Measurement of Length: Non-Standard Units

Active learning works well here because children need to physically engage with measurement to understand its purpose. By using their own bodies and familiar objects, they connect abstract numbers to tangible experiences, making the concept of length measurable and relatable. This hands-on approach builds a strong foundation before introducing standard units like centimetres.

• Class 3
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Compare the lengths of different objects measured using a single non-standard unit.
2. Construct a consistent method for measuring the length of an object using a chosen non-standard unit.
3. Analyze why measurements of the same object differ when using different non-standard units or different users.
4. Explain the difference between standard and non-standard units of measurement.

Hexagonal Thinking

⏱ 30 min·Pairs

Pair Measuring: Classroom Objects

Pairs choose five classroom items like erasers or benches. Each partner measures with hand spans or foot lengths, records counts, and compares results. Discuss why numbers differ.

Prepare & details

Differentiate between standard and non-standard units of measurement.

Facilitation Tip: During Pair Measuring, ask students to explain their counting method to each other to ensure accuracy and consistency in placing units.

Setup: Works in standard classroom rows — students push desks together into groups of four to six. Each group needs enough flat surface to spread fifteen to twenty hexagonal tiles. Can also be conducted on the floor in a circle if desks cannot be rearranged.

Materials: Pre-cut hexagonal tiles — one labelled set of 15 to 20 per group, Blank tiles for student-generated concepts, Markers or printed concept labels in the medium of instruction, A3 sheets or chart paper for mounting the final arrangement, Printable link-label strips for annotating connection sentences

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Hexagonal Thinking

⏱ 25 min·Small Groups

Small Group Challenge: Desk Length Race

Small groups race to measure a desk using uniform non-standard units like pencils or straws laid end-to-end. One records while others measure. Groups share and verify counts.

Prepare & details

Construct a method for measuring an object using a non-standard unit.

Facilitation Tip: For the Desk Length Race, remind groups to align units end-to-end without gaps or overlaps to avoid measurement errors.

Setup: Works in standard classroom rows — students push desks together into groups of four to six. Each group needs enough flat surface to spread fifteen to twenty hexagonal tiles. Can also be conducted on the floor in a circle if desks cannot be rearranged.

Materials: Pre-cut hexagonal tiles — one labelled set of 15 to 20 per group, Blank tiles for student-generated concepts, Markers or printed concept labels in the medium of instruction, A3 sheets or chart paper for mounting the final arrangement, Printable link-label strips for annotating connection sentences

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Hexagonal Thinking

⏱ 40 min·Whole Class

Whole Class: Playground Footsteps

Class lines up to measure playground distances with footsteps. Mark start and end, count steps collectively, then individuals recount. Chart variations on board.

Prepare & details

Analyze the limitations of using non-standard units for measurement.

Facilitation Tip: In Playground Footsteps, encourage students to walk heel-to-toe for the same step size so comparisons are fair.

Setup: Works in standard classroom rows — students push desks together into groups of four to six. Each group needs enough flat surface to spread fifteen to twenty hexagonal tiles. Can also be conducted on the floor in a circle if desks cannot be rearranged.

Materials: Pre-cut hexagonal tiles — one labelled set of 15 to 20 per group, Blank tiles for student-generated concepts, Markers or printed concept labels in the medium of instruction, A3 sheets or chart paper for mounting the final arrangement, Printable link-label strips for annotating connection sentences

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Hexagonal Thinking

⏱ 20 min·Individual

Individual: Personal Unit Book

Each student creates a 'measuring tool' from fingers or thumbs. Measure three personal items like arms or bags, draw and label in notebooks. Share one with class.

Prepare & details

Differentiate between standard and non-standard units of measurement.

Facilitation Tip: In Personal Unit Book, guide students to write their name and age next to their unit so variations in hand spans are visible later.

Setup: Works in standard classroom rows — students push desks together into groups of four to six. Each group needs enough flat surface to spread fifteen to twenty hexagonal tiles. Can also be conducted on the floor in a circle if desks cannot be rearranged.

Materials: Pre-cut hexagonal tiles — one labelled set of 15 to 20 per group, Blank tiles for student-generated concepts, Markers or printed concept labels in the medium of instruction, A3 sheets or chart paper for mounting the final arrangement, Printable link-label strips for annotating connection sentences

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Teaching This Topic

Experienced teachers begin with simple, familiar objects before moving to larger spaces. They avoid giving away answers and instead ask guiding questions like, 'How can we make sure both measurements are fair?' This approach lets students discover inconsistencies themselves. Research shows that peer discussion and repeated trials correct misconceptions more effectively than teacher explanations alone.

What to Expect

Successful learning is seen when students measure carefully, record results accurately, and discuss why measurements differ between peers. They should notice variations in their units and explain the need for consistency in measurement. Clear recording and sharing of findings indicate understanding of both the process and its limitations.

Watch Out for These Misconceptions

Common Misconception

During Pair Measuring, watch for students who assume their hand spans are identical to their partner's. Ask them to measure the same object together and compare results to highlight natural variations.

What to Teach Instead

During Pair Measuring, have partners swap objects and measure again to show that units differ. Ask, 'Why did each of you get a different number for the same object?' This leads to a class discussion on unit consistency.

Common Misconception

During Desk Length Race, watch for students who think a larger unit always means a bigger measurement. Ask them to compare their desk measurements using fingers versus palms to observe the inverse relation.

What to Teach Instead

During Desk Length Race, provide both finger lengths and palm lengths for measurement. Ask, 'Which unit gave a smaller number of counts? Why?' This helps students understand that unit size affects the count, not the actual length.

Common Misconception

During Playground Footsteps, watch for students who overlook gaps between steps or uneven strides. Ask them to measure the same path again using a continuous line to highlight inaccuracies.

What to Teach Instead

During Playground Footsteps, have students walk heel-to-toe along a rope laid on the ground. Then, ask them to measure a curved path like a circle to show the limitations of foot steps for non-straight objects.

Assessment Ideas

Quick Check

After Pair Measuring, observe students measuring the book, eraser, and pencil with paper clips. Note if they align units properly without gaps or overlaps and record counts consistently.

Discussion Prompt

After Pair Measuring, ask students to share their hand span measurements for the table. Prompt: 'Why did some of you get a different number of hand spans for the same table? What does this tell us about using hand spans to measure?'

Exit Ticket

After Personal Unit Book, collect students' cards. On the side with the drawing, check if they used their foot length to measure and recorded the count correctly. On the explanation side, look for their understanding of why a measuring tape is better than a hand span for a tailor.

Extensions & Scaffolding

• After measuring classroom objects with paper clips, challenge students to estimate the length of a longer object like a corridor and then measure it with their foot lengths to compare estimates with actual counts.
• For students struggling with alignment, provide a strip of paper to mark the end of each unit and tape it down to maintain accuracy.
• For extra time, ask students to create a bar graph showing the number of hand spans different classmates measured for the same book, prompting analysis of why the numbers vary.

Key Vocabulary

Non-standard unit	A unit of measurement that is not officially recognised or agreed upon, like a hand span or a pencil. Its size can vary.
Standard unit	An officially recognised and agreed-upon unit of measurement, such as a centimetre or a metre. Its size is fixed.
Hand span	The distance from the tip of the thumb to the tip of the little finger when the hand is stretched out wide. It is a non-standard unit.
Foot length	The length of a person's foot, used as a non-standard unit to measure other objects. Its size varies from person to person.
Measurement	The process of finding out the size, length, or amount of something, often by comparing it to a unit.