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 ProportionsMathematical 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 TargetStudents 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

• UNIT RATE A unit rate is a rate for which one of the numbers being compared is 1 unit.

An example:

is 140 miles 3.5 hours, or 40 miles per 1 hour is

The rate of miles to hours becomes miles PER hour, which is written mi/h.

The word “per” can be replaced with “for one.”

Getting Ready for Problem 1.2Referring 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 ?

Problem 1.2: Road Trip & Basketballs

Problem 1.2Have you thought about?

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 TargetReview & 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, 9Work & answers in your math workbook