Repetitiously

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

Sept 03

What is the last digit of the number 1 / 5^903 ?

Fractions Jigsaw

Stage: 3 Challenge Level:

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?

Can a set of pieces solve in more than one way ?
How does our answer to these questions change for different size jigsaws.

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.

Equivalent fractions, decimals and percentages. Calculating with fractions. Fractions. Visualising. Generalising. Practical Activity. smartphone. Area. Creating expressions/formulae. Working systematically.

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