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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? Information More Puzzles

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

How Many Triangles?

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:

One piece triangle

Correct Wrong

2. Next count the number of triangles made from two pieces. The green triangle shown here is one example:

Two piece triangle

Correct Wrong

3. Now count the number of triangles made from three pieces like this red one:

Three piece triangle

Correct Wrong

4. Count the number of triangles made from four pieces like this yellow one:

Four piece triangle

Correct Wrong

5. Count the number of triangles made from six pieces like this purple one:

Six piece triangle

Correct Wrong

6. Add up your answers above to calculate the total number of triangles in this design.

Six piece triangle

Correct Wrong

7. How many one piece triangles are in this design?

One piece triangle

Correct Wrong

8. How many four piece triangles are in this design?

Six piece triangle

Correct Wrong

9. How many triangles are there altogether in this design?

Triangle Design

Correct Wrong

10. How many triangles are there altogether in this design?

Square Design

Correct Wrong
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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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Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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

How Many Triangles?

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 don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

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