MS After School Intervention
Unit: Ratios & Proportions
Theme: Sports Park
Day 4 Lesson
Objective
Students will solve proportions.
Common Core Standards:
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems,
e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number
line diagrams, or equations.
6.RP.3a Make tables of equivalent ratios relating quantities with whole-number
measurements, find missing values in the tables, and plot the pairs of values on the
coordinate plane. Use tables to compare ratios.
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by
testing for equivalent ratios in a table or graphing on a coordinate plane and
observing whether the graph is a straight line through the origin.
Materials
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KWLS graphic organizer resource sheet
Cuisenaire® Rods (one per group)
Teaching Student-Centered Mathematics Grades 5-8, Activity 6.2
“Look-Alike Rectangles” resource sheet (one per group)
“Look-Alike Rectangles: Three Groups and an Odd Ball” resource sheets
(one per group)
Scissors
Color tiles (one per group)
Geoboard® (peg board) with bands (at least two boards per group)
Graph paper (at least two sheets per group)
“KWLS” resource sheets (one per student)
“Building a Playing Field” resource sheets (one per group)
“Which Has More?” resource sheet
Warm-Up (5 minutes)
Complete the “K” and the “W” of a KWLS graphic organizer. Prompt students to think
about what they already KNOW about proportions and WHAT they want to learn.
Students should create a KWLS graphic organizer and record ideas.
Which Has More? (15 minutes)
(Note: For this activity, refer to pages 158-159 of Teaching Student-Centered
Mathematics.)
Ask students to imagine themselves at the Sports Park. Ask students, “How many of you
have played Frisbee?” “Can anyone describe Ultimate Frisbee?” Discuss what Ultimate
Frisbee is. (Two teams compete against each other to get their Frisbee to the goal.
Players pass the Frisbee to each other and run as they attempt to score a goal. It is similar
to soccer except in soccer the teams are made up of all boys or all girls. In Ultimate
Frisbee teams are coed.)
Show students situation #1 on the “Which Has More?” resource sheet. Prompt students
to think-pair-square-share their responses. Accept all responses and elicit student
explanations. Possible follow-up questions could include:
 Explain how you got your answer.
 Why do you think your answer is correct? (Justify)
Note: Keep situation #2 covered for later use.
Proportions with Cuisenaire Rods (20 minutes)
Divide students into groups and give each group a set of Cuisenaire Rods. Students will
build a staircase of ten rods with white being the first rod and orange being the tenth.
Assign the number name of “one” to the white rod. Students are to number name the
other rods.
Ask students to select a purple rod, and place a brown rod underneath it.
Purple
Brown
This shows a comparison of 4 to 8. Ask students to find other combinations that
represent this same comparison. Some examples would be light green to dark green and
yellow to orange, and white to red. Have students share their method of exploring the
problem. Ask students to select a light green rod and place a blue rod under it. This
shows a comparison of 3 to 9. Ask students to find other combinations that represent this
same comparison. Have students share their method of exploring the problem.
Look-Alike Rectangles (20 minutes)
Assign students to pairs and complete the Look-Alike Rectangle Activity on page 160 of
Teaching Student-Centered Mathematics Grades 5-8. Go over answers as a class.
Building a Playing Field (20 minutes)
Divide students into groups of four and give each group a Geoboards®, color tiles, paper,
and graph paper. Read and display the following scenario:
“The Sports Park needs more ball fields. Your help is needed to determine the size of the
fields to accommodate different age groups. A regulation soccer field is 120 meters long
and 90 meters wide. Use the manipulatives provided to determine your solutions to the
following:
1. What is the ratio of length to width of the regulation size soccer field?
(Answer: 4 meters to 3 meters)
2. If a soccer field is 60 meters long, how many meters wide should the field be?
(Answer: 45 meters)
3. If the field is 40 meters wide, how many meters long should the field be?
(Answer: 30 meters long)
Pose the following discussion questions:
Explain how you determined the dimensions of each soccer field? (Answers will vary)
What is the relationship between the ratios of each soccer field? (Answer: When the
ratios of each soccer field are written in simplest form, all the ratios are equal. Two
equal ratios form a proportion.)
What if a soccer field was 90 meters long and 60 meters wide. Would it be proportional
to a regulation field? Why or why not? (Answer: It would not be proportional since the
ratio is 3 to 2, not 4 to 3.)
Closure (10 minutes)
Show students situation #1 on the “Which Has More?” resource sheet. Ask students again
to think-pair-share-square to answer the question. Follow-up by asking:
 Did your answer change? Why or why not?
 What did you learn today that helped you answer the question?
Show students situation #2 on the “Which Has More?” resource sheet. Prompt students
to, individually, think about the situation, answer the following question and justify their
answer.
Decide which sports bag has more Frisbees. Use words, pictures, and or numbers to
justify your answer.
Look-Alike Rectangles
(from Teaching Student-Centered Mathematics, Grades 5-8)
Look-Alike Rectangles
Three Groups and an Odd Ball
Rectangles
Group 1
(Letter of rect.)
Measures in cm
Long Side
Short Side
Ratio of Sides
Short/Long
Rectangles
Group 2
(Letter of rect.)
Measures in cm
Long Side
Short Side
Ratio of Sides
Short/Long
Rectangles
Group 3
(Letter of rect.)
Measures in cm
Long Side
Short Side
Ratio of Sides
Short/Long
Odd Ball
(Letter of rect.)
Measures in cm
Long Side
Short Side
Ratio of Sides
Short/Long
BLM 6 – Look alike rectangles recording sheet
K
W
L
S
The Sports Park needs more ball fields. Your help is needed to determine the
size of the fields to accommodate different age groups. A regulation soccer field
is 120 meters long and 90 meters wide.
Use the manipulatives and/or graph paper to help you solve the problem and
represent your solutions. Be prepared to explain your solutions to the class.
1. What is the ratio of length to width of the regulation size soccer field?
2. If a soccer field is 60 meters long, how many meters wide should the field be?
3. If the field is 40 meters wide, how many meters long should the field be?
Which Has More?
Situation 1: Which ultimate Frisbee team has more girls?
The Stars
The Comets
Situation 2: Which sports bag has more Frisbees?
John’s Bag
Peter’s Bag