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(1) Modeling Ratios


Learning Target:
  • You will learn how to build bar models to solve word problems that compare quantities using fraction and ratio.
  • You will also learn about the link between ratio and fraction by drawing models to organize and solve problems.
Follow along with the videos - take notes, pause, try to solve the problem yourself, rewind if needed, or just watch! 
When you are ready, try the online practice quiz.

Example 1: Paying for Lunch  
The goal of this lesson is to learn how to model a ratio word problem using a unit bar model.

Paying for Lunch


 Steps for Success

1. Read the problem and determine what the problem is about.
We are comparing the amount Jason paid to the amount Carmen paid.  
  
Part: Whole  (Jason’s share to the whole bill)  3 : 5
  Part: Part    (Jason’s share to Carmen’s share)
 3 : 2

2. Draw the unit bars to model the relationship between two or more quantities.

When we draw unit bars, we don’t yet know the exact value of the unit (or box), but we do know that each unit represents equal amounts.

3. Read again and use the facts of the problem to label the unit bars

We know that the total bill is $30, so Jason’s share combined with Carmen’s share totals $30. 

4. Identify the question or the "unknown" and label it on the unit bar as a  "?"

We want to know the amount of money Carmen and Jason each paid. 

5. Solve the problem – explain or justify all calculations.

Since 5 units equals $30, then 1 unit equals $30 ÷ 5 , or $ 6

Jason’s share is 3 units, and 3($6) = $18

Carmen’s share is 2 units, and 2($6) = $12

Check: $18 + $12 = $30                  


Example 2: Banana Cream Pie  The goal of this lesson is to learn how to model a ratio relationship that can also be expressed as a fraction.

Banana Cream Pie

 Steps for Success

1. Read the problem and determine what the problem is about.

We are comparing number of pies Will ate to the number of pies Kate ate.   We can create two comparisons:

Part: Whole     (Will’s pies to the total amount of pies)  4/7  


Part: Part    (Kate’s pies to Williams pies)   3 : 4

2. Draw the unit bars to model the relationship between two or more quantities.


When we draw unit bars, we don’t yet know the exact value of the unit (or box), but we do know that each unit represents equal amounts.  In this case, Will gets 4 units and Kate gets 3 units


3. Read again and use the facts of the problem to label the unit bars.

We know that 28 pies were eaten, so Will’s units combined with Kate’s units totals 28  

4. Identify the question or the "unknown" and label it on the unit bar as a  "?"

We want to know exactly how many pies they each ate.

5. Solve the problem – explain or justify all calculations.

Since 7 units equals 28 pies, then 1 unit equals 28 ÷ 7 , or 4 pies per unit

Will’s share is 4 units, and 4(4) = 16 pies                                                                                                       
Kate’s share is 3 units, and 3(4) = 12 pies

Check: 16 + 12 = 28 pies in total


Bonus Example: A more challenging problem with ratio and fraction!  

Payback


Steps for Success                                                                             
1. Read the problem and determine what the problem is about.            
2. Draw the unit bars to model the relationship between two or more      quantities                                                                                           
3. Read again and use the facts of the problem to label the unit bars     
4. Identify the question or the "unknown" and label it on the unit bar as a  "?"                                                                                                   
5. 
Solve the problem – explain or justify all calculations.                       


















Subpages (1): Practice Quiz (Module 1)
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Sarah Kurdziel,
Jul 26, 2011, 11:14 PM
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