|Module 12||Numbers Properties & Indices|
Number Properties & Indices - Teacher Notes
Solvemymaths has produced pages like this for lots of topics
NRICH Article: Divisibility
NRICH: One to Eight
NRICH: Factors and Multiples Game
NRICH: Factors and Multiples Puzzle
NRICH: Sissa's Reward
NRICH: What's Possible
NRICH: Always Perfect
NRICH: Ladder and Cube
NRICH: Where to Land
NRICH: Walking around a cube
NRICH: Inscribed in a Circle
NRICH: Where Is the Dot?
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?
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
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
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:
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?
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
Ever wondered why? - JustMaths (this is great for Year 12 too)
Giantburger task - Mathematics Assessment Project
Ever wondered why - JustMaths
Estimating length using scientific notation - Mathematics Assessment Project
Standard Form Exam Questions - mathsteaching.wordpress.com
Indices Inquiry Prompt -
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
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 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
Magnify by raising both to the power of 30 - Click here