Ratios and Proportions Day 2

```MS After School Intervention
Unit 3: Ratios, Rate, and Proportion
Theme: Sports Park
Day 2 Lesson
Objective
Students will solve problems involving unit rates.
Common Core Standards:
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with
b  0 , and use rate language in the context of a ratio relationship. For example, “This
recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is a 3/4 cup of flour for
each cup of sugar.” “We paid \$75 for 15 hamburgers, which is a rate of \$5 per
hamburger.”
7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of
lengths, areas and other quantities measured in like or different units. For example,
if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex
fraction &frac12;/&frac14; miles per hour, equivalently 2 miles per hour.
Materials
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Computer
Chart paper
Tape
LCD projector
Cuisenaire&reg; Rods (one set per group)
“What’s Your Rate” resource sheets (one per student)
Timers (or clocks) (one per pair)
“Food Gallery Walk” resource sheets
“Food Gallery Walk: Student Answer Sheet” resource sheets (one per student)
“Exit Ticket: Which Snack Do you Want” resource sheets (one per student)
Calculators (one per student)
Warm-Up: “Exploring with Cuisenaire&reg; Rods” (10 minutes)
Divide students into groups and give each group a set of Cuisenaire Rods. Have students
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 red rod underneath it.
P
R
This shows a comparison of 4 to 2. Ask students to find other combinations that
represent this same comparison. Some examples would be dark green to light green and
orange to yellow, and red to white. Have students share their method of exploring the
problem. Emphasize that the comparison of red to white, or two to one, models a unit
rate. Have students show other combinations for unit rates.
Introductory Activity (20 minutes)
Read and display the following scenario for students:
“Betsy is using the running track at the Sports Park to help her train for the cross country
meet and she is keeping a record of the data. On Monday, she ran around the track 5
times in 20 minutes. Betsy thinks it would be easier to compare her progress each day if
she knew about how long it takes her to complete each lap.”
Tell students that Betsy is trying to find a “unit rate.” Pair up students and have them
discuss what the unit rate would be for Monday. (Answer: 4 minutes per lap)
Next, pose the following situation and have students pair and then explain to the group
On Tuesday, Betsy ran around the track 10 times in 30 minutes.
Is the unit rate (minutes to times around) the same as the unit rate for Monday?
(Answer: No, Tuesday’s unit rate is 3 minutes per lap)
Do you think her running time was faster on Monday or Tuesday?
(Answer: Tuesday is faster since it only takes 3 minutes to complete one lap.)
Think-Pair-Share (15 minutes)
Give students 5 minutes to think of and list examples of unit rates. (Sample responses:
miles per hour, dollars per ounce, dollar a per pound, etc.)
Pair up students and give them 5 minutes to compare lists, looking for similarities and
examples that only appeared on one person’s list.
With the remaining 5 minutes, have the students share their examples with the class.
This is based on NCTM LESSON found at
http://illuminations.nctm.org/LessonDetail.aspx?ID=L511
Arrange students in pairs and distribute student answer sheets and timers (clocks can also
be used). Students will take turns completing four activities for one minute each:
saying their full name, jumping jacks, writing their initials, and hopping on one foot.
Their partner should keep time and record the number of complete activities (only use
whole numbers).
Once the data is collected, students should complete the answer sheet together. Have the
pairs record their data on the board to compare unit rates.
Discuss reasons for differences in the unit rates. (Sample responses: longer names vs.
shorter names, speed, energy level, handwriting, etc.)
Post the questions below on the board and have students answer on their papers.
1) Based on your unit rate, how many jumping jacks (or any of the activities) could you
do in ten minutes? How many in 30 minutes?
(Answers will vary: students should multiply their rate by 10, by 30)
2) Which of your answers is more likely to be accurate? Why?
(Answer: Ten minutes because most people would tire and slow down after 30 minutes of
the activity
Food Gallery Walk (15 minutes)
Display the following using the LCD projector:
“Your baseball team will be going to the Sports Park for a tournament. This will last
several days. The coach needs to buy food for the team to bring for the tournament. You
are going to help the coach find the unit rate of several foods that can be compared at
Display the first Food Gallery Walk station using the LCD projector. Distribute
calculators for students to utilize.
As a class, find the unit rate, cost per ounce, of the Lay’s Potato Chips.
(Answer: (using \$3 and 11 oz) -- \$0.27 per ounce)
Ask students to find the unit rate of the Fresh Express Salad Bags.
(Answer: students will need to find the cost per bag 1st -- \$0.50 per ounce)
Hang the Food Gallery Walk ads around the room. Distribute Student Answer sheets.
Instruct students to browse the grocery items and calculate the unit rates for the next 5
minutes using their calculators. Students should complete as many of the items as they
can in the time allotted. You may want to suggest rounding on some items. Discuss
Solutions:
\$4.00
 \$0.25 per ounce
16 ounces
\$1.80
Ketchup:
 \$0.05 per ounce
36 ounces
\$3.00

Ice Cream:
 \$0.20 per ounce
15 ounces
\$3.00
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Sugar
Snap Peas:
8 ounces
\$2.50
 Chips:
Tortilla
6 ounces
\$0.70
 Tuna:
Bumblebee
 \$0.14 per ounce
5 ounces
\$1.00

32 ounces
\$0.80
Macaroni&amp; Cheese:
 about \$0.13 per ounce ,
6 ounces
\$0.80

7.25 ounces
\$2.50

Cranberry Drink:
64 ounces
\$4.50
Orange Juice:
 \$0.05 per ounce
90 ounces
Beef Franks:
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Closure – Exit Ticket (10 minutes)
Pose 
the following closure questions:
1. What is the difference between a unit rate and a ratio?
(Sample answer: A unit rate has a denominator of 1 where a ratio can have any
denominator.)
2. Give two examples of unit rates in the real world.
(Sample answer: mph, mpg, \$ per lb., jumps per minute, etc.)
3. Why is it good to know unit rates for foods?
(Sample answer: to know if you are getting a good deal, saving \$, etc.)
Distribute “Exit Ticket: Which Snack Do You Want?” exit tickets to students.
1. items per ounce
2. 5 bears/ounce, 5.5 pieces/ounce, 4.5 fish/ounce
3. The fruit snacks give the most per ounce.
NAME ___________________________
1. Tally/count how many times you are able to complete the following activities in one
minute. (Only count the whole number of times each activity is completed. Do not count
half a jumping jack or a partial letter.)
Saying your full name ____________________ Doing jumping jacks _______________
Writing your initials _____________________ Hopping on one foot ________________
2. Record your answers below as a unit rate – don’t forget the unit!
Doing jumping jacks ___________________________
Hopping on one foot ___________________________
NAME ___________________________
1. Tally/count how many times you are able to complete the following activities in one
minute. (Only count the whole number of times each activity is completed. Do not count
half a jumping jack or a partial letter.)
Saying your full name ____________________ Doing jumping jacks _______________
Writing your initials _____________________ Hopping on one foot ________________
2. Record your answers below as a unit rate – don’t forget the unit!
Doing jumping jacks ___________________________
Hopping on one foot ___________________________
Food Gallery Walk Page 1
Food Gallery Walk Page 2
Food Gallery Walk Page 3
Food Gallery Walk Page 4
Food Gallery Walk Page 5
Food Gallery Walk Page 6
Food Gallery Walk Page 7
Food Gallery Walk Page 8
Food Gallery Walk Page 9
Food Gallery Walk Page 10
Food Gallery Walk Page 11
Name: ________________
Calculate the unit rate for each of the following food items.
Beef Franks ___________________________
Ketchup ______________________________
Ice Cream ____________________________
Sugar Snap Peas _______________________
Tortilla Chips __________________________
Bumblebee Tuna _______________________
Macaroni &amp; Cheese _____________________
Cranberry Drink ________________________
Orange Juice __________________________
Exit Ticket: Which snack do you want?
You can eat one ounce of any of the three snacks listed below.
Teddy Grahams: 45 bears in a 9 ounce package
Fruit Snacks: 55 pieces in a 10 ounce package
Goldfish: 54 fish in a 12 ounce package
1. What unit rate must be found? ____________________________
2. Find the unit rate for each snack ___________
___________ __________
3. If you are only allowed one ounce for a snack, which should you eat? Why?
_______________________________________________________________________
_______________________________________________________________________
Exit Ticket: Which snack do you want?
You can eat one ounce of any of the three snacks listed below.
Teddy Grahams: 45 bears in a 9 ounce package
Fruit Snacks: 55 pieces in a 10 ounce package
Goldfish: 54 fish in a 12 ounce package
1. What unit rate must be found? ____________________________
2. Find the unit rate for each snack ___________
___________ __________
3. If you are only allowed one ounce for a snack, which should you eat? Why?
_______________________________________________________________________
_______________________________________________________________________
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