### Plants

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

### Junior Frogs

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

### More Children and Plants

This challenge extends the Plants investigation so now four or more children are involved.

# More Plant Spaces

## More Plant Spaces

This activity has been particularly created as a possible follow-on to  More Children and Plants.

Here we look at similar problems of distributing a certain number of items across a larger number of sets, each needing a particular number of items.

So, set yourself a challenge like;

#### "Distribute 15 objects among four sets having 3 in one, 4 in another, 5 in another and 6 in the last."

Then take this further by having five sets with the extra set having just 1 object.

You'll be able to think of your own examples too.

Perhaps most important is to formulate some generalisations that can be tested.

One of the interesting and creative parts of this challenge may be to design the arrangement of sets. Here are some examples to start you off. Two for each of 4 and 5 sets.

If you want a start to see one solution click "show"

If you want to see a solution for 5 sets 3, 4, 5, 6, 7 using 12, click "show"

### Why do this problem?

This activity provides a good extension to the More Children and Plants activity when you have a pupil who you think could go so much further. It offers opportunities for both graphical and spreadsheet work. As with the more accessible version of this activity, it provides an opportunity for pupils to make use of their curiosity and perseverance in looking at the mathematics which they come across.

### Possible approach

Introduce the More Children and Plants activity and discuss with the pupils how what was learnt could be used to answer this extended challenge.

### Key questions

What ways are you finding for drawing the appropriate diagrams?
How are you deciding when the little items go?
Tell me about the areas you have obtained.
What have you set up on your spreadsheet/table?

### Possible Support

Some pupils will need to try this practically and large so using P.E. hoops overlapping each other and some easily moved objects like bean bags.