• 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. _________
Part 1:
Concrete Models
Tape Diagrams
Refresher!
• Remember we learned last week that a
RATIO is the RELATIONSHIP BETWEEN
TWO QUANTITIES
• There are 3 types of ratios
1. Part to Part
2. Part to Whole
3. 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 whole
Example: 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 units
Example: Distance compared to time (Miles per hour)
• 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 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
• 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
• 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.
2.
Draw a tape diagram by making a bar to indicate the total
number of assignments. Partition off five assignments and label
them math.
What is the ratio of math assignments to total assignments each
week?
»
X X X X X
5:25
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?
• You have 10 minutes to complete the
Independent Practice worksheet.
• Raise your hand if you have questions or
need help.
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 : 8
d. 6 : 8