Why do this problem?
This problem is short and suitable for an introductory
activity on representing and recording journeys, which is often
problematic. It brings together the idea of direction through
compass points, and the more difficult idea of constant speed.
Possible approach
You might choose to begin with a whole class activity
revisiting the points of the compass - perhaps having all the
children facing one direction which you denote as north, and
then turning to the west, south, north-west etc.
If your children have not done much recording of journeys
before, you might then ask one child to come to the front and
be given instructions to move. For example: take five steps
north, turn to face east, take five steps, turn to face south,
take five steps. Ask the class how s/he could get back to the
start. (Where was the start - did we mark it?) Model the
journey on the board, perhaps using a square grid to help the
children to see that the directions form three sides of a
square.
Then give out the problem and suggest that the children act it
out in pairs before recording it on grid paper.
Gather the class together and ask for solutions and methods of
working. Question them about how they know what the dimensions
and directions are for the return journey - listen for
explanations that include parallel, parallelogram, same angles
etc.
(Most children will not question the numbers $20$ and $50$ -
they will assume that this is the distance. If it is
appropriate you may want to question this and begin to make
links between the time taken and the speed travelled. It's
difficult to show time on a picture but if the bird travels at
the same speed for the whole journey then the time and distance
travelled are directly proportional to each other. Progamming
Beebot or Roamer may also bring up such questions.)
Key questions
What sort of drawing might help?
Shall we show where north is?
How do you know these lengths (on a parallelogram) are the
same?
Possible extension
You may wish to offer children the opportunity to make up their
own questions in the same vein, and post them somewhere central
for others to try. You could also try some 'What if ...?'
questions and encourage the children to make up their own of
these too, for example, what if the speed changed and the bird
flew back twice as fast?
Possible support
Some children will find the speed/distance complexity
difficult. Reword the question as: A bird flew north for $20$ km,
north-west for $50$ km, then south for $20$ km. How far, and in
what direction would the bird have to fly to return to its
starting point?