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.

• 1st Year
• Foundations of Mathematical Thinking
• 3 activities
• 15 min–25 min

Learning Objectives

1. Compare the lengths of different classroom objects using a consistent non-standard unit.
2. Explain why using the same size unit is crucial for accurate length measurement.
3. Analyze the impact of gaps or overlaps on the measurement of an object's length.
4. Demonstrate how to measure the height of objects located in different areas using a chosen non-standard unit.
5. Justify the selection of a specific non-standard unit for a given measurement task.

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

During Collaborative Investigation: The Mystery Weight, provide students with a set of five objects and ask them to order them from lightest to heaviest by balancing pairs in their hands. Observe if they use consistent comparisons and can explain their reasoning.

Exit Ticket

After Simulation: Human Scales, give each student a picture of two classroom objects and ask them to write one sentence explaining how they would compare their weights using their hands as human scales.

Discussion Prompt

During Think-Pair-Share: Big vs. Heavy, present the scenario of two desks in different classrooms and ask students to share their ideas for measuring and comparing their heights using shoes. Listen for explanations that include consistent unit placement and fair comparisons.

Extensions & Scaffolding

• Challenge: Ask students to find an object in the classroom that is approximately 5 paperclips long, then compare their findings with a partner to discuss any discrepancies.
• Scaffolding: Provide students with a template that shows how to align units end-to-end for accurate measuring, and allow them to practice with larger units like their own shoes before moving to smaller ones.
• Deeper: Introduce a comparison of two paths in the schoolyard using non-standard units, then discuss how different units affect the results and why standardization matters.

Key Vocabulary

Non-standard unit	A measurement tool that is not part of a formal system, such as paperclips, blocks, or hands. It must be uniform in size for accurate measurement.
Length	The measurement of how long an object is, from one end to the other.
Measure	To find out the size, amount, or degree of something, especially by using an instrument or device marked in units.
Uniform	The same size, shape, or amount. When measuring, each unit must be identical to the others.