Measure and compare length, capacity and mass

Measurement answers a question about an attribute. Length asks how long; capacity asks how much a container can hold; mass asks how heavy. A fair comparison uses the same kind and size of unit for both objects.

Best routine: Choose attribute → choose a suitable unit → place/use units with no gaps or overlaps → count → compare → explain.

If units are different sizes, the number you count is not a fair comparison. If units have gaps or overlaps, the measure is distorted.

Do not choose a unit just because it is nearby. Choose one that matches the attribute and is practical for the object.

A large unit may not fit the end of an object neatly. A smaller unit can describe the measurement more closely.

Important: smaller units usually produce a larger count, even though the object has not changed.

1. Length: A pencil measures 7 identical paperclips. Another measures 9 of the same paperclips. The second pencil is longer by 2 paperclips.
2. Capacity: Container A holds 6 equal cups; B holds 9 equal cups. B holds 3 cups more.
3. Mass: A toy balances with 8 equal blocks and a book with 11. The book has greater mass by 3 block-units.
4. Unit choice: Measuring the classroom width with tiny counters would work but be inefficient; larger equal footsteps or tiles are more suitable. Measuring a pencil with footsteps would be too coarse.

• Using mixed unit sizes: use identical units for a fair count.
• Leaving gaps or overlaps: place length units end-to-end.
• Comparing counts from different units: 8 small blocks cannot be directly compared with 5 large blocks unless the unit sizes are considered.
• Thinking larger count means larger object: the count depends on unit size.
• Judging mass by appearance: use hefting or a balance scale rather than size alone.
• Confusing capacity with how much is currently inside: capacity is how much the container can hold when filled.

• Choose the attribute first: length, capacity or mass.
• Use one uniform informal unit throughout a comparison.
• No gaps or overlaps for length.
• Use the same cup/scoop for capacity.
• Use equal-mass units on a balance scale.
• Smaller units can give a more accurate measure but usually create a larger count.

Mastery check: Explain why measuring the same table with adult shoe lengths and child shoe lengths can give different numbers even though the table has not changed.

Some elaborations invite investigation of First Nations measurement practices, including body-based units and interpreting animal-track dimensions. Use specific, reliable and community-approved sources. Identify the relevant Nation, People or community where known, and do not present diverse practices as one universal tradition. Follow local cultural and intellectual property protocols before reproducing cultural material or inviting community participation.

The mathematical focus remains the same: identify the measurable attribute, use a consistent reference or unit, compare carefully and explain what the measurement tells us.

• E1: choose suitable informal units for length, including larger units for long objects and smaller units for greater accuracy.
• E2: compare container capacity using the same unit, record results and explain the measurement process.
• E3: compare mass with balance scales and equal informal mass units.
• E4: recognise why the same informal unit is required and how unit size affects the count.
• E5: investigate specific First Nations uses of body-based uniform informal measurement in context.
• E6: investigate measurable attributes of animal tracks interpreted in specific First Nations contexts.