Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Estimating Quantities to 20

Estimating quantities helps young learners develop flexible number sense beyond rote counting. Active experiences with real objects let students see how benchmarks like 5 or 10 shape reasonable guesses. When students estimate and then check by counting, they build confidence that approximations are useful in everyday life.

• NCCA Curriculum Specifications
• NCCA: Primary - Number

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Carousel Brainstorm
• 25 min · Pairs

Pair Challenge: Handful Estimates

Partners take turns grabbing a handful of beans or counters from a bowl, up to 20 items, and estimate the quantity before counting to check. They record estimates and actual counts on a simple chart, then discuss what made their guess close. Switch roles after five turns.

Justify what makes a guess a 'good' estimate rather than just a wild guess.

Facilitation Tip

During Pair Challenge: Handful Estimates, remind partners to count their handful in a quick, organized way before making an estimate.

What to look for

Provide students with a small bag of counters (e.g., 15-20). Ask them to write down their estimate for the number of counters. Then, have them count the actual number and write one sentence explaining if their estimate was 'good' and why.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 02

• Carousel Brainstorm
• 30 min · Small Groups

Small Group: Benchmark Buckets

Provide buckets with 10-20 mixed objects like blocks or buttons. Groups estimate total using 5s and 10s as benchmarks, then sort and count to verify. Each student justifies their estimate to the group before recounting together.

Explain how knowing what ten looks like help us estimate larger groups.

Facilitation Tip

In Benchmark Buckets, circulate and listen for students who reference known quantities like 5 or 10 when explaining their estimates.

What to look for

Show students a picture with a group of objects (e.g., 12 apples on a table). Ask: 'How can knowing what 10 looks like help us guess how many apples there are? Is guessing exactly 12 the only 'good' estimate? What makes an estimate a 'good' guess?'

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 03

• Carousel Brainstorm
• 20 min · Whole Class

Whole Class: Picture Estimates

Project images of scattered items up to 20, like apples or stars. Students hold up fingers for their estimate, then count aloud as a class. Tally how many were within 2 of the actual number and note patterns.

Assess in what real life situations is an estimate better than an exact count.

Facilitation Tip

For Picture Estimates, give students a short think time before discussing to allow for careful observation of the image.

What to look for

Hold up a handful of 5-10 small objects. Ask students to quickly show you with their fingers how many they think are there. Then, hold up a group of 15-20 objects and ask them to use their fingers to show an estimate. Observe which students are using a benchmark like 10 to help them.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 04

• Carousel Brainstorm
• 15 min · Individual

Individual: Snack Estimates

Give each student a small pile of edible items like raisins or crackers, 10-20 total. They estimate silently, count to check, and note on a personal sheet if their guess used a benchmark like ten. Share one real-life example where they used it.

Justify what makes a guess a 'good' estimate rather than just a wild guess.

What to look for

Provide students with a small bag of counters (e.g., 15-20). Ask them to write down their estimate for the number of counters. Then, have them count the actual number and write one sentence explaining if their estimate was 'good' and why.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with concrete objects so students can see what a group of 5 or 10 looks like. Encourage students to verbalize their thought process so misconceptions become visible. Avoid rushing to correct; instead, ask questions that guide students to compare their estimate to the actual count themselves.

Students will practice using benchmarks to make close estimates, then justify why their guess was reasonable. They will explain their thinking in pairs, small groups, and whole-class discussions. By the end of the topic, students will recognize that estimates do not need to be exact to be valuable.

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Watch Out for These Misconceptions

• During Pair Challenge: Handful Estimates, watch for students who insist an estimate is only good if it is exactly right.

  Prompt pairs to discuss what a 'good' estimate means by asking, 'Is 3 close enough if the actual count is 5?' Have them adjust their thinking by seeing that small differences are normal and acceptable.

• During Benchmark Buckets, watch for students who guess any number without using benchmarks like 5 or 10.

  Ask students to sort the counters into groups of 5 or 10 first, then use those groups to make their estimate. Model how to say, 'I see about two groups of 5, so my estimate is around 10.'

• During Whole Class: Picture Estimates, watch for students who believe estimating always requires counting everything exactly.

  Have students quickly count just one row or section of the picture, then use that count to scaffold their estimate for the whole image. Discuss when exact counting is needed versus when an estimate is more practical.

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Methods used in this brief

• Carousel Brainstorm