Variations

How Many Seeds? (Grades K, 1, 2, 3, 4, 5, 6, 7)

Cut open a vegetable or fruit with many seeds, such as a pumpkin, squash or pomegranate. Children estimate and then count the number of seeds. This is a great way to mix math into Halloween pumpkin carving.

More or Less Than 100? (Grades 3, 4, 5, 6, 7)

Briefly display the jar, and ask children to make a quick judgment of whether it contains more or less than 100 items. Then, they count to find out.

Same Thing, Different Size (Grades 3, 4, 5, 6, 7)

Try this with items that come in different sizes. If you use big cotton balls one time, use smaller ones next time. Encourage children to use what they know about how many big cotton balls fit to figure out how many smaller ones fit.

Books and Other Resources

Animal Numbers (Grades K, 1, 2)
Kitchen, Bert. NY: Dial Books. 1987.

How Much Is a Million? (Grades 3, 4, 5, 6, 7)
Schwartz, David. NY: Mulberry Books. 1993.

Spotlight

Estimating number of objects

Estimation takes lots of practice. When first learning to estimate, children may think that a full jar contains a million beads. With experience, they learn to look at size and shape of the container and items inside and make more reasonable estimates.

One approach is to consider about how many fit in one layer, and how many layers fill the jar.

About 5 big buttons cover the bottom of the jar, and there are about 10 layers of buttons.

Another is to build on previous estimates:

We saw that about 50 big buttons filled the jar last time, and about 3 beans make up a button, so there are about 150 beans in the jar.

Connections

Decisions based on estimates

Many situations involve making decisions based only on a quick visual estimate. Before getting into line at a store, shoppers scan the checkout lines—how many people in each line and how much in their shopping carts—to decide which line is likely to be fastest. Shoppers also look at package designs and use visual estimates of size and number when deciding what to buy. Businesses spend millions of dollars each year on product and packaging design. Some packages are transparent so people think they’ll be getting a lot; others are opaque for the same reason.

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