# How Many Triangles?

## A self marking step by step approach to calculating the number of triangles in a design.

##### How Many Triangles?How Many Squares?How Many Rectangles?InformationMore Puzzles

The first few questions are about counting the number of triangles in this design:

 1. Let's start by counting the number of small triangles; the triangles that do not have any lines going through them like this blue one: 2. Next count the number of triangles made from two pieces. The green triangle shown here is one example: 3. Now count the number of triangles made from three pieces like this red one: 4. Count the number of triangles made from four pieces like this yellow one: 5. Count the number of triangles made from six pieces like this purple one: 6. Add up your answers above to calculate the total number of triangles in this design. 7. How many one piece triangles are in this design? 8. How many four piece triangles are in this design? 9. How many triangles are there altogether in this design? 10. How many triangles are there altogether in this design?
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## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London:

"I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable."

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Teachers

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Transum,

Friday, January 23, 2015

"This activity is all about breaking down a big difficult task into smaller, more achievable tasks. Not everyone can come up with an effective strategy for themselves so a structured guide like this exercise is a way of helping them learn. There are many other activities related to the process of counting strategies on the Combinations and Permutations section of this website."

Guillaume, France

Sunday, September 18, 2016

"Hi !
On the page "How many triangles", at question #2:
"Next count the number of triangles made from two pieces like this green one:" Your expected answer is 12 but I can only find 6 of them... Is there an error?
Best regards.

[Transum: Thank you Guillaume for your comment. The other green triangles are equilateral triangles so are not similar in shape to the example given. On reflection the wording of the question possibly suggested that it was shapes similar to the example that you should count and indeed there are only six of them. I have changed the wording of the question to make it more clear that it is all two-piece triangles that should be counted.]"

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## Information

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This self marking quiz takes you through the stages of a systematic approach to solving the 'How Many Triangles?' question.

You might find it helpful to print out this page containing a number of copies of the designs so that you can colour in the triangles you find.

More Puzzles including lesson Starters, visual aids and investigations.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you donâ€™t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.