RATES: Problem Solving Questions to Improve Multiplicative, Proportional, and Algebraic Reasoning (for Standardized

Tests and Life)

Jim OlsenWestern 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 ProjectReal-world Applications Teaching Everyday

Solutions

Mission StatementThe 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 Materialshttp://www.wiu.edu/users/mfjro1/wiu/RAT

ES/

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 worksheetsObjectives - 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.bSample worksheet Day 10.2 ~ 7.a

Rates Assessment (Post test)

Let’s solve some problems…

Implementation14-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