Algorithms and Number Patterns
Follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns.
Read this first
An algorithm is a set of steps. Follow them the same way every time.
Start at 3. Add 3 each time. That is the rule.
Words you need
- Algorithm
- A set of steps you follow in order.
- Rule
- What you do to get the next number.
- Pattern
- Numbers that follow a rule.
Worked example
e.g. Follow this rule: start at 4, add 5 each time. Write six numbers.
- Write the start number. It is 4.
- Do the rule. 4 + 5 = 9. Write 9.
- Do the rule again. 9 + 5 = 14. Write 14.
- Keep going. 4, 9, 14, 19, 24, 29.
Do the same step every time. That is what makes it an algorithm.
Practice
The pictures fade as you go. By the last few you are on your own.
1Start at 2. Add 4 each time. Write four numbers.with a picture
Answer2, 6, 10, 14.
2Start at 20. Take away 3 each time. Write four numbers.with a picture
Answer20, 17, 14, 11.
3Start at 1. Double each time. Write five numbers.with a hint
Need a hint?
Doubling means times 2.
Answer1, 2, 4, 8, 16.
4What is the rule for 5, 10, 15, 20?with a hint
Need a hint?
What do you add each time?
AnswerStart at 5, add 5.
5What is the rule for 100, 90, 80, 70?on your own
AnswerStart at 100, take away 10.
6Start at 6. Add 6 each time. What is the fifth number?on your own
Answer30.
7In 3, 6, 9, 12, are all the numbers odd or even?on your own
AnswerThey take turns. Odd, even, odd, even.
Think about it
1
Why must an algorithm have an order?
One good answerSo it gives the same answer every time.
2
What pattern do you see in the 5 times table?
One good answerEvery number ends in 5 or 0.
Common mistakes
Changing the rule part way.
The rule stays the same for the whole pattern.
Only checking the first two numbers.
Test the rule on every number in the list.