# 7th Grade Pre-Algebra Focus 1: Proportional Reasoning

```Standards: 7.RP.1, 7.RP2a, 7.RP.2d
Resource: Connected Math Program 2
Common Core Investigation 1
Common Core Investigation 1: Graphing Proportions
Mathematical Learning Goals
Compute unit rates associated with ratios of fractions,
including quantities measured in like or different units
Decide whether two quantities are in a proportional
relationship
Explain what any point (x,y), including (0,0) and (1,r)
where r is a unit rate, on a graph of a proportional
relationship means in terms of the situation
Problem 1.2: Learning Target
Students will extend their understanding of
ratios and develop understanding of
proportionality to solve problems by:
Converting rates to unit rates
Key Vocabulary Terms
• RATE
 A rate is a ratio that compares quantities in different units such as miles to
hours.
 An example of a rate is
140 𝑚𝑖𝑙𝑒𝑠
3.5 ℎ𝑜𝑢𝑟𝑠
• UNIT RATE
 A unit rate is a rate for which one of the numbers being compared is 1 unit.
 An example:
140 𝑚𝑖𝑙𝑒𝑠
3.5 ℎ𝑜𝑢𝑟𝑠
is 140 miles ÷ 3.5 hours, or 40 miles per 1 hour is
40 𝑚𝑖𝑙𝑒𝑠
1 ℎ𝑜𝑢𝑟
The rate of miles to hours becomes miles PER hour, which is written mi/h.
The word “per” can be replaced with “for one.”
Referring to the Key Vocabulary Terms examples, answer the following:
What two units are being compared in 140 miles in 3.5 hours?
How could you use this rate to find the distance that could be traveled in
7 hours?
Would it be helpful to find out how many miles are traveled in 1 hour?
Why?
How can you find the unit rate for the rate
140 𝑚𝑖𝑙𝑒𝑠
3.5 ℎ𝑜𝑢𝑟𝑠
?
Problem 1.2
How can converting rates to
unit rates make comparing
those rates easier?
Class Discussion & Sharing
Key Vocabulary Term
• PROPORTIONAL RELATIONSHIP
 Two quantities are in a proportional relationship if a change in
one quantities corresponds to a change by the same factor in the
other quantity.
 The ratios between the quantities do not change when the
quantities themselves change.
Problem 1.2: Learning Target
Review & Recap
Students will extend their understanding of
ratios and develop understanding of
proportionality to solve problems by:
Converting rates to unit rates
Pre-Algebra Homework
Exercises
#3, 5, 7, 9