Maths (Foundation) - Year 10

Maths (Foundation) Overview

Term 1: Expressions, Trigonometry & Angles

Terms and expressions.

Simplifying expressions.

Rules of indices.

Expanding and factorising into single brackets.

Trigonometric ratios to find missing angles and lengths in right-angled triangles and to solve problems.

Angles and parallel lines.

Angles in triangles and quadrilaterals.

Congruence and similar shapes.

Angles in polygons.

  1. Test on: Expressions, Calculations & Angles
Index

Power

Expand

Multiply out the brackets

factorise

Put an algebraic expression into brackets

Quadratic

A four sided 2D shape

Polygon

A 2D shape with straight sides

Congruence

Two shapes are congruent if they are exactly the same shape and size

Similar shapes

Two shapes are similar if one is an enlargement of the other

Alternate Angles

Alternate angles in parallel lines are equal

Corresponding Angles

Corresponding angles in parallel lines are equal

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

Skills such as confidence with numeracy and rounding benefit our students’ functioning in society. 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 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. Students learn geometrical reasoning through knowledge and application of angle rules and coditions for similarity and congruency. 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 2: Data Handling, Fractions, Decimals & Percentages

Sampling and data collection.

Organising data.

Representing data: two-way tables, frequency tables, stem and leaf diagrams, pictograms, bar charts, frequency trees.

Averages and the range.

Grouped frequency tables and estimating the mean from a grouped frequency table.

Scatter graphs and correlation.

Fractions, decimals and percentages.

Calculations with fractions.

Converting between fractions, decimals and percentages.

  1. Test on: T1 topics and Data Handling, Fractions, Decimals and Percentages
Random sample

A sample where everyone in the population has an equal chance of being chosen

Biased Sample

A sample where everyone in the population does not have an equal chance of being chosen

Stratified sample

A sample where different groups (e.g. boys and girls) are represented in sample in the same proportion as the population

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

Cumulative Frequency

The total of all the frequencies in a set of data

Interquartile Range

The difference between the upper quartile and the lower quartile

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:

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, and be able to compare statistical distributions. Competance with percentages benefits our students’ functioning in society: sales, interest rates, taxes.

Create a supportive community:

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

Term 3: Formulae & functions & working in 2D

Substituting into formulae, using standard formulae and rearranging formulae.

Equations, identities and functions.

Expanding and factorising double brackets.

Measuring lengths and angles.

Bearings

Area of 2D shapes: rectangle, triangle, parallelogram, trapezium, compound shapes.

Transformations: rotations, reflections, enlargements and translations.

  1. Test on: T1 and T2 topics. Formulae & functions & Working in 2D
Formula

A mathematical relationship or rule expressed in symbols

Function

A relation between a set of inputs and a set of permissible outputs

Inverse function

A mathematical operation or function that exactly reverses another operation or function

transformation

The act of moving or changing a shape

reflection

A reflection is an image that you can see in a mirror line

Rotation

The action of rotating about an axis or centre

Enlargement

The action of enlarging a shape or solid

Translation

The action of moving a shape along and up or down

Tesselation

Repeating a shape to cover an area with no gaps and no overlapping

Area

The amount of surface that a shape has

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

Students will learn about transformations of shapes. They will enlarge shapes by different scale factors. 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 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.

Create a supportive community:

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

Term 4: Probability, Measures & Accuracy, Compound Units

Probability experiments, expected outcomes and relative frequency.

Theoretical probability.

Mutually exclusive events.

Estimating calculations.

Using a calculator.

Metric units.

Limits of accuracy: error intervals and upper and lower bounds.

Calculating measures of speed, distance, time, density, mass and volume.

  1. Test on: All material covered in this term and previous terms

    1 Non-Calculator paper and 1 Calculator paper

Relative Frequency

Experimental probability

Theoretical probability

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

Probability space diagram

A list of all possible probability events

Mutually exclusive events

Two or more events are said to be mutually exclusive if they cannot occur at the same time

Independent events

Two events are independent if the occurrence of one does not affect the occurrence of the other

Estimate

An approximate calculation

Upper bound

The upper limit of a calculation

Lower Bound

The lower limit of a calculation

Error interval

The margin of error when rounding, usually expressed as an inequality

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

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. By exploring upper and lower bounds students will be able to understand limits of accuracy. This skill will benefit students’ functioning in society.

Create a supportive community:

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

Term 5: Solving equations & Inequalities, Ratio & Proportion, Factors and multiples, Circles

Solving linear equations with brackets and/or fractions.

Solving quadratic equations algebraically and by factorising.

Simultaneous equations.

Proportion and ratio.

Scales and scale diagrams.

Percentage change.

Factors and multiples, including HCF/LCM.

Product of prime factors

Parts of a circle.

The area and circumference of a circle.

  1. Test on: T1, T2, T3 and T4 topics and Equations & inequalities, Ratio & proportion, Factors and multiples, and Circles
Equation

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

Inequality

The relation between two expressions that are greater or less then each other

Surd

An expression containing one or more irrational roots of numbers, such as 2√3, 3√2 + 6

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

Tangent

A line that touches a circle

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

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. 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? When solving mathematical problems students will develop their creative skills. When solving mathematical problems students will develop their creative skills. 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.

Create a supportive community:

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

Term 6: Exams, Powers and roots, Further Circles, Constructions & Loci

Circles: calculating arc length and the area of a sector

Calculations involving powers and roots

Standard ruler and compass constructions: perpendicular bisector, angle bisector, constructing triangles

Solving problems using loci

  1. Test on:

    All material covered throughout Year 10

    1 Calculator paper and 1 non-calculator paper

Iteration

The repetition of a mathematical process applied to obtain successively closer approximations to the solution of a problem

Inequality

The relation between two expressions that are greater or less then each other

Perpendicular bisector

A line which cuts a line segment into two equal parts at 90°

Angle bisector

A line which cuts an angle into two equal parts

Loci

The set of all points that satisfy given conditions

Factor

A number that divides exactly into a given number e.g. the factors of 12 are 1 & 12, 2 & 6, 3 & 4

Multiple

A multiple is a number made by multiplying together two numbers

Prime factorisation

To express a number as the product of its prime factors

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

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 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. 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.. .