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Lots of Lollies


Lots of Lollies


Frances and Rishi were given a bag of lollies.




They shared them out evenly and had one left over.


How many lollies could there have been in the bag?



Sarah, Danielle and Sally said:




Poppy began like this:


$1$ lolly each - $7$ lollies
$2$ lollies each - $12$ lollies
$3$ lollies each - $17$ lollies
$4$ lollies each - $22$ lollies
$5$ lollies each - $27$ lollies
$6$ lollies each - $32$ lollies
$7$ lollies each - $37$ lollies
$8$ lollies each - $42$ lollies
$9$ lollies each - $47$ lollies
$10$ lollies each - $52$ lollies


Here is the start of Phoebe and Alice's work:




Why do this problem?


Possible approach

You could introduce this challenge by acting it out.  Invite two children to the front of the class and ask everyone to imagine that you have a bag of lollies.  Explain that you give them out to the two volunteers so that they have the same number each, but there is one left in the bag.  You could mime giving out some lollies so that everyone gets the idea.  Then invite three more children to the front.  Mime gathering the lollies back into the bag and then distributing them equally again, this time explaining that you have two left over.  Pose the question "I wonder how many lollies could have been in the bag?". 





Key questions

How many children are there altogether when they share the lollies the second time?
What is the smallest number of lollies there could be?
Is this the only number of lollies there could be?
Tell me about this approach.  What do you think she/they were doing?
How do you think this will help to solve the problem?
What do you think she/they would have done next?

Possible extension

At the highest level, encourage learners to articulate a full generalisation about what kind of numbers of lollies there could be in the bag. This might be worded in terms of multiples, or in terms of the units digit of possible solutions. Growing Garlic is a similar problem which pupils could have a go at as a follow-up to this one.

Possible support

Learners might request a range of different resources to help them tackle this challenge, for example a hundred square, or some counters/cubes.  Try not to pre-empt their requests by placing equipment out on tables at the start, but do make sure these kind of resources are easily accessible to the children, should they want to use them and do your best to accommodate any requests which you hadn't anticipated!