Getting Started

The student is unable to use ratio reasoning to convert measurement units.

The student:

• Adds or subtracts the measurement conversion factor and the given units.
• Consistently uses the wrong conversion factor.
  
  
  
   
• Incorrectly converts eight mile laps into an equivalent number of miles. 
• Makes a drawing to find the number of miles in 8 laps but is unable to show mathematical work or explain the answer. 

What are you trying to find? Do you know laps, miles, or feet? How can you convert between those different units?

How can you use your picture to help you write a math problem to convert laps to miles?

Can you build a ratio table to show the relationship between the units?

What does of a pizza look like? How much would eight pieces of pizza be all together?

What does a lap mean? How long is the lap? If he had run only 2 laps, how far would he have gone? If he ran 4 laps, how far did he run? How many laps does it take to make 1 mile? How many miles equal 8 laps?

Model completing each conversion. Use a triple number line to represent the relationship between number of laps, miles, and feet. Assist the student in using the number line diagram to determine how many feet Roger ran when running 8 laps. Have the student extend the diagram to 3 miles and then use it to create a table that contains corresponding numbers of laps and miles. Encourage the student to think multiplicatively about the relationship among values in the table, e.g., the number of laps is always four times the number of miles. Point out that associated values in ratio tables are related by a constant ratio and define this ratio as the constant of proportionality. Have the student use the constant of proportionality to extend the table to 10 miles and then determine how many more laps Roger will need to run in order to run 10 miles. Guide the student to select the appropriate conversion factor to convert 15,840 yards to miles. Assist the student in creating a double number line diagram or table to complete the conversion.

Guide the student to use ratio reasoning to complete measurement conversions. Model a variety of strategies for solving conversion problems and encourage the student to use ratio tables, tape diagrams, and double number lines to assist in making sense of the relationships among quantities. Provide additional opportunities to solve conversion problems.

Moving Forward

The student shows evidence of ratio reasoning but makes errors when converting measurement units.

The student:

• Finds the number of “miles more” rather than number of “laps more.”
  
  
  
   
• Uses the wrong conversion factor for one of the conversions.
  
  
  
   
• Uses a conversion factor incorrectly.
  
  
  
   
• Does not complete the problem, converting laps to miles but not miles to feet.
  
  
  
   

What units is the question asking for? What units did you change to? Can you try this problem again?

Why did you use this conversion factor? What units do you know and what do you need? Do you see a conversion ratio that relates the units you have to the units you're trying to find?

How did you decide whether to multiply or divide by the conversion factor? Does your answer make sense?

Guide the student to think about conversions in terms of equivalent ratios and their multiplicative relationship. Model a variety of strategies for solving conversion problems. Encourage the student to use ratio tables, tape diagrams, and double number lines to understand the relationship among units. For example, create a table that contains one of the conversion factors, e.g., 1 mile = 5280 feet, and have the student extend the table to include entries for 2 – 6 miles. Explain that the conversion factor reflects the constant of proportionality. Guide the student to use the constant of proportionality to calculate values for the table.

Provide feedback regarding any errors made and allow the student to revise the work. Provide additional opportunities to solve conversion problems.

Almost There

The student’s work contains a minor error or omission.

The student:

• Makes a calculation error.
  
  
  
   
• Finds the correct answer numerically but labels it with the wrong unit.
• Does not fully answer the question asked, e.g., finds the number of total laps needed to run 10 miles, rather than how many more laps.
  
  
  
   
• Provides unclear, insufficient, or mathematically incorrect work.
  
  
  
   

Can you read the question again? What units do you want? Is that what you found?

Do you want total miles or laps? How many miles has he run so far on Monday? How many miles does he have left? How many laps will that total?

Can you explain how you found your answer? Can you show work to support what you did?

Provide feedback concerning the error made and allow the student to revise the work. Show the student examples of appropriately written work of other classmates. Provide more opportunities for the student to solve conversion problems and encourage the student to show work appropriately.

Consider using other MFAS 6.RP.1.3 tasks to give the student more experience with proportional reasoning and percent.

Got It

The student provides complete and correct responses to all components of the task.

The student:

• Converts eight mile laps to 2 miles and converts 2 miles to 10,560 feet. 
• Determines that Roger will need to complete 8 more miles, which is equivalent to 32 more laps in order to complete 10 miles by the end of the week. 
• Converts 15,840 yards to 9 miles.

The student may multiply or divide by conversion factors or may set up a proportion to solve each problem.

   

Which week did Roger run more miles, last week or this week? How do you know?

How many laps would it take him to run 21,120 yards? How would you convert 10 miles to inches?

If he ran 10 miles every week for a year, how many miles would that be? How many yards?

Have the student convert between metric and standard units and work with rational measurement values.

Change the length of the lap to mile and have the student rework all problems.