Linear Measurement: Centimetres and Metres
Warm-up
How wide is your hand? How tall is your chair? Estimate first using personal referents, then measure to check. Track estimates vs. measurements. Whose estimate was closest? What referent did they use?
Explore
Measurement hunt: students measure 8 objects around the classroom, first estimating (using personal referents) then measuring. Record: estimate, actual measurement, difference. Identify the largest estimation error and discuss what referent would have helped.
Formalize
Unit selection: teacher shows a list of things to measure. For each: would you use centimetres or metres? Why? The width of a pencil (cm: too small for metres). The length of the hallway (m: too big for centimetres). The height of a bookshelf (could be either: 1.2 m or 120 cm). Discuss when precision matters.
Linear Measurement: Centimetres and Metres
Connect to place value: 100 cm = 1 m. How many centimetres is 2.5 metres? (250 cm.) This is not just measurement: it is place value applied to measurement units. Students who know 100 cm = 1 m can convert by multiplying or dividing by 100.
Practice
Students measure 6 objects (3 in cm, 3 in m), recording estimates and measurements for each. Exit ticket: estimate the length of the classroom in metres. Write your personal referent and your estimate.
Exit ticket
Students measure 6 objects (3 in cm, 3 in m), recording estimates and measurements for each. Exit ticket: estimate the length of the classroom in metres. Write your personal referent and your estimate.
Step 1: Measure a crayon with a normal ruler correctly: line the END of the crayon at 0, read the number at the other end: 9 cm.
Step 2: Now the diagnostic: hand out a "broken ruler" (starts at 4). Students measure the same crayon. Watch: many read the far end — "13!" — because they trust the printed number.
Step 3: Resolve it by counting UNITS, not reading labels: the crayon spans from the 4 mark to the 13 mark. Count the centimetre spaces it covers: 5, 6, 7, … 13 — that's 9 spaces. Still 9 cm.
Step 4: State what a ruler actually is: a line of centimetre spaces with labels for convenience. The measurement is how many SPACES the object covers — the labels only save you counting when you start at 0.
Students who pass the broken-ruler test understand measurement; students who read "13" understand only rulers.
Step 1: Pose the job: measure the gym's length. Offer the class ruler (30 cm) or the metre stick / trundle wheel.
Step 2: Let a pair actually START measuring the gym with the small ruler — three placements in, the class sees the problem: it'll take forever, and every placement risks gaps and slips. Small units for big distances multiply error and effort.
Step 3: Measure with the metre stick: about 18 metres, achieved quickly with fewer placements.
Step 4: Build the choosing-rule together: centimetres for things you can hold (pencil, book, handspan); metres for things you can walk (room, hallway, playground). And the connector fact, said with materials in hand: 1 metre IS 100 centimetres — the gym is 18 m, which is 1800 cm; same length, different unit.
Estimation habit: before any measuring, everyone writes an estimate. "About 20 metres" beats a silent shrug — calibrated eyes are the real product of measurement class.
What happened: the number was measured correctly; the unit was chosen by habit or guess. The student may not yet FEEL how different a centimetre and a metre are.
Step 1: Make the units physical: a centimetre is about a fingertip's width; a metre is about one giant step, or fingertip-to-nose with an arm out. Have the student show both with their body.
Step 2: Reality-check the claim: "a 6-METRE pencil would be six giant steps long — longer than the whiteboard! Could it fit in your pencil case?" Laughter is the sound of the error becoming un-makeable.
Step 3: Re-say the measurement with the body-check attached: "6 fingertips — 6 centimetres." ✓
Step 4: Build the habit that prevents relapse: every measurement gets a sanity sentence — "does that sound right for this object?" Numbers with units must survive a moment of imagination before they're written down.