Myriora Maths › 11+ maths › Chapter 3: Counting and logic
Matchstick patterns
11+Chapter 3 · Lesson 8✓ Watched
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Practise
Ten new questions every time. Answer them all, then check: you get your score, and the working for anything you missed.
In this lesson
- Count the first few patterns, and see how much each new one adds.
- That's the times part of the rule.
- Then find the extra one to start with, and check your rule on a small pattern.
Your turn
Now make a row of triangles. One triangle uses three matchsticks, two triangles use five, and three triangles use seven. How many matchsticks for fifty triangles?
Show the answer
Each new triangle adds two matchsticks. So it's two times the number of triangles, plus one. Two times fifty, plus one, is a hundred and one!
The common mistake
A common mistake is four matchsticks for every square: four hundred for a hundred squares. But the squares share their sides! Only the first square needs four. Every other square needs just three more.
Try it at home
Build squares in a row with pasta or matchsticks. Does 3 × squares + 1 work?
Read the whole lesson
Hello, and welcome to Myriora Maths! Here are rows of squares made of matchsticks: one square, two squares, three squares. How many matchsticks would you need for a hundred squares?
Count the matchsticks. One square uses four. Two squares use seven. Three squares use ten. Each new square adds three more matchsticks.
So the number of matchsticks is three times the number of squares, plus one. Check with three squares: three times three is nine, plus one is ten. It works!
Why plus one? Start with one matchstick on the left. Then every square needs three more: a top, a bottom and a right side. So it's one, plus three for each square.
So for a hundred squares, it's three times a hundred, plus one. That's three hundred and one matchsticks!
Exam questions go backwards too. A row uses sixty-one matchsticks. How many squares are there? Take away the one: sixty. Then divide by three: twenty squares.
A common mistake is four matchsticks for every square: four hundred for a hundred squares. But the squares share their sides! Only the first square needs four. Every other square needs just three more.
Your turn! Now make a row of triangles. One triangle uses three matchsticks, two triangles use five, and three triangles use seven. How many matchsticks for fifty triangles? You've got twenty seconds, or pause the video if you need more time. Go!
Time's up! Each new triangle adds two matchsticks. So it's two times the number of triangles, plus one. Two times fifty, plus one, is a hundred and one!
Quick review. Count the first few patterns, and see how much each new one adds. That's the times part of the rule. Then find the extra one to start with, and check your rule on a small pattern. See you next time!