Minds On
Discussion
Imagine I told you I had an object that measured 30 units. What do you think that object would be?
Action
Measuring with different metric units
In Minds On, you considered how your idea of an object might change depending on its unit of measurement. Choosing a unit of measure is important because it helps us communicate the correct information.
When using metric units, we know that we choose the unit that best matches with the object.
If we are measuring the length or area of a stadium, we might use kilometres and square kilometres.
In measuring the length or area of a piece of paper, we may use centimetres and square centimetres.
In measuring the capacity of a swimming pool, we might use litres. For a drinking glass, millilitres.
To measure the mass of a bushel of apples, we may use kilograms. For an apple, we may use grams.
We can expand our understanding of metric units by exploring the metric system.
The metric system
In the chart below are the most commonly used prefixes for units of measure.
Explore the prefix and the corresponding unit value.
| Metric Prefix | Unit Value | Place Value |
|---|---|---|
| kilo- | 1,000 units | thousand |
| hecto- | 100 units | hundred |
| deca- | 10 units | ten |
| UNIT | 1 unit | one |
| deci- | 1/10 unit | one tenth |
| centi- | 1/100 unit | one hundredth |
| milli- | 1/1,000 unit | one thousandth |
We can use the metric prefixes with different units of measurement. Let’s explore the chart using metres, litres, and grams.
| Metric Prefix | Unit Value | Place Value |
|---|---|---|
| Kilometre (km) | 1,000 metres | thousand |
| Hectometre (hm) | 100 metres | hundred |
| Decametre (dam) | 10 metres | ten |
| Metre (m) | 1 metre | one |
| Decimeter (dm) | 1/10 metre | one tenth |
| Centimetre (cm) | 1/100 metre | one hundredth |
| Millimetre (mm) | 1/1,000 metre | one thousandth |
| Metric Prefix | Unit Value | Place Value |
|---|---|---|
| Kilolitre (kL) | 1,000 litres | thousand |
| Hectolitre (hL) | 100 litres | hundred |
| Decalitre (daL) | 10 litres | ten |
| Litre (L) | 1 litre | one |
| Decilitre (dL) | 1/10 litre | one tenth |
| Centilitre (cL) | 1/100 litre | one hundredth |
| Millilitre (mL) | 1/1,000 litre | one thousandth |
| Metric Prefix | Unit Value | Place Value |
|---|---|---|
| Kilograms (kg) | 1,000 grams | thousand |
| Hectograms (hg) | 100 grams | hundred |
| Decagrams (dag) | 10 grams | ten |
| Grams (g) | 1 gram | one |
| Decigrams (dg) | 1/10 gram | one tenth |
| Centigrams (cg) | 1/100 gram | one hundredth |
| Milligrams (mg) | 1/1,000 gram | one thousandth |
Converting between metric units
A runner ran 10 kilometres. How else can that distance be represented?
Convert 10 kilometres into:
- hectometres
- decametre
- metres
- decimetres
- centimetres
- millimetres
What is happening as you convert between metric units?
Which unit would you choose to measure the distance the runner ran? Why?
Record your ideas in a notebook or a method of your choice.
When you are ready and have tried it yourself, you may press the ‘Answer’ button to reveal an explanation to the answer.
Solution
10 kilometres would equal to:- 100 hectometres
- 1,000 decametres
- 10,000 metres
- 100,000 decimetres
- 1,000,000 centimetres
- 10,000,000 millimetres
As we convert the metric units from smaller to larger metric units, we are multiplying by 10s, but when we go from larger to smaller metric units, we are dividing by 10s.
For example: If we were to convert from kilometers to millimeters, we would divide by 1,000,000, but going in the opposite way from millimetres to kilometres, we would divide by 1,000,000
If I wanted it to sound that the runner ran a very long distance, I might use 10,000 metres to describe the distance they ran. Although, I know that is that same as 10 kilometres which is equal to 10,000,000 millimetres. Once I decide what kind of information I am trying to clearly share, I can choose the metric unit.
| Metric Prefix | Unit Value | Place Value |
|---|---|---|
|
Kilometre (km) |
1,000 metres |
thousand |
|
Hectometre (hm) |
100 metres |
hundred |
|
Decametre (dam) |
10 metres |
ten |
|
Metre (m) |
1 metre |
one |
|
Decimetre (dm) |
1/10 metre |
one tenth |
|
Centimetre (cm) |
1/100 metre |
one hundredth |
|
Millimetre (mm) |
1/1,000 metre |
one thousandth |
If we convert using the metric prefix chart, we are multiplying or dividing by 10, 100 or 1,000.
Problem solving by converting metric units
A table measures 138 centimetres across. You need to get it through a door which is only 1 metre long. Will the table fit?
In order to check, we can convert the table from centimetres to metres.
Based on our metric units chart, we know that
1 m = 100 cm.
We take 138 cm and divide by 100.
138 ÷ 100 = 1.38 m
The table is 1.38 m and will not fit through the door.
Let’s practice
Explore the following examples. How can you use your understanding of converting metric units to solve the following word problems? Record your thinking using a method of your choice.
Press the ‘Answer’ button to reveal an explanation to the answer.
Solution
The correct answer is 6,400 millilitres.
We know there are , 1,000mL in a L, so we multiply 6.4 by 1,000.
6.4 × 1,000 = 6,400 mLPress the ‘Answer’ button to reveal an explanation to the answer.
Solution
The correct answer is 100 mL per container.
3 litres is split between 30 containers, because 3 is such a small number, it is easier to first convert 3 L to mL.
We know there are 1,000 mL in a L, so 3L is multiplied by 1,000 to convert to 3,000 mL.
Now, we know we have 3,000 mL and are dividing that among the 30 containers so each container gets 3,000 mL divided by 30 which is 100 mL.Consolidation
Converting metric units
Complete the following word problems. Record your thinking using a method of your choice.
Problem 1
Two runners complete a training course.
One runner describes the distance they ran in kilometres. The other runner describes the distance they ran in metres.
Justify both runners’ measurements.
Problem 2
A shape has a perimeter of less than 1m. It is put on a table that measures 24 cm by 26 cm.
Will the shape fit on the table? Explain your thinking.
Connections
Metric units in the real world
In what kinds of professions would it be important to convert metric units?
Record your ideas in a notebook or a method of your choice.
Reflection
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.