Algorithms That Make Numbers
Create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns.
Read this first
An algorithm is a set of steps with decisions. Follow it exactly and a pattern appears.
Start at 6. If it is even, halve it. If it is odd, add 7.
Words you need
- Algorithm
- Steps and decisions followed in order.
- Decision
- A question with a yes or no answer.
- Output
- A number the algorithm produces.
Worked example
e.g. Follow this rule from 6: if even, halve it. If odd, add 7.
- Start at 6. Ask the question. Is 6 even? Yes.
- So halve it. 6 becomes 3.
- Ask again. Is 3 even? No. So add 7.
- 3 becomes 10. The numbers so far are 6, 3, 10.
- Keep going. 10 is even, so 5. Then 5 is odd, so 12.
Ask the question every single time. Never assume the answer.
Practice
The pictures fade as you go. By the last few you are on your own.
1Start at 8. Halve if even, add 7 if odd. Next number?with a picture
Answer4.
2Start at 5. Same rule. Next number?with a picture
Answer12.
3Start at 12. Halve if even, add 1 if odd. Give four numbers.with a hint
Need a hint?
Ask the question each time.
Answer12, 6, 3, 4.
4An algorithm never stops. What is wrong with it?with a hint
Need a hint?
What must every algorithm do?
AnswerIt must end. It needs a stopping rule.
5Start at 20. Halve if even, add 5 if odd. Give four numbers.on your own
Answer20, 10, 5, 10.
6What pattern do you notice in that answer?on your own
AnswerIt repeats between 5 and 10.
7Why must the steps be in a fixed order?on your own
AnswerSo the algorithm gives the same result every time.
Think about it
1
What makes an algorithm different from a rule?
One good answerAn algorithm can include decisions, not just one step.
2
Why must an algorithm stop?
One good answerOtherwise it never gives an answer.
Common mistakes
Skipping the decision step.
Ask the question at every number.
Changing the rule when it gets boring.
The rule stays the same throughout.