Magic Plant
2 out of 3
On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?
Problem
On Friday at 9am, the magic plant was only 2 centimetres tall.
Every twenty four hours, it doubled its height.
How tall was it on Monday at 9am?
Getting Started
How tall will the plant be on Saturday at 9am?
How tall will the plant be on Sunday at 9am?
Student Solutions
Lots of you sent in your solutions to this problem - unfortunately far too many to mention everyone. Most of you worked out the plant's height each day, which is a very good way of approaching the problem. Here is an example of this method from Tom who goes to Linden Primary School:
So first you start with 2 centimetres.
On Saturday it's double 2. And double 2 is 4.
On Sunday is's double 4. And double 4 is 8.
On Monday it's double 8. And double 8 is 16.
So the answer is ...16 centimetres.
This is very clearly recorded - well done Tom. Hannah, Grace and Ellie, who were attending Royal Institution masterclasses, sent a very similar solution. So did Oliver from Webbers School, Livvy (who didn't say which school she is from) and someone from St Joseph's School in Harrogate. Ha Young from Wesley College wrote down the same calculations in a slightly different way, showing that doubling means multiplying by two:
On Friday at 9am, it was 2cm
On Saturday at 9am, it was 2x2=4cm
On Sunday at 9am, it was 2x2x2=8cm
On Monday at 9am, it was 2x2x2x2=16cm
So, the answer is 16cm.
Some pupils from Queens Crescent School also wrote down something a little different. Rather than recording multiplication, they representated the calculations as addition, like this:
2+2=4
4+4=8
8+8=16
Answer=16
In other words, doubling a number, or multiplying it by two, is the same as adding it to itself. Very well done all of you.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem offers learners a context in which to practise doubling. It also gives children the opportunity to choose their own representation and recording methods.
Possible approach
You could start by asking children a different question, for example, imagining a magic plant that grows one centimetre every day. Explain that you are particularly looking out for what they choose to write down or do and offer them use of anything in the classroom that they feel would be helpful. Once they have had a go at this introductory task, share some of the different representations they have made, making it clear that all of them have value and that each of us finds different things useful.
Then introduce the problem itself and again, leave children to work on it, perhaps in pairs. When you share their work this time, it will be interesting to see which children adopt a different form of representation than the one they used for the initial challenge. It might be worth finding out why some of them changed.
Key questions
How tall will the plant be on Saturday at 9am?
How tall will the plant be on Sunday at 9am?
Possible extension
Some children might like to predict the plant's height at later stages during the week as well before working it out. They may well be surprised at how quickly it grows!
Possible support
Some learners will find number line, number square or multiplication grid useful.