Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Capacity and Volume with Non-Standard Units

Active learning works because capacity and volume are abstract until students feel and count the units themselves. When children pour, scoop, and compare, they build mental images of volume that last beyond the lesson. Non-standard units let them focus on the concept of 'how much' without the distraction of standard labels like milliliters or inches.

• NCCA Curriculum Specifications
• NCCA: Primary - Measurement

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Container Match-Up: Water Cups

Provide pairs of differently shaped containers like tall thin glasses and short wide bowls. Students fill the first with water using small cups, count units, then match the second container exactly. They record counts and discuss shape differences.

Explain how a tall, thin container can hold the same amount as a short, wide one?

Facilitation Tip

During Container Match-Up, circulate with a timer and ask each pair to predict which container will hold more before they start pouring, then discuss surprises.

What to look for

Provide students with two containers of different shapes but equal capacity, and a set of non-standard units (e.g., small plastic cups). Ask them to: 1. Pour liquid into each container using the cups and count how many cups fill each. 2. Write one sentence explaining why the tall, thin container held the same amount as the short, wide one.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 35 min · Small Groups

Solid Capacity Hunt: Block Filling

Give small groups containers and unit blocks. Each member fills one container completely, counts blocks used, then compares with others. Groups predict and test if a new container holds more or fewer blocks.

Justify why we use different tools to measure milk versus measuring a book?

Facilitation Tip

For Solid Capacity Hunt, remind students to level the blocks in the container and avoid packing them, so their counts reflect true volume.

What to look for

Present students with a scenario: 'Imagine you need to measure out 10 spoonfuls of rice for a recipe, but you only have a large bowl. How could you do it?' Facilitate a class discussion where students propose and justify different strategies, focusing on the efficiency of their proposed methods.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 40 min · Pairs

Efficient Fill Challenge: Cup to Jug

Challenge pairs to design the fastest accurate way to fill a large jug using a small cup, testing straight pouring versus funnels or relays. They time trials, adjust methods, and share best strategies with the class.

Design the most efficient way to fill a large container using a small cup?

Facilitation Tip

In Efficient Fill Challenge, place measuring jugs at a separate station and ask students to plan their steps before fetching water, to reduce spills.

What to look for

Show students a picture of a measuring jug with water and a pile of building blocks. Ask: 'Which of these would be better for measuring the water, and why? Which would be better for measuring the blocks, and why?' Observe student responses to gauge their understanding of appropriate tools for different substances.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 45 min · Small Groups

Tool Choice Stations: Liquids and Solids

Set up stations with liquids for cups/spoons and solids for blocks. Students rotate, measure into target containers, and explain tool choices. Collect class data on most accurate tools.

Explain how a tall, thin container can hold the same amount as a short, wide one?

Facilitation Tip

At Tool Choice Stations, set out a tray of spilled sand or water to prompt reflections on why some tools work better than others.

What to look for

Provide students with two containers of different shapes but equal capacity, and a set of non-standard units (e.g., small plastic cups). Ask them to: 1. Pour liquid into each container using the cups and count how many cups fill each. 2. Write one sentence explaining why the tall, thin container held the same amount as the short, wide one.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with physical comparisons to confront misconceptions early. Use clear, short language like 'fill to the top' and 'count one spoon at a time' to avoid confusion. Avoid rushing to standard units; let the non-standard experience build the foundation. Research shows that young children grasp conservation through repeated, hands-on trials, so plan for multiple sessions with the same materials.

Successful learning looks like students using non-standard units to fill containers accurately, count reliably, and explain why shape does not always predict capacity. They should adjust their pouring based on spills or gaps and justify their choices when comparing tools for different substances.

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Watch Out for These Misconceptions

• During Container Match-Up, watch for students who assume the taller container holds more because of its height.

  Have students pour side-by-side using the same cups and count aloud together, then ask them to explain why the numbers match despite the difference in height.

• During Solid Capacity Hunt, watch for students who believe thin containers always hold less than wide ones.

  Ask them to fill a narrow box and a wide box with the same blocks, count each, and then rearrange the blocks to see the volume stays the same regardless of shape.

• During Tool Choice Stations, watch for students who use the same tool for liquids and solids without noticing mismatches.

  Prompt them to test a spoon with sand and water, observe the overflow or gaps, and then choose a different tool for one of the substances with a clear reason.

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Methods used in this brief

• Stations Rotation