**"Number patterns"**

## 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 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 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, […]

## Years 4 to 12 Table of Tables

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

What patterns do you notice in this table?

Continue the patterns to fill the empty squares.

Write a list describing all the patterns that you see.

What do you notice about the numbers on squares of the same colour?

Would the patterns […]

Can you find the chosen number from this square using the clues below?

1. The number is odd.

2. It is a multiple of three.

3. It is smaller than 7 x 4.

4. It has an even tens digit.

5. It is the greater of the two possibilities.

[…]

## LOWER SECONDARY A2 SEQUENCES AND PATTERNS

*By toni On 11 January, 2018 · Leave a Comment*

How to use beans, stones and other objects to form pattern sequences and to develop an understanding of algebraic formulas.

Click here to download a PDF with all you need to run your own professional development workshop.

## Years 4 – 7 Magic of 37

*By toni On 21 November, 2017 · Leave a Comment*

First complete the number sentences by putting = + – x or ÷ in the boxes. Then explain why the pattern occurs.

Explore the pattern you get when you carry on these multiplications up to 37 × 54.

Click here for the Notes for Teachers.

Inspired by Jain www.jainmathemagics.com

## Years 5 – 9 Magic Numbers

*By toni On 5 November, 2017 · Leave a Comment*

What patterns do you see in them?

Suppose you have to share 9872 gold coins between 8 people.

You give the coins out in thousands until there are less than 8000 left.

Then you give out one hundred at a time until there are less than 800, then […]

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