Term 1: Types of Numbers, Equations, Angles, Constructions and Probability
Students will find HCF’s and LCM’s, use powers and roots and find prime factors.
Students will solve simple and more complex equations. They will learn to form equations in order to solve problems.
Students will measure, draw and calculate angles in polygons and parallel lines. They will explore the properties of quadrilaterals and learn how to accurately construct polygons. Students will translate shapes and enlarge a shape by a given scale factor.
Students will create sample space diagrams in order to calculate probabilities. They will learn how to draw and use Venn diagrams to solve probability problems.
50 minute assessment on T1 topics (Non-calculator)
Negative Number
A number that is less than zero
Factor
Factors are numbers you can multiply together to get another number: Example: 2 and 3 are factors of 6, because 2 x 3 = 6.
Multiple
The result of multiplying a number by an integer (not a fraction). Examples: 12 is a multiple of 3, because 3 x 4 = 12. -6 is a multiple of 3, because 3 x -2 = -6. But 7 is NOT a multiple of 3
Index (Indices)
A superscript which tells you that you must multiply the number by itself that many times. E.g. 4³ = 4 x 4 x 4 = 64
Prime
A Prime Number can be divided evenly only by 1, or itself. And it must be a whole
number greater than 1. Example: 5 can only be divided evenly by 1 or 5, so it is a prime number.
Parallel
Lines that are always the same distance apart, however far they extend.
Quadrilateral
A 2D shape with four sides
Transformation
The process of changing a shape through translation, reflection, rotation or enlargement.
Translation (Translate)
Moving a shape a given number of spaces in the horizontal and vertical direction.
Enlarge (Enlargement)
Making a shape bigger or smaller.
Construct (Construction)
Draw angles, lines or shapes accurately, using compasses, a protractor and a ruler.
Outcome
The result of a single trial of a probability experiment.
Trial
Any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.
Mutually Exclusive
Events that cannot happen at the same time in a probability experiment. E.g. It is impossible to roll a die and get 3 and 5 at the same time.
Exhaustive
Fully complete.
Sample Space
The set of all possible outcomes from a probability experiment, often denoted S or Ω.
Relative Frequency
The frequency of each item in a data set, divided by the sum of all the frequencies.
Frequency
The number of times a particular event or item appears in a set of data.
Develop the individual:
When solving mathematical problems students will develop their creative skills. The topic of probability provides opportunities for students to consider whether situations are fair or biased and discuss gambling, betting, lotteries, raffles and games of chance. A knowledge of probability will benefit students’ functioning in society as they will understand bias and the chance of an event happening.
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .
Term 2: Percentages, Congruent Shapes, Further Sequences, Surface Area and the Volume of a Prism
Students will learn how to write one quantity as a percentage of another and how to calculate percentage change.
Students will learn how to recognise congruent shapes and solve geometrical problems using congruent triangles.
Students will find nth terms of more complex sequences and explore the Fibonacci sequence.
Students will learn how to convert between different metric units for both area and volume. They will also calculate the surface area and the volume of a prism.
50 minute assessment on T1 and T2 topics (Calculator)
Percentage
a percent or percentage is a fraction expressed as a number out of 100 followed by the % symbol.
Increase
get larger in size, number or quantity.
Decrease
get smaller in size, number or quantity.
Interest
interest is a fee paid for borrowing money or other assets.
Simple Interest
The amount paid in interest remains the same each year.
Compound Interest
Interest is paid each year on the balance at the end of the previous year (including any previous interest).
Congruent
having the same shape and the same size.
Face
flat surface of a three-dimensional shape.
Vertex (Vertices)
The point at which two lines meet in a 2D or 3D shape.
Edge
The side of a polygon or a line segment where two faces of a solid figure meet.
Surface Area
The total area of all the faces of a 3D shape.
Volume
Amount of space occupied by an object.
Develop the individual:
Competance 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. Students learn geometrical reasoning through knowledge and application of the rules for congruency.
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .
Term 3: Graphs, Powers & Significant Figures, Drawing & Interpreting Tables & Graphs
Students will learn about gradients and explore the connection between the equation of a straight line and the gradient. They will explore the properties of a quadratic graph and draw graphs to illustrate real life situations.
Students will multiply and divide negative powers of 10 and round numbers to a given number of significant figures. They will learn to use standard form.
Students will learn to construct and interpret scatter graphs. They will draw and use lines of best fit to understand the idea of correlation.
50 minute assessment on T1, T2 and T3 topics (Non-calculator)
Index (Indices)
A superscript which tells you that you must multiply the number by itself that many times. E.g. 4³ = 4 x 4 x 4 = 64
Gradient
gradient is the steepness and direction of a line as read from left to right.
linear equation
an equation whose graph is a straight line.
parabola
the graph of a quadratic equation.
significant figures
the digits that give most meaning to a number.
Quantitative
Data that can be quantified by counting or measuring.
Qualitative
data categories including characteristics, for example, names, ages, locations and occupations or personal preferences, for example, food, clothes and leisure activities.
Data
data is a collection of information gathered by observation, questioning or measurement.
Discrete
discrete data is quantitative data that can be counted and has a finite number of possible values
Continuous
Continuous data is quantitative data that can be measured, it has an infinite number of possible values within a selected range
Develop the individual:
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. Students learn about graphs in real-life situations.
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .
Term 4: Algebraic Expressions, Shape & Ratio
Students will simplify expressions and expand brackets. They will learn to write algebraic expressions involving powers.
Students will learn how to use ratio to compare lengths, areas and volumes, of 2D and 3D shapes. They will enlarge shapes using fractional and negative scale factors, and use different map scales.
50 minute assessment on T1, T2, T3 and T4 topics (Non-calculator)
Equation
a mathematical statement containing an equals sign, to show that two expressions are equal.
Formula
a mathematical rule written using symbols, usually as an equation describing a certain relationship between quantities.
Scale Factor
In scale drawings – the ratio of the measurement on the drawing compared to the measurement of the original subject. When comparing two similar geometric figures –the ratio of any two corresponding edge lengths.
Enlargement
a transformation where a shape is made larger or smaller without changing its position or direction.
Mixed Number
a number written as a whole number with a fraction.
Numerator
number above the line of a fraction, showing the number of parts of the whole.
Denominator
the bottom number in a fraction showing the number of parts the whole is divided into.
Expression
an expression is one or a group of terms and may include variables, constants, operators and grouping symbols.
Identity
an equation that holds true for all of its variables.
Develop the individual:
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 their experiences in order to describe and model situations. Students will learn about transformations of shapes. They will enlarge shapes by different scale factors.
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .
Term 5: Fractions & Decimals, Direct & Indirect Proportion & Circles
Students will add, subtract, multiply and divide fractions, mixed numbers and decimals.
Students will learn how to solve problems involving direct and indirect proportion. They will represent proportions of quantities using graphs and algebra.
Students will identify the parts of a circle. They will calculate the circumference and area of a circle. They will calculate the perimeter and area of semicircles and sectors of circles.
Year 8 examination - Two 50 assessments on all topics taught so far in Year 8 (Paper 1 non-calculator, Paper 2 calculator)
Equation
a mathematical statement containing an equals sign, to show that two expressions are equal.
Formula
a mathematical rule written using symbols, usually as an equation describing a certain relationship between quantities.
Direct Proportion
the relationship between two quantities whose ratio remains constant.
Inverse Proportion
the relationship between two quantities where as one quantity (x) increases the other quantity (y) decreases in proportion.
Radius
the distance from the centre of a circle to its circumference.
Diameter
a straight line passing through the centre of a circle to touch both sides of the circumference.
Circumference
the distance around a circle.
Chord
straight line joining two points on the circumference of a circle.
Tangent
a straight line touching a curve once at a given point.
Sector
section of a circle, bounded by two radii and an arc.
Segment
section of a circle, bounded by a chord and an arc.
Arc
section of a curve, part of a circle.
Expression
an expression is one or a group of terms and may include variables, constants, operators and grouping symbols.
Identity
an equation that holds true for all of its variables.
Develop the individual:
Numerical fluency and an understanding of proportion will benefit students’ functioning in society. For example to be able to convert between units, or state which is the better value for money? All mathematics has a rich history and a cultural context in which it was first discovered or used, for example, students will consider how pi was first discovered. 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 develop algebraic fluency throughout the curriculum.
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .
Term 6: Equations & Formulae, Comparing Statistical Distributions & Statistical Investigation
Students will solve a range of equations involving brackets and fractions and learn how to rearrange formulae.
They will learn how to use graphs to solve equations.
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 a hypothesis.
50 minute assessment on topics taught in Year 8
Data
data is a collection of information gathered by observation, questioning or measurement.
Quantitative
Data that can be quantified by counting or measuring.
Qualitative
data categories including characteristics, for example, names, ages, locations and occupations or personal preferences, for example, food, clothes and leisure activities.
Discrete
discrete data is quantitative data that can be counted and has a finite number of possible values
Continuous
Continuous data is quantitative data that can be measured, it has an infinite number of possible values within a selected range
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.
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .