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Make a star for Christmas

Sunday, 2 December 2012

Christmas gives some good opportunities for creative shape and measures activities. However, it is easy to forget the maths in all the cutting, sticking, shiny foil and glitter. Use this time to reinforce the language of shape and encourage them to measure accurately with a ruler.

This simple and rather pleasing paper folding method to create a 5-pointed star involves some measuring and certainly some good shape and angle language (right-angled triangle, bisect, acute, obtuse, regular pentagon, decagon, isosceles…).

With a slightly different cut you can also make a regular pentagon or a regular decagon.
Follow-up questions that could take the activity on further include:

What is the perimeter of the star?

Do you think it will be more or less than the pentagon? What about the decagon?

Can you think of a way to work out the area of the star?

What is the area of the rectangle piece of paper remaining?

paper star

Here are the step by step instructions to make a star.
1. Use a 25x20cm piece of paper, although it also works with A4 paper. Fold it in half with the crease on the left.
star  1
2. Find the middle of the base by folding and making a small crease.
star  2
 3. Fold the left hand top corner down to M and make a sharp crease.
star  3
star  4
4. Fold the bottom left hand right angled triangle back behind the rest of the paper so it is hidden.

5. Bring down the top edge so that the acute angle is bisected.
star  5
6. Flip the shape over. Choose one of these cuts: AS, AD or AP.
        AS to make a 5-pointed star.
        AD to make a regular decagon
        AP to make a regular pentagon

star  8
star  7
star  6
Cut 1 (AS), with angle ASO as an obtuse angle, gives a 5-pointed star.
Cut 2 (AD), with triangle ODA as an isosceles triangle, gives a regular decagon
Cut 3 (AP), with AP at right-angles to OA,  gives a regular pentagon 

Apparently this method of folding was suggested by a seamstress, Betty Ross, to George Washington when he wanted to make the stars for the flag of the USA.

If this is true it makes the method even more pleasing!

Related articles:
12 days of Christmas – a maths investigation
How many presents were sent altogether by the end of the 12th Day of Christmas?

A song to start 12 Days of Christmas investigation 
Hoopla Kidz has some good YouTube songs and it's 12 Days of Christmas is a nice start to this investigation

How many ways can a star be drawn?
Separate activities for KS1 and KS2 to explore this question.

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