Year 8 — Maths

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 less than 0

HCF

The Highest Common Factor of two or more numbers in the largest number that is a factor of each. The HCF of 15 and 40 is 5.

LCM

The Lowest Common Multiple of two or more numbers is the smallest number that is a multiple of each. The LCM of 2 and 3 is 6.

Prime

A number that can only be divided by 1 and itself. All prime numbers have exactly 2 factors.

Alternate angles

Alternate angles in parallel lines are equal.

Parallel

Two lines are parallel if they are the same distance apart and never meet.

Corresponding angles

Corresponding angles in parallel lines are equal.

Quadrilateral

A four sided shape.

Enlargement

The action of enlarging a shape or solid.

Probability

The chance of something happening.

Theoretical probability

The likeliness of an event happening based on all the possible outcomes.

Probability space diagram

A list of all possible probability events.

  • Spiritual
  • Moral
  • Social
  • Cultural

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

Out of 100.

Congruent

Two shapes that are exactly the same shape and size.

Sequence

A list of numbers that follow a pattern.

Surface area

The total area of the surface of a 3D object.

Volume

The amount of space that a 3D object occupies.

Prism

A solid that has a constant cross-sectional area.

  • Spiritual
  • Moral
  • Social
  • Cultural

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)

Equation

A mathematical statement where the values of two mathematical expressions are equal (indicated by the sign =).

Gradient

The slope of a line.

Quadratic expression

An expression that contains a squared term.

Standard Form

A number written in the form a × 〖10〗^b where a is a number between 1 and 10 (not including 10).

Positive correlation

As one quantity increases so does the other.

Negative correlation

As one quantity increases the other decreases.

  • Spiritual
  • Moral
  • Social
  • Cultural

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)

Expanding brackets

Multiply out the brackets.

Area

The amount of surface that a 2D shape has.

Volume

The amount of space that a 3D object occupies.

Enlargement

The action of enlarging a shape or solid.

  • Spiritual
  • Moral
  • Social
  • Cultural

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)

Integer

A whole number. May be positive or negative.

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.

Circumference

The distance round the outside of a circle.

Radius

The distance from the centre to the edge of a circle.

Diameter

The distance across a circle through the centre.

Chord

A chord is a straight line drawn through a circle which divides the circle into two parts. The line can be drawn anywhere in the circle EXCEPT the center where it becomes the diameter.

Sector

The sector of a circle is a portion of the circle enclosed by two radii and an arc.

Segment

The segment of a circle is a part of the circle bounded by a chord and an arc.

  • Spiritual
  • Moral
  • Social
  • Cultural

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

Equation

Equation - A mathematical statement where the values of two mathematical expressions are equal (indicated by the sign =).

Variable

An unknown number represented by a letter.

Formulae

A rule that is expressed algebraically. For example the area of a circle can be expressed by the formula πr^2.

Mean

An average found by totalling the numbers and dividing by how many there are.

Median

An average found by listing the numbers in order and finding the middle number.

Mode

An average found by finding the item that occurs the most often.

Range

The difference between the greatest and least values.

  • 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.

Create a supportive community:

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