Mathematical Investigations

Rectangles Investigation

How many rectangles can you find in this plaid pattern?

Investigations have no boundaries. You can make your study as big as you like but it is sometimes helpful to start small. Use the buttons here to vary the size of the plaid pattern visible.

1 row 1 column 1 row 2 columns 1 row 3 columns 1 row 4 columns 1 row 5 columns 1 row 6 columns
2 rows 1 column 2 rows 2 columns 2 rows 3 columns 2 rows 4 columns 2 rows 5 columns 2 rows 6 columns
3 rows 1 column 3 rows 2 columns 3 rows 3 columns 3 rows 4 columns 3 rows 5 columns 3 rows 6 columns

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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


Investigations Home

Vijaya, Jodh

Friday, April 30, 2010

"There are eleven rectangle."

Mark, Holland

Friday, September 24, 2010

"Every square here contains 9 rectangles."

Class 4T, Kaimes School

Wednesday, January 12, 2011

"We had a go and we got various answers. When we discussed the rules and the boundaries of the shapes we found that allowed more. We also concluded that squares are also rectangles. We are going with 232. But there is probably more."

Wonhang Lee, Korea

Friday, January 27, 2012

""There are forty-one rectangles."brown color 33 &yellow color 8."

Callum , Year 8, Carisbrooke, Isle Of Wight

Friday, May 4, 2012

"We have reached 206 rectangles of various sizes and there are still a few more!"

Spruce Class - Year 5, East Borough Primary , Kent

Tuesday, March 19, 2013

"We found 173 at most, but we are still looking! Does anyone have an accurate answer?"

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.


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