Puzzles: Number Patterns in a Table

Contributor: Ashley Nail. Lesson ID: 13079

Do you Sudoku or Sudon't? It is easy when you know the trick! Learn how to discover number patterns and solve math puzzles. You will even create your own puzzles!


Elementary, Numbers & Operations

learning style
personality style
Otter, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!


Do you love puzzles?

Math puzzles, like Sudoku, are some of the trickiest puzzles to solve! In order to complete a math puzzle, you have to figure out the rule first. Then, you can fill in the missing pieces and solve the puzzle.

Today, you are going to learn about a new kind of math puzzle! Once you learn the trick to solving it, you will get a chance to create your own math puzzles!

Do you think your family and friends can solve a math puzzle you make?

Before we solve and make our own math puzzles, we need to learn about number patterns and input/ouput tables!

A pattern is when something is repeated with a rule. For example, this row of shapes (below) has a pattern. The pattern has two rules. The first rule in this pattern is that the color of the shapes are red, then blue. The rule repeats over and over again to make the pattern. The second rule of this pattern is that the shapes are triangle, triangle, circle. This rule also repeats, creating a pattern.

shape pattern

If we follow these rules, we can guess what the next shape in the pattern will look like. The next shape will be a red triangle!

You can have patterns just like this with numbers, too! I bet you already know a lot of these patterns and their rules.

Look at this number pattern that you already know.

2, 4, 6, ____

The next number in this pattern is 8. We know this because we are counting by twos. That is the rule of this pattern. You add 2 each time you repeat the pattern. Can you think of other number patterns you know?

Sometimes number patterns are organized in a table. These tables are also called function tables or input/output tables. They all have rules. The rule helps you figure out the pattern and the relationship between the numbers in the two columns of the table. Once you know the rule of a table, you can solve it! Just like a puzzle!

Look at the first table (below). Just like a puzzle, we need to figure out the missing piece. We need to find which number goes in the red box. In order to solve the puzzle, we need to first notice any patterns to figure out the rule of the table.

table 1

Let's look at the relationship between the numbers in the first row of the table. In order to go from 1 to 5, there are two possible rules. We could add 4 or multiply by 5.

table 2

Let's test our possible rules on the next row in the table. The rule of the table has to be the same for every row.

table 3

Only one of our possible rules worked on this row. Multiply by 5 works as a rule on both rows. Let's check to see if it's true for all rows!

table 4

Now we can solve the puzzle! Since we figured out the rule of the table was multiply by 5, we can find the missing piece!

table 5

The missing piece to the table was 20! We solved the puzzle!

Now, go to the Got It? section to practice more puzzles.

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