Fractional Triangles
Fractional Triangles
Use the lines on this figure to show how the pattern of triangles can be used to divide the square into two halves, three thirds, six sixths and nine ninths.
More lines are needed to divide it into four quarters.
What is the least amount of line needed to do this if the quarters are in one piece and all the same shape?
How many ways can you divide it into halves using just the lines given?
Why do this problem?
This problem could be used as part of a lesson on finding fractions of various shapes. It should help develop an understanding of the relationship between the part and the whole. It allows children to explore fractions in a non-threatening, open-ended way and yet it does contain some real challenge.
Possible approach
This sheet (which contains six copies of the image) could be used both to work on and record answers to the problem. Coloured pencils would be useful to emphasise the different shapes within the design.
Key questions
Possible extension
Children could explore the design further and find the fraction of other shapes within the design such as the diagonally placed squares formed by four small triangles.
Possible support
Those experiencing difficulty with this problem may find it easier to start by looking at a $3 \times3$ grid. Even if the rest of the class are not using it, this sheet could be useful. Some learners may find it helpful to cut out the different fractions of the square to check that they are identical. (If
this is the case, several copies of the image will be needed!)You may also like
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