# Math Strategies: Problem Solving by Finding a Pattern

One important math concept that children begin to learn and apply in elementary school is reading and using a table. This is essential knowledge, because we encounter tables of data all the time in our everyday lives! But it’s not just important that kids can read and answer questions based on information in a table, it’s also important that they know how to create their own table and then use it to solve problems, find patterns, graph equations, and so on. And while some may think of these as two different things, I think **problem solving by making a table and finding a pattern** go hand in hand!

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**Finding Patterns in Math Problems: **

So when should kids use **problem solving by finding a pattern**? Well, when the problem gives a set of data, or a pattern that is continuing and can be arranged in a table, it’s good to consider looking for the pattern and determining the “rule” of the pattern.

As I mentioned when I discussed **problem solving by making a list**, **finding a pattern** can be immensely helpful and save a lot of time when working on a word problem. Sometimes, however, a student may not recognize the pattern right away, or may get bogged down with all the details of the question.

Setting up a table and filling in the information given in the question is a great way to **organize things and provide a visual** so that the “rule” of the pattern can be determined. The “rule” can then be used to find the answer to the question. This removes the tedious work of completing a table, which is especially nice if a lot of computation is involved.

But a table is also great for kids who struggle with math, because it gives them a way to get to the solution even if they have a hard time finding the pattern, or aren’t confident that they are using the “rule” correctly.

Because even though using a known pattern can save you time, and eliminate the need to fill out the entire table, it’s not necessary. A student who is unsure could simply continue filling out their table until they reach the solution they’re looking for.

Helping students learn how to set up a table is also helpful because they can use it to organize information (much like making a list) even if there isn’t a pattern to be found, because it can be done in a systematic way, ensuring that nothing is left out.

If your students are just learning how to read and create tables, I would suggest having them **circle their answer in the table** to show that they understood the question and knew where in the table to find the answer.

If you have older students, encourage them to **find a pattern in the table and explain it in words**, and then also with mathematical symbols and/or an equation. This will help them form connections and increase number sense. It will also help them see how to use their “rule” or equation to solve the given question as well as make predictions about the data.

**It’s also important for students to consider whether or not their pattern will continue predictably**. In some instances, the pattern may look one way for the first few entries, then change, so this is important to consider as the problems get more challenging.

There are tons of examples of problems where creating a table and finding a pattern is a useful strategy, but here’s just one example for you:

Ben decides to prepare for a marathon by running ten minutes a day, six days a week. Each week, he increases his time running by two minutes per day. How many minutes will he run in week 8?

Included in the table is the week number (we’re looking at weeks 1-8), as well as the number of minutes per day and the total minutes for the week. The first step is to fill in the first couple of weeks by calculating the total time.

Once you’ve found weeks 1-3, you may **see a pattern** and be able to calculate the total minutes for week 8. For example, in this case, the total number of minutes increases by 12 each week, meaning in week 8 he will run for 144 minutes.

If not, however, simply continue with the table until you get to week 8, and then you will have your answer.

I think it is especially important to make it clear to students that it is **perfectly acceptable to complete the entire table** (or continue a given table) if they don’t see or don’t know how to use the pattern to solve the problem.

I was working with a student once and she was given a table, but was then asked a question about information *not included in that table*. She was able to tell me the pattern she saw, but wasn’t able to correctly use the “rule” to find the answer. I insisted that she simply extend the table until she found what she needed. *Then* I showed her how to use the “rule” of the pattern to get the same answer.

I hope you find this helpful! Looking for and finding patterns is such an essential part of mathematics education! If you’re looking for more ideas for **exploring patterns **with younger kids, **check out this post for making patterns with Skittles candy**.

#### And of course, don’t miss the other posts in this Math Problem Solving Series:

- Problem Solving by Solving an Easier Problem
- Problem Solving by Drawing a Picture
- Problem Solving by Working Backwards
- Problem Solving by Making a List

I had so much trouble spotting patterns when I was in school. Fortunately for her, my daughter rocks at it! This technique will be helpful for her when she’s a bit older! #ThoughtfulSpot