Part 1: Concrete Models Tape Diagrams Representing Ratios 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 Part to Part Part to Whole 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 __________________ Rate _________________________

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)

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 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

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

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?   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

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?