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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. Part 1:

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Warm up

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

Representing Ratios

Part 1:

Concrete Models

Tape Diagrams


Refresher

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


Refresher1

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 ______________________


Refresher2

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

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

  • 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____


Partitioning1

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

    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

    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

    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 models1

    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

    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 diagram1

    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

    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


    Tape diagram example1

    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

    Real World Application!


    Independent practice

    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

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


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