Chapter 3 Ratios and Rates

Chapter 3Ratios and

Rates

Day…..1. Introducing Rates

2. Unit Rates

3. Graphing Rates of Change

4. Rates and Ratios in Review

5. 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….

Explore rates using models.

Introducing RatesEssential Understanding: • A rate is a ratio that compares two quantities with

different kinds of units. For example: 120 miles in two hours.

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

• Just like before we must be careful to write the units in the order they are given.

• Because rates are ratios, they can be written in all three forms; colon 120 miles: 2 hours, 120 miles in two hours, and .

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)

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 2

Bell WorkMark 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?

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

No NewVocabulary

Rate

Unit Rate

I Can….Determine unit rates

AndSolve unit rate problems including those involving unit pricing and constant

speed.

Unit RatesEssential Understanding:

• A unit rate is a rate that has been simplified to a

denominator of 1.

• Remember a rate is a ratio and it must be scaled down by

division.

• To determine a unit rate, you simply divide the numerator

by the denominator and place the quotient over a

denominator of 1.

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)

Practice

Please take out your maker boards

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 3

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?

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

No NewVocabulary

Rate

Unit Rate

I Can….Plot a rate of change

on a graph.

Rate of ChangeEssential Understanding:• A graph can be used to illustrate a rate of

change, such as changes over time and distance.

Please open your book to page 162

Watch This• http://

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

(7 minutes)

Your Turn….

• Clear your desk of everything but a pencil and a calculator.

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 4

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

at this rate, how many DVDs can the expect to

sell in 30 days?

Graph the rate of change for each day on the

given 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

No NewVocabulary

Rate

Unit Rate

I Can….Use ratio and rate

reasoning to solve real-world and

mathematical problems

Station Rotations1. Write your exit ticket.

2. Pack up everything but a pencil.

3. You will have 15 minutes to complete each rotation

1st Rotation

2nd Rotation

3rd Rotation

4th Rotation

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 5

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

No NewVocabulary

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.

Let’s Review

PleaseTake out your Study Guide

pOp Quiz

• Take out a pencil and a calculator

• Clear everything else from your desk

Wrap it Up

• Classroom Store

• Exit Tickets

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)