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- 1. Strategies for Solving Proportional Ratios With Missing Values<br />
- 2. EightStrategies for Solving Missing Value Problems for Proportional Ratios<br />(*Cross multiplication is the least recommended of the ten as it often neglects the understanding of the ratios and instead gets user to use a shortcut that may often be used erroneously)<br />Unit Rate <br />Scale Factor<br />Table Strategy<br />Graphing Strategy<br />Double Number Line<br />Unit Bars<br />Fraction Strategy<br />Cross Multiplication*<br />
- 3. The Problem: Mobile Phone Minutes<br />Janie Lou just bought a pay-as-you-go mobile phone. According to this plan, $5.00 gets 20 minutes of talk time. If Janie wants to limit her plan to $25.00 per month, how many minutes will she be limited to each month? <br />Let’s investigate!<br />
- 4. Strategy #1: Unit Rate ApproachUnit Rate approach is looking at units of measure across or between the two measure spaces<br />In order to determine how many minutes $25 will get us, let’s look at the relationship between 5 dollars and 20 minutes. In order to get to 20 from 5, we need to multiply 5 by 4, or apply a UNIT RATE of 4. Likewise, to get from 20 to 5 we can apply a unit rate of 20/5 or 0.25 to 20<br />Let’s put the information that we know into the table below<br />4<br />0.25<br />Applying a unit rate of 4 to 25, we can solve: 25x4=100 <br />4<br />
- 5. Strategy #2: Scale Factor ApproachScale Factor approaches problems much in the way that Unit Rate did, however, instead of looking across the measure spaces, we are looking at the multiplicative relationship vertically<br />In order to determine how many minutes $25 will get us, let’s look at the relationship between 5 dollars and 25 dollars. In order to get to 25 from 5, we need to multiply 5 by 5, or apply a SCALE FACTOR of 5. Likewise, to get from 25 to 5 we can apply a scale factor of .2 to 25<br />Let’s put the information that we know into the table below<br />x5<br />x 5<br />x.2<br />Applying a scale factor of 5 to 20, we can solve: 20x5=100<br />
- 6. Strategy #3: Table Strategy<br />This strategy uses table to highlight interaction of additive & multiplicative thinking<br />We know that $5 is 20 minutes, so if we pay $10, or twice the original amount, we should get twice the number of minutes. Using this same line of thinking, we can figure out the minutes for $20 and $40 dollars<br />25 is ¼ of the way from 20 to 40, the minutes should be ¼ of the way between 80 and 160, or 100 minutes<br />
- 7. Strategy #4: Graphing <br />Graphing allows us to see visually the relationship between dollars and minutes, then use the graph to determine what $25 will get us.<br />When the line has 25 on the x or Dollars axis, we have 100 on the y or Minutes axis<br />
- 8. Strategy #5: Double Number Line<br />Each tick on the number line has two values associated with it. The double number line helps us visualize or see the relationships between minutes and dollars at any point on the line<br />Minutes<br />0 20 40 60 80 100 120 140 160 <br />0 5 10 15 20 25 30 35 40 <br />Dollars<br />
- 9. Strategy #6: Unit Bars<br />Unit bars show a picture of a proportional situation. Here, each box represents a unit of 4 minutes. 4 minute bars are grouped into chunks of 5 each as 5 dollars gets Janie Lou 20 minutes. If we go to the 5th box of 5 dollars, we will have spent $25. Counting the groups of 5 boxes of 4 minutes each, 5 boxes x 20 minutes per box, we get 100 minutes.<br />
- 10. Strategy #7: Fraction Strategy<br />5 dollars = 25 dollars<br /> 20 minutes ? Minutes<br />I have to multiply the numerator by 5 to get 25 so I have to multiply the bottom by 5, as 5/5 will maintain the proportion. This yields 100 minutes.<br />
- 11. Strategy #8: Cross Multiplication<br /> 5m = 20x25<br /> 5 25<br /> =<br /> 20 m<br />5m = 500<br /> m=100<br />

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