Grade by Grade
B. Number · Number Sense: Numbers to 200 and Fractions

Estimating Big Collections

B1.3 B1.4 A1About 30 minutes
Learning goals
  • I can make a smart guess (estimate) of how many objects there are, up to 200.
  • I can use a group I know, like 10 or 25, to help me estimate.
  • I can check my estimate by counting in groups.

Words to know

estimate
A thoughtful guess about how many, made without counting every object.
about
Close to, but not exact. "About 100" could be 96 or 104.
benchmark
An amount you already know well, like 10 or 25, that helps you estimate.
verify
To check if something is true. We verify an estimate by counting.

How many geese?

In the fall, Canada geese fly south in big V shapes. Sometimes a huge flock lands in a field. There are too many to count one by one before they fly away!

When we can't count every one, we can estimate. An estimate is a smart guess that is close to the real number.

A large flock of Canada geese resting in a harvested corn field with orange and red autumn trees behind.
There are far too many geese here to count one by one. Picture a group of 10 geese, then think about how many groups like that fit in the field to make your estimate. AI-generated image

Remember from Grade 1

In Grade 1 you estimated small groups, up to 50. This year you will estimate collections up to 200.

A good estimate is not a wild guess. You use what you already know.

Use a benchmark

A benchmark is a group you know well. Look at this group of 10 snowflakes. Remember how much space 10 takes up.

❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️
A benchmark: 10 snowflakes.
❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️❄️
About how many snowflakes here? Picture how many groups of 10 would fit.
Worked example

Example 1: Estimate with groups of 10

About how many snowflakes are in the big group above?

  1. Look at the benchmark of 10.
  2. Picture the big group cut into pieces the size of 10. It looks like about 4 pieces.
  3. Count by 10s: 10, 20, 30, 40.
  4. Estimate: about 40. Now verify! Count them in groups of 10.

There are exactly 40. An estimate of 35, 40 or 45 would all be great estimates.

Is it a good estimate?

An estimate doesn't have to be exactly right. It should be close.

If there are 40 snowflakes, an estimate of 40 or 45 is close. An estimate of 150 is too far away.

It's okay to change your estimate when you learn more! That's what good thinkers do.

Worked example

Example 2: A jar of beans

Raj fills a scoop with 25 beans. He pours it into a jar. The jar looks about 4 scoops full. About how many beans can the jar hold?

  1. The benchmark is 25, so count by 25s for each scoop.
  2. 25, 50, 75, 100.

About 100 beans.

Worked example

Example 3: Verify by counting in groups

Zoe estimated 120 pieces of cereal in a bowl. She checked by making groups of 10 on a plate. She made 13 groups of 10 and had 7 left over. Was her estimate close?

  1. Count the groups by 10s: 10, 20, 30, ... 100, 110, 120, 130.
  2. Count on the 7 leftovers: 131, 132, ... 137.
  3. 137 and 120 are close. They are less than 20 apart.

There were 137 pieces. Zoe's estimate of 120 was close.

Steps for estimating

  1. Look at the whole collection.
  2. Find a benchmark: a group of 10, 20 or 25.
  3. Think: About how many benchmark groups fit?
  4. Skip count to make your estimate.
  5. Verify: Count in groups of 10 (or 20, 25, 50) to check.
Just for fun

Why did the goose never finish counting the flock?

Every time it got close to 100, somebody honked and it lost count. That goose should have estimated!

Hands-on activity

Estimation jar

You need: a clear jar or container, and a few small things like dry pasta, buttons, Lego bricks or cotton balls. Also paper and a pencil.

  1. A grown-up fills the jar (somewhere between 50 and 200 things).
  2. Count out 10 of the same things and put them beside the jar. This is your benchmark.
  3. Write your estimate.
  4. Pour everything out. Count it in groups of 10 on paper plates (or groups of 20 or 25).
  5. Was your estimate close? Write the exact number next to it.
  6. Try again with a new jar. Did your estimates get closer?

Math talk: "What helped you make your estimate?"

Your turn

1

🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁🍁

Estimate how many maple leaves, then count to verify.

2

A cup holds about 20 marbles. A bag fills about 5 cups. About how many marbles are in the bag?

3

There are about 50 birds on one tree. There are 3 trees, each with about the same number of birds. About how many birds?

4

Nick estimated 60 crayons. There were 64. Was his estimate close?

5

You count a pile of buttons and get 11 groups of 10 and 5 extra. How many buttons?

6

Which is the best estimate for the number of students in a whole school gym assembly: 15, 150, or 1500?

More practice: warm-up

1

🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟

Is this closer to 10 or to 20?

2

What does "about 100" mean?

3

Is an estimate the same as counting?

4

Estimate first: are there more than 50 or fewer than 50 days in one month?

5

Count by 10s to check: 4 groups of 10. How many?

More practice: on your own

1

A box of 25 pencils fills a pencil cup. There are 6 full cups. About how many pencils?

2

Ali estimated 90 snowballs. The real number was 160. Was that a close estimate? What could Ali do next time?

3

You estimate a jar has 80 beads. Then you see that a group of 10 takes up only a tiny part of the jar. Should you change your estimate up or down?

4

Pine cones in a pile: you make 9 groups of 20. How many pine cones?

5

Three friends estimate stickers on a sheet: 50, 100, 180. The real number is 96. Whose estimate is closest?

Challenge

1

A row of chairs has 10 chairs. The gym has 14 rows. How many chairs are there? Then: 6 chairs are taken out. Exactly how many are left?

2

Explain why counting a big pile in groups of 10 is better than counting one by one.

3

Emma estimates there are 75 people in line at a hockey game. She counts 3 groups of 25 people. Then 25 more people join. About how many are in line now?

Check your understanding

Quiz

1.

What is an estimate?

2.

There are 104 apples. Which estimate is closest?

3.

A scoop holds about 25 berries. You fill 4 scoops. About how many berries?

4.

You count 12 groups of 10 and 3 leftovers. How many is that?

5.

Why do we use a benchmark like 10?

6.

Which is the best way to verify an estimate of 150 beads?

For parents and teachers

Big idea: Estimating is reasoning, not guessing. Children use a benchmark (a known group like 10 or 25) to picture how many groups fit, then skip count. They verify by counting in groups.

Common difficulties:

  • Wanting the exact answer. Some children feel upset if their estimate is "wrong". Praise close estimates and good reasons. Changing an estimate after new information is a smart move, not a mistake.
  • Wild guesses ("a million!"). Ask, "How did you decide? Show me what 10 looks like."
  • Counting one by one to check. Encourage grouping in 10s, 20s or 25s.

Social-emotional learning: This lesson is a great time to practise taking safe risks and staying positive when an answer isn't exact.

How to help: Estimate often: grapes in a bowl, cars in a parking lot, steps to the corner. Then count together in groups.