When I first started teaching, I struggled to find a way to help my students with their problem solving skills in a way that was rigorous yet consistent. I often found myself blaming my students' low reasoning skills on their lack of reading comprehension but I soon found this thinking to be extremely false. As the years went on and my delivery of instruction improved due to professional development, I finally feel that I am at a place where I am confident in my ability to help my students develop their problem skills.
First you want to give students a consistent process for solving word problems. My students use the acronym UPESC which stands for Understand, Plan, Estimate, Solve and Check.
Understand- To understand the problem, I teach my students to read and annotate word problems by circling important numbers with the units, underlining key information (important information without numbers) and labeling the important information. To keep my students from randomly circling and underlining, I try to stress that anything that is circled/underlined should have a specific smart note on why that information is important. Without naming this stipulation, it is almost guaranteed that students will underline the entire problem and circle every single number that they see without trying to fully understand what is being asked. The two questions that help the most during this process are: what do we have? and, what do we need to find?
Plan- During the planning process, students should use their annotations to help them choose the operation. Visual models definitely help students choose the appropriate operation by forcing them to represent the situation of the problem. My students use bar models as their visual representations and with consistent practice and feedback, choosing the appropriate operation becomes a breeze even for my students with the most gaps in their reasoning ability. Once students have shown mastery of choosing the appropriate operation on a consistent basis, I allow them to simply list the steps for solving.
Estimate- There are several estimation strategies that I teach my students to choose from throughout the course of the school year, the strategy that they use depends on the problem. The most common strategy that students can use to estimate is rounding. When dealing with fractions students can use benchmarking or their understanding of relative magnitude to help them estimate their final answer. The purpose of this component is to help students gauge the range of their final answer so that they can readily recognize when they have made a mistake after solving. There are countless occurrences where my students were able to avoid silly mistakes based on estimating their answer before hand.
Solve- Once students fully understand the problem and have a clear plan of execution, they can solve but they must show clear, complete work. I do not accept work with just an answer. My reasoning for this is because it becomes more difficult to give feedback for students to fix mistakes when its not clear they've done incorrectly.
Check- Finally students should wrap up their problem solving by checking their work. They should start by checking their work against their estimate; if their answer is close then they most likely solved correctly. To check their work more thoroughly students have the option of checking using the inverse operation, re-working the problem, or using models if they chose to solve with the standard algorithm. Any checking strategy is acceptable as long as students are showing strategic thinking for checking to see if they solved correctly.
I usually start teaching this process for solving word problems in the very beginning of the year with lots of guided practice, questioning around reasoning and feedback. I have found that students make faster progress when they have exemplars to refer back to when they are working independently. Posters and interactive math notebooks come in handy for my students when developing their independence with problem solving.
If you are looking for resources to start helping your students with problem solving check out my UPESC Problem Solving Pack and my Interactive Math Notebooks for Bar Models. These products along with consistent practice and feedback, are sure to help develop the reasoning skills that students need to tackle word problems.
What do you do to help your students with their problem solving? Share your strategies by leaving a comment down below!
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