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'Biscuit Decorations' printed from http://nrich.maths.org/

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We had over 80 solutions sent in for this challenge, thank you. Here are just a few showing the variety the pupils offer.

Francesca sent in a spreadsheet as follows;


Francesca
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Jack sent in his result as pictures.


pic2
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Mia sent in a spreadsheet in this way.

 
pic3
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Christabel wrote as follows;



What I did before: I first drew 20 cakes and then I put icing on the second one, cherries on the third one and then choc buttons on the next one and then I missed one and I kept on doing that until I got to the end.

What I'm doing now: I made cakes and then labelled them 1,2,3 ...Then I put icing on the ones that are in the 2 times table. I put cherries on the ones in the 3 times table and choc buttons on the cakes if they're in the 4 times table. Then I would count how many toppings they have.
Q1. 1,5,7,11,13,17,19.
Q2.Number 12 did which had icing on, cherries on and choc buttons. Which means that there was only one.
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Zahrah wrote it out in this way;



1st biscuit= nothing
2nd biscuit= Icing
3rd biscuit= Cherry
4th biscuit= Chocolate Button, Icing
5th biscuit= Nothing
6th biscuit= Cherry, Icing
7th bicuit= Nothing
8th biscuit= Chocolate Button, Icing
9th biscuit= Cherry
10th biscuit= Icing
11th biscuit= Nothing
12th biscuit= Chocolate Button, Icing, Cherry
13th biscuit= Nothing
14th biscuit= Icing
15th biscuit= Cherry
16th biscuit= Chocolate Button, Icing
17th biscuit= Nothing
18th biscuit= Cherry, Icing
19th biscuit= Nothing
20th biscuit= Chocolate Button, Icing

7 Biscuits had no decorations.
1 got all three decorations.

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Adam sent in this chart;



Adam
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Eboselumen described her working as a set of instructions;



you label the biscuits 1-20
you draw the icing on 2, 4 6, 8, 10, 12, 14, 16, 18, 20
the cherry on 4th, 8th, 12th, 16th, 20th
the chocolate button on 3, 6, 9 , 12, 15, 18
so 5 cakes did not get anything
nos 5, 11, 13,  17,  19
it's simple, the logic is that only prime nos can have nothing so all numbers that are a multiple of either 2, 3, 4 will have something on it, the only one with everything on it is 12 which is a multiple of all three nos
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and finally Lorne used a spreadsheet to show her working;



Lorne
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Well done all of you! This may be a help for teachers to see the variety of approaches that we can start to expect from pupils.