Proof Through Words - Geometry

In this feature for Primary teachers, we offer a selection of geometrical tasks that lend themselves to 'proof through words'. In the accompanying article, we outline three essential features of proof and illustrate what they might look like in the context of words, as opposed to algebraic symbols. The tasks we have included in this feature will help develop your learners' understanding of what constitutes a proof, so that they are well equipped on the mathematical journeys ahead.

You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these activities.

You may also like to take a look at our Proof Through Words - Number feature which offers similar experiences but in a numerical context.

In this article for Primary teachers, Ems explores three essential features of proof, all of which can be developed in the context of primary mathematics through talk.

Break it Up! 

Age 5 to 11
Challenge Level
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Counting Stick Conjectures 

Age 5 to 11
Challenge Level
How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?

School Fair Necklaces 

Age 5 to 11
Challenge Level
How many possible symmetrical necklaces can you find? How do you know you've found them all?

Diagonally Square 

Age 7 to 11
Challenge Level
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

Brush Loads 

Age 7 to 11
Challenge Level
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Triangle in a Square 

Age 7 to 11
Challenge Level
Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?