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. 5 Copy the 4. Do it 9 times 4•9 = $36 4 $4 on dog food 4 4 4 4 4 4 4 4
1).
Out of 5
Out of 5
Out of 10
Out of 15
Out of 20
Out of 25
Out of 30
Out of 35 5
Adds up to 2 2 2 2 2 2 2 2
Answer: x = 14 = 14 14
2).
Justin loves his dogs. Out of every $6 he spends on them, about $4 goes towards dog food. In March, he spent $54 on his dogs. How much did he probably spend on dog food?
Copy the 4. Do it 9 times
4•9 = $36 4
$4 on dog food 4 4 4 4 4 4 4 4 4
$6 total $6
total
$12
total
$18
total
$24
total
$30
total
$36
total
$42
total
$48
total
$54
total
Copied 9 times
He spent $36 on dog food in March.

5. 3).
4).
Please fill in the missing heights on the number line.
Please fill in the missing numbers on the x- and y-axis.
Distance run (miles)
3.2 ?
49.2 ft.
2.0
2.8 ?
= each
0.4
(8.2)(5) = ? 41 5
2.4 ?
(8.2)(4) = ?
32.8 6
pieces
2.0
(8.2)(3) = ?
(0.4)(4) =
24.6
1.6 ?
(8.2)(2) = ?
16.4
(0.4)(3) =
1.2 ?
2.0
broken into 5 pieces
(0.4)(2) =
0.8 ? ? ?
0 ft. 2 4 6 8 10 12
49.2 ft
Time (min.)
= each
8.2
6 pieces
Hint: the total height is broken down into how many pieces?