# Patterns and Sequences - Stage 3

This is part of ourĀ Secondary Curriculum collection of favourite rich tasks arranged by topic.

### Frogs

##### Stage: 3 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### Growing Surprises

##### Stage: 3 Challenge Level:

Can you find the connections between linear and quadratic patterns?

### 1 Step 2 Step

##### Stage: 3 Challenge Level:

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

### Odds, Evens and More Evens

##### Stage: 3 Challenge Level:

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

### Picturing Triangle Numbers

##### Stage: 3 Challenge Level:

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

### Elevenses

##### Stage: 3 Challenge Level:

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

### Picturing Square Numbers

##### Stage: 3 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

### Days and Dates

##### Stage: 3 Challenge Level:

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Shifting Times Tables

##### Stage: 3 Challenge Level:

Can you find a way to identify times tables after they have been shifted up?

### Beach Huts

##### Stage: 3 Challenge Level:

Can you figure out how sequences of beach huts are generated?

### Summing Consecutive Numbers

##### Stage: 3 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### Squares in Rectangles

##### Stage: 3 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

### Triangle Numbers

##### Stage: 3 Challenge Level:

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

### Tower of Hanoi

##### Stage: 3 Challenge Level:

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

### Seven Squares - Group-worthy Task

##### Stage: 3 Challenge Level:

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

### Coordinate Patterns

##### Stage: 3 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

##### Stage: 3 and 4

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

### Spaces for Exploration

##### Stage: 3

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

### Charlie's Delightful Machine

##### Stage: 3 and 4 Challenge Level:

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### Seven Squares

##### Stage: 3 Challenge Level:

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

### What Numbers Can We Make Now?

##### Stage: 3 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

### Patterns and Sequences Stage 3 - Short Problems

##### Stage: 3

A collection of short Stage 3 problems on patterns and sequences.