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Compare Lengths Indirectly Using a Third Object

Students will compare the lengths of two objects that cannot be placed side by side by measuring each with a third object (e.g., a string or strip) and using transitivity to determine which original object is longer.

How it is taught

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A third object can compare lengths.

Longer than longer means longest.

Read it: Compare through the one in the middle

The rope is longer than the stick. The stick is longer than the ribbon. So the rope is longer than the ribbon, without putting them side by side.

  1. Compare the first thing with the one in the middle.
  2. Compare the one in the middle with the last thing.
  3. The first is longer than the middle, and the middle is longer than the last, so the first is longer than the last.

The rope and the ribbon may be too far apart to line up.

The stick is compared with each, so it carries the length across.

A thing that matches the stick is as long as the stick.

Compare each with the one in the middle. The rope is longer than both, so it is the longest.

Picking the stick in the middle, or saying you cannot tell.

The rope is longer than the stick, and the stick is longer than the ribbon. The rope is the longest.

A rope is 9 cubes long. A bench matches the rope. How long is the bench? — 9. The bench matches the rope, so it is 9 cubes long too.

Bed vs. bathtub — measured with a string

Which is longer — your bed or your bathtub? They are big, and they live in different rooms!

Here is the bed in the bedroom, and the bathtub in the bathroom.

We can't carry a bed or a bathtub to compare them side by side. So how can we tell which is longer?

We can use a string! A string is easy to carry from room to room.

First, lay the string along the bed. Make the string the same length as the bed.

Now carefully carry the string over to the bathtub.

Lay the string along the bathtub and line them up at one end.

Look — the string sticks out past the end of the bathtub. The string is longer than the bathtub!

The string is the same length as the bed. So the bed must be longer than the bathtub too!

Which is longer — bed or bathtub?They are in different rooms!Bedroom — the bedBathroom — the bathtubWe can't put them next to each other!Use a string!stringcarry it!stringlonger than the bathtub!String = Bed, and String > Bathtubso Bed > Bathtub!LONGERBed(than the bathtub)
Grade 1 · Use a string to compare two things you can't move

The bed is longer than the bathtub. We figured it out using a string in the middle.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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