**toni**

## Five in a Line Game

*By toni On 10 December, 2019 · Leave a Comment*

This is a game for two players. It requires a lot of thinking and strategic play.

Each player has 5 counters, bottle tops, buttons or stones that look different from the counters used by the other player.

To win the player must be the first to get his or her 5 counters […]

## Some Mathematical Games

*By toni On 3 December, 2019 · Leave a Comment*

GAMES FOR THE WHOLE CLASS

Grades 6 and 7 HALF A MILLION GAME

Grades 7 to 10 THE FUNCTION GAME

GAMES FOR 2 PLAYERS

Grades 4 to 8 SCISSORS, PAPER, ROCK

Grades 5 to 9 CHANCY OPERATIONS

[…]

## Years 9 – 12 Differences of Squares Investigation

*By toni On 15 November, 2019 · Leave a Comment*

1. What do you see in this picture?

Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .

2. What do you notice about the difference between squares of consecutive numbers?

Compare the differences between squares of numbers that differ by 1 […]

## Years 10 – 12 Construct Geometrical Patterns

*By toni On 21 October, 2019 · Leave a Comment*

1. ENVELOPE PATTERNS WITH STRAIGHT LINES

These straight lines form a family and the curves that you see, called envelopes, are tangent to each line in the family.

Draw two base lines and mark the same number of points at equal distances along each line. Join the outermost point on one base […]

## Years 2 – 10 30-minute Fractals Lesson and Follow Up

*By toni On 16 September, 2019 · Leave a Comment*

Start by watching the video https://youtu.be/B2dkNPaTmDY

Each student should have a stage 3 Sierpinski triangle of edge length about 6.5 cm and a colouring pen, and should colour their triangle as shown by the black filling in the small diagram.

The class will make poster of a stage […]

## Years 7 – 12 Squareflake Fractal

*By toni On 14 September, 2019 · Leave a Comment*

1. If the red square has area 1 square unit. What is the area enclosed by the stage 1 squareflake?

2. What is the area enclosed by the stage 2 squareflake? What about the stages 3 and 4 squareflakes?

3. If replacing each line segment on the edge with the zig-zag is […]

## Years 4 – 10 Make a von Koch Poster

*By toni On 12 September, 2019 · Leave a Comment*

The curve, also known as the ‘snowflake curve’, was invented in 1904 by the Swedish mathematician Helge von Koch.

Take a large piece of backing paper, and either draw an equilateral triangle with edges of length 27 cm or cut a triangle from coloured paper and stick it on […]

## Years 6 – 12 Sierpinski Number and Shape Patterns

*By toni On 11 September, 2019 · 2 Comments*

In March 2014 and February 2015 Bubblz the Mathematical Clown and the Pyraloons built Guinness World Record breaking Balloon Model Sierpinski Pyramids to raise funds for AIMSSEC. The photo shows the triumphant team in a shopping mall in Cambridge, UK and their 6.5 metre high pyramid.

The smallest pyramid is made from […]

## Years 10 to 12 The von Koch Curve

*By toni On 10 September, 2019 · Leave a Comment*

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 […]

## Years 9 to 12 Pascal’s Triangle and Fractal Patterns

*By toni On 8 September, 2019 · Leave a Comment*

Can you see what the rule is for filling numbers in the hexagons? Continue the pattern using the same rule. If you get it right the bottom row will start 1, 9, 36, 84, …

Shade the hexagons where the number inside is odd all in one colour. Using a contrasting colour, […]

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