# 10 Math Problem Solving Activities for Middle School

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Looking for some math problem-solving activities for middle school? Good, you’re at the right page then.

Right before children enter Middle School (around the age of 11 or 12), they enter a critical developmental stage known as Piaget’s fourth and final stage of cognitive development.  It’s at this stage that children demonstrate marked growth in a number of areas, ranging from making hypotheses and inferences to thinking abstractly and using advanced reasoning skills.  In line with this crucial phase of a child’s development, Middle School Math curricula are designed to stretch the bounds of adolescent thinking while also helping them to establish new skills and sound mathematical habits.

One way that educators try to ensure this is through common core standards that can be applied to Middle School-aged students.  These standards seek to achieve eight distinct objectives, which help foster the developmental transition addressed by Piaget.  The objectives:

1. Make sense of problems and persevere in solving them;
2. Reason abstractly and quantitatively;
3. Construct viable arguments and critique the reasoning of others;
4. Model with mathematics;
5. Use appropriate tools strategically;
6. Attend to precision;
7. Look for and make use of structure;
8. Look for and express regularity in repeated reasoning

allow for a lot of leeways as well as creativity in the way that problems are both presented to and solved by students.

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The first objective, for example, emphasizes a student’s ability to not simply apply an algorithm to a problem, but more pointedly, make a decision and implement it.  This process can draw out drastically different reactions in different students.  For some, the prospect of being creative and innovative in thinking of ways to solve brain-bending problems is exciting, and often even addicting.  On the other hand, getting past the roadblocks that come along with solving a tough problem can be frustrating and, at times, discouraging for students.  It is in these moments that establishing math skills that promote perseverance are most critical.

A quick and easy way of avoiding that anticipated frustration that students might encounter in the face of challenging math problems is equipping them with an arsenal of tools and approaches through which they can tackle such problems.

If, for example, you told me that I was a bird with a short, stubby beak that had to find a way to drink water from a glass that was only half-full with only a pile of stones at hand, I might get frustrated pretty quickly upon realizing that my beak did not reach far enough down to allow me to drink.  I might peck a few times in vain but would remain parched.

With the right set of dynamic problem-solving skills at my disposal, however, I might think of the problem in a different light, and realize that by dropping enough stones into the glass, I could make the water level rise enough that my beak could easily extract all the water I desired.

Applying these kinds of problem-solving skills to questions that are appropriate for Middle School students can fortify grit, the quality of not giving up easily, and help students to solve problems they may face in their own lives.

Taking all of this into consideration, there are a few basic skills and approaches that students can use to help them crack just about any age-appropriate problem that you, the teacher, throw at them.  In the interest of time, we’ll introduce just four here, though plenty of others can certainly be applied where appropriate. The most common methods for solving problems that students may encounter are:

• Guess and Check;
• Draw a picture;
• Work Backward; and
• Use an Equation with a variable.

The first method on our list of math problem-solving activities for middle school is fairly self-explanatory. In a sense, it involves a bit of reverse-engineering, as the student starts with a proposed solution and works his or her way back to the beginning of the problem to see if that solution is effective.

Drawing a picture may be more effective for visual learners, as it enables students to lay eyes on the problem and conceive of a solution in ways that they may not have otherwise.

Working backward is like a more scientific version of guessing and checking.  Students can use the information provided to step backward one piece at a time, like Guy Pearce in Memento, until they reach the solution that is in accordance with all of the details provided in the problem.

Finally, an equation that uses a variable can be effective when information is missing, or when an approach unlike the first three is required.

Again–these approaches are mere suggestions that students can apply to solving problems that they may encounter.  Ultimately, a healthy combination of different tactics can serve a student well in handling any problem thrown their way.  Skills such as these, though tough to develop at first, can go a long way toward helping US students stand up to their peers around the world in global math benchmarks, while also making day-to-day problems that they face easier to solve.

Without further ado, here are ten math problem-solving activities for middle school students that can help them develop a number of crucial skills.  If you find these interesting, you may also like our article on the Best Problem Solving Activities For Middle School. Beyond just math, there are other areas where problem-solving can be extremely useful for that age group.  And now, the problems.

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