Start here

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.

   Let's do one together: 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. Write the conversion fact in the first column. (1 lb : 0.45 kg) 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) 31 pounds is a little more than 30. Does the package fit? (Yes. A little more than 13.5 kg is between 10 and 25 kg.)

   My first step is ___ , because the problem asks for ___ .

   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
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
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

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
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.

   I chose ___ because ___ .
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?

   Inside one system the units are defined to be ___, but across systems the conversion factor is ___, so I write ___.

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?

   Each row multiplies BOTH parts of 1 : 0.6 by ___, giving ___ : ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 3.6Quick check — you've got this: 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
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

Be honest — this tells your teacher what to do next