Proportional Relationships
Unit 3 – Lesson 2
Learning Goals for this Lesson:
Standards: MAFS.7.RP.1.2
MAFS.K12.MP.1.1, MAFS.K12.MP.2.1, MAFS.K12.MP.3.1,
MAFS.K12.MP.4.1,
LAFS.68.WHST.2.4, LAFS.7.SL.2.4, LAFS.7.SL.1.1
Students Will Know:
Students Will Be Able To:
Proportional relationships and the constant of
proportionality are found through tables, graphs,
and equaitons.
Identify proportional relationships in tables,
graphs, and equations. Identify the constant of
proportionality (unit rates) in tables, graphs, and
equations. Represent proportional relationships by
equations. Interpret the graphic representation of
proportional relationship.
Lesson Essential Question:
How are proportional relationships recognized and represented?
Activating Strategy:
Pizza Party – Glencoe p. 33
Students will begin to discover proportional relationships by looking at the cost for x number of
pizzas when planning a pizza party.
Key Vocabulary to Preview and Vocabulary Strategy:
Proportional
Non-Proportional Quadrants
Cross Product Cross Product Property Rate of
Change
Constant Rate of Change Slope Direct Variation Constant of Variation Constant of
Proportionality
Lesson Instruction:
Learning Activity 1:
(Have students complete the I Think section of the Proportional
Relationships Anticipation Guide.) Use the Cornell Note format to
take notes on the key vocabulary. (Preview of the vocabulary.)
Graphic Organizer:
Anticipation Guide
Cornell Notes
Assessment Prompt for LA 1:
Students will complete the I Know section of Proportional
Relationships Anticipation Guide and correct the statements if false.
Differentiation 1:
Ability Levels: Paired Groupings (stronger/slightly weaker
students)
Learning Styles: visual, auditory, interpersonal, intrapersonal,
kinetic
Varied Interest: Students will be allowed to choose 2 of the new
vocabulary
words to create a Frayer Model.
*** See the document at the end of the unit for more
information.
Learning Activity 2:
Assignment:
Discuss the error points and model problems involving solving
equations.
Be sure to point out/review:
 When writing a proportion, remind students to line up their
units.
 Tables:
- A pattern in the table does not necessarily indicate
proportionality.
- The arrangement of the table may not match the
desired ratio.
- The entire table must be checked for proportionality.
 Remind students that slope is always rise over run. (Run is
on the bottom because you run with your legs.)
 Proportional relationships have graphs that pass through the
origin.
 .
After each example section, students complete the “Got It?”
questions with their partners. (Ink-Pair-Share.)
Assessment Prompt for LA 2:
Question: “What relationship exists between rate of change,
slope, and direct variation?” Write-Pair-Share As tell the Bs their
answer and give their reasoning. Bs follow up – do you agree,
disagree, or need to add to? Call on Bs to answer aloud for the class.
Differentiation 2:
Ability Levels: Paired Groupings (stronger/slightly weaker
students)
Learning Styles: visual, auditory, interpersonal, intrapersonal,
kinetic
*** See the document at the end of the unit for more
information.
Learning Activity 3:
Review Marking the Text to students. Review the 4 parts
(underline the question, circle operational words, highlight values,
and translate word problems into a numerical sentence). Remind
students that Marking the Text can help them to solve word
problems by helping to better understand the questions before
solving it. Review how to use Marking the Text with students using
a problem involving equations. Provide students with an additional
word problem (proportional relationsips) to solve. (Ink-Pair-Share)
Assessment Prompt for LA 3:
Complete word problems pertaining to the LEQ using the Marking
the Text Strategy with their partners.
Differentiation 3:
Ability Levels: Paired Groupings (stronger/slightly weaker
students)
Learning Styles: visual, auditory, interpersonal, intrapersonal,
kinetic
Varied Interest: Create and solve their own word problem.
*** See the document at the end of the unit for more
Performance Task–
Road Trip
(Textbook p. 93)
In this activity, students apply
their knowledge of proportional
relationships in the real-world
context of calculating gas
mileage.
Rubric:
See p. PT1
information.
Learning Activity 4:
Review the Higher Order Thinking Skills to the students.
Review how to solve word problem involving a H.O.T. skill that
involve equations. Remind students to use the Marking the Text
strategy. Provide students with an additional H.O.T. problem to
solve. (Ink-Pair-Share)
Assessment Prompt for LA 4:
Complete H.O.T problems pertaining to the LEQ using the Marking
the Text
Strategy with their partners.
Differentiation 4:
Ability Levels: Paired Groupings (stronger/slightly weaker
students)
Learning Styles: interpersonal, intrapersonal, kinetic
Varied Interest: Choose two of the H.O.T questions from the
textbook related
content.
*** See the document at the end of the unit for more
information.
Summarizing Strategy:
Students will review their Cornell Notes to answer the LEQ in the Summary section.
Students:
Modifications/Accomodations:
1. Seat student near teacher.
2. Stand near student when giving
directions/presenting.
3. Provide visual aids/graphic organizers.
4. Ensure oral directions are understood.
5. Allow extra time to complete tasks.
6. Simplify complex written directions.
7. Give test items orally.
8. Provide peer assistance/study groups.
Proportional Relationships
Anticipation Guide
Please answer the following statements/problems as True or False in the “I think” column first. At the
end of class you will review these statements/problems again and then you will write the correct True or
False answer in the “I know” column. If the answer if false, then correct the statement somehow to
make it true.
I Think
I Know
Statement
Two quantities that have a constant ratio or unit
rate are proportional.
Two quantities that do not have a constant ratio
or unit rate are non-proportional.
The three regions of a coordinate plane are called
quadrants.
The Cross Product Property states that the cross
products of any proportion are equal.
The cross product is a rate that describes how one
quantity changes in relation to another.
A non-linear relationship has a constant rate of
change.
Slope is the rate of change between any two
points on a line.
When two variables have a constant ratio, their
relationship is called an Inverse Variation.
The constant ratio is not called the constant rate
of change.
The constant of variation is also know as the
constant of proportionality.