Lesson 1 Unit Rates

Name: ______

Lesson 1 – Unit Rates

Objective: Determine a unit rate involving one or more fractional quantities and use the unit rate to solve problems

A.Words to Know:

Unit Rate: ______

Ratio: ______

Complex Fraction: ______

B. REVIEW: How find a unit rate (review from 6th grade)

Example 1: Tommy types 700 words in 10 minutes. How many words can he type per minute?

Example 2: A 10 kg bag of apples cost $15. What does it cost per kg?

C. Classwork: Finding Unit Rates Worksheet #1-20

D. New Concept: find unit rates for ratios of fractional quantities with unlike units

Example 3: Carl’s mother buys pound of Rainier cherries for $2.80 and pound of Bing cherries for $1.50. Which cherries are more expensive?

Lesson 2 – Identify Proportional Relationships

Objective: Compare unit rates or use a graph to determine whether a set of paired data points have a proportional relationship.

A.Words to Know:

Proportional Relationship: ______

Origin: ______

B. Understand: Using a table to test for a proportional relationship.

Example 1: Which table represents a proportional relationship?

Table 1

The unit rate(s) ______

The relationship between the two quantities is ______for each ratio.

Table 2

The unit rate(s) ______

The relationship between the two quantities in each pair is ______.

C. Understand: Using a graph to test for a proportional relationship.

Example 2: Eliza makes these four servings of orange-cranberry juice. If the pairs of quantities in the table are in equivalent proportional relationships, each serving will taste the same. Does the table show proportional relationships that are the same?

*You can test to see if there is a proportional relationship by graphing the ratio parts. The quantities are in equivalent proportional relationships if

1) Points lie in a straight line AND 2) pass through the origin (0,0).

Answer: ______

Example 2: Eliza makes the four servings of mango-pear juice shown in the table. Does the table of ratios show equivalent proportional relationship?

Answer: ______

D. Think/Pair/Share

Unit Rate Method
Advantages / Disadvantages
Graphing Method
Advantages / Disadvantages

Lesson 3 – Identify the Constant of Proportionality

Objective: Use tables, graphs, equations, and diagrams to compute the constant of proportionality (unit rate) for a proportional relationship

A. Words to Know:

Constant of Proportionality: ______

B. Understand: Identify the unit rate from a graph or from an equation

Example 1:

*You can find the constant of proportionality (unit rate) by:______

Therefore, the unit rate is: ______

Proportional Equation: Any proportional relationship can be written as an equation in the form of: ______

k: ______

So, the equation for the relationship in the graph above is: ______

C. Understand: Identifying a unit rate from a double number line diagram

Example 2:

The double number line diagram at the right shows the proportional relationship between the cups of flour and the cups of milk in the recipe.

To find the unit rate: ______

D. Connect - Different ways to identify a unit rate

Verbal description
Martha drives miles in 2.5 hours.
The unit rate is: ______/ Table:
The unit rate is _____ foot per second.
Graph

The point ______shows the unit rate. The
unit rate is _____ cup of milk per cup of flour. / Equation
Let x = the number of cups of yellow paint
Let y = the number of cups of blue paint
Equation: y = 4x
The unit rate is ______of blue paint per cup of yellow paint.
Diagram
/ The point for _____ on the top line lines up with the point for 1 on the bottom line.
The unit rate is ______pound of cheese per pound of chicken.

Lesson 4 – Represent Proportional Relationships with equations

Objective: write equations for proportional relationships and use the equations to solve problems.

A. Understand: Representing a proportional relationship with an equation

Example 1: Liam buys a new car. She travels 96 miles using 4 gallons of gasoline. Write two equations to represent this proportional relationship.

*You can use variables

Let m = ______

Let g = ______

Equation 1: ______Equation 2: ______

The equations ______and ______represent the proportional relationship.

*Keep in mind – every word problem presents a unique solution. Therefore, the equation you write to represent a proportional relationship should depend on the information you are given and the information you need to find.*

Example 1a: How far can Lina travel on 1 gallon of gasoline? ______

Which equation from above will get you the information you need to find? ______

Example 1b: How many gallons of gasoline will Lina need to travel 1 mile? ______

Which equation from above will get you the information you need to find? ______

B. Guided Practice: See workbook page 38 and complete #1-4

C. Connect: Using an equation to find the unknown in a proportional relationship

Example 2: Adam runs 13 miles in 2 hours. If he keeps up the same pace, how far can he run in 5 hours?

Write a proportional relationship:

So, you need to find the unknown miles Adam runs in 5 hours.

Method 1: Use an equationMethod 2: Use cross products

(review from 6th grade)

In 5 hours, Adam can run ______.

Lesson 4 – Guided Practice

Solve the following problems using BOTH methods.

1. 110 miles in 11 hours = ______miles in 24 hours