Help Middle School Math Students Improve Problem Solving Skills

• We’d typically underline or highlight important information and cross out extra information.
• Instead of just highlighting/underlining, students also wrote the information, putting it into their own words as much as possible.
• Writing the information helps solidify it in their minds, and if they reword it or add detail to clarify the meaning, they understand it a bit better.

For “what I need to know,” students highlight/underline what the question is asking and then wrote it in their own words.

For example, with a problem like this:
Steve runs every other day and trains with weights every 3rd day. If he does both on Monday, how many times will he do both on the same day during the next 2 weeks?

Students might write:
What I know:

• Runs every 2 days. I know this because every other day means the same things as every 2 days.
• Weights every 3rd day – the problem states this information. 
• Runs and uses weights on Monday – the problem states that he does both activities on Monday.

What I need to know:

• I need to figure out how many times will Steve run and use weights on the same day, during the next 14 days – I know that 2 weeks is the same as 14 days. 

After students completed these written parts, we’d discuss what they identified as what they knew and what they needed to know,  before getting started with the solving. Then students would solve on their own and write a paragraph to explain exactly what they did to solve the problem.

Solution Explanation Example:
To solve this problem, I decided to make a table to find how many days Steve will do both activities.

• Since I want to know how many times this happened in 2 weeks, I made the table 2 rows of 7, and I labeled the days of the week at the top of the table, starting with Monday.
• In the first square of the table, I wrote an R and a W, since Steve did both on Monday.
• Then I wrote an R in every other square, and I wrote a W in every 3rd square.
• When I was finished, I counted how many squares had both R and W in them. There were 3 days total (including the Monday he started), so the answer is: Steve will do both activities on the same day 3 different times in 2 weeks.

Once students finished solving and writing their paragraphs, several of them would read their paragraphs to the class, giving students the opportunity to see if they could follow their peers’ explanations, compare the explanations to their own to see how similar they were, and learn/consider a new method if a student had solved a different way.

While this process did take a while, it was SO worth it. It really helped students break down the problems, become more in tune with how they were solving, and resulted in less “random” use of operations/solving methods. It also greatly improved their math communication abilities.

These days, with shorter math classes:-(, and therefore less time to write, I’ve consolidated the “what I know” and “what I need to know” into ‘Find out,’ so it encompasses both the important info the question that needs to be answered. Where I used to have several students read their examples with the class, I now have students do a quick “pair-share” after the first stages, and then share a couple of the final explanations with the entire class. It still takes a good chunk of time, but I believe that time is made up with fewer struggles as we move through the year.