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Points of Departure
Points of Departure is a great publication from ATM. Packed full of little ideas that can grow into great investigations.
A collection of 70 starting points for investigative work covering many aspects of the National Curriculum. It is compiled from the popular Points of Departure 1-4 series and brings together starting points specifically aimed at the Key Stage 2 (8-11 year olds) programme of study for mathematics.
We reproduce some examples here.
Breaking Sticks
A stick is broken into three pieces. When can the pieces make a triangle. What is the probability that this will happen?
If the stick is broken into four pieces, what is the probability that they could make a quadrilateral?
Cuboids
We know that it is easy to find cuboids which have the same volume but different surface area.
Investigate cuboids which have the same surface area and different volumes.
Folding Stamps
Six postage stamps are in a block. How many different ways can you find of folding them into one pile?
Geodesics
Investigate how to find the shortest distance between two points on the surface of a solid. The diagram shows three examples.
Hiccup Numbers
Choose a three-digit number, say 327, and repeat it, 327327.
Divide the number by 11; by 13; by 7 - what happens?
Investigate other ‘hiccup’ numbers and other situations like this/
How Great?
Use the digits 1, 2, 3, 4, 5 exactly once each to make two or more numbers, for example: 4 21 53
Multiply these numbers together:
4 x 21 x 53 = 4452
Try other arrangements of the digits 1 to 5. What is the greatest product that can be made?
-->Primes
Fermat discovered that exactly half the prime numbers are the sum of two squares. See example in the diagram. Make a list of the primes that you can form in this way, and a list of those you can’t form like this.
Try to find a rule which tests whether or not a prime can be made like this.
Sixes
What sums can you find with answer six?
Sticky Triangles
Using twelve sticks of equal length, what triangles can you make?
Try with other numbers of sticks. Does the number of triangles depend on the number of sticks?
Worms
Worms leave tracks in layers of mud.
A worm forms a piece of track, turns through 90°, forms another piece, turns, forms another piece, turns...
The drawing shows a 1, 2, 3 worm; it makes one unit of track, turns, makes two units of track, turns, makes three units of track, turns, makes on unit of track …
- Why not use Logo to investigate worms?
