How to Solve a Math Pattern

Make sure to have plenty of erasers!

Some math problems can be easy to solve, but others can be more difficult. One type of math problem that many people feel are fun to solve are math patterns. Math patterns take a bit of logic, some observation skills, and some basic math knowledge to figure out. A few of the easier math patterns can probably be solved in your head. If you encouter a more difficult pattern, you may need paper and pencil to figure it out. Read on to see how to solve a math pattern.

Difficulty:

Moderate

Instructions

Things You'll Need

• paper
• pencil
• calculator (optional)

How to Solve a Math Pattern

1. Look at the entire math pattern from the beginning to the end.

2. Ask yourself basic questions. Are the numbers increasing or decreasing? If they are increasing, does it look like the numbers are increasing by adding a number or multiplying a number? If they are decreasing, does it look like the numbers are going down by subtracting or dividing?

3. Study the first three to four numbers in the pattern. Ask yourself what is the relationship between these numbers. For example in this math pattern, the first three to four numbers are 1,3,6,10. The numbers are increasing, and it seems like you need to add to get the next number. First you add 2, then you add 3, then you add 4. So, if you write this down on paper, you probably see a pattern developing.

4. Try the rest of the pattern that is given to you to see if your solution works. Using the example in Step 3, the pattern given to you would be: 1,3,6,10,15,21,28. You can test your pattern solution to see if you are correct. So, if you think you should add 5 next, then ask yourself if it fits the pattern. In this example, your theory is correct.

5. Write the pattern in words, and do some more examples. So, with the above example, it could be written like: each time you add a number, you increase the number you add by one, starting with the number 2. So, first you add 2, then you add 3, then add 4, and so on. To do more of this pattern, it would look like this: 1,3,6,10,15,21,28,36,45,55.

Tips & Warnings

• If you are having difficulty solving a math pattern, writing anything you notice can be helpful. So, for example if you notice the relationship between the first 2 numbers is adding 6, then write it down, even if it doesn't fit the rest of the pattern. Sometimes, when you write down clues, it will help you see the pattern.

• Another tip for solving patterns is to walk away from the pattern for a while and then come back and look at it with fresh eyes.

Resources

• Margo Dill's website