1. Part 1: Concrete Models Tape Diagrams
Representing Ratios
Part 1:
Concrete Models
Tape Diagrams

2. Refresher!
Remember we learned last week that a RATIO is the RELATIONSHIP BETWEEN TWO QUANTITIES
There are 3 types of ratios
Part to Part
Part to Whole
Rates

3. 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 __________________
Rate _________________________

4. Define and give an example of EACH TYPE of ratio in your notes.
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)

5. 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

6. 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____

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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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?
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?
5:25 X

14. 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?