# Maths - Year 9

### Term 1: Percentages, Equations & Formulae, and Polygons

Students will learn to calculate simple interest, percentage increases and decreases, reverse percentages, repeated percentage change and compound interest.

Students will learn to expand brackets, factorise algebraic expressions and solve equations with fractions.

Students will explore the properties of polygons, find internal and external angles of regular polygons and learn why some polygons tessellate and some do not.

1. 50 minute assessment on T1 topics (Calculator)
###### Expression

A mathematical statement containing constant terms (numbers) and variables (unknown values)

###### Equation

Mathematical expressions that are equal in value and denoted with a '=' sign

###### Polygon

A closed shape with straight sides

###### Regular Polygon

A polygon where all sides are equal and angles are equal

###### Sum of interior angles

The total angles inside a polygon. Found by using formula 180(n-2) where n is the number of sides

###### Exterior Angle

The angle on the outside of a polygon. In a regular polygon is found by dividing 360 degrees by the number of sides

###### Multiplier

Number used to represent a percentage change: increase is 100% + percentage increase, decrease is 100% - percentage change

###### Exponential

A function with an ever increasing gradient

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Competence with percentages benefits our students’ functioning in society: sales, interest rates, taxes. Students are encouraged to question “why”; they compose proofs and arguments and make assumptions when analysing a problem. For example, students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to describe and model situations. The topic of algebra provides opportunities for students to develop a sense of “awe and wonder” by using letters to represent variables. Students are encouraged to question “why”; they compose proofs and arguments and make assumptions. Students learn geometrical reasoning through knowledge and application of angle rules.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 2: Using Data, Applications of Graphs & Pythagoras

Students will learn about scatter graphs and correlation. Draw and interpret cumulative frequency diagrams and estimate the mean from grouped data. They will use two-way tables to solve problems.

Students will learn about distance/time graphs and exponential growth.

Students will discover Pythagoras’ Theorem and use it to find missing sides in a right-angled triangle. They will use Pythagoras’ Theorem to solve problems.

1. 50 minute assessment on T1 and T2 topics (Calculator)
###### Hypotenuse

The longest side of a right angled triangle, always opposite the right angle

###### Pythagoras Theorem

a^2 + b^2 = h^2 where a & b are the shorter sides and h is the hypotenuse

###### Correlation

How two variables are related- can be positive (as one goes up so does the other), negative (as one goes up the other goes down) or none

###### Cumulative Frequency

The running total of frequencies from a frequency table

###### Time Graph

A graph that shows how a variable changes over time

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Student’s understanding of statistics is developed to a depth that will equip them to identify when statistics are meaningful or when they are being used inappropriately (eg in newspapers or on social media). The skill of interpreting data will benefit students’ functioning in society. Students will understand how to interpret graphs and charts. When solving mathematical problems students will develop their creative skills. All mathematics has a rich history and a cultural context in which it was first discovered or used. The opportunity to consider the lives of specific mathematicians is promoted when studying Pythagoras’ Theorem.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 3: Fractions, Algebra, Standard Form, Upper & Lower Bounds

Students will review addition, subtraction, multiplication and division of fractions and mixed numbers. They use this knowledge and understanding to complete calculations using simple algebraic fractions.

Students will learn how to expand the product of two and more brackets, factorise quadratic expressions and find the difference of two squares.

Students will learn how to write numbers in standard form, and complete calculations involving standard form.

They will learn how to calculate upper and lower bounds.

1. 50 minute assessment on T1, T2 and T3 topics (Non-calculator)
###### Expansion

The process of multiplying out two brackets to create an expression

###### Factorising

The process of finding the factors of an expression (in other words: put into brackets). Can be done using the grid method

###### Difference of Two Squares

Method of factorising when one square number is subtracting another. a^2 - b^2 = (a+b)(a-b)

###### Standard Form

Numbers in the form a x 10^n where a is between 1 and 10 (but not including 10) and n is an integer

###### Upper and Lower Bound

The largest and smallest possible value that will round to a given number

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Students are encouraged to question “why”; they will explore the links between area and algebra. The topic of algebra provides opportunities for students to develop a sense of “awe and wonder” by using letters to represent variables. Students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to reflect on experiences in order to describe and model situations. Mathematics provides opportunities for students to develop a sense of “awe and wonder”. Standard form promotes “awe and wonder” by providing a way for students to write extremely large and extremely small numbers.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 4: Surface Area and Volume of Cylinders & Solving Equations Graphically

Students will learn how to find the surface area and volume of a cylinder and of composite solids involving cylinders.

Students will learn how to plot straight line graphs with and without a table. They will use graphs to solve simultaneous equations, quadratic equations and cubic equations.

1. 50 minute assessment on T1, T2, T3 and T4 topics (Calculator)
###### Cylinder

A prism with a circle as a cross section

###### Volume of a cylinder

V = π(r^2)h where r is the radius and h is the height

###### Surface Area of a Cyclinder

A=2πr^2 + 2πrh where r=radius and h=height

###### Simultaneous Equation

The process of solving two or more equations at the same time

###### Graphing Equations

The process of plotting equations on a coordinate grid so they can be solved by finding intersections

An expression where the highest power is squared (x^2)

###### Cubic

Expression where the highest power is cubed (x^3)

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to describe and model situations. The topic of algebra provides opportunities for students to develop a sense of “awe and wonder” by using letters to represent variables.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 5: Compound Units & Trigonometry

Students will calculate measures of speed, distance, time, density, mass and volume.

Students will learn how to find trigonometric ratios. They will use trigonometric ratios to find missing angles and lengths in right-angled triangles. They will use trigonometry to solve problems.

1. 50 minute assessment on T1, T2, T3, T4 and T5 topics (Calculator)
###### Speed-Distance-Time

Speed=Distance/Time, Distance = Speed x Time, Time = Distance/Speed

###### Density-Mass-Volume

Density= Mass/Volume, Mass = Density x Volume, Volume= Mass/Density

###### Sine

The ratio between the opposite side and the hypotenuse of a right angled triangle

###### Cosine

The ratio between the adjecent side and the hypotenuse of a right angled triangle

###### Tangent

The ratio between the opposite side and adjacent side of a right angled triangle

###### Inverse Trigonometry

The process of finding the size of an angle in a right angled triangle

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Understanding compound units will benefit students’ functioning in society, as they will be able to calculate speeds, distances, times etc. When solving mathematical problems students will develop their creative skills.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 6: Venn Diagrams & Frequency Trees, Sequences, Proportion & Simultaneous Equations

Students will use Venn diagrams and frequency trees to solve problems.

Students will learn how to find nth terms of quadratic sequences and those involving fractions and indices. Students will explore and generalise Fibonacci type sequences.

Students will convert between fractions, ratios and percentages. They will be able to find the proportion of a shape that is shaded and solve problems involving proportion.

Some students will solve simple simultaneous equations.

1. End of year examination - two 50 minute assessments on all topics taught in Year 9 (Paper 1 non-calculator, Paper 2 calculator)
###### Venn Diagram

A diagram that shows how data can be sorted into different sets

###### Set

A collection of data, e.g. students who study Mandarin, students who study Spanish

###### Union

In a Venn Diagram: the data that is in one set or the other

###### Intersection

In a Venn Diagram: data that is in both sets

###### Universal Set

The set in which all data is contained

###### Null Set

The set in which no data is contained

###### Frequency Tree

A branching diagram that shows how sucessive probabilities are calculated

###### 'And' Rule

the probability of two events occurring: multiply the probabilities

###### 'Or' Rule

The probability of one event or a different event occurring: add the probabilities

###### Mutually Exclusive

Sets which have no overlap-a coin toss cannot return a heads and a tails at the same time

###### Independence

Probabilities which have no influence on each other, e.g. rolling a 6 on a dice will not change the probability of rolling a 6 on the next roll

###### Subtended Angle

The angle made between a line and an arc

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

When solving mathematical problems students will develop their creative skills.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .