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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 needs flea medicine for a dog weighing 31 pounds, but the packages are labeled in kilograms. The conversion factor is 1 pound ≈ 0.45 kilogram, so the ratio is 1 : 0.45. Scale it with a ratio table: 10 lb ≈ 4.5 kg, 20 lb ≈ 9 kg, 30 lb ≈ 13.5 kg, 40 lb ≈ 18 kg. 31 pounds is just past 30, so the dog is a little more than 13.5 kilograms. That falls inside the package for dogs between 10 and 25 kilograms. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

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

   1. A12 cups
   2. B7 cups
   3. C3/4 cup
   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. A2.4 m
   2. B24 m
   3. C0.24 m
   4. D240 m

   How do you know?
4. 4

   Warm restartWhich conversion factor changes feet into inches?

   1. A12 in / 1 ft
   2. B1 ft / 12 in
   3. C3 ft / 1 yd
   4. D1 in / 12 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. A6 miles
   2. B0.06 mile
   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. A13.5 kg
   2. B30.45 kg
   3. C66 kg
   4. D4.5 kg

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

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

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

   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.

• Rewriting a customary measurement as a metric one gives an ___ answer, not an exact one.
• 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.

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. A20 cups, because cups are smaller so I multiply: 5 × 4
   2. B1.25 cups, because I divide 5 by 4
   3. C9 cups, because I add 5 + 4
   4. D5 cups, because the amount does not change

   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. ASmaller, because pounds are the larger unit
   2. BBigger, because 96 is already large
   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