Online Investigations

Scroll down to browse the listor use the filter on the left to select a topic.

Welcome to hours of mathematical enjoyment!

(Ages 8-11): Areas of Squares (FREE!)

Discuss the meaning of the area of a square as the flat space inside it. Establish the idea that you can find the area of a square by counting the 1cm squares that would fit into it.

Investigate the areas of different squares and, in the process, revise how to find simple squares and square roots.

Consider what might happen to the area if you double the size of a square. Investigate and discover that if you double the width, the area is multiplied by 4. (This idea is explored further in the section How similar shapes work.)

Go to this

(Ages 8-11): Perimeters of Squares (FREE!)

Discuss the meaning of perimeter. Establish how to find the perimeter of a square if you know the width. Set the children the challenge of finding different perimeters and notice the link with the 4x table.

Consider how to find the width if you know the perimeter. Set the challenge of finding widths of different squares, including those where the perimeter is not a multiple of 4. Through investigating this, revise how to quarter a number and express remainders in different ways. (Links are given to earlier investigations to help with this.)

Go to this

(Ages 8-11): Areas of Rectangles (FREE!)

Discuss the meaning of the area of a rectangle as the flat space inside it. Establish the idea that you can find the area of a rectangle by counting the 1cm squares that would fit into it (p1).

Investigate the areas of different rectangles, exploring what happens if you fix either the length or the width and change the other one (p3). Note note the link with multiplication. Establish that to find the length or width when you know the area you have to divide (p6). Practise this.

Explore to find rectangles that have an area of 30 (p10), and then an area of 100 (p13). Note the link with factors and factor rainbows.

Note: This investigation suggests that the children draw rectangles and tables to record their findings.

Go to this

(Ages 8-11): Perimeters of Rectangles (FREE!)

Discuss the meaning of perimeter for a rectangle (p1). Speculate on what will happen to the perimeter if you fix the width and made the length go up in ones (p3). What will happen if you fix the width and increase the length by a different amount (pp7/8). Investigate!

Next, consider what will happen if you increase the width and the length at the same time (p10). Suppose you make the width and length increase at different rates. What then (p14)? Investigate!

Next, discuss what happens if you work backwards. Can you find the length if you know the width and the perimeter (p17)? What happens if the perimeter is an odd number (p18)?

What happens if you fix the perimeter and make the width increase (p21)? etc, etc.

Loads to investigate here! Once the pupils have worked through the investigation given, they may have their own ideas for further exploration.

Go to this

(Ages 10-13): Perimeters and Areas of Polygons (FREE!)

Establish the meaning of polygon(p1) and regular polygon (p2).

Recap on how to find the perimeter of a square and a rectangle. Then consider how you could find the area of a regular hexagon if you know its width (p6). Consider if this would work for other regular polygons (p9).

Recap on how to find the area of a rectangle and a triangle. Then consider a rhombus (p13) and a kite (p17). Investigate areas of these and other quadrilaterals by drawing them on cm squared paper.

Extend these ideas to find the area of a regular hexagon (p20).

Go to this

(Ages 10-13): Interior Angles of Regular Polygons (FREE!)

Investigate the interior angles around the inside edge of a square, equilateral triangle and regular hexagon (p2). What are their totals?

What about the angles at the centre (p7)? Is there a link?

Could you use what you have discovered to find the angles in a regular pentagon (p9)?

Consider the factor rainbow for 360 (p16). What does this have to do with the angles at the centre of different polygons?

Investigate polygons with more sides. What are their angles?

Establish and test formulas for the interior and centre angles (p21).

Go to this

(Ages 10-13): Circle Circumference (FREE!)

A new take on PI.

Explore the relationship between the circumference of a circle and its diameter by investigating the perimeter of the circumscribed square (round the outside of the circle) and the inscribed hexagon (on the inside)!

Go to this

(Ages 10-13): Circle Area (FREE!)

Investigate how the area of a circle is connected to the square of the radius.

Go to this

(Ages 11-14): Perimeters of Similar Shapes (FREE!)

Explore how, when you double the size of a shape, the perimeter also doubles. Then look at what happens when the shape is made 3x or 4x larger. Does the same thing work?

Go to this

(Ages 11-14): Areas of Simliar Shapes (FREE!)

What happens to the area of a shape when you double its size? It doesn't just double...

And what happens when the shape is made 3x or 4x larger?

Go to this

(Ages 11-14): Pythagorean Triple Hunt (FREE!)

Find out how to make a spreadsheet to hunt for Pythagorean triples.

Go to this

(Ages 11-14): Pythagorean Triple Patterns (FREE!)

Pythagorean triples are groups of whole numbers that fit Pythagoras Theorem. 3, 4, 5 is one. 5, 12, 13 is another. Are there any more? Are there any connections between them?

Use a spreadsheet and the online pattern builder to venture deep into unknown territory!

Go to this