Count the Crayons
Problem
Estimate how many pencils you can see in each one.
What was your method?
How else could you do it?
Is there one way that is particularly useful? Why?
Getting Started
Here is an example which leads me to believe that there are approximately 50 items in this picture. To be on the safe side, I will give a range as my answer and say that I think there are between 40 and 60 items.
PICTURE
Can you use a similar approach? Can you use a different approach?
Student Solutions
These solutions refer to a previous version of this activity which used different pictures.
We had a small number of solutions sent in for this activity. This is a different kind of activity and maybe you found it hard to write about it.
Seb from Caen School Primary School wrote;
I think that the first one has around 30, I think this because if you look at the bottom set of the first picture then there are around 15 pencils. The second picture looks like it's in the 60 or 70's. It is not as easy to estimate as the first picture because it's all mixed up.
Bob from Paddington Green Primary School wrote;
The answer is 30 but my estimate was 28. So close. My method was estimate the top then double the answer.
Thank you for these two ideas for performing an estimate.
Teachers' Resources
Count the Crayons
Take a look at these pictures:
Estimate how many pencils you can see in each one.
What was your method?
How else could you do it?
Is there one way that is particularly useful? Why?
Why do this activity?
This activity is designed to support children as they begin to estimate by grouping in 10s.
It will encourage the idea of different possible answers and children talking about, and justifying, their methods.
Possible approach
Empty a tray of pens or pencils onto the floor and ask the class how they could go about working out how many there are. This is a good opportunity for talk partners and you are likely to just get counting strategies at this stage.
As the class share their ideas, get them to consider how long each approach would take.
You might need to jumble the pens up and maybe add/remove some before challenging the class to now decide how many pens there are, given only a very short amount of time. The pens could be hidden and then revealed briefly. What do the class discover? Counting strategies take too long but are very accurate.
Tell the class that you do not need an exact amount, an approximation will do. Ask children to talk to a partner about how they could do this. Then test the strategies as the pens are briefly revealed again. Collate ideas and draw out the idea that grouping into 10s is useful.
The pens can then be revealed a final time and the class can be challenged to use this grouping into 10s strategy. Collate answers and suggest that this is our range of possible solutions.
Key questions
How did you come to your answer?
Did imagining grouping the items into 10s help you?
Did anyone on your table use a different approach?
How many do you think there are?
Does everyone agree?
What is the range of answers?
Possible extensions
You could show either a tray or an image of a large number of pencils to children and challenge them to do a similar thing. How about grouping in 100s?
Possible support
Tracing paper or a transparent sheet that can be placed over an image may help the children to group items in the picture into 10s.