Year 7 — Maths

Term 1: Introduction to Algebra , Positive & Negative Numbers & Perimeter, Area & Volume

This topic will involve students in learning the rules of algebra. They will learn how to write algebraic expressions, simplify expressions and substitute values into formulae.

Students will learn about negative numbers in real life and carry out calculations incorporating positive and negative numbers.

Students will find the area of rectangles, triangles, parallelograms, trapeziums and compound shapes. Students will calculate the surface area and volume of cubes and cuboids.

50 minute assessment on T1 topics (Non calculator)

Expression

An expression is one or a group of terms and may include variables, constants, operators and grouping symbols.

Substitute

Replacing letters (variables) with numbers.

Term

One of the numbers in a sequence.

Variable

A quantity that can change or vary, taking on different values.

Coefficient

A number which multiplies a variable.

Like Terms

Are exactly the same except for their coefficients.

Simplify

To remove brackets, unnecessary terms and numbers.

Formula (formulae)

A mathematical rule written using symbols, usually as an equation describing a certain relationship between quantities.

Greater

More than.

Less

Smaller than.

Negative

A number less than zero, written with a minus sign.

Positive

A number greater than zero.

Brackets

A pair of symbols used to enclose sections of a mathematical expression. Whatever is inside brackets needs to be done first.

Subtract

To take one quantity away from another.

Area

The size a surface takes up, measured in square units.

Length

Distance from one end to the other.

Perimeter

Distance around the outside of a shape, calculated by adding the length of all sides together.

Formula

A mathematical rule describing a relationship between two or more quantities.

Rectangle

A rectangle is a quadrilateral with four right angles and opposite sides equal.

Square

A square is a quadrilateral with four equal sides and four right angles.

Width

Distance across from side to side.

Compound shape

A shape made up from a combination of shapes.

Capacity

The amount a container or something can hold.

Cube

A cube is a three-dimensional solid that has six square faces.

Cuboid

A 3D shape with 6 rectangular faces.

Height

The measurement from top to bottom.

Litre

A metric unit for measuring capacity or fluid volume.

Volume

Amount of space occupied by an object.

Dimension

The measurable size of something.

Metric

A decimal system of measurement based on 10.

  • Spiritual
  • Moral
  • Social
  • Cultural

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. Learning about negative numbers benefits our students’ functioning in society through bank balances and temperatures. When solving mathematical problems students will develop their creative skills. Students enjoy solving real life problems involving area and perimeter.

Create a supportive community:

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

Term 2: Fractions, Working with Numbers, Statistics

Students will find equivalent fractions, compare and order fractions, and add and subtract fractions. They will convert between mixed numbers and improper fractions.

Students will use square numbers and square roots, round numbers using decimal places and significant figures, and carry out non-calculator methods of multiplication and division to solve problems.

Students will find and interpret the mean, median, mode and range. They will use discrete and continuous data and read and interpret statistical diagrams, including grouped frequency tables.

50 minute assessment on T1 and T2 topics (Non-calculator)

Equivalent

Fractions with the same value.

Denominator

The bottom number in a fraction showing the number of parts the whole is divided into.

Numerator

Number above the line of a fraction, showing the number of parts of the whole.

Simplify

To simplify a fraction to its simplest form: to reduce the numerator and denominator in a fraction to the smallest numbers possible.

Convert

The process of changing quantities to equivalent amounts in a different system.

Improper fraction

A fraction larger than one whole. The numerator is larger than the denominator.

Mixed numbers

A number written as a whole number with a fraction.

Squaring

Multiplying a number by itself

Square number

A square number is the answer when a whole number has been multiplied by itself.

Square root

A number which when multiplied by itself gives the original number.

Decimal places

The number of digits to the right of the decimal point.

Rounding

To change a number to a more convenient value.

Order of operations

The order in which mathematical operations should be done.

Remainder

Amount left over after dividing a number, for example, 9 ÷ 4 leaves a remainder of 1.

Quotient

The number resulting from dividing one number by another.

Conversion

The process of changing quantities to equivalent amounts in a different system.

Metric

A decimal system of measurement based on 10.

Operation

Mathematical procedure or process used to work something out.

Interpret

Explain the meaning of.

Compare

Note the similarity or difference between.

Average

An average is a measure of central tendency of a data set.

Mode

A type of average. The most common value in a set of data.

Median

A type of average which is the middle value of an ordered set of data values.

Range

The difference between the lowest and highest values in a data set.

Outlier

A value far away from most of the rest in a set of data.

Bar chart

A graph using bars to show quantities or numbers so they can be easily compared.

Pictogram

A graph which uses pictures to show data.

Grouped data

Data that has been ordered and sorted into groups called classes, often displayed in a frequency table.

Line graph

Uses lines to join points which represent a data set.

Pie chart

A graph using a divided circle where each section represents a percentage of the total.

Frequency

The number of times a particular event or item appears in a set of data.

Sample

A section of a whole group.

Tally chart

A record of an amount using small lines.

Mean

Usually called the average and may be called the arithmetic mean. The mean is the total of all the scores or amounts, divided by, how many scores or amounts there were.

  • Spiritual
  • Moral
  • Social
  • Cultural

Develop the individual:

Skills such as confidence with numeracy and rounding benefit our students’ functioning in society. 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).

Create a supportive community:

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

Term 3: Sequences & Functions, Decimal Numbers, Angles in Triangles, Quadrilaterals & Parallel Lines

Students will explore sequences and rules, find missing terms and nth terms, and use functions and mappings.

Students will learn more about decimals; they will order decimals and complete calculations involving decimals. They will learn how to estimate calculations.

Students will delve deeper into geometrical reasoning: they will measure and draw angles, calculate angles in different types of triangles and quadrilaterals and explore angles in parallel lines. They will use geometrical reasoning to solve problems.

50 minute assessment on T1, T2 and T3 topics (Non-calculator)

Function

A mathematical relationship from a set of inputs to a set of outputs.

Term

One of the numbers in a sequence.

Sequence

Ordered sets of numbers, shapes or other mathematical objects, arranged according to a rule.

Linear/arithmetic

A common number sequence where the same value is added each time.

Geometric

A number sequence where successive numbers are multiplied by the same value each time.

Square

To square a number means to multiply it by itself.

Order

Arrangement according to size, amount or value.

Place value

The value of a digit depending on its place in a number. In the decimal system, each place is 10 times bigger than the place to its right.

Inverse

The opposite or reverse operation. Addition and subtraction are inverse operations and multiplication and division are inverse operations.

Estimate

To make an approximate calculation, often based on rounding.

Acute

An angle measuring less than 90 degrees.

Obtuse

Any angle between 90º and 180º.

Reflex

Any angle between 180º and 360º.

Degrees

A unit for measuring the size of an angle, symbol º.

Protractor

An instrument used to measure angles in degrees.

Right angle

An angle measuring 90º.

Point

A defined position in space.

Straight line

A line with no bends or curves, the shortest distance between two points.

Calculate

To work something out.

Vertically opposite

Pair of angles directly opposite each other, formed by the intersection of two straight lines.

Isosceles

Triangle with two equal sides and two equal angles.

Triangle

Two dimensional shape with three edges and three vertices.

Quadrilateral

Two dimensional shape with four edges and four vertices.

Diagonal

A line joining two non-adjacent vertices of a polygon.

Parallel lines

Equidistant lines that are the same distance apart, never touching.

Perpendicular lines

Two lines at right angles to each other.

  • Spiritual
  • Moral
  • Social
  • Cultural

Develop the individual:

Mathematics provides opportunities for students to develop a sense of “awe and wonder”. Mathematical investigations produce beautiful elegance in their surprising symmetries, patterns or results. Students enjoy exploring patterns and sequences, making predictions and generalisations. Numerical fluency and estimation skills will benefit students’ functioning in society. What does my shopping cost? Which is the better value for money? Approximately how long will it take to get to another location? . 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. The topic of angles provides opportunities for students to develop a sense of “awe and wonder” when they explore the relationships between angles in quadrilaterals and parallel lines.

Create a supportive community:

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

Term 4: Co-ordinates and Graphs, Percentages & Probability

Students will plot co-ordinates in all four quadrants and draw graphs from given equations. They will use graphs that represent real life situations.

Students will convert between fractions, decimals and percentages. They will calculate percentages with and without a calculator and find percentage increases and decreases.

Students will use probability scales, find the probability of combined events and calculate experimental probability.

50 minute assessment on T1, T2, T3 and T4 topics (Non-calculator)

Axis (axes)

The reference lines on a graph.

Origin

The point of intersection of the x and y axis on a coordinate or Cartesian graph with the coordinates (0,0).

Graph

A visual diagram used to represent statistical information or functions and equations.

Straight-line graph

A graph of a linear function, written in the form y=mx+c.

Conversion graph

A line graph used to convert one unit to another.

Equation

A mathematical statement containing an equals sign, to show that two expressions are equal.

Decrease

Get smaller in size, number or quantity.

Increase

Get larger in size, number or quantity.

Percentage

A percent or percentage is a fraction expressed as a number out of 100 followed by the % symbol.

Random

Without any particular order or pattern.

Chance

The likelihood that a particular outcome will occur.

Event

One outcome in a probability experiment.

Probability

The chance that an event will occur.

Outcome

The result of a single trial of a probability experiment.

Likely

Will probably happen.

Unlikely

Will probably not happen.

Certain

Will definitely happen.

Impossible

Will definitely not happen.

Biased

Unfairly prejudiced for or against someone or something.

Fair

Without bias.

Theoretical probability

The number of ways that the event can occur, divided by the total number of outcomes.

  • Spiritual
  • Moral
  • Social
  • Cultural

Develop the individual:

Competance with percentages benefits our students’ functioning in society: sales, interest rates, taxe? Competance with percentages benefits our students’ functioning in societ? 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 chanc? A knowledge of probability will benefit students’ functioning in society as they will understand bias and the chance of an event happenin?

Create a supportive community:

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

Term 5: Symmetry, Equations & Interpreting Data

Students will learn about line symmetry and rotational symmetry. They will reflect, rotate shapes and tessellate shapes.

Students will solve simple and more complex equations. They will learn to form equations in order to solve problems.

Students will use charts and diagrams to interpret data, including the use of pie charts. They will analyse sets of data by comparing averages.

50 minute assessment on T1, T2, T3, T4 and T5 topics (Non-calculator)

Line of symmetry

A line which divides a shape in to two equal parts which are mirror images of each other.

Reflect/reflection

A geometric transformation resulting in a mirror image.

Rotational symmetry

The number of times a shape will fit exactly on to itself in a 360º turn.

Image

The result of a transformation.

Object

The original shape which is to be transformed.

Tessellation

A pattern of shapes that fits together without any gaps.

Equation

A mathematical statement containing an equals sign, to show that two expressions are equal.

Solve

Find numerical values for all the variables that make the equation true.

Inverse

The opposite or reverse process.

Operation

Mathematical procedure or process used to work something out.

Frequency

The number of times a particular event or item appears in a set of data.

Percentage

A percent or percentage is a fraction expressed as a number out of 100 followed by the % symbol.

Pie chart

A graph using a divided circle where each section represents a proportion of the total.

Sector

Section of a circle, bounded by two radii and an arc.

Data

A collection of information.

Range

The difference between the lowest and highest values in a data set.

Mean

Usually called the average and may be called the arithmetic mean. The mean is the total of all the scores or amounts, divided by, how many scores or amounts there were.

Questionnaire

A set of printed or written questions with a choice of answers, devised for the purposes of a survey or statistical study.

Statistical survey

A method of collecting a sample of data by asking people questions.

  • Spiritual
  • Moral
  • Social
  • Cultural

Develop the individual:

Mathematics provides opportunities for students to develop a sense of “awe and wonder? Mathematical investigations produce beautiful elegance in their surprising symmetries, patterns or result? Students will learn about line symmetry and rotational symmetr? They will reflect, rotate shapes and tessellate shape? Students develop algebraic fluency throughout the curriculu? Algebra is a uniquely powerful language that enables students to describe and model situation? 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 societ? Students will understand how to interpret graphs and chart?

Create a supportive community:

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

Term 6: 3D Shapes & Ratio

Students will draw and construct 2D representations of 3D solids using isometric dotty paper. They will create nets of 3D solids and explore the relationship between faces, edges and vertices.

Students will learn to use ratio notation. They will simplify ratios, share a quantity into a given ratio, and solve problems involving ratios.

They will convert between ratios and fractions.

End of year examination - two 50 minute assessments on all topics taught in year 7 (Paper 1 non calculator, Paper 2 calculator)

3D

Flat surface of a three-dimensional shape.

Prism

A solid three-dimensional shape with a constant cross section.

Tetrahedron

A triangular pyramid.

Construct

Draw accurately using a ruler, compasses and protractor.

Net

A flat shape which can be folded up into a three-dimensional solid.

  • Spiritual
  • Moral
  • Social
  • Cultural

Develop the individual:

When solving mathematical problems students will develop their creative skills. Students enjoy solving real life problems involving 3D ratios. Students will draw and construct 2D representations of 3D solids using isometric dotty paper. They will create nets of 3D solids. When solving mathematical problems students will develop their creative skills. Students enjoy solving real life problems involving 3D shapes.

Create a supportive community:

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