E. Spatial Sense · Shapes, Maps and Measurement

Measuring with Units: Big Units and Small Units

E2.1About 30 minutes

Learning goals

I can measure length by laying units end to end with no gaps and no overlaps.
I can choose a sensible unit for what I am measuring.
I can explain why I need more small units than big units to measure the same thing.

Words to know

length
How long something is from one end to the other.

unit
The thing we use over and over to measure, like a paper clip, a cube or a footstep. All the units must be the same size.

non-standard unit
A unit that is not the same everywhere, like a hand span or a shoe. Your hand and a grown-up's hand are different sizes.

estimate
A smart guess about how long something is, before you measure.

How long is a hockey stick?

You could say "It's long!" But how long? To answer, we need to measure it. To measure, we count units.

In Grade 1 you compared lengths by lining things up. Now you will measure lengths by counting units.

How to measure with units

Line up the first unit with the start of the object.
Lay the units end to end in a straight line.
Leave no gaps and make no overlaps.
Use units that are all the same size.
Count the units. Say the number and the unit: "5 erasers long", not just "5".

Gaps make the count too small. Overlaps make it too big. End to end is just right.

What if it doesn't fit exactly?

Sometimes the last unit sticks out. Then say "about 6 paper clips long" or "a bit more than 5 paper clips long". That's OK!

Big units and small units

Let's measure the same scarf two ways.

The same scarf is 5 big blocks long, or 10 small cubes long.

Did the scarf change? No! The scarf is the same length. We just used different units.

With big units, we need fewer of them.
With small units, we need more of them.

So when you share a measurement, always say which unit you used.

Worked example

Example 1: Hand spans

Dad measures the kitchen table with his hand spans. He gets 8 hand spans. Zoe measures the same table with her hand spans. Will Zoe get more than 8, fewer than 8, or exactly 8?

The table is the same table. Its length does not change.
Zoe's hand is smaller than Dad's hand.
Smaller units means we need more of them.

Zoe will get more than 8 hand spans.

Worked example

Example 2: Choosing a good unit

Which unit would you choose to measure the length of a hallway: paper clips, crayons or footsteps (heel to toe)?

A hallway is long. Paper clips are tiny. You would need hundreds and it would take forever!
Crayons would also take a long time.
Footsteps, heel to toe, are bigger. You can count them quickly.

Footsteps. Choose a big unit for long things and a small unit for short things.

What to measure	Good unit choice	Why
a crayon	paper clips or small cubes	short object, small unit
a book	crayons or paper clips	medium object
a rug	shoes or footsteps	long object, bigger unit
a soccer field	big walking steps	very long, very big unit

Matching units to objects

Just for fun

Long ago, people really did measure with body parts. That's why we still have a unit called a foot! The problem? Everyone's foot is a different size. (Can you guess what the next lesson is about?)

Hands-on activity

Measure the same thing three ways

You need: paper clips (or LEGO bricks), spoons, and your own feet.

Pick a table or a bed.
Estimate first: about how many spoons long is it? Write your guess.
Measure with spoons, laid end to end. Write the number.
Measure the same thing with paper clips. Then with your feet (heel to toe).
Make a chart: unit, estimate, measurement.
Which unit gave the biggest number? Which gave the smallest? Why?

Math talk: "Which unit was easiest to use for this object? Why?"

Your turn

When measuring with paper clips, should you leave gaps between them?

A book is 6 erasers long. Would it be more or fewer than 6 if you used paper clips that are shorter than erasers?

Which unit is best to measure the length of a toothbrush: footsteps or paper clips?

Nia measured a rug: "It's 9." What is missing from her answer?

Kai measured a pencil with some long erasers and some short erasers mixed together. Why is that a problem?

The same rope is 4 skipping-rope handles long and 12 paper clips long. Which unit is bigger?

More practice: warm-up

What does length mean?

Where do you put the first unit?

Which is a better unit to measure a driveway: paper clips or big steps?

True or false: the units must all be the same size.

If the last paper clip sticks out past the end, what word can you use?

More practice: on your own

A table is 10 spoons long. Ben says it will also be 10 forks long, but his forks are longer than the spoons. Is Ben right?

Ali measured a shelf with overlapping blocks and got 12. Is the real number of blocks more or less than 12?

Grandpa's foot is longer than Maya's foot. They both measure the same rug in footsteps. Who gets the bigger number?

A desk is 6 crayons long. A crayon is the same length as 2 paper clips. How many paper clips long is the desk?

Why do you think people invented units like centimetres that are the same everywhere?

Challenge

A mat is 4 big blocks long. One big block is as long as 3 small cubes. How many small cubes long is the mat?

Lucas measured a window as 5 hand spans. His mom measured it as 4 hand spans. Did one of them make a mistake? Explain.

You want to measure a baseboard along a wall, about as long as 3 beds. You have 10 paper clips and 10 rulers. Which would you use? Why?

Check your understanding

Quiz

How should units be placed when measuring?

A shelf is 5 crayons long. If you measure it with paper clips that are shorter than crayons, you will get...

Which unit is best for measuring the length of a classroom?

A rug is 6 big blocks long or 12 small cubes long. Which is the bigger unit?

Leo measured a book with overlapping erasers. His count will be...

Why should you always say the unit, like "7 paper clips"?

For parents and teachers

Big idea: Measuring means counting equal units laid end to end. The smaller the unit, the more of them you need (an inverse relationship). Children should choose units that make sense for the size of the object.

Common difficulties:

Gaps, overlaps, or not starting at the end. Show what happens to the count when you do each one.
Thinking a bigger number means a longer object, even when different units were used. Measure the same object with two units side by side.
Forgetting the unit name. Ask, "7 what?"

How to help: Measure furniture with spoons, shoes, LEGO bricks or hand spans. Compare your measurement with your child's for the same object and talk about why they differ. This prepares children to see why we need standard units (centimetres and metres), coming next.