Learning Focused Lesson Plan Lynn W. Evans

Topic: Ratio and Rates

Scheduled time: Math 7 2+ days Total time 3 days Accelerated math 2 days Total time 2 days

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Standard: 7.RP.1

Students will know: The definition of unit rate.

Students will be able to: Analyze unit rates comparing fractions to fractions. Compute unit rates, including ratios of lengths, areas, and other quantities measured in

like or different units.

Learning essential question: How can we use ratios and rates to help describe real life problems?

Activating strategy: Finding rates, Simplifying expressions with rates, ratio tables, unit analysis workbook pages 85-87

Key vocabulary to preview and vocabulary strategy:

Unit rate, ratio, complex fractions (text page 164)

Ratio a comparison of two quantities using division. 3/4, 3 to 4, 3:4

Rate is a ratio of two quantities with different units. 60 miles/2 hours

unit rate a rate with a denominator of 1. 30 miles/1 hour

Complex fraction has at least one fraction in the numerator, denominator or both. Complex fractions may need to be simplified to find unit rates.

Lesson Instruction:Learning activity #1: Finding Ratios and Rates

There are 45 males and 60 females in a subway car. The subway car travels 2.5 miles in 5 minutes.

Find the ration of males to females males/females = 45/60 = 3/4

find the speed of the subway car 2.5 miles/5 minutes = 0.5 mile /1 minute

https://www.youtube.com/watch?v=RQ2nYUBVvqI

Assessment prompt for LA #1 (text page 167 #'s 1- 20)

Find the product. List the units.

8 hours times 9$/hour8 pounds times 3.5$/pound29/2 sec times 60 MB/sec

Write the ratio in simplest form.

25 to 4563:2835 girls : 15 boys16 dogs to 12 cats

Find the unit rate.

180 miles in 3 hours256 miles per 8 gallons$9.60 for 4 pounds

Learning activity #2 Finding a Rate from a ratio table

A ratio table shows the cost for different amounts of artificial turf. Find the unit rate in dollars per square foot.

Amount (square feet)

25 100 400 1600

Cost (dollars) 100 400 1600 6400

Use a ratio from the table to compute the rate and then the unit rate.

rate = 100$/25sf

unit rate = 4$/1 sf the unit rate is 4$ per square foot

Assessment prompt for LA#2

Use the ratio table to find the unit rate with the specified units

servings per packagepackages 3 6 9 12servings 13.5 27 40.5 54

feet per yearyears 2 6 10 14feet 7.2 21.6 36 50.4

Learning activity #3 Finding a rate from a graph (example 3 in text on page 165)

Given a graph of a straight line that goes thru the point (0,0)Step 1....chose a point on the line The point (1/2,1/4) shows the car travels 1/4 mile in 1/2 minute

step 2 find the speed distance/time =( 1/4 mile)/(1/2 min) = 1/2 mile/minute

Be sure to notice the units and the unit sequence.

https://www.youtube.com/watch?v=HKg5Xl8OLmg

Assessment prompt for LA#3

What is a rate? What is the unit rate?

Learning activity #4 Solving a Ratio problem

You mix 1/2 cup of yellow paint for every 3/4 cup of blue paint to make 15 cups of green paint. How much yellow paint and blue paint do you use?

Method 1 Ratio Table

Yellow (cups) Blue (cups) Total (cups)1/2 3/4 1/2 + 3/4 = 5/42 3 2 + 3 = 56 9 6 + 9 =15We multiplied row 1 by 4 to get the 2nd row. We multiplied the 2nd row by 3 to get the third row. Our target total was 15. So, we use 6 cups of yellow and 9 cups of blue.

Method 2 Algebraic using ratio of a part to the total.

We use 1/2 cup of yellow with 3/4 cup of blue to make 5/4 cup of green.

yellow/total =( 1/2) / (5/4) = 1/2 times 4/5 = 2/5 so the ratio of yellow to the total is 2/5 2/5 times the total of 15 = 6 cups of yellow. If 6 cups are yellow, 9 must be green. 3/5 times 15 = 9

https://www.youtube.com/watch?v=qlO61eyo6co

Assessment prompt for LA#4

An auto dealership sells minivans and sedans. In January, they sold 12 minivans and 14 sedans. In February, they sold 7 minivans and 10 sedans. During which month did the auto dealership sell a higher ratio of minivans to sedans?

Graphic organizer

Assignment

Workbook page 88

Summarizing strategy

We learned about ratios, rate and unit rate. We learned to read rates from a graph and a table. We learned how to use a ratio to solve a problem.