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Display the first image of beach huts.
To work on these questions, students could generate sequences of beach huts of their own and look for rules linking the numbers between huts. You may wish to introduce an algebraic representation where the middle two numbers in the hut are $a$ and $b$, and invite students to work out other terms in the sequences algebraically.
At the end of the session, bring the students together and set them a challenge: "Here is a beach hut. Without drawing all the huts in between, quickly draw for me the 5th and 8th hut to the right." If you have mini whiteboards the students could draw their huts and then hold them up to see if everyone agrees. Finally, invite students to compare how they worked out the numbers.
Challenge them to go both to the right and to the left.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?