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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Terrance's dog weighs 31 pounds. Flea medicine comes in a package for dogs from 10 to 25 kilograms. Does this package fit his dog? Use 1 pound ≈ 0.45 kilogram. What is the scale factor from 1 lb to 30 lb? (× 30) Multiply 0.45 by the same factor. About how many kilograms is 30 pounds? (0.45 × 30 = 13.5 kg) Is a little more than 13.5 kg between 10 and 25 kg? (Yes, so the package fits.) 31 is more than 25. Why is the dog not too heavy? (31 is in pounds and 25 is in kilograms. We must convert before we compare.)

   Show your work
2. 2

   Warm restartHow many cups are in 3 quarts? (1 quart = 4 cups)

   1. A3/4 cup
   2. B7 cups
   3. C12 cups
   4. D16 cups

   How do you know?
3. 3

   Warm restartA rope is 240 centimetres long. How many metres is that? (1 m = 100 cm)

   1. A0.24 m
   2. B2.4 m
   3. C24 m
   4. D240 m

   How do you know?
4. 4

   Warm restartWhich conversion factor changes feet into inches?

   1. A1 ft / 12 in
   2. B1 in / 12 ft
   3. C3 ft / 1 yd
   4. D12 in / 1 ft

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughUsing 1 km ≈ 0.6 mi, about how many miles is 10 kilometers?

   1. A0.06 mile
   2. B6 miles
   3. C16 miles
   4. D60 miles

   Why is that the answer?
2. 6

   Think it throughUsing 1 lb ≈ 0.45 kg, about how many kilograms is a 30-pound dog?

   1. A4.5 kg
   2. B13.5 kg
   3. C30.45 kg
   4. D66 kg

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhy do conversions between systems use ≈ rather than =?

   1. ABecause metric units are always bigger
   2. BBecause the amounts are actually different
   3. CBecause ratios cannot be exact
   4. DThe conversion factors are rounded approximations

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelWhy is a conversion between two systems written with ≈ instead of =, when a conversion inside one system (12 in = 1 ft) is exact?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• mile
• kilometer
• pound
• kilogram
• inch
• centimeter
• gallon
• liter

Use the words

Fill each blank with a word from the bank.

• The ratio that trades one unit for another is a ___ ___.
• Inches, pounds and gallons belong to the ___ system.
• Centimeters, grams and liters belong to the ___ system, built on tens.
• Close to but not exactly equal is ___ — written with ≈.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake converting between systems is comparing the bare numbers without converting at all — deciding that 5 kilometers and 5 miles are the same distance because both say 5.
2. 10

   Say moreTo convert between systems you used a conversion factor like 1 km ≈ 0.6 mi as a RATIO. How does writing it as the ratio 1 : 0.6 let a table do the converting for you?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Two smoothie stands at Chef Academy report their morning sales. Stand A sold 45 smoothies in 9 hours. Stand B sold 56 smoothies in 8 hours.

   Show your work

Last check

These two come from Lesson 3.6. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A highway sign in Canada reads 100 km/h. Using 1 km ≈ 0.6 mi, is that faster or slower than 100 mi/h?

   1. ASlower — 100 km/h is about 60 mi/h
   2. BFaster — 100 km/h is about 160 mi/h
   3. CThe same, because both numbers are 100
   4. DYou cannot compare two different systems

   Explain your choice.
2. 13

   From Lesson 3.6Explain your thinking — There are 4 cups in 1 quart. A soup recipe calls for 5 quarts of broth. How many cups is that, and why?

   1. A1.25 cups, because I divide 5 by 4
   2. B5 cups, because the amount does not change
   3. C9 cups, because I add 5 + 4
   4. D20 cups, because cups are smaller so I multiply: 5 × 4

   How do you know?
3. 14

   From Lesson 3.6You convert 96 ounces to pounds (16 ounces = 1 pound). Should the number get bigger or smaller?

   1. ABigger, because 96 is already large
   2. BSmaller, because pounds are the larger unit
   3. CIt stays the same
   4. DYou cannot tell without the ratio table

   How do you know?

Be honest — this tells your teacher what to do next