Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Measuring Length with Non-Standard Units

Active learning helps students grasp the abstract concept of length measurement by using familiar objects they can handle and compare directly. When children manipulate non-standard units like blocks or paperclips, they build an intuitive sense of measurement before moving to formal units, making the transition smoother and more meaningful.

• NCCA Curriculum Specifications
• NCCA: Primary - Measurement

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 25 min · Small Groups

Inquiry Circle: The Mystery Weight

Give each group a 'mystery' wrapped box and a set of wooden blocks. They must use a balance scale to find out exactly how many blocks it takes to make the scale level, recording their 'weight' in blocks.

Justify why we must use the same size unit when measuring two different things?

Facilitation Tip

During Collaborative Investigation: The Mystery Weight, circulate with a small basket of contrasting objects for students to explore, ensuring they feel the weight difference before discussing their findings.

What to look for

Provide students with a collection of uniform non-standard units (e.g., 10 identical blocks). Ask them to measure the length of a pencil and record the number of blocks. Then, ask them to measure the width of a book using the same blocks and record the number. Observe if they maintain consistent unit placement and count accurately.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Simulation Game
• 15 min · Pairs

Simulation Game: Human Scales

Students stand with arms out like a scale. A partner places a heavy book in one hand and a light pencil in the other. The 'scale' student must tilt their body to show which is heavier, while the class describes the movement.

Analyze what happens if we leave gaps between our measuring tools?

Facilitation Tip

For Simulation: Human Scales, model how to balance carefully by holding objects steady and gently adjusting hand positions to avoid frustration with the concept of equal weight.

What to look for

Give each student a card with a picture of two objects of different lengths. Ask them to write one sentence explaining how they would compare the lengths using paperclips. Then, ask them to write one sentence explaining why it's important that all the paperclips are the same size.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Big vs. Heavy

Show a large sponge and a small stone. Ask students to predict which is heavier. After testing on a scale, they discuss in pairs why the 'big' thing wasn't the 'heavy' thing.

Explain how we can compare the height of two things that are in different rooms?

Facilitation Tip

In Think-Pair-Share: Big vs. Heavy, provide a set of objects with clear size and weight differences so students can articulate their observations with concrete evidence.

What to look for

Present students with a scenario: 'Imagine you need to measure the height of your desk and your friend's desk, but your desks are in different classrooms. How could you use your shoes to compare their heights?' Facilitate a class discussion, guiding students to explain how they would measure each desk with shoes and then compare the number of shoes used.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with hands-on comparisons before introducing any tools, as research shows students learn weight concepts better through direct sensory experience. Avoid rushing to formal scales; instead, let students internalize the idea of balance by using their own bodies and familiar objects. Emphasize the importance of consistent unit size, as this foundational skill transfers to standard measurement later.

Successful learning looks like students confidently using consistent units to measure objects, explaining why unit size matters, and recognizing that size does not always determine weight. They should also demonstrate patience with measurement tools and describe their process clearly to peers.

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Watch Out for These Misconceptions

• During Collaborative Investigation: The Mystery Weight, watch for students assuming the larger object is always heavier when holding the large balloon and small apple.

  Guide students to feel the difference in weight by holding both objects, then use a balance scale to show that the small apple is heavier, reinforcing that size does not determine weight.

• During Simulation: Human Scales, watch for students expecting the balance to tip immediately when comparing objects of similar weight.

  Demonstrate how to wait for the scale to settle and explain that small differences may not be visible on a classroom scale, preparing them for more sensitive tools later.

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Methods used in this brief

• Inquiry Circle
• Simulation Game
• Think-Pair-Share