Warm Up• Use the pictures below to answer the

questions that follow.

• Write the ratio of ice cream cones to fortune cookies. ________

• Write the ratio of fortune cookies to total treats. ________

• Write the ratio of total treats to ice cream cones. _________

Representing Ratios

Concrete ModelsTape Diagrams

Double Number LinesTables

Refresher!

• Remember we learned last week that a RATIO is the RELATIONSHIP BETWEEN TWO QUANTITIES

• There are 3 types of ratios1. Part to Part2. Part to Whole3. Rates

Refresher!Define and give an example of EACH TYPE of ratio in your notes. You have

2 minutes!• Part to Part ____________________

Example ______________________• Part to Whole __________________

Example ______________________• Rate _________________________

Example ______________________

Refresher!Define and give an example of EACH TYPE

of ratio in your notes. • Part to Part: Relates One part of the

whole to another part of the wholeExample: The ratio of boys to girls in the line

• Part to Whole: Relates one part of a whole to the whole

Example: The ratio of boys to children in the line

• Rate: Ratio that relates different unitsExample: Distance compared to time (Miles per

hour)

The relationship stays the SAME!

• Remember that you can SIMPLIFY a ratio - but the relationship always stays the same

Let’s take a closer look at this:• A ratio of 3 blue paper clips to 9 red

paper clips is written 3:9• Can this ratio be simplified? To what?• 1:3 – Divide both 3 and 9 by 3

Partitioning

• Partitioning means SPLITTING a unit

• Let’s look at an example:– Sam bikes 20 miles in 1 hour. Sam’s

rate is the same no matter how long or short his bike ride is.

Miles _0_ 5 __10___20____40___Hours _0__1/4__1/2____1_____2____

Partitioning

Miles _0_ 5 __10___20____40___Hours _0__1/4__1/2____1_____2____

• If Sam’s ride is only 10 miles – how long does it take?

– 1/2 hour

• How do you know?– Because the distance is cut in half – so is the time (keep the

ratio the same!)

• What if Sam’s ride is 5 miles – how long does it take?

– ¼ of an hour

Iteration

• Iterating means repeating a unit• Let’s look at our example with Sam:

Miles _0_ 5 __10___20____40___60___80

Hours _0__1/4__1/2____1_____2____3____4

Sam bikes 20 miles in 1 hour. So if Sam bikes 40 miles how long will it take?

• 2 hours because the distance doubled, so does the time

What if Sam bikes 80 miles? • 4 hours because the distance was 4 times greater

– so is the time

Brain Break!

• Musical Chairs!• When the music stops – quickly find

your seat• The last person standing will answer

a question on ratios!• Ready, set, go!

Concrete Models

• There are many different ways of drawing/representing ratios

• A concrete model uses pictures to represent each quantity in the ratio

• Example: 2 eggs for every 1 cup of milk

Concrete Models

• Example: 2 eggs for every 1 cup of milk

• Now, iterate to show the ratio for 6 eggs

• 6 eggs for every 3 cups of milk

Tape Diagram

• A tape diagram looks like a piece of tape and shows the relationship in a given ratio

• It is also called:– Strip diagram– Bar model– Fraction Strip– Length model

Tape Diagram

• Tape diagrams work very well to show PART to PART and PART to WHOLE ratios

Example:• School A has 500 students, which is 2 ½

times as many students as School B. How many more students attend school A?

School A

School B

Tape Diagram - Example

Keenan has 25 homework assignments per week. Of the 25, five of the assignments are for math

and the other assignments are for other subjects. In 125 total assignments, how many

non-math assignments  does Keenan have? 1. Draw a tape diagram by making a bar to indicate the total

number of assignments. Partition off five assignments and label them math.

2. What is the ratio of math assignments to total assignments each week?

» 5:25

 

X X X X X

Tape Diagram - Example

Keenan has 25 homework assignments per week. Of the 25, five of the assignments are for math and the other

assignments are for other subjects. In 125 total assignments, how many non-math assignments  does

Keenan have? • What is the ratio of math assignments to total assignments?

• 25:125

• How many assignments are non-math?• 100

• Other assignments to total assignments?• 100:25

• Math assignments to other assignments?• 25:100

 Turn and talk: Which ratio was needed to solve this problem? Why?

Real World Application!

Independent Practice

• You have 10 minutes to complete the Independent Practice worksheet.

• Raise your hand if you have questions or need help.

Exit Ticket Show your work using a Concrete Model

or Tape Diagram!

1. For every two peonies in a flower arrangement there are three gardenias. There are 15 flowers in the flower arrangement. How many flowers are gardenias?

2. For every piece of broccoli Devaunte eats, his mother will give him half of a Chips Ahoy cookie. How many pieces of broccoli does Devaunte need to eat to get three Chips Ahoy cookies?

3. Read the problem below. Then choose the correct ratio to solve the problem. 

In his garden, Mr. Warshawer has two cucumbers for every six cherry tomatoes. In the garden, there are currently 80 vegetables (cucumbers and cherry tomatoes) growing. How many of the vegetables are cucumbers?

a. 2 : 6 b. 6 : 2 c. 2 : 8d. 6 : 8