RATES: Problem Solving Questions to Improve
Multiplicative, Proportional, and Algebraic
Reasoning (for Standardized Tests and Life)
Jim Olsen
Western Illinois University
http://www.wiu.edu/users/mfjro1/wiu/RATES/
First Samples:
1.
Jackie and Sallie buy 120 craft beads for 6 dollars.
a)
Jackie takes 120 ÷ 6 and gets 20. Explain what the 20 means.
b)
Sallie takes 6 ÷ 120 and gets .05. Explain what the .05 means.
2.
Chocolate covered raisins cost $4.35 per pound. You have $3. How much (in
pounds) can you buy? Round your answer to two decimal places.
3.
Robin mowed three yards. At the first yard Robin was paid $6 per hour
and it took 2 hours to mow the yard. The second yard also took 2 hours
to mow, but the pay was $5 per hour. The third yard took 4 hours to
mow and the pay was $8 per hour. What is Robin’s average pay per hour?
RATES Project
Real-world Applications Teaching Everyday Solutions
Mission Statement


The purpose of this project is to increase
student understanding of rates and students’
ability to use rates flexibly to solve real-world
problems. Our goal is to help teachers and
students realize the importance of teaching
and learning about rates and provide them
with curriculum materials for teaching and
learning about rates in the classroom.
Examples of rates:
◦ calories per serving; $/pound; mpg.
Why is it important?
Why should we teach about rates?
 Why should students learn about rates?

The Guiding Principles For Writing
Questions and Instructional Materials

http://www.wiu.edu/users/mfjro1/wiu/RATES/
Overview of curriculum so far
Eighth Grade Curriculum
 14-week, Problem-of-the-Day curriculum
 Designed to be done three days per week.
 Worksheets are designed to be done in 10 minutes or less per day.
The quizzes take about 15 minutes. The Pretest and Posttest take
about 50 minutes.
 The Pretest and Posttest contain a no-calculator and calculator-allowed
portions.
 The curriculum is based on 9 Objectives (which are further broken
down, making a total of 29 sub-objectives).
 The curriculum consists of:
 A Pretest
 38 Problem-of-the-Day worksheets (29 worksheets, keyed to the
objectives, covering new material and 9 mixed practice worksheets)
 3 quizzes
 A Posttest

Request – If you’d like to use this new curriculum, we request
that you help us measure the effectiveness of this curriculum.
Objectives and sample worksheets
 Objectives
- See packet.
Example Problems-of-the-Day sheets (in
packet)
 Sample worksheet “Day: 1.2 ~ Obj.: 1.b”
◦ Week 1, day 2, Objective 1.a
Sample worksheet Day 4.2 ~ 2.b
 Sample worksheet Day 10.2 ~ 7.a


Rates Assessment (Post test)
Let’s solve some problems…
Implementation
14-week timetable on the web site.
http://www.wiu.edu/users/mfjro1/wiu/RATES/
 How much direct instruction?

◦ Flexible – up to the teacher.
◦ Very little is needed. Worksheets have
examples.
◦ We assume that the students have seen (but
have not fully mastered) decimals, mixed
numbers, percent, and the word “per.”

Scoring Rubric online.
--Session Evaluation