This activity gives students a chance to apply the different strategies they have learned to solve part-part-whole ratio problems. It is also an opportunity to decide on methods that would make the most sense in given situations.

Each problem may lend itself better to a particular representation than to others. For example:

• The problem about power sources can be well represented by all three representations because it involves small numbers and simple multiplication.
• The problem about power used for cooling might be inefficient to represent with a number line diagram, since it would require marking 8 increments of 4.25 to find the total of 34. Using a tape diagram or a table with more straightforward multiplication would be more efficient.

The time needed to solve the problems may depend on the representation students choose to use.
 

Solicit or share the solutions to the problems, and ask students about their choice(s) of representations. Here are some questions for discussion:

• “Is there a particular representation you tend to try first?” 
• “Does one seem more efficient than the others?” 
• “Did the situation in a problem affect your choice? If so, what features of a problem might steer you toward or away from a particular strategy?” 
• “A family wants their home to be comfortable in the summer while also minimizing their energy use. What recommendations would you make to them?” (Ceiling fans use less energy than air conditioners use. Some homes or rooms in homes do not have ceiling fans, so a combination of fans and air conditioners would be better than just air conditioners.)