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 earned 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
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.
50 minute assessment on T1 and T2 topics (Calculator)
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.
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
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 equations
Two equations with two unknowns.
Quadratic equation
An equation containing an x² coefficient
Cubic equation
An equation containing an x³ coefficient
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
Hypotenuse
The longest side of a right-angled triangle. The side opposite the right-angle.
Adjacent
Next to (the side next to an angle (not the hypotenuse)
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
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.
Students will explore the addition and subtraction of simultaneous equations and find the first unknown.
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 an arc of a circle and a chord
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.. .