Transcript Topic A: Proportional Relationships

Topic A: Proportional
Relationships
Lesson 4
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 4: Identifying Proportional & Non-Proportional Relationships in Tables
Today I can determine if data in a table represents a proportional or non-proportional
relationship by determining if there’s a constant of proportionality for each set of x and y
values.
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
• (5 min) Review Key Vocabulary
• (10 min) Warm-Up: Which Team Will Win
the Race?
• (10 min) Share Solutions
• (10 min) MODEL: Finding the Constant
of Proportionality
• (10 min) Proportional or NonProportional?
• (10 min) Extension
• (5 min) Exit Ticket
• (30 min) Online Practice
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: Which Team Will Win the Race?
You have decided to run in a long distance race. There are two
teams that you can join. Team A runs at a constant rate of 2.5
miles per hour. Team B runs 4 miles the first hour and then 2
miles per hour after that.
Task: Create a table for each team showing the distances that
would be run for times of 1-6 hours.
Team A
Time (hrs)
Team B
Distance
(miles)
Time (hrs)
1
1
2
2
3
3
4
4
5
5
6
6
Distance
(miles)
MODEL: Finding the Constant of Proportionality
Team A runs at a constant rate of 2.5 miles per
hour.
Team A
Time (hrs)
1
2
3
4
5
6
Distance (miles)
MODEL: Finding the Constant of Proportionality
Team B runs 4 miles the first hour and then 2
miles per hour after that.
Team B
Time (hrs)
1
2
3
4
5
6
Distance (miles)
Proportional or Non-Proportional?
1. For which team is distance proportional to
time? Explain your reasoning.
2. Explain how you know the distance for the
other team is not proportional to time?
Extension
1. If the race were 2.5 miles long, which team
would win? Explain.
2. If the race were 3.5 miles long, which team
would win? Explain.
3. If the race were 4.5 miles long, which team
would win? Explain.
Exit Ticket
The table below shows the relationship between
the side lengths of a regular octagon and its
perimeter.
Side Length, s Perimeter, P
1. Complete the table.
2. If Gabby wants to make an octagon
with a side length of 20 inches using
wire, how much wire does she
need? Justify your reasoning with an
explanation of whether perimeter is
proportional to the side length.
(inches)
1
2
(inches)
8
16
3
4
9
24
32
12
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 by determining if there’s a constant of proportionality for each set of x and y
values.
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
• (10 min) Warm-Up
• (5 min) Review Key Vocabulary
• (5 min) Review: Which Team Will Win the
Race?
• (20 min) Discussion
• (25 min) Lesson 4 Problem Set
• (30 min) Lesson 4 Quiz
Warm-Up: Day 2
Does the table show that y is proportional to x?
Explain.
X
1
2
3
4
Y
4
8
12
16
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.
Review: Which Team Will Win the Race?
You have decided to run in a long distance race. There are two
teams that you can join. Team A runs at a constant rate of 2.5
miles per hour. Team B runs 4 miles the first hour and then 2
miles per hour after that.
Task: Create a table for each team showing the distances that
would be run for times of 1-6 hours.
Team A
Time (hrs)
Team B
Distance
(miles)
Time (hrs)
1
1
2
2
3
3
4
4
5
5
6
6
Distance
(miles)
Discussion
1. For what length race would it be better to be
on Team B than Team A? Explain.
2. Using the relationship, if the members on the
team ran for 10 hours, how far would each
member run on each team?
3. Will there always be a winning team, no
matter what length of the course? Why or
why not?
Discussion Continued…
4. If the race were 12 miles long, which team
should you choose to be on if you wish to
win? Why would you choose this team?
5. How much sooner would you finish on that
team compared to the other team?
Lesson 4 – 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 4 – 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