How long is the object?

I have an object that is 200 units long. What do you think it could be?

If I measured the object with a unit the length of a pencil, does that change your idea of the object?

If I measured the object with a unit the length of a table, does that change your idea of the object?

If I measured the object with a unit the length of a car, does that change your idea of the object?

Measuring length

In the Minds On section, you considered how different units of measure can change our perspective on the length of an object.

We can use metric units to measure the length of shapes, objects, and spaces. When we measure a length using large metric units, we might be measuring a distance (a space between 2 locations).

If a teacher is in one location and they move to the other side of the room, they could measure the distance that they moved.

We can also measure dimension. Dimension is the distance between 2 points on an object. Some examples of dimensions are length, width, and height.

Measuring height or width, and distances can be done using the following units.

Task 1: Measurement search

Now that we’ve reviewed the benchmark measurement units, find as many objects as you can in the space you are in, or think of objects that would match the following criteria. Which objects did you find or think about?

Complete the Measurement Search Checklist in your notebook or using the following fillable and printable document. When you are ready to check some suggested answers, access the Measurement Search Checklist Sample Response using the next printable document.

Task 2: A closer look at units

The following table outlines all the units that you can use to measure distances or dimensions.

Which of the units have you used before? Which is the smallest unit? The biggest unit? How do you know?

Millimetre is the smallest unit (in this table) that you can use to measure a distance, and each unit to the right gets bigger and bigger. Smaller units should be used for objects that are smaller, or measurements that must be more precise and detailed.

Smaller units should be used for objects that are smaller, or measurements that must be more precise and detailed.

Bigger units are better for larger objects, or when you need to estimate the measurement.

Choose the most appropriate unit that should be used for each of the following items. Estimate the measurement of each item.

1. A pencil
2. A football field
3. A classroom
4. The width of a book
5. The height of a statue
6. The distance from the front door of the school to your classroom
7. A paper clip
8. The width of a ring

Record your estimates in a notebook or a method of your choice.

Task 3: Measurement challenges

Measurement Challenge #1: If you needed to determine the length of a room and could choose any object to help you do so, what object would you choose?

• Step 1: Estimate or measure the length of the object. What unit could you use to measure this object? Could your object be more than 1m? Why is it important to measure accurately when determining the room length?
• Step 2: Count how many of these objects it will take to reach the opposite side of the room. Does it matter if you place the object along a straight line? Why might this be important?
• Step 3: Multiply the number of objects it took by the length of the object. This will tell you the length of the room.
• Step 4: Can you figure out this distance in a different unit?

Record your ideas in a notebook or a method of your choice.

Measurement Challenge #2: Figure out the height of the Big Apple in front of the Big R’ Apple Farm in Brampton, Ontario, using the height of a pencil or any other item that you’re familiar with.

Task 4: Calculating conversions

When we switch from one unit of measurement to another, it is called a conversion. To convert between units, we can relate units to the place value of each unit. One metre is the basic or benchmark unit of measurement, like the ones column of a place value chart.

What do you think the height of the Big Apple is? What did you do to find the answer? What object did you use to estimate the measurement? What strategies did you use to convert between units?

According to the place value and units chart, how many m are in a km? How many mm are in a m?

The units get smaller as you move from the left of the chart to the right of the chart. Each unit is 10 times smaller than the unit to its left. Therefore, every time you move one unit to the right or one unit smaller, you multiply by 10.

For example, if you have 1 km, you will have:

• 10 hm (1 × 10 = 10)
• 100 dam (10 × 10 = 100)
• 1,000 m (100 × 10 = 1,000)
• 10,000 dm (1,000 × 10 = 10,000)
• 100,000 cm (10,000 × 10 = 100,000)
• 1,000,000 mm (100,000 × 10 = 1,000,000)

You move the decimal one place to the right.

Every time you move one unit to the left or one unit bigger, you do the opposite and divide by 10.

For example, if you have 1 mm you will have:

• 0.1 cm (1 mm ÷ 10 = 0.1)
• 0.01 dm (0.1 cm ÷ 10 = 0.01)
• 0.001 m (0.01 dm ÷ 10 = 0.001)

and so on...

For example, if you have 1 mm you will have:

• 0.1 cm (1 ÷ 10 = 0.1)
• 0.01 dm (0.1 ÷ 10 = 0.01)
• 0.001 cm (0.01 ÷ 10 = 0.01)
• and so on…

You move the decimal one place to the left.

As you can see, there is an inverse or ‘opposite’ relationship between the size of a unit and the count of units. This means that larger units produce a smaller measure, and smaller units produce a larger measure. This will help you when estimating whether a conversion will result in a having larger or smaller count of units.

Task 5: Estimating conversions

Estimate how tall the following towers are:

• Leaning Tower of Pisa
• Taj Mahal
• Lotus Tower
• CN Tower

What unit is the most reasonable to measure a tower?

Record your ideas in a notebook or a method of your choice.

What unit did you use to estimate? You should use m. Without calculating the conversion, make another estimate for how many cm each of these towers are? How many mm? Which unit gives you the largest number?

When you use a smaller unit, you need more of them (or a bigger number) to measure the length. When you use a bigger unit, you need less of them (or a smaller number) to measure the same distance.

Therefore, when you are switching from bigger units to smaller units, the number will always get bigger. When you are moving from smaller units to bigger units, the number will always get smaller.

How can this discovery help you when you are calculating or estimating conversions?

Here are a few estimates for the towers we explored. Are your estimates similar?

Press ‘Solutions’ to check your work.

Solutions

Task 6: Word problems

Complete the conversions in the following questions. First make an estimate and then calculate the answer. Record your ideas using a method of your choice. After you have answered the questions on paper or in your notebook, press ‘Solutions’ to check your work.

Question 1: To make one bracelet, 16 cm of string is used. How many bracelets can you make with 1.92 m of string?

Solutions

Question 2: A parking lot is 75 m wide. There are 25 spots, side by side. How many centimetres wide is each spot?

Solution

Question 3: A bus travelled 50 km. A train travelled one quarter of that. How many metres did the train travel?

Solution

Designing to scale

Task 1: Design a statue

A local artist has been asked to design a statue that represents the community. Create a two-dimensional example or describe your plan in a way that is to scale. This means that you need to choose a unit that the statue will be built in (should be bigger than the size of a door!) and convert it to a smaller unit that you can fit onto a page.

Describe the statue in a notebook or a method of your choice. Record the actual height and width of your statue and the conversion to the measurements it should be when it is built.

Be prepared to share and discuss the following:

1. Explain how you decided on the size of your plan.
2. Explain why you chose the unit of measurement for your statue.

If you would like, you can complete the activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Press the ‘TVOMathify’ button to access this resource and the ‘Activity’ button for your note-taking document.

TVO Mathify (Opens in a new window) Activity(Open PDF in a new window)

Questions to explore

Reflect on and answer the following questions:

1. Why is it a useful skill to know how to measure objects and convert to different units?
2. How does it help to compare the units of measurement to place values?

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.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Connect with a TVO Mathify tutor