Problem Solving Strategies

After reading Comprehending Math, I decided to ask students three essential questions while solving problems. Those questions are only a few that I took from Arthur Hyde's Braided Model. Those three questions help students to break down a word problem, understand it and develop strategies for solving. As a classroom teacher, you can turn these questions into a routine every time they come across word problems. Students can write down their responses or simply exchange ideas to help others lead to a solution. 

 

Here is an example:  The sum of three numbers is 98. The ratio of the first to the second is 2:3, and the ratio of the second to the third is 5:8. What is the value of the second number?

 

1) WHAT DO I KNOW FOR SURE?

Sample response: I know that the sum of the three numbers in 98. The ratio of the first number to the second is 2 to 3 and the ratio of the second number to the third is 5 to 8. 

2) WHAT DO I WANT TO KNOW, FIGURE OUT OR DO?

Sample response: We would like to know what the second number is. 

3) HOW CAN I SOLVE THIS PROBLEM?

Sample response: Since the second number is mentioned twice, I need to find the greatest common multiple of 3 and 5 and then represent the numbers as algebraic expressions. GCF (3,5)=15 so I can use the following expressions for each number:

Number one= 10x

Number two = 15x 

Number three= 24x

You can see that these numbers will satisfy the ratios mentioned in the problem: 

(10 to 15 is same as 2 to 3) and (15 to 24 is same as 5 to 8)

I will then add these three expressions 10x+15x+24x = 49x 

Since 49x = 98 x=2 and now we can tell the numbers are 20, 30 and 48 respectively.