Julie Buckholt
CCLM^2 Project
Summer 2012
DRAFT DOCUMENT. This material was developed as part of the
Leadership for the Common Core in Mathematics (CCLM^2) project at the University of Wisconsin-Milwaukee.
Part 1:
Grade 7
Domain: Ratios and Proportional Relationships (7.RP)
Cluster: Analyze proportional relationships and use them to solve real-world and
mathematical problems.
Standard:
3) Use proportional relationships to solve multi-step ratio and percent problems.
Examples: simple interest, tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease, percent error.
Part 2:
Explanation and Examples of the Standard
This standard focuses on Proportional reasoning with an emphasis on using real world
math problems.
The examples for this standard are already listed in the standard, which are:
simple interest, tax, markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, and percent error. When teaching a multi-step problem,
involving percent increase or decrease, the student needs to pay attention to the whole.
Example of a Real World Problem: iPod problem 1: After a 15% discount, the price of
the iPod is $150.00. What was the price of the iPod before the discount?
iPod problem 2: An iPod currently costs $150.00, its price will go up by 15%. What will
the new price be after the increase?
In both of these problems the solutions are different because the 15% refers to different
wholes or 100% amounts. In the first problem, 15% is 15% of the larger percent
discount amount, but in the second problem the 15% is 15% of the smaller percent
increase amount.
Key Terms:
Percent: Per “100”. Example: If 20 liters out of every 100 liters in a mix are orange
juice, then the juice mixture is 20% orange juice.
Proportional Relationship: Mathematical relationship between two quantities as an
equality of two ratios. Example a/b=c/d
Ratio: A relationship between two quantities. A ratio can be indicated in words, such as
3 to 2, and 3 for every 2, 3 out of 5, and 3 parts to 2 parts. Ratios can also be written in
fraction form 3/2 or 3:2
Teacher friendly language:
Students should be able to solve real world examples that show proportional
relationships, that include multi-step ratio and percent problems.
Part 3: School Mathematics Textbook Program
A. Textbook Development:
The textbook that I am currently using is CMP2. The series begins to address Ratios
and Proportional Relationships in the 7th grade book, Stretching and Shrinking, which
can be found in Investigations 1-5. This book starts with looking at similarity which
would come before proportional relationships. This begins with a geometric approach
and then moves into solving the problems algebraically. For example, in Investigation 1
the students begin with enlarging a figure using a “rubber band stretcher” , and then
they compare the figures, using vocabulary such as corresponding sides and angles, no
numbers are used at this time; students are looking at the figures geometrically. Also, in
Investigation 1 ACE problems (Applications, Connections and Extensions) there are
specific problems where the students would have to calculate sales tax, income tax, and
gratuities . In investigation 2, students make similar figures using algebra and
coordinate pairs, they are drawing the “Wump Family” and then comparing the different
Wumps. In Investigation 3, students begin to set up proportions to solve problems.
Proportion problems can also be found in the ACE of Investigation 3, these are not realworld problems. Investigation 4 begins to address equivalency using ratios. This is done
by comparing similar shapes, looking at length, height and width. The students will need
to set up proportions showing the comparisons. This is an important idea because it
exposes students to different ways of exploring proportional reasoning and
relationships. In the last investigation, which is Investigation 5, the students get into the
process of solving proportions. I think this is a good progression, the way the book
teaches Proportional Relationships. Logically, the book introduces the concepts and the
building blocks that students need to have to understand standard 7.RP.3
Comparing and Scaling is the other CMP2 that meets standard 7.RP.3. This is the main
book that addresses ratios, proportions, and percents. Investigations 1 and 2 begins
with making comparisons using real world application. In these first two investigations
students learn how to write ratios in three different forms, making comparative
statements, in the form of 3:2, in fraction and percent form. Investigation 3 address unit
rates, mark downs, percent decrease, and sales tax. The real world application in this
Investigation is comparing CD prices at two different stores. The last investigation is
Investigation 4, this defines proportion and explains many different methods of solving
proportions.
In the 6th grade CMP2 books, standard 7.RP.3 can be found in Bits and Pieces 111
investigations 4 and 5. Investigation 4 involves finding percents of numbers. Students
will also compute discounts, sale prices, gratuities, and sales tax. In Investigation 5,
students solved real world problems where they had to find the original cost of an item if
they know the amount and the percent of the discount. Students had to solve problems
with a fixed amount of money to spend and would have to pay a percent of it for tax.
They would have to figure out if they had enough money for the purchase and for the
tax. In both investigations, students would have to show more than one strategy.
8th grade CMP2 does not meet any standard 7.RP.3. The domain Ratios and
Proportional Relationship is not one of the domains in 8th grade.
Conclusions:
In the CMP2 series, the book Stretching and Shrinking met standard 7.RP.3. This
standard was found in Comparing and Scaling Investigations 4 and 5. The 7th grade
books cover Proportional Relationships and Ratios. The 6th grade CMP2 books covers
this standard in Bits and Pieces 111, Investigations 4 and 5. It covers discounts,
percents, gratuities, and sales tax. Both 6th and 7th grade use real world problems in
their investigations.
By 8th grade, students are expected to be fluent in Ratios and Proportional
Relationships.
In helping to write the Pacing guides in Milwaukee Public Schools, the current 7th grade
CMP2 aligns with the CCSSM. Therefore, choosing this curriculum would help increase
state testing scores because CMP2 satisfies the standards and demands of the
CCSSM.
Suggestions:
As was previously mentioned in my conclusion, I feel that it is important that
Milwaukee Public Schools implement CMP2 throughout the district; which in my opinion
would raise test scores significantly. Not only is this a rich curriculum, it also helps to
improve classroom management. I believe that when a curriculum is strong and the
students are engaged students tend not to disrupt the classroom.
As I review the formative testing, also known as Classroom Assessments Based on
Standards, needs to be revised to meet the new CCSSM. These were originally written
to meet the Milwaukee Public Schools Learning Targets and the State Descriptors.