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When Centimetres Are Not Enough
The Need for Smaller Units · Inductive
Build the intuition that whole centimetres are too coarse before any notation is introduced — the cognitive need for smaller units must feel genuine. A common early error is reading the tenths tick as a new whole unit; confirm that ten such ticks span exactly one centimetre. No worked examples are formally defined in this section, so class discussion and measurement drive the entire unit.
0–8Hold up two visually similar objects (a pen and a pencil) and invite students to say which is longer. Guide a brief discussion about how ordinary whole-centimetre readings fail to distinguish lengths that differ by a small fraction. Introduce Sonu's mother's screw problem from section 3.1 to crystallise why subdividing a centimetre is necessary.
8–20Distribute rulers. Students place their pen and sharpener on the millimetre-ruled scale and attempt to record lengths in whole centimetres, noticing the gap. Teacher models reading a length such as 2 7/10 cm by counting tenths of a centimetre, writing the mixed-number notation on the board and naming each part.
20–35Figure it Out, section 3.1 p.47 ("Measure the lengths of a pen, sharpener, and an object....") — students measure three objects, record each length in the form 'whole number and tenths' notation, and share readings aloud with a partner to check for consistency.
35–40Whole-class close: students name one situation from their own life where a whole-unit measurement would be insufficient, and explain which smaller unit they would want. Teacher collects two or three examples to anchor the language of 'tenths of a centimetre'.
Figure it Out, section 3.1 p.47 — Measure the lengths of a pen, sharpener, and an object of the student's choice using a scale; record the measurements in centimetres using tenth notation as modelled in the section.
A student places a pencil on a millimetre-ruled scale. The pencil ends between the 12 cm and 13 cm marks, at the seventh small division past 12 cm. Which expression correctly records the pencil's length?
- A 1 27/10 cm
- B 12 7/10 cm
- C 12 7/100 cm
- D 127 cm
B. 12 7/10 cm
What each wrong option reveals
- A The student mis-groups the digits, reading '1 ten and 27 tenths' rather than '12 whole centimetres and 7 tenths'.
- C The student confuses the size of a millimetre division with one hundredth of a centimetre, placing the digit in the wrong fractional position.
- D The student concatenates the whole-centimetre reading and the tick count without inserting any fractional notation, treating the length as 127 whole centimetres.
Also saved as 5 periods or 7 periods.
- 2Building Lengths from Tenths
A Tenth Part - 3Adding and Subtracting Tenth Lengths
A Tenth Part - 4Folding into Hundredths
A Hundredth Part - 5Column Arithmetic with Hundredths
A Hundredth Part - 6Why Ten? Extending the Place Value Chain
Decimal Place Value - 7Decimals in Measurement and on the Number Line
Units of Measurement - 8Zooming In, Adding Up, and Real-World Decimals
Locating and Comparing Decimals - 9Putting Decimals to Work
Synthesis
- 1. Large Numbers Around Us
- 2. Arithmetic Expressions
- 3. A Peek Beyond the Point
- 4. Expressions Using Letter-Numbers
- 5. Parallel and Intersecting Lines
- 6. Number Play
- 7. A Tale of Three Intersecting Lines
- 8. Working with Fractions
- 9. Geometric Twins
- 10. Operations with Integers
- 11. Finding Common Ground
- 12. Another Peek Beyond the Point
- 13. Connecting the Dots
- 14. Constructions and Tilings
- 15. Finding the Unknown
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