These lessons will involve the students in investigating and understanding:
• N, Z, Q and representing these numbers on a number line
video Number sets
Khan
Negative numbers on the number line
Negative numbers on the number line without reference to zero
Recognizing rational and irrational numbers
• Factors, multiples and prime numbers in N
Khan
• How to express numbers in terms of their prime factors
Khan
The fundamental theorem of arithmetic
• Highest Common Factor and Lowest Common Multiple
Khan
Project Maths LCM and HCF(Geogebra File)
• How to make and justify estimates and approximations of calculations
• How to make estimates of the world around them e.g. how many books in a library
Khan
Approximating irrational numbers
Adding and subtracting rational numbers
Project Maths Estimating Quiz (Interactive File)
Webpage Estimation (Introduction)
• How to calculate percentage error and tolerance
• How to calculate accumulated error ( due to addition or subtraction only)
Webpage Error in Measurement
IXL
E.1Convert rates and measurements
Video: Calculating % Error
IXL
E.4Minimum and maximum area and volume
E.6Percent error: area and volume
• Terminating and non-terminating decimals
Webpage Definition of Terminating Decimal
• Irrational numbers R\Q
Khan
Recognizing rational and irrational numbers
Recognizing rational and irrational expressions
Alison Rational or irrational
• The number system R, appreciating that R ≠ Q and representing R on a number line
Khan
video Number sets
• How to geometrically construct Root(2) and Root(3)
Project Maths Root 2
video Construct root 2 units on a number line - YouTube
Project Maths Root 3
video Construct root 3 units on a number line - YouTube
How to construct Root 3 by using a 30-60-90 triangle with compass and straightedge or ruler
• Proof by contradiction that Root(2) is an irrational number
Proof that square root of 2 is irrational-Khan
Root 2 is Irrational – Proof by contradiction - Alison.com
Proof by Contradiction: Re-order the steps
Proof by Contradiction & Converse statements: Download Powerpoint
Note: Students need to know the concept of proof by contradiction, not necessarily any particular proof. This one suggested above could serve as an example of such a proof.
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