Module 12 Numbers Properties & Indices

Number Properties & Indices - Teacher Notes

Solvemymaths has produced pages like this for lots of topics


NRICH Article: Divisibility Tests
NRICH: One to Eight
Factors and Multiples Game 
Factors and Multiples Puzzle 
NRICH: Sissa's Reward
 What's Possible 
 Always Perfect
NRICH: Tilted Squares
Ladder and Cube
Where to Land
Walking around a cube
Inscribed in a Circle
Where Is the Dot?

Video: Horrible Histories​
Distances around school
Visualising Indices



Multiples and Factors

Interactive Factors Tasks - Click here

Robot Stepper: Idea taken from here

Imagine that you have several robots:

a two-stepper, a three-stepper, a four-stepper, all the way to a nine-stepper.

Ask pupils how this task might develop and give them ownership of the task

Some suggestions might be:

ü  If all robots start from 0 how many will land on 100

ü  What if you take two robots on which numbers will they both land?

ü  What about 3 robots?



Factors/Number Properties
[Thanks to Jo @mathsjam]

Number Type Cards - Churchill Maths

Factor Frenzy - Teachit Maths

HCF and LCM worded problems - Median Don Steward

HCF and LCM star matching - Teachit Maths

See my blog post on HCF/LCM for methods

Fact cards - The Chalk Face

Prime Factor decomposition activity - The Chalk Face


FlashMaths: Properties of Numbers - Venn Diagrams – Click here

Factors Inquiry Prompt - Click here

Primes: Ideas from Mr Hill's blog - Click here @MathsWithMrHill

ü  I like the links to Area (which they may not make straight away, depending on ability). I recommend doing this using multilink cubes: Idea taken from Don Steward

ü  Give 25 cubes and ask the students to record how many ways they could rearrange cubes to represent the numbers from 1 - 25:  Then this leads to discussions about Factors, Square Numbers and what it takes to be a prime number. 

ü   If you want to go onto Prime factorisation, then try it a different way - show how powerful prime numbers can be. Set a target - make it a game - after a while allow them to choose one more number to add to the list. Ask them why they wanted that number..


I can't believe I have never heard of Shikaku until this week. It is also referred to as rectangles. It's so perfect to consolidate factors (i.e. knowing that 10 could be one strip of ten or two strips of five) and also help with Area too.

This website allows you to choose loads of different levels of difficulty, meaning differentiation is easy! Also can be done on the website (with timings for extra competition) or printed. There are also a bunch of apps too with the game - Click here

ü  My last resource this post is Factors bingo - if you haven't played this before I will be surprised, but nevertheless here are the rules:

Factor Trees

Brilliant Video showing the numbers from 1 to 10,000 visually displayed as a product of Primes

Prime Factors for Small Numbers

What would this look like if you split the circles in the ratio of the numbers?

[Thanks to Jo @mathsjam]

Simplifying Indices Code Breaker - Teachit Maths

Index Laws dominoes - Teachit Maths

Using Indices  - Standards Unit

Powers of y eliminator - Teachit Maths

Properties of Exponents - Mathematics Assessment Project

Mental Powers Code Breaker -Teachit Maths

Collect a Joke - Number Loving

Treasure hunts: simple index laws and negative & fractional indices - Teachit Maths

Ever wondered why? - JustMaths (this is great for Year 12 too)



Standard Form
[Thanks to Jo @mathsjam]

Standard Form Visually
Standard Form Random
Questions Converting

Giantburger task - Mathematics Assessment Project

Ever wondered why - JustMaths

Estimating length using scientific notation  - Mathematics Assessment Project

Standard Form Exam Questions -

Large and Small - student sheet and teacher notes


Indices Inquiry Prompt - Click here


Finding the HCF and LCM

An alternative to the method of listing all factors or multiples or the more powerful use of Venn Diagrams

LCM = 2 x 2 x 2 x 3 x 3 = 72     HCF = 2 x 2 x 3 = 12

Say we want to find the Highest Common Factor and Lowest Common Multiple of 24 and 36.
Write down the two numbers, then (to the left, as in my example below) write down any common factor (ie 2, 3, 4, 6 or 12).  I've chosen 6.  Now divide 24 and 36 by 6 and write the answers underneath (4 and 6 in this case).  Keep repeating this process until the two numbers have no common factors (ie 2 and 3 below).  Now, your Highest Common Factor is simply the product of numbers on the left. And for the Lowest Common Multiple, find the product of the numbers on the left and the numbers in the bottom row.

Even better if you try this method and the Venn Diagram method and get pupils to explain what is happening.


Rules of Indices


See the Teacher Notes for Module 14 for proofs of Pythagoras' Theorem

Show that it works for any 3 similar shapes and not just squares, can you explain why?

Extending Pythagoras into 3D Co-ordinates

Measuring User Preferences

Let’s say you do a survey to find movie preferences:

1.     How did you like Rambo? (1-10)

2.    How did you like Bambi? (1-10)

3.    How did you like Seinfeld? (1-10)

How do we compare people’s ratings? Find similar preferences? Pythagoras to the rescue!

If we represent ratings as a “point” (Rambo, Bambi, Seinfeld) we can represent our survey responses like this:

§  Tough Guy: (10, 1, 3)

§  Average Joe: (5, 5, 5)

§  Sensitive Guy: (1, 10, 7)

And using the theorem, we can see how “different” people are:

§  Tough Guy to Average Joe: (10−5,1−5,3−5)=(5,−4,−2)= √(25+16+4)=6.7

§  Tough Guy to Sensitive Guy: (10−1,1−10,3−7)=(9,−9,−4)= √(81+81+16)=13.34

§  For further ideas - Click here




Answer = 15cm2



Surds Decimal Approximations

Angry Surds Game – Click here 


Two methods for introducing simplifying Surds


[Thanks to Jo @mathsjam]

See my blog post on Surds for ideas and resources

The width to height ratio of A4 paper remains unchanged when cut in half to make A5.  What must the ratio of the sides be to make this true?

When an A4 sheet is folded as shown, prove that length  is equal to length :

Click here for solution


Magic Square

Magnify by raising both to the power of 30 - Click here