How Many Sides?

An open-ended mathematical investigation

On a 3 x 3 grid you can make polygons with 3, 4, 6,and 7 sides.

Have a go!

How many different polygons can you make on

4 x 4, 5 x 5, 6 x 6 grids?

Online Pin Board

Area shapes

Investigate polygons with an area of 4 square units. This is your starting point, you can decide how to proceed.

Transum.org/go/?to=areashapes

How Many Squares? 2

How many different sets of four dots can be joined to form a square?

Transum.org/go/?to=how

Tridots

Find all the triangles that can be drawn by joining dots on a 3 by 3 grid of dots.

Transum.org/go/?to=tridots

Investigations Home

Transum,

Friday, December 6, 2013

"Here are some grids of dots (3x3) you might want to print out to help with the first part of this investigation. As you develop the investigation further this dotty paper may be of use."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.

For Students:

For All: