Draw a pentagon and draw in all the diagonals (lines joining the vertices not including the edges of the pentagon), how many diagonals is this?
This is called a pentagram. How many diagonals are there in a hexagram, heptagram, octagram, nonagram, decagram etc. up to a 20 sided shape.
Does any pattern occur when looking at the number of diagonals?
Why is this so?
Can you find a formula?
The council wants to create 85 flowerbeds and surround them with hexagonal paving slabs according to the pattern shown. In this example, 18 paving slabs surround four flowerbeds.
How many paving slabs will the council need for 85 flowerbeds?
Try to find a rule or two-stage function machine that the council can use to decide the number of paving slabs needed for any number of flowerbeds.
Pupils learn to translate between words, symbols, tables, and area representations of algebraic expressions, recognise the order of operations, recognise equivalent expressions and understand the distributive laws of multiplication and division over addition (expansion of brackets).
Pupils learn to create and solve their own equations, where the unknown appears once. Building equations is easier than solving them because it postpones the second difficulty and so is an easier place to start.
Pupils learn to distinguish between and interpret equations, inequations and identities and substitute into algebraic statements in order to test their validity in special cases.
Pupils interpret linear and non-linear distance-time graphs using the computer programme Traffic. This program provides a simple yet powerful way of helping learners to visualise distance–time graphs from first principles. The program generates situations involving traffic moving up and down a straight section of road. It then allows the user to take ‘photographs’ of this situation at one-second intervals, places these side-by-side, and then gradually transforms this sequence of pictures into a distance–time graph. In this way, direct correspondences between speeds and gradients are obtained.
Pupils learn to interpret and construct distance–time graphs; relating speeds to gradients of the graphs and accelerations to changes in these speeds.
Pupils learn to understand the relationship between graphical, algebraic and tabular representations of functions, the nature of proportional, linear, quadratic and inverse functions and doubling and squaring.
Pupils will learn to: use past examination papers creatively, explore, identify, and use pattern and symmetry in algebraic contexts, investigate whether a particular case can be generalised further, understand the importance of counter-examples, develop the ability to generalise from geometric patterns and devise and explore their own questions in this context.