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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

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Thank you for your valuable time!

Free worksheets and simulator:

www.mathsatsharp.co.za