February 8 More Lesson Activities to Develop Understanding and Skills
REPETITION – writing rational numbers as fractions
DIFFERENCES OF SQUARES AND AREA
DIFFERENCES OF SQUARES INVESTIGATION
INTERSECTIONS Simultaneous Linear Equations
GP ALGEBRAICALLY Geometric series
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Sierpinski Number and Shape Patterns
There are many investigations and projects you could do based on the Sierpinski Tetrahedron.
For a start: how many small tetrahedra, like the blue model shown, were used to make the 6.5 metre high red balloon model shown below.
The smallest tetrahedron (Stage 0), the blue model, is made from 6 balloons, each […]
The von Koch Curve
Image starting with an equilateral triangle and replacing each edge by a zig-zag curve made up of 4 pieces. Each of the 4 pieces is one third of the length of the line segment it replaces so it looks as if equilateral triangles have been attached to the shape. Now imagine repeating […]
NA5 GROWTH AND DECAY – FINANCIAL MATHEMATICS
This workshop guide provides learning activities that explore the ways in which arithmetic and geometric series are used in simple and compound interest calculations related to loans (including pay-day loans) , investments, annuities, hire-purchase, inflation etc. and there is an explanation of how APR is calculated. Ideas are given for practical ways […]
Multiply out these expressions:
What do you notice?
Does this pattern continue?
Can you prove it?
What does this tell you about the sum to n terms of the geometric series with first term 1 and common ratio r?
Why do we get a formula for all values of r except r = 1?
The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .
South Africa COVID-19 News
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