Chapter 3Ratios and Rates

(Part 2)

Day…..

1. Introducing Rates

2. Graphing Rate of Change

3. Unit Rates

4. Pop Quiz

Day 1

Bell Work

Walt can mow 500ft2 in10 minutes. If he

does not slow down, how long will it take

him to mow his parents lawn that measures

3,500ft2?

Justify your Response

Vocabulary• Rate –

(Example: 4 tires: 1 car)• Unit Rate –

(Example: )• – A comparison of two quantities by division.

(Example: a:b, a to b, ) • – ratios the express the same relationship between two

quantities. (Example: 10:15 is equivalent to 2:3 and 20:30)• – to multiply or divide two related quantities by the same number.

(Example: x )• – a table with columns filled with pairs of numbers that have

the same ratio.

Example: Nails Used 5 10 15Shelves Hung 1 2 3

A ratio comparing two quantities with different kinds of units.

a rate that is simplified so that it has a denominator of one.

Ratio

Equivalent Ratio

Scaling

Ratio Table

I Can….

Identify and determine

equivalent rates.

Introducing RatesEssential Understanding:

• A rate is a ratio that compares two quantities with different kinds of units.

Examples:

1) Driving 120 miles in two hours.

2) Paying $2.49 per gallon.

3) Reading 15 pages in 20 minutes.

4) Making $15 an hour.

• Because rates compare quantities with different units, the units must be included when writing or solving rates.

Example:

• Just like before we must be careful to write the units (labels) in the order they are given or answer the question in the order the units are asked.

Example:

Introducing RatesEssential Understanding: • Because rates are ratios (just like fractions are ratios) all the

rules and procedures for ratios apply. Such as….. Rates can be written in three forms

Example: Rates can be scaled up and down to generate equivalent

rates or determine an unknown variable.

Example: You can also determined if rates are equivalent by finding

their cross products, unit rates, or simplest form.

Example:

Watch This• http://

learnzillion.com/lessons/839-understand-rates-as-a-type-of-ratio

(6 minutes)• http://

learnzillion.com/lessons/614-solve-rate-problems-using-multiplicative-reasoning

(7 minutes)

Practice

Clear your desk of everything except for a pencil and a calculator.

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 2

Bell Work

Mark works in a factory where he is paid buy the piece to put together roof vents. He clocked himself one day and found he could

make one roof vent in 20 minutes. If he works an 8 hour shift, how many roofs vents

can he make in one day?

How many vents can he make it two days? A week?

Homework Check

Vocabulary• –

(Example: 4 tires: 1 car)• –

(Example: )• – A comparison of two quantities by division.

(Example: a:b, a to b, ) • – ratios the express the same relationship between two

quantities. (Example: 10:15 is equivalent to 2:3 and 20:30)• – to multiply or divide two related quantities by the same number.

(Example: x )• – a table with columns filled with pairs of numbers that have

the same ratio.

Example: Nails Used 5 10 15Shelves Hung 1 2 3

A ratio comparing two quantities with different kinds of units.

a rate that is simplified so that it has a denominator of one.

Ratio

Equivalent Ratio

Scaling

Ratio Table

Rate

Unit Rate

I Can….

Determine unit rates and plot the rate of

change on a graph to determine an unknown

variable.

Unit RatesEssential Understanding: • A unit rate is a rate that has been simplified to a

denominator of 1.Example:

• Remember a rate is a ratio and it must be scaled down by division (not subtraction) to find its simplest form.

Example:

• However, the quickest way to determine a unit rate is to divide the numerator by the denominator and place the quotient over a 1.

Example:

Watch This

• http://learnzillion.com/lessons/840-create-unit-rate-using-diagram

(5 Minutes)• http://

learnzillion.com/lessons/841-create-unit-rate-using-tape-diagram

(5 minutes)

Rate of ChangeEssential Understanding:• A line graph can be used to organize and

illustrate equivalent rates. This is preferable to a ratio table, when illustrating rate of change. Such as changes over time, speed, distance, and profit/loss ($).

Please open your book to page 162

Watch This• http://

learnzillion.com/lessons/615-graphing-rate-problems-using-a-table

(7 minutes)

Practice

Take out your white boards.

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 3

Bell WorkA store sold 255 DVDs in 5 days. If sales continue

at this rate, how many DVDs can the expect to

sell by the 10th day? 15th day? 30th day?

Graph the rate of change for each day given on

the provided graph card.

Homework Check

Vocabulary• –

(Example: 4 tires: 1 car)• –

(Example: )• – A comparison of two quantities by division.

(Example: a:b, a to b, ) • – ratios the express the same relationship between two

quantities. (Example: 10:15 is equivalent to 2:3 and 20:30)• – to multiply or divide two related quantities by the same number.

(Example: x )• – a table with columns filled with pairs of numbers that have

the same ratio.

Example: Nails Used 5 10 15Shelves Hung 1 2 3

A ratio comparing two quantities with different kinds of units.

a rate that is simplified so that it has a denominator of one.

Ratio

Equivalent Ratio

Scaling

Ratio Table

Rate

Unit Rate

I Can….

Solve unit rate problems including those involving unit pricing and constant

speed.

Station Rotations

1. Write your exit ticket.

2. Pack up everything but a pencil and a calculator.

3. You will have 15 minutes per station

1st Rotation

2nd Rotation

3rd Rotation

4th Rotation

Computer Station• http://

learnzillion.com/lessons/842-define-unit-rate-using-double-number-line

• http://learnzillion.com/lessons/613-solve-rate-problems-using-double-number-lines

• http://learnzillion.com/lessons/612-solve-for-missing-values-in-rate-problems-using-a-table

(6 minutes per video)

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 4

Bell Work1. A 5lb sack of potatoes cost $4.32. An 8lb sack of

potatoes cost $6.78. Which is the better deal?

2. Jessie says she will charge Jim $45.00 for 3 hours of

tutoring. Mark says he will charge Jim $90.00 for 5

hours of tutoring. Who offers Jim the better hourly

rate of pay?

Homework Check

Vocabulary• –

(Example: 4 tires: 1 car)• –

(Example: )• – A comparison of two quantities by division.

(Example: a:b, a to b, ) • – ratios the express the same relationship between two

quantities. (Example: 10:15 is equivalent to 2:3 and 20:30)• – to multiply or divide two related quantities by the same number.

(Example: x )• – a table with columns filled with pairs of numbers that have

the same ratio.

Example: Nails Used 5 10 15Shelves Hung 1 2 3

A ratio comparing two quantities with different kinds of units.

a rate that is simplified so that it has a denominator of one.

Ratio

Equivalent Ratio

Scaling

Ratio Table

Rate

Unit Rate

I Can….

• Relate ratios and rates to the

multiplication and division of fractions.

• Look at my answer to check that I answered what was asked and see if

my answer makes sense.

pOp Quiz

• Take out a pencil and a calculator.

• Clear your desk of everything else.

Let’s Review

Complete Chapter Study Guide

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 5

No School

I Can….

Use ratio and rate reasoning to solve

real-world and mathematical

problems

Bell Work1. Mr. Vanderson drove 110 miles in 2 hours. How

fast did Mr. Vanderson drive?

2. Nikki can bounce a basket ball 900 times in 20

minutes. How may times can Nikki bounce a

basketball in one minute.

3. Dakota walked 12 blocks to his uncle’s house in

30 minutes. How many minutes did it take

Dakota to walk 1 block?

Vocabulary• –

(Example: 4 tires: 1 car)• –

(Example: )• – A comparison of two quantities by division.

(Example: a:b, a to b, ) • – ratios the express the same relationship between two

quantities. (Example: 10:15 is equivalent to 2:3 and 20:30)• – to multiply or divide two related quantities by the same number.

(Example: x )• – a table with columns filled with pairs of numbers that have

the same ratio.

Example: Nails Used 5 10 15Shelves Hung 1 2 3

A ratio comparing two quantities with different kinds of units.

a rate that is simplified so that it has a denominator of one.

Ratio

Equivalent Ratio

Scaling

Ratio Table

Rate

Unit Rate