MS After School Intervention
Unit: Ratios, Rate, and Proportion
Theme: Sports Park
Day 5 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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Overhead projector or document camera
KWLS graphic organizer from previous day
Moving with Math: Percent & Probability (MH3)
Color tiles (blue and yellow in addition to other colors)
Calculators
“Equal Ratio Cards” resource sheets (print multiple copies)
“Mix-N-Match Ratio Cards” resource sheets (cut prior to class)
“Mix-N-Match Answer Cards” resource sheet
“Stir-the-Class” resource sheet
“Exit Ticket” resource sheets (one exit ticket per student)
Warm-Up: “K-W-L-S” (5 minutes)
Return to the K-W-L-S graphic organizer started in the warm-up from the Day 4 lesson.
Allow students time to consider:
L – What have you LEARNED about proportions?
S – What do you still want to KNOW?
“Painters Wanted!” (15 minutes)
Share the following scenario with students:
After years of neglect the concession stand at the Sports Park is in need of a fresh coat of
paint. You and your friends have been hired to paint the Concession Stand green. To
your surprise the only colors left are blue and yellow.
Ask students what they can do to make green paint. Elicit information about making
green by combining yellow and blue.
Next, complete the Introductory Activities on page 24 (Ratio and Proportion) of Moving
with Math: Percent & Probability (MH3). Begin with the activity that explains how to
make green paint. Once completed write the following examples on the board and have
students solve.
Example 1: After painting, your friend’s heart is beating 100 times in 1 minute. What is
the ratio of minutes to heart beats? (1/100) What is the ratio for 2 minutes? (2/200)
for 5 minutes? (5/500)
Example 2: Use cross products to determine if the ratios are equal, in other words form
a proportion.
8
2
3
2
and
a)
b)
and
10
6
12
3
(no 20  18)
( yes 24=24)
“Mix-N-Match” (15 minutes)
Give each student a “Mix-N-Match” card. Instruct students to think about some possible
equivalent ratios that would form a proportion.
Direct students to stand and on the signal find another classmate with an equivalent ratio
that will form a proportion. After students pair up, instruct them to pair up with another
pair of equivalent ratios, so they can form several different proportions with equivalent
ratios.
After students have formed groups of four, they may check their accuracy by going to the
‘Answer Board’. Answer cards could be made available in a variety of ways: taped to
the chalkboard, placed on a table, put in a clear pocket chart, hung on a clothes line, etc.
Each group should determine which of their ratios is in simplest form, go to the answer
board and find that ratio. Next to the simplest form ratio are the other equivalent ratios.
“Cookie Fundraiser” (20 minutes)
Share the following scenario:
Each year some equipment is lost or damaged. This year the Sports Park is holding a
bake sale to raise money for new equipment such as soccer balls, footballs, bats, baseball
gloves, Frisbees, etc. You and your friends have gotten together at your house to bake
cookies to sell at the concession stand. Discuss basic ingredients needed to make
cookies.
Next, complete the Introductory Activities on page 25, “Proportion: Two equal Ratios
and The Missing Number in a Proportion,” of Moving with Math: Percent & Probability
(MH3). The activity begins by explaining the ratio of sugar to flour. Once completed
write examples on the board and have students solve.
3 n

4 12

8 40

3 n
4 n

6 9
(n = 9)
(n = 15)
(n = 6)
“Stir-The-Class” (20 minutes)


Group students into fours. Assign each person a number 1 through 4.
Display the sports problems on the board/overhead/LCD:
Have students work in their group to agree upon an answer to each question. Have the
groups signal you when ready (raising hand, standing, etc.).
Call out a number 1 through 4 and that person must rotate to a new group and share their
group’s answer and explanation before being given the next question. Continue this
process with each question, changing the number called and the direction in which they
rotate.
Questions:
1. Crusher Calhoun of the Wilde Lake Wildcats hit 12 homeruns in his first 25 games. If
he continues hitting at the same pace how many homeruns can he expect to hit in a 75
game season?
12 n
n  36

25 75


2. Kiara struck out 3 batters for every 8 players up at bat. If 120 players come up to bat,
 players could she expect to strike out?
how many
3
n
n  45

8 120
1
3.A baseball team with 20 players has of the players needing catching practice. The
5
rest will work on batting practice. How many will work on batting practice?

1 n

5 20
n4

4. One of your team’s best players batting average is 0.40. If he is at bat 200 times in the

season,
how many hits can you expect?
4
n
( n  80 )

10 200

5. A baseball team has a record of winning 5 games and 2 losses. If they continue with
 pattern and play a total of 105 games this year, how many will they win?
this
5
n
( n  75 )

7 105


6. The #1 team in the league has a record of losing only 2 games for every 9 games they
 If they play 45 games, how many games can you expect them to win?
play.
7 n
( n  35 )

9 45
Exit Ticket (10 minutes)
 students complete the exit ticket and turn in. Check for accuracy to see how well
Have
students mastered the lesson. Offer interventions as needed. See “Equal Ratio” Card
Game resource sheet for intervention.
1. Kalina bought 3 bags of chips for $2.40 at the concession stand. At the same price,
how much would 10 bags of chips cost?
3
10

( n  $8.00 )
$2.40 n


2. Miguel bought 4 hot dogs for $3.75. How much would a dozen hot dogs cost?

4
12

(n= $11.25)
$3.75 n
(Note: These problems can be solved using different methods. A student might use cross

multiplication
or a unit rate approach to the first problem. On the second problem the
numbers are compatible so multiplying is the most efficient strategy.)
3-2-1 Closure (5 minutes)
On a piece of paper or back of the Exit Ticket have students write down:
3 key terms from what they have learned about proportions
2 ideas they would like to learn more about
1 concept or skill they believe they have mastered.
Have students share responses.
“Equal Ratio” Card Game (15-20 minutes) Resource Sheet
Note: This activity is an optional remediation activity for students who are still
struggling.
Assign students to pairs. Complete the “Proportion Card Game” described on page 24 of
Moving with Math: Percent & Probability (MH3). If playing cards are not available, use
the attached number cards, making four copies per “deck.” One deck of cards is needed
for each pair of students.
EQUAL RATIO CARDS
1
2
3
4
5
8
9
10
1
6
7
MIX-N-MATCH RATIO CARDS (Use as sets of four as needed for your class)
1:2
5
10
24:48
7
14
3
4
75:100
6:8
9
12
2:3
18
27
8 : 12

80
120
8 : 10
40
50
12
15
1:5
2
10
30
150

3 : 15
1
3
30
90
2:6
5 : 15

4
5


1:4
2
 5
25
100
4
16
8 : 32
20 : 50
4
10
6 : 15

3:5
60
100

9 : 15
6
10
2
 9
4:18
20:90
6
27

1:6

2
7

10
60
2
12
4 : 24
4
14

20:70
6:21
MIX-N-MATCH ANSWER CARDS
1:2
5/10
24:48
7/14
3/4
75:100
6:8
9/12
2:3
18/27
8:12
80/120
4/5
8:10
40/50
12/15
1:4
25/100
4/16
8:32
2/9
4:18
20:90
6/27
1:5
2/10
30/150
3:15
2/5
20:50
4/10
6:15
1:6
10/60
2/12
4:24
1/3
30/90
2:6
5:15
3:5
60/100
9:15
6/10
2/7
4/14
20:70
6:21
Questions
1. Crusher Calhoun of the Wilde Lake Wildcats hit
12 homeruns in his first 25 games. If he continues
hitting at the same pace how many homeruns can he
expect to hit in a 75 game season?
2. Kiara struck out 3 batters for every 8 players up at
bat. If 120 players come up to bat, how many players
could she expect to strike out?
1
of the
5
players needing catching practice. The rest will work
on batting practice. How many will work on batting
practice?

3. A baseball team with 20 players has
4. One of your team’s best players batting average is
0.40. If he is at bat 200 times in the season, how
many hits can you expect?
5. A baseball team has a record of winning 5 games
and 2 losses. If they continue this pattern and play a
total of 105 games this year, how many will they
win?
6. The #1 team in the league has a record of losing
only 2 games for every 9 games they play. If they
play 45 games, how many games can you expect
them to win?
Exit Ticket
1. Kalina bought 3 bags of chips for $2.40 at the concession stand. At the same price,
how much would 10 bags of chips cost?
2. Miguel bought 4 hot dogs for $3.75. How much would a dozen hot dogs cost?
Exit Ticket
1. Kalina bought 3 bags of chips for $2.40 at the concession stand. At the same price,
how much would 10 bags of chips cost?
2. Miguel bought 4 hot dogs for $3.75. How much would a dozen hot dogs cost?
Exit Ticket
1. Kalina bought 3 bags of chips for $2.40 at the concession stand. At the same price,
how much would 10 bags of chips cost?
2. Miguel bought 4 hot dogs for $3.75. How much would a dozen hot dogs cost?