**Multiplication, Division, Fractions & Decimals**

There are just three photocopiable investigations in this section. But they will keep your pupils busy for hours!

Between the three investigations you will cover the following skills and concepts:

- how multiplication is a rectangle
- what factors are
- how to make a factor rainbow
- the inverse relationship between multiplication and division
- interpreting remainders in division
- rounding calculator answers appropriately
- finding fractions of numbers.

###### Numbers Between Numbers

Explore where simple fractions and decimals sit on the number line and how they relate to each other.

###### Multiplication Rectangles and Factor Rainbows

An engaging investigation into multiplication and the concept of factors. Investigate which numbers have few factors and which have lots. Explore square numbers and look at the ‘specialness’ of the...

###### Chopping up a Metre Stick

Well, not ACTUALLY cutting it up – but imagine… Suppose you wanted to make 4 pieces or 5 pieces. Where would you chop? How about 3 pieces? Get totally immersed in how division, fractions and...

**Shapes and Angles**

Shapes are fascinating! There are so many things you can investigate about them and they provide a brilliant context for practising all your number skills.

There are five suggested areas for investigation here and each of them is BIG – so you can come back to them again and again to explore in more depth. Here are the skills you will cover…

- identifying different types of angle
- identifying and describing the different types of triangle and quadrilateral
- understanding the difference between perimeter and area
- measuring accurately with a ruler
- calculating perimeters and areas of triangles and quadrilaterals
- measuring and drawing angles
- constructing shapes using a pair of compasses and a straight edge
- understanding Pythagoras’ theorem.

###### Pythagoras Puzzle

Have fun making this simple puzzle which very beautifully illustrates Pythagoras’ Theorem that the sum of the squares on two sides of a right-angled triangle = the square on the third side. Make...

###### How Many Different Kinds of Triangle Are There?

How many different kinds of triangle are there? Can you have a triangle with two obtuse angles? These and other questions are all explored in this practical investigation using geostrips (or...

###### Constructing Shapes

Constructing shapes with compasses is always great fun because you get pretty patterns. But this investigation goes well beyond regular activities with pupils being given an open-ended challenge to...

###### Angles in Triangles and Quadrilaterals

Investigate the angles in different triangles and quadrilaterals and discover the facts about their totals.

###### Perimeter and Areas of Triangles and Quadrilaterals

You may be able to calculate the perimeters and areas of a rectangle and a triangle, but can you explain why the formulas work? Build on this to explore other quadrilaterals: rhombus, kite,...

###### Angles in Polygons

Investigate the total interior and exterior angles of polygons (triangle, quadrilateral, pentagon, hexagon etc.) Explore patterns in the numbers and establish rules and experiment with formulas.

###### The Egyptian Triangle

Discover the special triangle that the Egyptians used in their buildings, while learning about how simple decimals work, the importance of accurate measuring and how to work systematically to solve...

###### Properties of Quadrilaterals

Find out why a square is a special kind of rectangle but a rectangle is not a special kind of square!Explore the differences rhombuses and parallelograms, kites and trapeziums.Investigate questions...