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February 6, 2018
Modifying Proportional Problems Based on Problem Structures

Proportional tasks involve a variety of structures that can be modified to make the problem more or less challenging. Some of the structures that can be altered include:

- Multiplicative Relationships (integral vs non-integral)
- Context
- Complexity of the Numbers
- Parallel vs Non-Parallel Structure
Look at the problem above. Some of the main structures of the problem are:

1.  Multiplicative relationships : both the within (pounds to pounds) and between (pounds to days) ratios are non-integral
2.  Complexity of numbers : the numbers are all whole numbers
3.  Non-Parallel : the story is pounds to days, but the question asks for days to pounds
You can alter any of these structures in order to change the difficulty of the problem to meet the needs of your students.

To make the problem easier, you could:
- Make one or both relationships integral
- Change the numbers to make them both even
- Make the problem parallel (Paul's dog ate a 45 lb bag of dog food. How long did it take?)
- Present the information in a table to make it parallel

To make the problem harder, you could:
- Change the numbers to fractions or decimals
- Make the problem multi-step
- Change the within ratio to something more difficult than 1.5
Action Item

Look at the two items below from the OGAP Proportional Item Bank. Which problem is easier and which is more difficult? What structures were changed between the two problems?
Now, find a proportional word problem in your textbook. Identify the structures in the problem. How can you adjust the structures to make the problem easier or harder?
Did you know?

You can access the OGAP Item Banks online in two ways: find our new searchable OGAP item bank  here ( bookmark it! ) or view the PDFs at  www.ogapmath.com/item-bank .

Also, you can access past issues of OGAP Teacher Tips by visiting  www.ogapmath.com/ogap-teacher-tips-archive.