More about Maths (Foundation)

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.

- Test on: Expressions, Calculations & Angles

Power

Multiply out the brackets

Put an algebraic expression into brackets

A four sided 2D shape

A 2D shape with straight sides

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

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

Alternate angles in parallel lines are equal

Corresponding angles in parallel lines are equal

- Spiritual
- Moral
- Social
- Cultural

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.

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

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.

- Test on: T1 topics and Data Handling, Fractions, Decimals and Percentages

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

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

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

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

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

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

The difference between the greatest and least values

The total of all the frequencies in a set of data

The difference between the upper quartile and the lower quartile

As one quantity increases so does the other

As one quantity increases the other decreases

- Spiritual
- Moral
- Social
- Cultural

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.

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

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.

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

A mathematical relationship or rule expressed in symbols

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

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

The act of moving or changing a shape

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

The action of rotating about an axis or centre

The action of enlarging a shape or solid

The action of moving a shape along and up or down

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

The amount of surface that a shape has

- Spiritual
- Moral
- Social
- Cultural

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.

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

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.

- Test on: All material covered in this term and previous terms
1 Non-Calculator paper and 1 Calculator paper

Experimental probability

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

A list of all possible probability events

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

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

An approximate calculation

The upper limit of a calculation

The lower limit of a calculation

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

- Spiritual
- Moral
- Social
- Cultural

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.

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.

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

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

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

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

The distance round the outside of a circle

The distance from the centre to the edge of a circle

The distance across a circle through the centre

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

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

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

A line that touches a circle

- Spiritual
- Moral
- Social
- Cultural

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.

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

- Test on:
All material covered throughout Year 10

1 Calculator paper and 1 non-calculator paper

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

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

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

A line which cuts an angle into two equal parts

The set of all points that satisfy given conditions

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

A multiple is a number made by multiplying together two numbers

To express a number as the product of its prime factors

- Spiritual
- Moral
- Social
- Cultural

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.