Lesson 4 Ratio Tables.notebookWarm Up
Examples
Click on box for video tutors
Lesson 4 Ratio Tables.notebook
September 16, 2013
Lesson 4 Ratio Tables.notebook
September 16, 2013
Lesson 4 Ratio Tables.notebook
September 16, 2013
Lesson 4 Ratio Tables.notebook
September 16, 2013
Attachments
MSM3.07.01.Act.xhtml
Lesson_13__Setting_Up_Tables_to_Work_Ratio_Problems.asf
How can you make a comparison using unit rates?
The relationship between two quantities measured in different units
can be expressed as a unit rate. A unit rate is a rate that has a
denominator of 1 unit. A unit rate can be found by dividing one
quantity by the other. For example, a student can do 6 math
problems in 3 minutes. To find the unit rate, you can divide to get
6 math problems3 minutes = 2 math problems1 minute.
So, the unit rate is 2 math problems per 1 minute.
EXPLORE
STEP 1 Set up the experiment
Your teacher will choose five students to do jumping jacks. Write
the names of those students in the first column of the table.
Student
Time
10 seconds
15 seconds
5 seconds
12 seconds
6 seconds
STEP 2 Conduct the experiment
When your teacher says, “go,” the first student starts doing
jumping jacks. You should count the number of jumping jacks
completed until your teacher says, “stop.” Record the number of
jumping jacks in the third column of the table in Step 1.
STEP 3 Repeat the experiment
Repeat Step 2 for each student in the table.
STEP 4 Calculate unit rates
Complete the fourth and fifth columns of the table to find a unit
rate for each student. Round your answers to the nearest
hundredth.
DRAW CONCLUSIONS
Why might it be hard to compare the speeds at which the five
students do jumping jacks based on the information in just the
first three columns of the table?
Which student has the greatest unit rate?
Which student can do jumping jacks the fastest? Explain how you
know.
How could you find how many jumping jacks each student could do in
1 minute?
Find how many jumping jacks each student could do in 1
minute.
Which student could do the most jumping jacks in 1 minute? How does
this compare to your answer to Exercise 3? Explain.
Do your answers to Exercise 5 seem realistic? Why or why not?
Answer Key
DRAW CONCLUSIONS
It would be hard to compare the speeds because each student did
jumping jacks for a different amount of time. It makes sense for
the student who was timed for 15 seconds to have done more jumping
jacks than the person who was timed for 5 seconds, even though the
second student may have done them faster.
Answers will vary.
Answer should be the same as answer for Exercise 2. Students should
realize that the greater the unit rate, the faster the student can
do jumping jacks.
Multiply the unit rates by the number of seconds in one minute, or
60.
Answers will vary.
Answer should be the same as answer for Exercise 3. Students should
realize that the unit rates do not change when the amount of time
changes. This means that the same student will be able to do the
most jumping jacks for any given amount of time.
These numbers are probably unrealistic. Chances are that a student
will be able to do jumping jacks faster in the beginning of the
minute. As more time passes, the student will get tired and slow
down.
Teacher Notes
ACTIVITY PREPARATION
Clear out an area at the front of the classroom so that a student
can do jumping jacks without hitting anything or anyone.
Each student should be supplied with a calculator.
ACTIVITY MANAGEMENT
Go over how the fourth and fifth columns of the example row in the
table were completed before students calculate the unit
rates.
Remind students to check that each unit rate makes sense. For
example, a unit rate of 15.00 would not make sense because no one
could do 15 jumping jacks in 1 second. This is a good way to avoid
misplacing a decimal point.
A-Level Alternative 1: Encourage students to get in the habit of
always labeling the two terms of a rate so it is easy to see what
the rate is comparing.
A-Level Alternative 2: Discuss Draw Conclusions Exercise 7 together
as a class. You may wish to have students come up with a real-world
rate which is really a constant rate (e.g., price per pound) and a
real-world rate that really changes over time (e.g., speed of a
runner which is actually an average rate over a period of
time).
C-Level Alternative: Instead of giving students the full table to
fill in, just have them record the Student, the Time, and the
Number of jumping jacks and have them try to compare the speeds at
which the students do jumping jacks. Once they realize the
difficulties, challenge them to come up with a way way to better
express the relationships between the numbers to compare them.
(Approaches may vary. For example, rather than dividing to find the
number of jumping jacks per second, students could multiply by 6
for the people with 10 seconds, multiply by 4 for the person with
15 seconds, etc. to get each up to a time of 60 seconds.) After
students have found their own approach, you can discuss unit rates
and have students find the unit rate per second if they didn’t
already find it.
Activity and Closure Questions
Why are unit rates useful for making a comparison?
Answer: Unit rates give a quantity in relation to one unit of
another quantity so that a direct comparison can be made.
Suppose student A can do 6 jumping jacks in 10 seconds and student
B can do 11 jumping jacks in 15 seconds. Which student is faster at
doing jumping jacks? Explain.
Answer: student B; The unit rate for student A is 0.60 jumping
jacks per second, and the unit rate for student B is about 0.73
jumping jacks per second.
Give an example of how you can you use a unit rate to make a
prediction.
Answer: Answers may vary. An example is given. If you know the
miles per hour you are traveling, you can predict the number of
miles you will travel after 3 hours my multiplying by 3.
LESSON TRANSITION
After completing this activity students should have a basic
understanding of unit rates and their usefulness in making a
comparison. You can skip Example 3 is you feel that students have a
solid understanding of how to find a unit rate. The rest of the
lesson still needs to be covered in its entirety, however, so that
students will understand the relationship between ratios, rates,
and unit rates.
SMART Notebook
SMART Notebook
Page 1
Page 2
Page 3
Page 4
Page 5
Page 6
Page 7
Page 8
Page 9
Page 10
Page 11
