Understand Valid Counter Examples
Lesson
Topic Index| Grade 5 Math | Intermediate Test Prep | StudyZone

There is more than one way to skin a cat.
In other words there are many ways in which to solve a problem and come up with the correct answer.

Example 1:

Jack did 28% of his work on the computer. What fraction of the work does Jack have left to do?

 Valid Solutions

Valid

Step 1: You can change the percent to a fraction 28/100.

Step 2: Reduce 28/100 to 7/25 by dividing 28 and 100 each by 4.

Step 3: Subtract 25/25 - 7/25 = 18/25

Step 4: He has 18/25 of the job left to do.

Counter Valid

Step 1: Subtract 100% - 28% = 72%

Step 2: You can change the percent to a fraction 72/100.

Step 3: Reduce 72/100 to 18/25 by dividing 72 and 100 each by 4.

Step 4: He has 18/25 of the job left to do.

Counter Valid

 

Step 1: You can change the percent to a fraction 28/100.

Step 2: Subtract 100/100 - 28/100 = 72/100.

Step 3: Reduce 72/100 to 18/25 by dividing 72 and 100 each by 4.

Step 4: He has 18/25 of the job left to do.

Example 2:

Mackenzie is making Surprise Punch for her birthday, The recipe makes 2 quarts. If she make 8 times the recipe because she is very popular and has many friends coming to her party. How many gallons of Surprise Punch will she have?
 

 

Valid

Step 1: You can multiply 2 x 8 = 16 quarts.

Step 2: There are 4 quarts in a gallon, so 16 ÷ 4 = 4 gallons.

Step 3: Mackenzie has 4 gallons of Surprise Punch.

Counter Valid

Step 1: You can change 2 quarts to 0.5 gallons.

Step 2: Then multiply 0.5 x 8 =4 gallons.

Step 3: Mackenzie has 4 gallons of Surprise Punch.
 

Counter Valid

 

Step 1: You can multiply 2 x 8 = 16 quarts.
 
Step 2: Quarts are 1/4 of a gallon so, 1/4 of 16 =4 gallons.

Step 3: Mackenzie has 4 gallons of Surprise Punch.
 

 

Let's Practice

Remember: Use the method of solving a problem that you're most comfortable with. Then when the problem is done ask yourself " Is this what the question is asking for? Is the problem solved correctly?"

 

 
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