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## 'Fractions Jigsaw' printed from http://nrich.maths.org/

### Why do this problem:

This
problem provides an opportunity to find equivalent fractions
and carry out some simple additions and subtractions of fractions
in a context that may challenge and motivate students.

For some students this will also invite questions like:

How has this puzzle been created, and how much freedom is
there in this structure?

### Possible approach :

Give the jigsaw to pairs of students to complete, being ready
for discussion that may follow about fractions or puzzles of this
type.

Here
is a blank outline of the jigsaw for students to create their own,
harder/easier versions of the puzzle.

You can create, print out, save and exchange customised jigsaws,
domino activities and a variety of rectangular card sort activities
using "Formulator Tarsia", free software available from the

Hermitech Laboratory website .

### Key questions :

- How did you start with this puzzle?
- At what stage did it get hard?
- How did you get through that block?
- How could it be made harder?

### Possible extension :

Would it have been harder if the numbers did not have to be
"the right way up"? What if the same answer occured more than once?
What if there were calculations on the outside edges, rather than
grey? Can you make a harder (but still possible) puzzle?

Or consider the structure that makes this puzzle possible.
Matching here is specified to be by equivalent fractions but the
means of matching is unimportant. If we use a letter to stand for
each 'match' : a to a, b to b etc., and if we release the
constraint that 'numbers are the right way up', how easy is it to
arrive at the arrangement which is the solution?

### Possible support :

Use the blank template and create a jigsaw using only simple
fractions. Give some of the piece positions at the start. Get the
group creating appropriate jigsaws for each other to try. There may
be good discussions in what makes one puzzle harder than
another.