Unit 1 · Essential SkillsE4 · Units · Ground Ops

Units & Conversions

Build conversion chains whose units cancel and keep squared and cubed units honest.

29 min
Unlocks: Conversion Console
Desmos way

Ready when you are

7 steps · about 29 minutes

Start with the warm-up.

Start

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Warm-up

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Key terms

Conversion factor: A ratio equal to 1 used to change units.
Dimensional analysis: A conversion chain arranged so units cancel.
Squared unit: An area unit requiring the conversion factor to be squared.

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Try it first

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Take a shot before the lesson. Write one relationship from the stem, even if you do not finish.

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The big idea

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See the structure

Treat a conversion factor as a fraction equal to 1. Orient it so the unwanted unit cancels and the wanted unit remains.

Key idea

Name quantities before calculating

Write what each number measures. A correct calculation with the wrong quantity or unit still misses the question.

Build a reliable method

For area, square the conversion factor; for volume, cube it. If $1$ foot equals $12$ inches, then $1$ square foot equals $144$ square inches.

Explore in Desmos

Compare linear and area conversions

For 9 feet of cable, line 1 gives 108 inches. For 9 square feet of tile, line 2 gives 1,296 square inches. Identify why area needs two factors of 12.

The calculator is live: change anything and see what happens.

Compare linear and area conversions

Degree mode

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Stretch to a 36

Write the units on every factor. They expose a reversed conversion before the arithmetic can hide it.

Trap

A believable answer to the wrong question

The choices often include a correct intermediate number. Before selecting it, reread the highlighted ask and check the unit, sign, and domain.

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Worked examples

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Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1: Convert one length dimension

Problem

A 14-foot cable is how many inches long?

Multiply by the unit fraction

12\text{ in}/1\text{ ft}

Which conversion factor matches the dimension?

14(12)=168

inches.

Which reverse conversion confirms the unit change?

Worked example

Example 2: Square a conversion factor for area

Problem

A 5-square-foot panel has how many square inches?

One square foot is

(12\text{ in})^2=144\text{ in}^2

Which conversion factor matches the dimension?

5(144)=720

square inches.

Which reverse conversion confirms the unit change?

Faded example · you finish it

Example 3: Complete the setup and result

Problem

How many seconds are in 2.5 hours?

Choose the setup that follows the stated relationship.

Choose the resulting value.

Desmos way

Chain unit factors and reverse the conversion

Type 2.5*60 to read 150 minutes, then 2.5*60*60 to read 9,000 seconds. Each factor of 60 changes one time unit.

Type 9000/(60*60) and read 2.5 hours. Reversing both factors checks the conversion and catches a missing factor of 60.

Chain unit factors and reverse the conversion

Degree mode

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Practice

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Spot the mistake

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Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

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Exit ticket

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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.