Post on 02-Feb-2022
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Maths Senior Phase Term 2 Content
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Agenda
• Sharpies
• Basics
• Topics• Decimal Fractions
• Integers
• Numeric and Geometric Patterns
• Functions and Relationships
• Exponents
• Algebraic Expressions
• Algebraic Equations
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Free Downloads and Resources
• Download the simulator• Link
• Download Geogebra• Link
• Worksheets• www.mathsatsharp.co.za• www.e-classroom.co.za• www.math-drills.com• https://www.mathx.net/• https://www.worksheetworks.com/ (one of my favourites for younger grades
and fully customisable)• https://www.mathwarehouse.com/sheets/ (FET mostly)
• ATP documents (link)
Calculator Basics
• Turn the calculator on
• 2nd Function – used to activate orange functions
• Turn the calculator off by pressing 2nd F and ON
• ALPHA – used to activate teal functions
• Mode – change to different modes
• BS – backspace – to delete something.
• Change – change between mixed, improper and decimal answers.
• Equals – to find an answer or used as enter.
Modes
• Press
• 0: Normal• Fractions, integers, probability,
trigonometry and much more
• 1: Stat• Single data, linear regression and
more
• 2: Table• Functions but can also be used for
teaching finance
• 3: Drill• Mental maths fun!
Decimal FractionsGrade 7 and 8
Decimals
• Need to be able to add and subtract
• Multiply decimals with 2 decimals places by another with one decimal place (grade 7)
• Divide a number with 3 decimal places by a whole number (grade 7)
• Grade 8 – two decimal places divided by two decimal places
This Photo by Unknown Author is licensed under CC BY-SA-NC
Practice rounding off
• Press
Equivalence between decimals and fractions
• We can use the change button to check our answers.
• E.g. Press
• Or,
Recurring Decimals
• To turn the recurring decimal function on:
Squares, Cubes and Roots of Decimals
• We use
• Examples: • Find 3.52
•
• Find 30.125
•
IntegersGrade 7
Adding and Subtracting Integers
• When the signs are the same, we add the digits and keep the signs.
• E.g. 7 + 3 = 10• E.g. -7 – 3 = -10
• When the signs are different we subtract the “small” digits from the “big” digits, and keep the sign of the big digits.
• E.g. 7 – 3 = 4• E.g. -7 + 3 = -4
Associative and Commutative Properties
• Associative property• We can rearrange the way we
group things when we are multiplying or adding.
• E.g. (2 x 3) x 5 = 2 x (3 x 5)• Algebraicly: 2 × 3𝑥 = 2 × 3 𝑥= 6𝑥
• Commutative property• When we multiply or add, the
order in which we multiply or add the numbers doesn’t matter
• E.g. 5 x 4 x 2 = 4 x 2 x 5 and so on.
• Or, 5 + 4 + 2 = 4 + 2 + 5 etc
Numeric and Geometric PatternsGrade 7
Grade 8
Grade 9
Is it a difference or ratio?
• Linear patterns• The same “distance” between
each part of the pattern• E.g. 2 4 6 8 10
• Counting in from a certain point• E.g. 2 5 8 11 14
• Geometric Patterns• We multiply or divide by the
same number each time• E.g. 3 9 27 81
• E.g. 625 125 25 5
Investigating Patterns
• Our formula is: Tn = 3𝑛 + 5
• Press
General Rules: Linear Pattern
• The pattern formula is: 𝑇𝑛= 𝑑𝑛 + 𝑐
• E.g. 11, 14, 17 • Common difference = __
• To find c we subtract the common difference (d) from the first term: 11 – __ = __
• So we can say our formula is: 𝑇𝑛 = __ 𝑛 + __
• Let’s check that we are correct
• Press
• Type in the formula for the pattern:
Geometric Patterns
• Are like exponents
• Formula: 𝑇𝑛 = 𝑎. 𝑟𝑛−1
• E.g. 3, 12, 48, 192
• We are multiplying by a common ratio of ___
• a is our first term = ___
• So our formula is: 𝑇𝑛 = _________________
• Let’s check that we are correct.
• Press
• Type in the formula for the pattern:
Functions and RelationshipsGrade 7
Grade 8
Input and Output Values
• 3 ways to show these:• Tables (like in table mode)
• Flow diagrams
• Formula
• We need to be able to give the other two from the one we are given.
Tables and Formulae
• We can also use the table mode to create patterns, and explore them.
• E.g. linear pattern: 4𝑥 + 3
• Press
• E.g. Geometric Pattern
• Press
ExponentsGrade 8
Scientific Notation
• 2 options: or
• E.g. 3.4 × 105 × 7.9 × 106
• Type in
Setting Scientific Notation
• Press
And back to Normal Notation
• Press
Exponent Laws
• Teaching the multiplication rule:
• Press
• Two ways to prove it:
• Press
• Now we can use:
• Now scroll up to previous example:
Squares, Cubes and Roots
• To square a number press
• To cube a number press
• To find the square root press
• E.g. 22 press
• E.g. 33 press
• E.g. 16 press
Algebraic ExpressionsGrade 8
Grade 9
Like and Unlike Terms
• What is a term? • Separated by a plus or minus. • Fractions are considered one
term. • Multiplication also considered one
term• E.g. 3𝑥 4 + 5𝑥 - 1 term
• Like terms have the same variables and the same exponents.
• Unlike terms either don’t have the same variables, or have the same variables but with different exponents.
Theory• Coefficients
• The number and/or variable(s) attached to variable you are looking at.
• Constants• A value that doesn’t change
• Degree • The highest power of the expression
or equation
• Expression• One sided• Can only be simplified
• Equation• Two sides• Can be solved for a variable
Polynomials
• Monomials• A single term • E.g. 3𝑥 𝑜𝑟 4𝑥𝑦2
• Binomials• Two terms• E.g. 3𝑥 + 1
• Trinomials• Three terms• E.g. 4𝑥2 + 4𝑥 + 1
• Polynomials• More than 3 terms
FOIL
• FOIL• Firsts
• Outers
• Inners
• Lasts
• Or use Kitty cat ears
• E.g. 3𝑥 + 1 6𝑥 − 7
Algebraic EquationsGrade 9
Highest Common Factor
• Lets find the highest common factor of 85 and 100
• Press
Lowest Common Multiple
• Lets find the lowest common multiple of 85 and 100
• Press
Factor Pairs
• Press
• Lets find the factors of 36
• Press
Factorising Trinomials
• Rules to remember:• 𝑎𝑥2 + 𝑏𝑥 + 𝑐• Look at the sign in front of the
c:• If it is plus the signs in both
brackets are the same, and you add your two factors to find the value of b.
• The sign in front of b tells you which sign to put into your two brackets.
• If the sign is negative, subtract one factor from the other, and the signs in the brackets are different.
• E.g. 𝑥2 + 5𝑥 + 6
• 𝑥2 − 5𝑥 + 6
• 𝑥2 − 𝑥 − 6
Solving for x: linear
• We can check our answers using table mode.
• E.g. 4𝑥 + 5 = 1
• First manipulate the equation so that it is equal to zero.
• 4𝑥 + 5 − 1 = 0
• 4𝑥 + 4 = 0
• Press
Solving for x: trinomial
• E.g. 𝑥2 + 5𝑥 + 4 = 0
• Press
Junior Calculator
• EL-W535SA – cheaper and 422 functions
• Ideal for grade 7 – 9 students
• 500 000 calculators given to No-Fee school students in Gauteng by the department of education
• With a 40% improvement between the pre- and post-tests after training.
Thank you for your valuable time!
Free worksheets and simulator:
www.mathsatsharp.co.za