Task
2
By the Pound
Topic
Proportional Relationships,
Lines & Linear Equations
Common Core State Standards
8EE5
Copyright @ 2016 The Regents of the University of California
This work was supported by grant number #DRL-1020393 from the National Science Foundation
and grant number 2012-8075 from the William and Flora Hewlett Foundation.
Agenda
Set Up
Whole class, 5 min
Mind Stretch
Whole class, 5 min
Workout
Check Your Pulse
Final Lift
Individual, 10-15 min
Pairs, Individual, Whole class, 10 min
Individual, 15 min
How can we use
math to get a fair
deal?
Setup
Learning Goals & Expectations
We are
learning to…
We will be
successful
when we…
Reason about unit rate.
Compare two rates or ratios using graphs &
other representations.
Can correctly determine unit rate (cost per
pound).
Compare rates or ratios within a graph &
create a table or equation that represents a
graph.
Use words and other representations to justify
our thinking.
High Quality Work
Work is
accurate &
precise
Explanations
Problem is set up in a way that helps you solve it.
Scale: responses use appropriate units.
Work has been checked for calculation errors.
Describe what you did and why you did it.
Use multiple representations to show your
thinking about math.
Include a logical argument and evidence to
support each answer. It makes sense.
Multiple Representations
Use multiple representations to help you think and to
show your thinking to others.
Representations
Create a chart or table
Set up an equation or an algebraic rule
Sketch a graph
Use words to explain and justify
Prior Knowledge
In ordinary life, where do you see slopes?
Ratio: a ratio tells us, for every amount of one
thing, how many times more (or less) there is of
another thing.
Rate: a ratio comparing two different kinds of
quantities
Unit rate: a ratio of a quantity to one unit of another
quantity
•
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓𝐴
𝟏 𝑜𝑓 𝐵
• any number of quantity A : 1 of quantity B
• 50 miles per 1 hour
• $4 per 1 gallon
Unit Rate = slope of the line
The story so far…
You want to buy some fruit, but you have
only a few dollars to spend.
Mind Stretch
Mind Stretch
Describe what you see in the graph.
List at least one fact or idea suggested by the graph.
Mind Stretch
Complete the following sentences. Be sure to explain
your thinking.
For $5, I can buy more pounds of _______.
I know this because….
Student Work Example
Would you agree with this student? Why can you buy more plums
if the line for peaches goes up faster (i.e., has greater slope)?
Workout
Workout
Cherries cost more by the pound
than do peaches and plums.
1. Draw a line on the graph used for peaches and plums to
represent the cost of cherries by the pound.
Remember: (x,y) represents (number of pounds, total cost).
2. Describe in writing what you notice in this graph about the
cost of cherries, peaches and plums.
3. Create table(s) and/or equation(s) that you believe represent
the same information shown in the graph. Provide evidence
for your thinking.
Check
Your Pulse
Student Work Example
Here is what one student did to answer the last question. What do
you think?
Student Work Example
Turn to your elbow partner and discuss… about how much you would
pay if you bought 0 pounds of cherries based on the graph?
Student Work Example
Here is what another student did to answer the last question.
What do you think?
Student Work Example
Turn to your elbow partner and discuss… about how much you would
pay if you bought 0 pounds of cherries based on this graph?
Check Your Pulse
Explain, in writing, why you think your tables and/or
equations are accurate. Use evidence from the graph,
table, and/or equation(s) to support your answer.
Compare your answers with a partner.
Then discuss…
•
Where do you agree or disagree with your partner’s answer?
•
What part(s) were difficult for you?
Check Your Pulse
On your own… self-assess:
1. Circle your level of understanding for the Workout.
I have lots of
questions. I need help
Almost got it, but I
need practice
Got it. I can explain
this to a clssmate.
Final Lift
Final Lift
Sara paid $4.00 for a 2-pound box of strawberries.
Matt paid $7.00 for a 5-pound box of mangos.
1. What is the unit rate or cost per pound for strawberries? For
mangos?
2. Which graph best shows these relationships?
3. In your own words, explain how you know this is the correct
graph. Be sure to describe the meaning of the lines.
Final Lift
Last year the cost of oranges rose from $2 per
pound to $4 per pound and the cost of pineapples
rose from $8 per pound to $11 per pound.
4. What is the ratio of the new price of oranges to the
previous price of oranges?
5. What is the ratio of the new price of pineapples to the
previous price of pineapples?
6. Are the ratios proportional? If not, which ratio is larger?
Explain your thinking.
Challenge
The trend of prices to increase over time is called
inflation and a measure of inflation is called the
inflation rate. This rate is often calculated as a
percent increase – just like you calculated in 7th
grade.
7. What is the percent increase in the cost of oranges?
8. What is the percent increase in the cost of pineapples?
9. Do you think either of these two values would be a good
measure of inflation overall? Why or why not?