Chapter 3 Ratios and Rates. Day….. 1.Expressing ratios in all formsExpressing ratios in all forms...

Chapter 3Ratios and

Rates

Day…..1. Expressing ratios in all forms

2. Equivalent ratios

3. Creating and interpreting ratio t

ables to represent and solve pro

blems involving equivalent ratio

s

.

4. Exploring ratios using models

5. Creating and simplifying equival

ent ratios

Day 1

Bell WorkDuring one year Mrs. Laymon sent 484 text messages.

This number was 1/3 the number of text messages her

son sent during the same year. How Many text

message did her son send?

Draw a diagram and justify your response.

If he sent the same number of messages each month, how many messages did he send in one month?

I Can….

express ratios in all forms.

(ex. a:b, a to b, and )

Vocabulary• Ratio – A comparison of two quantities by division.

(Example: a:b, a to b, )

• Equivalent Ratio – ratios the express the same relationship between two quantities.

(Example: 10:15 is equivalent to 2:3 and 20:30)

• Scaling – to multiply or divide two related quantities by the same number. (Example: x )

• Ratio Table – a table with columns filled with pairs of numbers that have the same ratio.

Example:

Nails Used 5 10 15

Shelves Hung 1 2 3

Introducing Ratios

Essential Understanding: • A ratio compares two quantities. It can compare a part to a

part, part to whole, or whole to part. Examples:

• Ratios can be written 3 different ways 1:2, 1 to 2, or ½ Examples:

• Ratios can be written in simplest form by dividing each quantity by the greatest common factor. Example: can be reduced to ½ by dividing both qualities by 2.

Examples:

Ratio Scavenger Hunt

1. Write your exit ticket.

2. Pack up everything but a pencil.

3. When told, place your backpack or other belongings in your chair

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 2

Bell WorkA recipe requires a ratio of 2 cups of flour to

3 cups of water. How much water will you need if you have 12 cups of flour?

The ratio of Tennessee representatives to total representatives in the U.S Congress is 3 to 145. If the U.S. Congress has 435 representatives, how many represent Tennessee?

Homework Check

Vocabulary• – 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 15

Shelves Hung 1 2 3

Ratio

Equivalent Ratio

Scaling

Ratio Table

I Can….

determine if two ratios are

equivalent.

Equivalent RatiosEssential Understanding: • To create equivalent ratios, scale them up or down

(multiply or divide each quantity by the same amount). You can use a ratio table or T Chart to organize your work.

• There are many ways to determine if two ratios are equivalent. For instance, you can determine their cross products, calculate their unit rates, or scale both ratios down to simplest form.

**** A word to the wise…Label, Label, Label! ****

Notes Continued…… To determine cross products, begin by writing each ratios in fraction form.

Then ,multiplying the numerator of one ratio by the denominator of the other (cross multiplication). If the cross products are equivalent then the ratios are equivalent.

(This type of equation is called a proportion and can be used to solve for a missing value. To be discussed at a later time….)

Example:

To calculate the unit rate of a ratio, divide the numerator by the denominator and place the quotient over a 1.

Examples:

To simplify ratios, begin by writing the ratio in fraction form . Then, scale the ratio down by dividing both parts by the greatest common factor.

Examples:

Watch This

• http://learnzillion.com/lessons/606-create-equivalent-ratios

• http://learnzillion.com/lessons/607-simplify-ratios-using-common-factors

Practice

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 3

Bell WorkThe ratio of walkers to bikers on a trail is about

10 to 6. If there are 20 walkers, about how

many bikers would there be?

Draw a diagram and justify your response.

Homework Check

Vocabulary• – 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 15

Shelves Hung 1 2 3

Ratio

Equivalent Ratio

Scaling

Ratio Table

I Can….

create and use ratio tables to represent and

solve problems involving equivalent

ratios.

Ratio TablesEssential Understanding:• Ratio tables can be used to find equivalent

ratios. Remember equivalent ratios express the same

relationship between two quantities.

Example: Ratio of eggs to servings in a recipe for cake

Servings 8 16 24 32 40 48 56

Eggs 2 4 6 8 10 12 14

Watch This

• http://learnzillion.com/lessons/587-solve-ratio-problems-using-tables-and-multiplication

• http://learnzillion.com/lessons/608-solve-missing-values-in-ratio-problems-using-a-table

Practice

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 4

Bell WorkPacks of gum are on sale this week 5 for $4. If Mrs. E wanted to

buy gum for the class how much would it cost to buy each

student a pack?

Create a ratio table to find the price for 10, 15, 20, and 25 packs.# of Packs 5 10 15 20 25

Price $4

Wow! That’s a lot of money for gum, when you have 90 students! Mrs. E decides to buy every student one piece of gum instead.

For a total of 90 pieces. Each pack had 5 pieces. How many packs did she buy in all?

Homework Check

Vocabulary• – 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 15

Shelves Hung 1 2 3

Ratio

Equivalent Ratio

Scaling

Ratio Table

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 everything else from your desk

Wrap it Up

• Review

• Questions

• Quiz

Ratio Bingo

Day 5

Bell WorkThe table below shows how students in two classes arrive at

school most mornings.

Based on the results in the table, how many how many can be

expected to take the bus if there are 250 students in the

school?

Method Number of StudentsBus 14

Walk 18Bike 10Car 8

Vocabulary• – 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 15

Shelves Hung 1 2 3

Ratio

Equivalent Ratio

Scaling

Ratio Table

Let’s Review

PleaseTake out your

Study Guide

I Can….

explore ratios using models.

Lego Creation Station

Clear your desk

Wrap it Up

• Review

• Questions

• Exit Tickets