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# Generating Number Patterns

In this lesson you will learn how to describe, extend, and make generalizations about numeric patterns. Working with number patterns is an very useful skill for solving many types of problem.

Identifying a pattern when you look at individual examples helps you to generalize and find a broader solution to a problem.

Work through the examples and explanations in this lesson with your children and then try the worksheet that you will find at the bottom of this page.

Probably without even knowing it, you have been observing and creating patterns ever since you were a very small child. You probably made repeating patterns with shapes, such the one below with triangles, circles, and squares.

Get your children to explain the pattern they see in the above sequence of shapes.

When you got just a little bit older, you probably learned skip-counting, which is nothing more than applying a pattern to counting.

### Skip Counting

Skip-count by 2’s:  2, 4, 6, 8, 10, 12,  14,  16…

Skip-count by 5’s:  5, 10, 15, 20, 25, 30, 35, 40 …

Skip-count by 10’s: 10,  20,  30,  40,  50,  60,  70…

All of these are patterns, or mathematical rules.

### Generating & Analyzing Number Patterns

A fun part of math is creating and playing with patterns. Math is organized with rules to follow. If you know what the rule is, you can create a pattern. The rule is often organized on a function table as shown in the examples below.

### Function Table Example: x – 3 = y

Work through the next set of number pattern examples with your children. You can check your answers by clicking the empty boxes to show and hide the Y numbers.

### Function Table Example: x + 9 = y

How did you do filling in the missing information on the Y side? Click in the boxes to check your answers . Since the rule is X +9 = Y, you add 9 to each of the X numbers to get the corresponding Y number.

### Function Table Example: x – 7 = y

How did you do filling in the missing information on the Y side? Check your answers by clicking the boxes. Since the rule is X -7 = Y, you should have subtracted 7 from each of the X numbers to get the corresponding Y number.

### Function Table Example: 5x = y

How did you do filling in the missing information? Since the rule for this function table is “multiply by 5,” the first missing number is 15, since 3 x 5 = 15. For the next missing number, you have to think “what number times 5 would give me 25?” You can also think of it as division: “25 divided by 5 = what number?” since division is the inverse, or opposite of multiplication. The final missing number is 5 x 7, or 35.

### Function Table Example: What is the Rule?

How did you do? Were you able to figure out the pattern? This table shows “multiply a number by 3.” You can use the filled in numbers to figure out the rule by asking, “what is the relationship between the X numbers and their corresponding Y numbers?” Look for patterns. Once you have determined the pattern, it is a simple matter to fill in the missing numbers. Here, 21 (3 x 7) and 33 (3 x 11) were missing. If you were asked to extend the table, you would get the pair: 13, 39.

### Generating & Analyzing Number Patterns With Function Tables: Recap

So when it comes to number patterns, remember these things:

• Look for a relationship between the input “X” side, and the output “Y” side.
• Check the pattern against every row. It has to be true for the whole table, or it’s not the rule.
• Use the rule, and the numbers you know, to complete or extend the pattern.

### Number Patterns and Function Tables Worksheets

Click the link below and get your children to try the Number Patterns and Function Tables worksheet. This worksheet has 3 pages and includes a recap of the above, guided practice, and independent questions.