1. Licensing information
Users should treat this material as a working draft. This material can be used in its current form, customized, and/or printed or displayed by the user.
The author(s) request feedback on all materials so that they can be continually improved and updated.
This material is licensed under the Creative Commons Attribution-Share Alike license: (
Author: Kevin Hall
This is part of a larger unit on Proportional Reasoning available at
Wording for the legal statement above is adapted from the legal statement for Trigonometry, published in 2009 by The CK-12 Foundation:

2. Teaching notes
These are NOT lecture notes. Students should try the questions on their own, before you show the answers.
While they are practicing, you want to be walking around praising and coaching them.
Before getting to class, be sure to print out the answers and have them handy. Otherwise you’ll be stuck solving the questions for yourself while they work, rather than walking around praising and coaching students.
Using a remote mouse clicker, you can slowly display the answers. Time it so each answer appears soon after most students have finished that question.

3. Teaching Notes
The purpose of these slides is to keep you, the teacher, mobile. Instead of being stuck in the front at the blackboard/projector, you can walk around.
This works best if it takes less than 5 s. for you to look at each student’s work, praise or coach, and move on, “working the crowd” as Fred Jones would say.
The student blackline is designed to make all students solve each question in the same part of their page, so you can see at a glance whether it’s right. That lets you work the crowd more efficiently and praise or coach many more students.

4. What’s the total cost of the cans of soup below? Each can is the same.
1).
What’s the total cost of the cans of soup below? Each can is the same.
2).
What’s the price per can of soup below? Each can is the same.
Total cost = ______? $
Total cost =$9 ??
1.80 ??
1.80 ??
1.80 ??
1.80 ??
1.54
1.54
1.54
1.54
1.54
$/can = _____?
$/can = $1.54
To split up $9 into equal parts, we DIVIDE.
Easy way to add it up is to MULTIPLY:
1.54 • 5 =
7.70
7.70
9 ÷ 5 = $
1.80
1.80
per can 2 2 $8 $8
Each circle
represents 1 ______ 2
candy. 2
So the rate is 2 _______
for $
each
candy.
_________
4 candies
4 candies

5. 4).
0.5
0.5
0.5
0.5
4 candies
4 candies
0.5
0.5
0.5
So the rate
is 0.5 _______
for
Each circle rep-
resents 1 _____
0.5
candies
dollar.
each
dollar.
______
8 dollars
8 dollars
5).
You ran a 3-mile race in 18 minutes.
a). What was your rate in minutes per mile?
b). What was your rate in miles per minute? 18 3 =
6 minutes/mile =
0.133 minutes/mile 3 18
If you don’t understand #5, don’t worry. We’ll go over the idea in class later.