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Connecting kilometres, metres, centimetres and millimetres


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Last updated 26 October 2012 15:30 by NZTecAdmin
Connecting kilometres, metres, centimetres and millimetres (PDF, 54 KB)

Measurement progression, 5th step

The purpose of the activity

In this activity, the learners develop understanding of the relative size of metres, centimetres and millimetres by measuring the length of objects, using a variety of measuring tools and scales.

The teaching points

  • The learners will be able to determine the appropriate standard unit for measuring a given length.
  • The learners will use knowledge of place value to understand the conversions between millimetres, centimetres and metres.
  • Discuss with the learners relevant or authentic situations where the conversion between units of length is applicable.
  • Ensure the learners understand that the unit needs to be included with the length measure so the size or value of the measure is not misunderstood.
  • Use personal benchmarks to estimate the length of objects.

Resource

  • A variety of rulers or measuring tapes marked in millimetres, centimetres and metres. Include some ‘broken’ rulers that do not have a zero starting point.
  • Conversion dominoes for the follow-up activity ( Appendix A (PDF, 35kB)).

The guided teaching and learning sequence

1. Give the learners a piece of paper with an unlabelled 25-centimetre line drawn on it and ask the learners to estimate its length.

2. Ask the learners to share their estimates. As they give their estimates, ask the learners to explain what they used to make those estimates.

“Why did you think it was that length?”
“What do you use to guide your length estimates? in centimetres? in metres? in millimetres?”

Their answers will allow you to see if the learners have established personal benchmarks for centimetres, millimetres or metres.

3. Next ask the learners to use a ruler or measuring tape to measure the length of the line and record this beside the line.

4. Ask the learners to work in groups to compare their recorded lengths.

“Is your recorded length the same as everyone else’s? If not, why are they different?”
“Did you all use the same measurement unit?”
“How can you use a ‘broken’ ruler to measure an object?”

5. Ask the groups to share their records with the class. Record the lengths on the board. If the group has not given a unit, then do not record it with the length.

6. Discuss any differences in the recorded lengths.

“Is 25 the same as 25 centimetres?”
“Is 250 millimetres the same as 25?”

Encourage the learners to realise that the unit must be included or the length may be misunderstood.

7. Write “37 centimetres” on the board and ask volunteers to draw a line that length on the board without using a ruler or measuring tape. Ask the learners to explain what they are using to make their estimate of 37 centimetres.

“What do you use to estimate 37 centimetres?”
“How accurate do you think you are?”

8. If they have no reference point, suggest that they think of a 30-centimetre ruler and add about another quarter of a ruler length. Alternatively, they may know the length of their hand span (about 20 centimetres) and use slightly less than two hand spans to estimate 37 centimetres.

9. Ask the learners how else the measure 37 centimetres could be recorded.

“How else can we correctly record the length 37 centimetres?”

Record the responses on the board. Encourage the learners to explain why their answer is correct.

“Why is 370 millimetres the same as 37 centimetres?”
“Why can this be also written as .37 metres?”

10. Draw a place-value chart on the board as follows:

Image of place-value chart.

“Is 37 correctly recorded?”

The answer “yes” to this requires the learners to identify that the “unit” for the ones column is centimetres.

11. Record centimetres with the ‘ones’ and then ask the learners to identify where millimetres, metres, and kilometres are in relation to the centimetres. Discuss the placement of the decimal point between ones and tenths.

Centimetres

Image of place-value chart.

Ask the learners to record the following measurements on a copy of the chart above:

  • 3.5 metres (350 centimetres)
  • 45 millimetres (4.5 centimetres)
  • 500 centimetres.

12. Record metres with the ‘ones’ and then ask the learners to identify where millimetres, centimetres and kilometres are in relation to the metre. Note this requires the addition of an extra column (thousandths of metres or millimetres).

Metres

Image of place-value chart.

Ask where 3.7 centimetres would be recorded on this chart. Discuss why this is recorded as 0.037 metres.

13. Ask the learners to record the following measurements on the chart and then write the measure in relation to metres:

  • 56 centimetres (0.56 metres)
  • 45 millimetres (0.045 metres)
  • 500 centimetres (5 metres)
  • 45 kilometres (45,000 metres).

14. Discuss how measurements can be converted without the use of a chart.

“How do you convert metres to centimetres without using the chart?” Or: “Why do you multiply the number of metres by 100 to convert to centimetres?”
“How do you convert metres to kilometres?” Or: “Why do you divide the number of metres by 1,000 to convert to kilometres?”
“How do you convert millimetres to kilometres?” Or: “Why do you divide the number of millimetres by 1,000,000 (million) to convert to kilometres?”

Follow-up activity

Conversion dominoes played by groups of two to four learners.

1. The dominoes are placed face down on the table and mixed well.

2. Each player takes up dominoes to make up their hand. The number of dominoes taken up depends on the number of players: two players draw seven dominoes each, three players draw five dominoes each, and four players draw five dominoes each. The remainder of the dominoes are held in reserve.

3. The player with the double domino that has the ‘longest’ length recorded on it places the first domino. Play proceeds in a clockwise direction. Each player adds a domino to an open end of the layout, if possible.

4. If a player is unable to make a move, they take up a domino from the reserve and the turn passes to the next player. If there are no dominoes left for the player to take up, then the player must pass.

5. A game ends either when a player plays all their tiles or when a game is blocked. A game is blocked when no player is able to add another tile to the layout.

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