Year 9 — Maths

Term 1: Percentages, Comparing Statistical Distributions, Formulae & Polygons

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

Students will use grouped frequency tables and construct frequency polygons. They will calculate statistics from given data and use this information to compare distributions. Students will learn to recognise misleading graphs. Students will collect, present and interpret data in order to test an hypothesis.

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.

50 minute assessment on T1 topics (Calculator)

Percent

Out of 100

Compound Interest

Interest earnt on interest

Expand

Multiply out the brackets

Simplify

Combine the like terms of an algebraic expression

Factorise

Put into brackets

Equation

Is solved by finding the value of unknown variables

Polygon

A 2D shape with straight sides

Interior Angle

The inside angle of a 2D shape

Exterior Angle

The angle between an edge of a polygon and another edge extended. 180° - the interior angle

Tessellate

To cover an area with a shape without any gaps or the shape overlapping

  • 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. Students will 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.

50 minute assessment on T1 and T2 topics (Calculator)

Scatter Graph

Two sets of numerical data are plotted on each axes

Correlation

A measure of how strongly two sets of data are related

Positive Correlation

As one quantity increases, so does the other

Negative Correlation

As one quantity increases, the other decreases

Causation

The capacity of one variable to influence another

Cumulative Frequency Graph

A graph where the total of all the frequencies are plotted

Grouped Frequency Distribution

The data is grouped into class widths

Two-way Table

A table that shows two sets of data

Exponential Function

A function involving indices/powers

Pythagoras’ Theorem

Pythagoras discovered that for a right-angled triangle a² + b² = c², where a, b and c are the lengths of the sides of the triangle and c is the length of the hypotenuse.

Hypotenuse

The longest side of a right-angled triangle. It is the side opposite the right-angle.

  • 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.

50 minute assessment on T1, T2 and T3 topics (Non-calculator)

Algebraic Fraction

A fraction containing algebraic terms

Product

To find the product of two numbers, multiply the numbers together

Difference of Two Squares

An algebraic expression of the form a² - b² can be factorized into the form (a + b)(a – b)

Standard Form

Numbers written in the form a x 〖10〗^b where a is a number 1≤ a< 10

Upper Bound

The upper limit of a calculation

Lower Bound

The lower limit of a calculation

  • 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.

50 minute assessment on T1, T2, T3 and T4 topics (Calculator)

Surface Area

The sum of the area of all the faces of a 3D solid

Volume

The amount of space inside a shape. Measured in mm³, cm³, m³ etc.

Cylinder

A prism with a circular cross-sectional area, for example, a baked bean can

Prism

A solid with a constant cross-sectional area, for example, a Toblerone box is a triangular based prism.

Simultaneous Equation

Two equations with two unknowns

Quadratic Equation

An equation containing an x² coefficient

Cubic Equation

An equation containing an x³ coefficient

  • 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.

50 minute assessment on T1, T2, T3, T4 and T5 topics (Calculator)

Speed

How fast something travels. The distance travelled per one unit of time.

Density

The mass per one unit of volume

Mass

The amount of matter that a body contains. Measured in g or kg

Trigonometry

The mathematics of triangles

Hypothenuse

The longest side of a right-angled triangle. The side opposite the right-angle

Adjacent

Next to

Sine Ratio (sin)

The ratio of the opposite side divided by the hypotenuse in a right-angled triangle

Cosine Ratio (cos)

The ratio of the adjacent side divided by the hypotenuse in a right-angled triangle

Tangent Ratio (tan)

The ratio of the opposite side divided by the adjacent in a right-angled triangle

Tangent

The tangent to a curve is a straight line that touches a curve

  • 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 & Circle Theorems

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 explore the circle theorems and use these theorems to solve problems.

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 pictorial view, using overlapping circles, of the relationships between elements in sets

Union

The union of two or more sets is the combination of all of the elements in the sets

Intersection

The intersection of two or more sets is the single set containing ONLY elements common to the sets

Sequence

A set of numbers, patterns or objects in order according to a mathematical rule

Linear(arithmetic) Sequence

A sequence in which each term is obtained by adding a constant number to the preceding term e.g. 1, 4, 7, 10, 13,…

Geometric Sequence

A sequence in which each term after the first term a is obtained by multiplying the previous term by a constant r, called the common ratio e.g. 1, 2, 4, 8, 16, 32, . . .

Index (indices)

Power (powers)

Fibonacci Sequence

A sequence formed by adding the previous two terms

Direct Proportion

Two quantities are directly proportional when one quantity increases the other increases by the same amount. If y is directly proportional to x, this can be written as y ∝ x or y = kx

Inverse Proportion

Two quantities are inversely proportional when one quantity increases the other decreases. If y is inversely proportional to x, this can be written as y ∝ 1/x or y= k/x

Tangent

A straight line that touches a circle

Chord

A straight line passing from one point on the circumference of a circle to another

Sector

A part of a circle formed by an arc and two radii

Segment

A part of a circle formed by a n arc of a circle and a chord

  • 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.. .