Transcript Topic A: Proportional Relationships

Topic A: Proportional
Relationships
Lesson 3
Identifying Proportional and
Non-Proportional Relationships in Table
Topic A Overview
Lesson 1: An Experience in Relationships as
Measuring Rate
Lesson 2: Proportional Relationships
Lessons 3-4: Identifying Proportional and NonProportional Relationships in Tables
Lessons 5-6: Identifying Proportional and NonProportional Relationships in Graphs
LEARNING TARGET
Lesson 3: Identifying Proportional & Non-Proportional Relationships in Tables
Today I can determine if data in a table represents a proportional or non-proportional
relationship and explain my reasoning.
STANDARDS
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.
KEY VOCABULARY
Proportional
Constant
Constant of Proportionality
AGENDA – Day 1
• (10 min) Warm-Up
• (5 min) Review Key Vocabulary
• (10 min) Warm-Up: Babysitting
• (10 min) Discussion
• (5 min) Teacher Model: Example 1
• (10 min) Class Model: Example 2
• (10 min) Partner Model: Example 3
• (10 min) Discussion
• (10 min) Partner Model: Example 4
• (10 min) Discussion
• (5 min) Exit Ticket
Warm-Up: Day 1
Review Key Vocabulary
• Proportional – when two quantities simplify to the
same ratio.
• Constant – a quantity having a value that does not
change or vary.
• Constant of Proportionality - a constant value of the
ratio of two proportional quantities.
Exercise: Babysitting
You have been hired by your neighbors to babysit their
children on Friday night. You are paid $8 per hour.
Complete the table relating your pay to the number of
hours you worked.
Hours Worked
Pay ($)
1
2
3
4
4.5
5
6
6.5
Discussion
1. Describe the relationship between the
amount of money earned and the number of
hours worked in this example.
2. How can multiplication and division be used
to show the earnings are proportional to
number of hours worked?
Discussion
1. Explain how you completed the table.
2. How did you determine the pay for 4 ½ hours?
3. How could you use the information to
determine the pay for a week in which you
worked 20 hours?
4. How many other ways can the answer be
determined?
5. If the quantities in the table were graphed,
would the point (0, 0) be on the graph? What
would mean in the context of the problem.
TEACHER MODEL: Example 1
Determine if y is proportional to x. Justify your
answer.
The table below represents the amount of snow
fall in 5 countries (in inches) to hours of a recent
x
y
winter storm.
Time (hrs)
Snowfall (in)
2
10
6
12
8
16
2.5
5
7
14
CLASS MODEL: Example 2
Determine if y is proportional to x. Justify your
answer.
The table below shows the relationship between
cost of renting a movie to the number of days
x
y
on rent.
Number of Days
Cost
6
2
9
3
24
8
3
1
PARTNER MODEL: Example 3
Determine if y is proportional to x. Justify your
answer.
The table below shows the relationship between
the amount of candy (pounds) bought and the
x
y
total cost.
Pounds
Cost
5
10
4
8
6
12
8
16
10
20
Discussion
1. When looking at ratios that describe two
quantities that are proportional in the same
order, do the ratios always have to be
equivalent?
2. For example, if the quantities in the table were
graphed, would point (0,0) be on the graph?
Describe what the point (0,0) would represent in
each table.
3. Do the x and y values need to go up at a
constant rate? In other words, when the x and y
values both go up at constant rate, does this
always indicate the relationship is proportional?
PARTNER MODEL: Example 4
Randy is planning to drive from New Jersey to
Florida. Randy recorded the distance traveled
and the total number of gallons used every time
he stopped for gas.
Assume miles driven is proportional to Gallons
Consumed in order to complete the table.
Gallons
Consumed
2
Miles Driven
54
4
8
189
216
10
12
Discussion
1. Why is it important for you to know that
miles are proportional to the gallons used?
2. Describe the approach you used to complete
the table.
3. What is the value of the constant? Explain
how the constant was determined.
4. Explain how to use multiplication and
division to complete the table.
Exit Ticket – Day 1
1. Explain how we found the constant of
proportionality?
2. Explain how we used the constant of
proportionality to find missing values in the
table.
LEARNING TARGET
Lesson 3: Identifying Proportional & Non-Proportional Relationships in Tables
Today I can determine if data in a table represents a proportional or non-proportional
relationship and explain my reasoning.
STANDARDS
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.
KEY VOCABULARY
Proportional
Constant
Constant of Proportionality
AGENDA – Day 2
• (5 min) Review Key Vocabulary
• (10 min) Warm-Up: Price of Roses
• (10 min) Lesson Summary
• (25 min) Lesson 3 Problem Set
• (30 min) Lesson 3 Quiz
Review Key Vocabulary
• Proportional – when two quantities simplify to the
same ratio.
• Constant – a quantity having a value that does not
change or vary.
• Constant of Proportionality - a constant value of the
ratio of two proportional quantities.
Warm-Up: Price of Roses
The table below shows the price for the number
of roses indicated.
Number of Roses
3
6
7
12
15
Price (Dollars)
9
18
27
36
45
1. Is the price proportional to the number of roses?
How do you know?
2. Find the cost of purchasing 30 roses.
Lesson Summary
One quantity is proportional to a second if a constant
(number) exists such that each measure in the first quantity
multiplied by this constant gives the corresponding measure
in the second quantity.
Steps to determine if two quantities in a table are
proportional to each other:
1. For each given measure of Quantity A and Quantity B, find
𝐵
the value of .
𝐴
𝐵
2. If the value of is the same for each pair of numbers, then
𝐴
the quantities are proportional to each other.
Lesson 3 - Problem Set
1 Point
(Unsatisfactory)
2 Points
(Partially Proficient)
3 Points
(Proficient)
A correct answer
Missing or incorrect Missing or incorrect with some evidence
answer and little
answer but
of reasoning or an
evidence of
evidence of some
incorrect answer
reasoning
reasoning
with substantial
evidence
4 Points
(Advanced)
A correct answer
supported by
substantial
evidence of solid
reasoning
Lesson 3 - Quiz
1 Point
2 Points
(Unsatisfactory)
(Partially Proficient)
3 Points
(Proficient)
A correct answer
Missing or incorrect Missing or incorrect with some evidence
answer and little
answer but
of reasoning or an
evidence of
evidence of some
incorrect answer
reasoning
reasoning
with substantial
evidence
4 Points
(Advanced)
A correct answer
supported by
substantial
evidence of solid
reasoning