Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

A Flying Holiday

A Flying Holiday

A bird flew north for $20$ minutes, north-west for $50$ minutes, then south for $20$ minutes.

The bird keeps flying at about the same speed.

For how long, and in what direction, would the bird have to fly to return to its starting point?

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?
For some pupils this activity might also be an opportunity to experiment with LOGO (freely downloadable from http://www.softronix.com/logo.html ).

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?