**Key Concepts **

Use a rule to extend a number pattern, identify features of the number pattern, and use the number pattern to solve a problem.

## I**ntroduction**

**Patterns**

A pattern is a series of objects or numbers which repeat in a pre-designed manner.

**Number rules:**

**Example1: **A function machine used a rule to change Lucy’s numbers into different numbers. The table shows Lucy’s numbers and the function machine’s changed numbers.

What is the function machine’s number of Lucy’s number 4?

What is the function machine’s number of Lucy’s number 5?

Use the rule to complete the table. Describe the feature of the pattern.

Lucy’s Numbers | Function Machine’s Numbers |

1 | 7 |

2 | 14 |

3 | 21 |

4 | |

5 | |

6 |

From the above table, the number 1 changes to 7, 2 changes to 14, and 3 changes to 21.

The rule: Multiply by 7.

Lucy’s Numbers | Function Machine’s Numbers |

1 | 7 |

2 | 14 |

3 | 21 |

4 | 28 |

5 | 35 |

6 | 45 |

So, 4 changes to 28, 5 changes to 35, and 6 changes to 42

The function machine’s numbers 7, 14, 21, 28, 35, 42, …

One of the features of this pattern is all of the function machine’s numbers are multiples of 7.

**Example2: **There are 3 vertices in 1 triangle and 6 vertices in 2 triangles. How many vertices are there in 3 triangles, 4 triangles?

**Solution: **

Rule: Multiply by 3

Number of Triangles | Number of Vertices |

1 | 3 |

2 | 6 |

3 | 9 |

4 | 12 |

### What have we Learnt:

A pattern is a series of objects or numbers which repeat in a pre-designed manner.

**Concept map:**

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