Biscuit decorations
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Problem
Biscuit Decorations printable sheet
Andrew decorated $20$ biscuits to take to a party.
He lined them up and put icing on every second biscuit.
Then he put a cherry on every third biscuit.
Then he put a chocolate button on every fourth biscuit.
So there was nothing on the first biscuit.
How many other biscuits had no decoration? Did any biscuits get all three decorations?
Printable NRICH Roadshow resource.
Getting Started
Perhaps you could sketch the biscuits?
The second biscuit has icing on it. Which other biscuits have icing on?
Which biscuits have a cherry on them as well as the third one?
What about the biscuits with a chocolate button on them? Which ones are they?
Student Solutions
We had a good number of solutions sent in for this challenge. There were also some good descriptions as to how you did it and some recording ideas for everyone to see.
First from Ellie at Stanley Park Junior School:
There are 20 biscuits.
0= Biscuits
O= Cherry
\= Chocolate Buttons
D= Icing
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
D D D D D D D D D D
O O O O O O
\ \ \ \ \
Seven have nothing on.
Next, from Brampton Primary School, we had two emails sent in.
First from Toby:
Secondly from Brampton we have Georgia and Joe:
Two Alfies at Christ the King Catholic Primary School wrote:
There is one biscuit with all three decorations on...it is biscuit 12
This is because it is in the 2, 3 and 4 times table.
Miss Martin bought us biscuits, cherries and buttons and we put 20 biscuits in a line.
We followed the instructions on the problem. We noticed it was a number pattern.
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3, 6, 9, 12, 15, 18
4, 8, 12, 16, 20
There are some biscuits with nothing on. 1, 5, 7, 11, 13, 17, 19
Next JJ, JU, IA and DM at Ardley Hill Academy, Dunstable, sent in the following creative account of what happened:
Cookie problem
JU said “We stuck 20 pieces of paper in our books and numbered them.”
IA said “Then we drew a circle on every 2nd one for the icing.”
JJ said “Then we drew a red dot on every 3rd one for the cherries.”
“What about the brown dot on every 4th one for the chocolate button,” said DM.
IA said, “We found that only odd numbers have no icing on.”
“Even numbers all have some decoration on,” said JJ.
“There was nothing on 1, 5, 7, 11, 13, 17 and 19,” they read out.
“They are all odd numbers,” said JU”.
“But some are missing,” added DM.
“Number 12 got all decorations.” They all agreed.
Then Mrs Clarke helped us to draw a Venn Diagram.
After this, we tried it with real biscuits using “randoms” instead of cherries!!!
Lastly, we had the following from Aymen at Arnhem Wharf School:
I drew pictures of the biscuits. I used a key to then show all the decorations. I then counted all the biscuits that did not have decorations.
Well done all of you and thanks for sending in your recordings and explanations. We look forward to seeing other solutions you send in in the future.
Teachers' Resources
Biscuit Decorations
Biscuit Decorations printable sheet
Andrew decorated $20$ biscuits to take to a party.
He lined them up and put icing on every second biscuit.
Then he put a cherry on every third biscuit.
Then he put a chocolate button on every fourth biscuit.
So there was nothing on the first biscuit.
How many other biscuits had no decoration? Did any biscuits get all three decorations?
Why do this problem?
Possible approach
Key questions
Possible extension
Possible support