- 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.
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.
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.
2. Draw the unit bars to model the relationship between two or more quantities.Part: Whole (Jason’s share to the whole bill) 3 : 5 Part: Part (Jason’s share to Carmen’s share) 3 : 2 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 barsWe 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 |
Steps for Success 1. Read the problem and determine what the problem is about.
Part: Whole (Will’s pies to the total amount of pies) 4/7 Part: Part (Kate’s pies to Williams pies) 3 : 4
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
We want to know exactly how many pies they each ate.
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!
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.