# Problems with patterns with rational numbers

Lesson

In Looking for Patterns, we discovered that if a sequence of numbers increase or decrease by a regular amount, we can describe this as a number pattern. So far, we've only looked at numbers that increase or decrease by a whole number. Now we are going to build on that knowledge and find patterns with fractions and decimals as well.

Let's start by watching a video.

## Summary

1. Decide whether the numbers are increasing or decreasing.
2. Work out how much they are increasing/ decreasing by each time.
3. Now you can write a rule to describe the pattern and to find the next number in the pattern (e.g. "Add $0.7$0.7 each time," or "Subtract $\frac{1}{3}$13 each time.")
4. Use the rule you found to work out the next number in the pattern.

#### Worked Examples

##### Question 1

Complete the pattern.

1.  $\frac{1}{10}$110​ $\frac{2}{10}$210​ $\frac{3}{10}$310​ $\editable{}$ $\editable{}$ $\editable{}$

##### Question 2

Complete the pattern.

1.  $4.2$4.2 $4.0$4.0 $3.8$3.8 $\editable{}$ $\editable{}$ $\editable{}$

##### Question 3

Complete the pattern.

1.  $\frac{1}{10}$110​ $\frac{2}{10}$210​ $\frac{3}{10}$310​ $\editable{}$ $\editable{}$ $\editable{}$
2. What is the rule for finding the next number in the pattern?

Subtract $\frac{1}{10}$110

A

Add $1$1

B

Add $\frac{1}{10}$110

C

Subtract $1$1

D

Subtract $\frac{1}{10}$110

A

Add $1$1

B

Add $\frac{1}{10}$110

C

Subtract $1$1

D

### Outcomes

#### 5.PA1.01

Create, identify, and extend numeric and geometric patterns, using a variety of tools