Patterns and Sequences - Stage 3

Days and Dates

Stage: 3 Challenge Level: Challenge Level:1

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

Summing Consecutive Numbers

Stage: 3 Challenge Level: Challenge Level:1

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?

1 Step 2 Step

Stage: 3 Challenge Level: Challenge Level:1

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?

Frogs

Stage: 3 Challenge Level: Challenge Level:1

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

Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

Coordinate Patterns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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

Elevenses

Stage: 3 Challenge Level: Challenge Level:1

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

Tower of Hanoi

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Shifting Times Tables

Stage: 3 Challenge Level: Challenge Level:1

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

Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Odds, Evens and More Evens

Stage: 3 Challenge Level: Challenge Level:1

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

Seven Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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

Beach Huts

Stage: 3 Challenge Level: Challenge Level:1

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

Growing Surprises

Stage: 3 Challenge Level: Challenge Level:1

Can you find the connections between linear and quadratic patterns?