**toni**

## Years 4 – 7 Tangram Pattern

*By toni On 11 August, 2020 · Leave a Comment*

Arrange the 7 tangram pieces to make the shape in the grey picture.

What do you notice about this shape?

Describe the shapes of the tangram pieces.

What is the same and what is different about the shapes of the tangram pieces?

Make a pattern of your own using all 7 pieces.

[…]

## Years 6 – 9 Magic Egg Tangram Puzzle

*By toni On 10 August, 2020 · Leave a Comment*

We know birds come from eggs.

You can make many birds from the 9 puzzle pieces of the Magic Tangram Egg.

Break the egg and re-assemble the 9 pieces to hatch one of many varieties of birds.

Construction

Draw a circle with radius […]

## Years 5 – 9 Path to the Stars

*By toni On 29 July, 2020 · Leave a Comment*

Is it possible to draw a 5-pointed star without taking your pencil off the paper?

When you turn this star around it looks exactly the same in 5 different positions so we say it has ROTATIONAL SYMMETRY of order 5.

Is it possible to draw a 6-pointed star in the same way […]

## Years 4 – 7 Digit Detective

*By toni On 27 July, 2020 · Leave a Comment*

You are a detective and you have to discover what digits the question marks stand for. They can be any digit from 0 to 9 and they can be the same digit or different digits.

How will you find the missing digits?

What do you notice?

How many solutions are there to the calculations?

What clues […]

## Years 4 – 12 Symmetry Challenge

*By toni On 27 July, 2020 · Leave a Comment*

How many symmetric patterns can you make by shading whole squares in a 3 by 3 grid?

Where are the mirror lines (lines of symmetry)?

Which of your patterns also have rotational symmetry?

Here is just one pattern. Can you find more than 60 different patterns? Patterns that are […]

## Years 5 – 7 Cups and Capacity

*By toni On 21 July, 2020 · Leave a Comment*

(1) You will need a collection of cups, either disposable cups like the ones shown or any mugs and cups you have available. You will also need some water and a measuring jug.

Which cup would you fill with water if you are really thirsty and want a lot to drink?

Arrange […]

## Years 10-12 Tops

*By toni On 19 July, 2020 · Leave a Comment*

For your company, you have to design spinning tops made from two pieces glued together, a hemisphere and a cone, and you have to plan how they will be manufactured, packaged and sold.

(1) The radius of the circular surface where the pieces are glued together is 3 cm. The slant […]

## Years 3 – 12 Frogs Puzzle

*By toni On 18 July, 2020 · Leave a Comment*

Five red-eye frogs and five orange frogs line up in a row with a space between them.

They have to change places but they can only hop, one frog over another frog or slide to an empty space next to them.

Red-eye frogs can […]

## Years 5 – 9 Magic Numbers

*By toni On 16 July, 2020 · 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 […]

## Year 12 Pythagoras Similarly

*By toni On 12 July, 2020 · Leave a Comment*

There are hundreds of proofs of Pythagoras Theorem.

This diagram shows a proof.

Look carefully. Can you see three squares?

Assuming that they are squares, can you prove that four of the triangles are congruent?

Can you now write down a proof of Pythagoras’ Theorem and explain the proof?

The second diagram […]

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