How Many Triangles? 3

A Mathematics Lesson Starter Of The Day

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Topics: Starter | Combinations | Problem Solving | Shape

  • B Unit, Texas
  • There are 39, not 37
  • Ryan Ames, Edmonton
  • I count 51
    Not double counting anything
    and remembering that a triangle is just that three angles in which all angles together equal 180 and there is a bunch in there that are not right angles... Would love to know the correct answer though.
  • Ricardo Estopier-Ayala, Strake Jesuit College Prep, Houston, Texas
  • The correct answer is 37 triangles:
    There are:
    12 single triangles
    12 triangles composed of 2 single triangles
    6 triangles composed of 3 single triangles
    6 triangles composed of 4 single triangles and
    1 triangle composed of 6 single triangles.

    - The triangles composed of 3 single triangles were the hardest to find, but u can use the giant(composed of 6 single triangles) triangle to find them; they are all contained in it.
    - The triangle composed of 4 single triangles are the same triangles as the ones composed of 3 single triangles, except for the fact that they have just added one triangle to the end.
    - I am unsure how to respond to the person who found 51 triangles other than to say that he/she might have confused the definition of a triangle: A plane geometric figure with three angles and three sides.
  • Australia Class, Preston, Lancashire, England
  • Our class found different ways and strategies to solve this puzzle. We found 37 triangles and we enjoyed it! Thank you.
  • Mr Kavanagh's Fifth Class, Cork, Ireland
  • Most of the class got lower numbers than 37. The teacher found 27 and when we looked at the answer we realised that there were 37. Abbie got the closest with 30.
  • Transum,
  • As you can see by clicking on the button underneath the title at the top of this page we have provided a dynamic answer to this question. The challenge is for pupils to show their solution in a clear, organised way of their own. It could be a static series if diagrams or they too may decide to show their solutiion in a dynamic way using the animation tools of PowerPoint, Prezi or similar. Feel free to send Transum any examples of your pupils' work, we may post them on this page.

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Show Answer

Click the button above to see all of the triangles in the diagram.

There are:

A total of 37 triangles

There is a printable worksheet to go with this activity.


Other shape counting starters:

How Many Squares 1? | How Many Squares 2?
How Many Triangles 1? | How Many Triangles 2? | How Many Triangles 3?
How Many Rectangles? | Rectangles Investigation | Icosahedron | Mystic Rose

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Laptops In Lessons

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Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

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Student Activity


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