Lesson 14Four Representations
Learning Goal
Let’s contrast relationships that are and are not proportional in four different ways.
Learning Targets
I can make connections between the graphs, tables, and equations of a proportional relationship.
I can use units to help me understand information about proportional relationships.
Warm Up: Which Is the Bluest?
Problem 1
Which group of blocks is the bluest?
Problem 2
Order the groups of blocks from least blue to bluest.
Activity 1: One Scenario, Four Representations
Problem 1
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Select two things from different lists. Make up a situation where there is a proportional relationship between quantities that involve these things.
creatures
starfish
centipedes
earthworms
dinosaurs
length
centimeters
cubits
kilometers
parsecs
time
nanoseconds
minutes
years
millennia
volume
milliliters
gallons
bushels
cubic miles
body parts
legs
eyes
neurons
digits
area
square microns
acres
hides
square light-years
weight
nanograms
ounces
deben
metric tonnes
substance
helium
oobleck
pitch
glue
Select two other things from the lists, and make up a situation where there is a relationship between quantities that involve these things, but the relationship is not proportional.
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Your teacher will give you two copies of the “One Scenario, Four Representations” sheet. For each of your situations, describe the relationships in detail. If you get stuck, consider asking your teacher for a copy of the sample response.
Write one or more sentences describing the relationship between the things you chose.
Make a table with titles in each column and at least 6 pairs of numbers relating the two things.
Graph the situation and label the axes.
Write an equation showing the relationship and explain in your own words what each number and letter in your equation means.
Explain how you know whether each relationship is proportional or not proportional. Give as many reasons as you can.
Activity 2: Make a Poster
Problem 1
Create a visual display of your two situations that includes all the information from the previous activity.
Lesson Summary
The constant of proportionality for a proportional relationship can often be easily identified in a graph, a table, and an equation that represents it. Here is an example of all three representations for the same relationship. The constant of proportionality is circled:
On the other hand, some relationships are not proportional. If the graph of a relationship is not a straight line through the origin, if the equation cannot be expressed in the form