Module 12  Numbers Properties & Indices 
Number Properties & Indices  Teacher Notes
Solvemymaths has produced pages like this for lots of topics
NRICH Tasks
NRICH: Two
Primes Make One Square 
NRICH Article: Divisibility
Tests NRICH: One to Eight NRICH: Factors and Multiples Game NRICH: Factors and Multiples Puzzle NRICH: Sissa's Reward NRICH: Facfinding NRICH: What's Possible NRICH: Always Perfect 
NRICH: Tilted
Squares NRICH: Ladder and Cube NRICH: Where to Land NRICH: Walking around a cube NRICH: Inscribed in a Circle NRICH: Semidetached NRICH: Where Is the Dot? 
Extras
Video: Horrible
Histories 
Multiples and Factors Interactive Factors Tasks  Click here Robot Stepper: Idea taken from here Imagine that you have several robots: a twostepper, a threestepper, a fourstepper, all the way to a ninestepper.
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 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
www.datapointed.net/visualizations/math/factorization/animateddiagrams/ 
Prime Factors for Small Numbers
What would this look like if you split the circles in the
ratio of the numbers?

Indices 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
Standard Form
Visually Giantburger task  Mathematics Assessment Project Ever wondered why  JustMaths Estimating length using scientific notation  Mathematics Assessment Project Standard Form Exam Questions  mathsteaching.wordpress.com 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.
Even better if you try this method and the Venn Diagram method and get pupils to explain what is happening. 
Rules of Indices

Pythagoras 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 Coordinates
Measuring User PreferencesLet’s say you do a survey to find movie preferences: 1. How did you like Rambo? (110) 2. How did you like Bambi? (110) 3. How did you like Seinfeld? (110) 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 = 15cm^{2}

Surds Decimal Approximations Angry Surds Game – Click here

Surds Two methods for introducing simplifying Surds

[Thanks to Jo @mathsjam http://www.resourceaholic.com/]
See my blog
post on Surds for
ideas and resources 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 

