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Connecting tonnes, kilograms and grams


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Last updated 26 October 2012 15:30 by NZTecAdmin
Connecting tonnes, kilograms and grams (PDF, 64 KB)

Measurement progression, 5th step

The purpose of the activity

In this activity, the learners develop an understanding of the relative size of tonnes, kilograms and grams and the conversions between the units.

The teaching points

  • The learners will be able to determine the appropriate standard unit for a given measuring (weight) context.
  • The learners will use knowledge of place value to understand the conversions between tonnes, kilograms and grams.
  • The learners will know that measuring weight to appropriate levels of precision depends on the task and the scale being used.
  • The learners will understand that mass and weight are not the same thing. Mass is the amount of matter in an object and a measure of the force needed to accelerate it. Weight is a measure of the pull or force of gravity on an object. If the same force is applied to several objects, those with a smaller mass will be affected the most. The weight of an object is its mass under the force of gravity. Because gravity is close to constant on Earth, we judge an object’s mass by weighing it. If an object were taken to the moon, its mass would be the same as on Earth, but its weight would be considerably less because the gravity on the moon is far weaker than on Earth. For practical purposes, the measures of mass and weight are about the same, and the terms are used interchangeably.
  • The learners will understand that mass is not proportional to volume. For example, a piece of lead has a far greater mass than a similar-sized piece of foam plastic.
  • Discuss with the learners relevant or authentic situations where the conversion between units of weight is applicable.

Resources

  • A range of measuring devices.
  • Several ‘filled’ bags that weigh 1.4 kilograms.
  • Conversion dominoes for the follow-up activity ( Appendix B (PDF, 30kB)).

The guided teaching and learning sequence

1. Give the learners an unlabelled bag that weighs 1.4 kilograms and ask them to estimate its weight.

2. Ask the learners to share their estimates. As they give their estimates, write the estimates on the board and ask the learners to explain what they used to make their estimate.

“Why did you think it was that weight?”
“What do you use to guide your weight estimates – in grams? in kilograms? in tonnes?”

3. Their answers will allow you to see if the learners have established personal benchmarks for units of weight.

4. Next ask the learners to use one of the weighing devices to weigh the bag. Ask the learners to work in groups of three or four to compare their recorded weight with the weights from others in the group.

“Is your recorded weight the same as everyone else’s? If not, why are they different?”
“Did you all use the same measurement unit?”

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

6. Discuss any differences in the recorded weights.

“Is 1.4 the same as 1.4 kilograms?”
“Is 1,400 grams the same as 1.4 kilograms or 1.4?”

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

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

Image of place-value chart.

“Is 1.4 kilograms correctly recorded?”

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

8. Record kilograms with the ‘ones’ and then ask the learners to identify where grams and tonnes are in relation to the kilograms. Discuss the placement of the decimal point between ones and tenths.

Kilograms

Image of place-value chart.

Using this chart, ask the learners to record the following measurements on it:

  • 600 grams (0.6 kilograms)
  • 5,560 kilograms (5.56 tonnes)
  • 3,055 grams (3.055 kilograms).

9. Record grams with the ‘ones’ and then ask the learners to identify where kilograms and tonnes are in relation to the grams. Note that this requires the addition and relabelling of columns.

Grams

Image of place-value chart.

Ask how 3,500 grams would be written on this chart. Discuss how else this could be recorded.

“How else could you record 3,500 grams?” (3.5 kilograms)
“How do you write 2.5 tonnes on this chart?”
“How else could you record 2.5 tonnes?” (2,500,000 grams, 2.5 million grams, 2,500 kilograms)

10. Give each of the learners, or pairs of learners, a grams chart and ask them to record the following weights on the chart and then convert to kilograms and tonnes. Discuss their answers.

  • 34,500 grams (34.5 kilograms, 0.0345 tonnes).
  • 124,589 grams (124.589 kilograms, 0.124589 tonnes).

11. Ask the learners to record the following weights on their grams chart and then convert to grams and kilograms.

  • 6.7 tonnes (6,700,000 grams, 6,700 kilograms).
  • 30 tonnes (30 million grams, 30,000 kilograms).
  • 0.05 tonnes (50 kilograms, 50,000 grams).

12. Discuss how measurements can be converted without using a chart.

“How do you convert kilograms to grams without using the chart?” Or: “Why do you multiply the number of kilograms by 1000 to convert to grams?”
“How do you convert grams to kilograms?” Or: “Why do you divide the number of grams by 1,000 to convert to kilograms?”
“How do you convert grams to tonnes?” Or: “Why do you divide the number of grams by 1,000,000 (one million) to convert to tonnes?”

13. Discuss with the learners the difference between mass and weight using their existing understandings as a starting point for the discussion.

“Sometimes the weight of an object is called its mass. Are they the same thing?”

Follow-up activities

  • Ask the learners to give their weight in kilograms, grams and tonnes.
  • Have the learners play conversion dominoes* as groups of two to four learners.

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

2. Each player draws dominoes to make up their hand. The number of dominoes drawn 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 with the ‘largest’ weight recorded on it places the first domino. Play proceeds clockwise. 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 draw a domino from the reserve and the turn passes to the next player. If there are no dominoes left, then the player must pass.

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

* Conversion dominoes activity courtesy of BMET tutor, Emily Harrop.

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