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Junior Frogs

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Junior Frogs

This challenge is based on the game Frogs which you may have seen before. 

There are two green frogs and two brown toads:

A frog or toad can jump over one other creature onto an empty lilypad or it can slide onto an empty lilypad which is immediately next to it.  
Only one creature, at a time, is allowed on each lilypad.
Now the idea is for the frogs and toads to change places.  So, the frogs will end up on the side where the toads started and the toads will end up where the frogs began.

The challenge is to do this in as few slides and jumps as possible. 
You could use the interactivity below to help you try out your ideas.
To move a frog or toad, click on it.  If it is not able to jump or slide, it won't move. The toads and frogs in the interactivity only move in the direction they are facing.

This button button 1takes you back to the start.

This buttonbutton 2takes you back one step at a time.

This scorekeeps a record for you - you may also be interested in the grand total of all four parts added together.

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How do you know you have found the smallest possible number of slides and jumps?

Why not try three frogs and three toads?  
What is the smallest number of slides and jumps now?

Why do this problem?

This game allows pupils to think strategically in an engaging context. They will need to work very systematically, and may also want to develop their own recording system.  With very young pupils it helps to re-inforce following rules.

Possible approach

You could introduce this challenge using the interactivity, but it works just as well to have pupils replacing the frogs and toads.  The four chosen children can be sat on chairs with the rest of the group offering ideas. Having a go at the initial challenge as a whole class to begin with will help reinforce the rules and may also bring about the need for some sort of recording.
Having got the idea, learners could work in pairs or small groups.  At this stage, depending on your focus, you may offer them the interactivity, or some pupils will prefer to have a physical representation in front of them in the manner of small counters, blocks etc. to move around. Keep a watch out for pupils who don't have set places or items representing the lilypads, as it is easy to lose the empty place!
Emphasise that you are looking out for those pairs/groups who are able to justify their thinking and convince everyone that there really isn't a way of doing it in fewer moves.  

Key questions

Tell me about what you are thinking.
Why that move?
You seem to have some system going on, can you tell me about it?

Possible extension

Some learners will be keen to try larger numbers of frogs and toads.  Being able to predict the total number of slides and jumps needed for a given number of frogs/toads is not straightforward but there is still value in encouraging pupils to convince you there is no quicker way to complete the challenge.
Some children may be intrigued by the Towers of Hanoi problem, which is similar in the necessity to work systematically.  There are three pegs, and on the first peg is a stack of discs of different sizes, arranged in order of descending size. The object of the game is to move all of the discs to another peg. However, only one disc can be moved at a time, and a disc cannot be placed on top of a smaller disc.  The interactivity in this problem might help.

Possible support

Some pupils may need reminding of the rules but the interactivity may help in this respect.