# Mathematics

**Year 7**

Maths is a subject that incorporates many skills in order to apply these skills to problem solving. It is important that every child leaves year 7 with a good basis to build on for the next four years in order to gain a good grade at GCSE.

We feel that it is essential to be confident with the manipulation of numbers. With this in mind, all year 7 students will have a learning focus of core skills teaching. They will be regularly assessed in order to ensure that they are making progress at their own level. The assessments will take the form of day to day marking and formal tests; the results of these tests will inform the teaching of individuals and of the class. Students will have the opportunity to learn using resources to aid their understanding of number concepts.

The core skills learning incorporates the following:

- understand and use negative numbers in context of temperature
- read and write numbers that include zero as a place holder
- find the value of the digits in a number
- multiplication – moving from arrays to grid method
- division by grouping
- missing numbers – inverse operations +-x÷ (understand that = represents equality)
- solve two step problems - money
- Formal written methods for all 4 operations (+ and – decimals)
- use known facts and place value to answer simple calculations involving decimals
- multiply and divide numbers by 10, 100, 1000
- round and order decimal numbers
- read time
- solve two step problems –measures
- fractions of a shape
- proof by contradiction (always sometimes never)
- understand and use negative numbers
- solve multi step problems
- find fraction/decimal and % of numbers
- equivalent fractions/percentages/decimals
- algebra – forming expressions/substitution
- round numbers to decimal places and significant figures
- BIDMAS

The core skills will be taught and assessed for the first two modules. From module 3 onwards, other concepts will be taught and assessed alongside the core skills teaching. The normal scheme of work follows the following structure:

M**e, Myself and I**

Aim: For pupils to collect data on themselves and others and use the data over a series of lessons to explore topics within Handling Data. By the end of the topic pupils can produce a poster about themselves with comparisons between their peers.**Farmer**

Aim: For pupils to gain basic understanding on the difference between perimeter, area and volume. To recognise and discuss difference between 2D shapes. To calculate the perimeter for most shapes and calculate the area of a rectangle and triangle. This can be done using the theme of farmers and their fields and how much yield they create etc.**Food (Chocolate/Pizza)**

Aim: For pupils to use food as a visual representation of fractions and how things are split/shared. For pupils to think about numbers in terms of out of 100. To start to recognise the relationship between fractions, decimals and percentages.**Tiles and Matchsticks**

Aim: For pupils to recognise and describe sequences. To use kinaesthetic resources to show patterns and develop thinking onto introducing algebra. For pupils to identify sequences in real life contexts.**Number Shuffling**

Aim: A very basic introduction into Algebra with the main emphasis on reverse operations of each other.**Turn, turn, turn**

Aim: For pupils to learn about angles and notation used when dealing with angles. Pupils to develop this onto looking at transformations in a basic sense.**Take a chance**

Aim: For pupils to understand the basic concept of probability. Pupils over the course of the unit will design and create their own fair ground game with outcomes and probabilities. Last lesson of the session will be run as a fairground.**Guess what**

Aim: For pupils to make approximations and estimations for numbers. Pupils should be introduced to rounding and significant figures through the unit. This can be used in the context of money, populations etc**Trains, Planes & Automobiles**

Aim: For pupils to fully understand the basics of dealing with time, timetables, distance maps and everyday tables/graphs.**Blocks, Balls & Ice Cream**

Aim: For pupils to look at 3D shapes and identify features on 3D shapes. To use nets to create 3D shapes and identify 3D shapes through nets. Spend last lesson in computer room using webpage for naming types of 3D shapes to create poster.**Twist & Flip**

Aim: Having looked at a basic introduction into transformations early in the year, this is a chance to recap their knowledge and develop their understanding further into transformations.**Shopping**

Aim: To use their knowledge from previous units and apply it to the topic of shopping. Introduce more percentage work and introduce ratio. Make sure that some lessons are delivered using a calculator and pupils are encouraged to buy their own.**Battleships**

Aim: For pupils to be able to plot and identify co-ordinates in all 4 quadrants. Introduce and discuss the lines of y=a and x=b.**Measure It**

Aim: For pupils to understand the difference between metric and imperial measure. To be able to convert between measure and understand the difference between length, mass and capacity.**What’s Special about me?**

Aim: For pupils to learn about factors, multiples, primes, squares, cubes and roots. Pupils should be identify numbers and their qualities by the end of the unit and discuss with peers what’s special about them.**Year 8**

At the beginning of year 8 students are placed in sets based on a combination of their year 7 tests results and teacher assessments. By the start of year 8 students will be familiar with completing their APP sheets which are designed to track their progress through each year at the Academy.**Topic Examples of student learning objectives by level**

Addition and subtraction

I can use mental methods of addition and subtraction in 2 digit numbers (L3)

I can add and subtract decimal numbers up to 2 decimal places (L4)

I can add and subtract decimal numbers with more than 2 decimal places (L5)

I can add or subtract negative numbers from a starting number (L6)

I can add and subtract mixed numbers and simplify my answer (L7)

Shapes and angles

I can name 2-D and 3-D shapes (L3)

I can accurately measure and draw angles using a protractor (L4)

I can identify and list the properties of quadrilaterals (including kites) (L5)

I can use the properties of quadrilaterals and triangles to find missing angles (L6)

I can use Pythagoras’ theorem to find a missing side in a right-angled triangle (L7)

Manipulating algebra

I can use letter symbols to represent numbers in algebra (L3)

I can write simple expressions to represent information e.g. 2a + 3b (L4)

I can substitute two or more numbers into an algebraic expression (L5)

I can expand and factorise single brackets (L6)

I can substitute values into quadratic and cubic expressions (L7)

**Term 1 assessment**

During the last week of the first term students sit both a calculator and non-calculator based solely on the topics covered in the first term. This is then recorded on their student progress sheet and allows students to see their progress over the first three modules.**Term 2**

Topic Examples of student learning objectives by level

Multiplication and division I can solve whole number problems up to 12 x 12 involving multiplication or division, including remainders (L3)

I can read worded problems and decide whether to use multiplication or division (L4)

I can check my answers by estimating to the nearest whole number (L5)

I can simplify multiplication of fractions by first cancelling common factors (L6)

I can multiply and divide powers of a number using laws of indices e.g. 5² x 5³ = 55 (L7)

Representing Data

I can construct bar charts and pictograms (L3)

I can group data in equal class intervals (L4)

I recognise that a change in one variable can affect another (L5)

I can construct and interpret pie charts and frequency polygons (L6)

I can use a line of best fit to interpolate/extrapolate (L7)

Sequences and Graphs

I can read values from simple diagrams and graphs (L3)

I can recognise simple number patterns (L4)

I can find the coordinates of the point of intersection of two lines (L5)

I can follow an algebraic rule to find a sequence of numbers (L6)

I can draw quadratic graphs by generating a table of values and plotting points (L7)**Term 2 assessment **

Students sit a National standards test which compromises of a calculator paper, a non-calculator paper and a mental arithmetic test. These tests give an accurate level which reflects a pupils overall mathematical ability. The results from this are also recorded on the student progress sheet and show the progress made since the end of Year 7.**Term 3Topic Examples of student learning objectives by level**

Properties of numbers and accuracy

I can define odd and even numbers (L3)

I can find factors and multiples of a number (L4)

I understand how to apply BIDMAS e.g. work out 12 x 5 – 24 ÷ 8 (L5)

I can write a number as a product of its prime factors (L6)

I can find the reciprocal of whole numbers, fractions and decimals (L7)

Construction and measures

I can accurately draw and measure straight lines with a ruler (L3)

I can use various metric units of measure (L4)

I can make sensible estimates of length, mass, capacity and time (L5)

I can convert between less familiar units e.g. cm³ to litres (L6)

I can construct an accurate scale drawing from a sketch (L7)

**Term 3 assessment**

During the last week of the third term students sit both a calculator and non-calculator based solely on the topics covered in this term. This is then recorded on their student progress sheet.**Term 4Topic Examples of student learning objectives by level**

Perimeter, area and volume

I can accurately draw and measure straight lines with a ruler (L3)

I can find the perimeter of simple shapes (L4)

I can find the surface area of a cuboid by counting squares (L5)

I can calculate the volume of a cuboid using length x width x height (or equivalent) (L6)

I can find the volume and surface area of a cylinder (L7)

Fractions and decimals

I can use decimal notation in problems with money (L3)

I can understand decimal numbers in real life problems (L4)

I can use a calculator to add, subtract, multiply and divide fractions (L5)

I can convert between mixed numbers and improper fractions (L6)

I can apply my knowledge of fractions and decimals to solve real-life problems (L7)

**Term 4 assessment**

Students sit a National standards test which compromises of a calculator paper, a non-calculator paper and a mental arithmetic test. These tests give an accurate level which reflects a pupils overall mathematical ability. The results from this are also recorded on the student progress sheet and show the progress made since the end of term 2.

**Term 5**

Topic Examples of student learning objectives by level

Topic Examples of student learning objectives by level

Averages

I can understand information from simple charts (L3)

I can understand how to use range and mode (L4)

I can use a stem and leaf diagram to sort data (L5)

I can find a missing value in a set of data if the mean is known (L6)

I can draw a cumulative frequency curve and find the median value (L7)

Transformation and symmetry

I can reflect a 2-D shape in a mirror line, including using isometric paper (L3)

I can describe the rotational symmetry of a 2-D shape (L4)

I can make the centre of rotation on a diagram of an object that has been rotated (L5)

I can rotate a 3-D object and draw its image on isometric paper (L6)

I can enlarge objects using fractional scale factors (L7)

**Term 5 assessment**

During the last week of the fifth term students sit both a calculator and non-calculator based solely on the topics covered in this term. This is then recorded on their student progress sheet.**Term 6Topic Examples of student learning objectives by level**

Fractions, percentages and ratios

I understand the a fraction is ‘part of a whole unit’ (L3)

I can express a small integer as a fraction of a larger integer (L4)

I can simplify a ratio and find equivalent ratios (L5)

I can share an amount in a given ratio (L6)

I can interpret map scales or model scales given as a ratio (L6)

Solving equations and inequalities

I can recognise terms, expressions and equations in algebra (L3)

I can use simple formulae given in words (L4)

I can construct and use simple formulae using symbols (L5)

I can find the solution to a problem by writing an equation and solving it (L6)

I can solve simultaneous equations, algebraically and graphically (L7)

Probability

I can recognise that some events are more likely than others (L3)

I can represent key words for probability on a number line (L4)

I can find probabilities for event described in tables, charts and graphs (L5)

I can play simple probability games and predict outcomes (L6)

I can estimate a probability by using data collected about an event (L7)

**Term 6 assessment**

Students sit their end of year assessment which compromises of a calculator paper, a non-calculator paper and a mental arithmetic test. These tests cover all of the work taught during the course of year 8. An accurate level is then calculated which reflects a pupils overall mathematical ability. The results from this are also recorded on the student progress sheet and show the progress made over the course of the year.

The results from this test along with other assessments carried out through the course of the year help determine which set would be most appropriate for each individual student.

At the beginning of year 9 students are placed into ability sets based on a combination of their Year 8 test results and teacher assessments. During Year 8 students would have completed APP unit stickers at the end of each module that has allowed students to monitor their progression throughout the year. This Academic year 2014-5 students will be completing a revised APP sheet to monitor their progress.

**Term 1 Students study the following topices to the appropriate leel based on their ability.****Topic Examples of student learning objectives by level**

Fractions, decimals, multiplication and division

I can use written methods for multiplying whole numbers up to 3 digits times 2 digits (L4)

I can arrange decimals and fractions into ascending and descending order (L5)

I can check my answers by estimating to the nearest whole number (L5)

I can multiply by 0.1, 0.01 and 0.001 and I know that 13.5 ÷ 0.5 is equal to 135 ÷ 5 (L6)

I can add, subtract, multiply and divide fractions without a calculator (L6)

I can divide fractions and mixed numbers (C)

Manipulating algebra

I can simplify algebraic expressions by adding and subtracting like terms (L4)

I can use brackets in expressions (L5)

I can expand and factorise single brackets (L6)

I can collect like terms where each term may consist of more than one letter e.g. 3ab + 4ab (L6)

I can substitute values into quadratic and cubic expressions (L7)

I can multiply out expressions with brackets such as y(3y – 8) (C)

Representing data and correlation

I can collect and record data using tally tables and frequency tables (L4)

I can plot a scatter graph from a set of data (L5)

I can read information given in a two-way table (L5)

I can design a suitable question for a questionnaire and understand about bias in sampling (L6)

I can represent data as a time series and identify trends in data over time (L7)**Term 1 Assessment** - During the last week of the first term students will sit both a calculator and non-calculator paper based solely on the topics covered in the first term. This is then recorded on their student progress sheet and allows students to see their progress over the first three modules.**Term 2****Topic Examples of student learning objectives by level**

Angles and circles

I can count the vertices, faces and edges of 3-D shapes (L4)

I can identify and list the properties of quadrilaterals (including kites) (L5)

I know that angles on a straight line add up to 180˚ and that angles about a point add up to 360 ˚ and can use this to find missing angles (L5)

I know that the sum of the exterior angles of any polygon is 360˚ (L6)

I can identify congruence in similar triangles and give reasons (L7)

I can solve problems involving circles such as finding the perimeter or area of a semicircle (C)

Fractions, percentages and ratios

I can use a fraction wall to compare the size of fractions and find equivalent fractions (L4)

I can reduce a fraction to its simplest form (L5)

I can increase or decrease an amount by a given percentage (L6)

I can share an amount in a given ratio (L6)

I can find a missing value in a ratio e.g. Ann and Bob shared their lottery win in the ration 2:3, if Ann got £110 how much did Bob get? (L7)

I can use exchange rates to convert between different currencies (C)

Constructions

I can make 3-D models from multi-link cubes and count faces, edges and vertices (L4)

I can make an isometric drawing of cuboids and shapes made from cuboids (L5)

I can make an isometric drawing of cuboids and shapes made from cuboids (L5)

I can use a ruler and compass to construct accurate triangles and other 2-D shapes given information about their sides lengths and angles (L6)

I can find the Locus of an object moving using a rule (L7)

I can construct angles of 60º and 90º and the bisector of an angle (C)

Project 1 – Paradise in Pembroke

A Functional skills activity that allows students to investigate a mathematical problem. This allows students to puts they’re learning, skills and understanding of Term 4 modules into practice to enable them to answer the problem.

**Term 2 - **Assessment

Students sit a National Standard test which compromises of a calculator paper, non-calculator paper and a mental arithmetic test. These test give an accurate level which reflects a pupils overall mathematical ability. The results from this are recorded on the student progress sheet and show the progress made since the end of Year 8.**Term 3**

Topic Examples of student learning objectives by level

Averages

I can collect and record data using tally tables and frequency tables (L4)

I can calculate the mean, median, mode and range for a set of numbers (L5)

I can find averages from graphs and diagrams, including pie charts (L5)

I can calculate averages from data presented in a stem and leaf diagram (L6)

I can calculate the mean, median, mode and range for a set of numbers including negatives (L7)

I can find the mean, median class and modal class for grouped data (C)

Indices, factors and multiples

I can find squares, cubes, square roots and cube roots of numbers using a calculator (L4)

I can recognise and define prime numbers (L5)

I can classify integers into different categories e.g. multiples of 5, factors of 12 etc. (L5)

I can calculate the HCF and LCM of two numbers by using lists (L6)

I know that 0 does not have a reciprocal and that a number multiplied by its reciprocal is 1 (L7)

I can write a number as a product of prime factors (C)

**Term 3 - **Assessment

During the last week of the third term students sit both a calculator and non-calculator paper based solely on the topic covered in this term. This is then recorded on their student progress sheet.**Term 4Topic Examples of student learning objectives by level**

Sequences and graphs

I can read and plot positive coordinates (L4)

I can find rules for sequences and write them down in words (including Fibonacci) (L5)

I can draw graphs of the form y=mx+c by generating a table of values and plotting points (L6)

I can solve real-life problems involving patterns and sequences e.g. tiles, match-sticks (L6)

I can draw quadratic graphs by generating a table of values and plotting points (L7)

I can use and understand coordinates in three dimensions (C)

Transformations

I can shade a shape with two or more lines of symmetry to make a symmetrical pattern (L4)

I can describe the rotational symmetry of a 2-D shape (L4)

I can describe the rotational symmetry and line symmetry of a 2-D shape (L5)

I can enlarge an object by a positive scale factor, including when given the centre of enlargement (L6)

I can find missing lengths in similar shapes following an enlargement (L7)

I can describe fully a single transformation (C)

Project 2 – 3D jigsaw

A Functional skills activity that allows students to investigate a mathematical problem. This allows students to puts they’re learning, skills and understanding of Term 4 modules into practice to enable them to answer the problem.

**Term 4 - Assessment **

Students sit a National Standard test which compromises of a calculator paper, non-calculator paper and a mental arithmetic test. These test give an accurate level which reflects a pupils overall mathematical ability. The results from this are recorded on the student progress sheet and show the progress made since the end of term 2.**Term 5Topic Examples of student learning objectives by level**

Solving equations

I can find missing numbers in calculations e.g. 5 x ? = 20 (L4)

I can find rules and write them down using letters e.g. if Tina’s age is n years then in three years time Tina’s age will be n + 3 years (L5)

I can solve simple two-step equations including brackets e.g. 2y + 11 = 17(L5)

I can solve linear equations with unknown on both sides e.g. 75 + 2t = 100 – 2t (L6)

I can solve complex equations by trial and improvement (L7)

I can solve more complex linear equations such as 3x – 12 = 2(x – 5) (C)

Perimeter, area, volume and error

I can find the area of a shape by counting squares (L4)

I can calculate the area of a rectangle using base x height (or equivalent) (L5)

I can calculate the area of compound shapes made from rectangles and triangles (L5)

I can calculate the circumference and area of a circle (L6)

I can calculate areas using formulas e.g. for a trapezium (L7)

I can calculate volumes of prisms and cylinders (C)

**Term 5 - Assessment **

During the last week of the third term students sit both a calculator and non-calculator paper based solely on the topic covered in this term. This is then recorded on their student progress sheet.**Term 6Topic Examples of student learning objectives by level**

Pythagoras and trigonometry

I can round a number to one significant figure (E)

I can use Pythagoras’ theorem to find a missing side in a right-angled triangle (L7)

I can use Pythagoras’ Theorem to find the length of a line segment on a co-ordinate grid (L7)

I can use Pythagoras’ theorem to decide whether a triangle has a right-angle (C)

I can use Pythagoras’ theorem to find the height of an isosceles triangle (C)

I can find the midpoint of a line segment (C)

Probability

I can understand events described in words and in pictures e.g. spinners (L4)

I can write down probabilities of events that may or may not happen (L5)

I can find probabilities for event described in tables, charts and graphs (L5)

I can identify all outcomes when dealing with 2 events using diagrams and tables (L6)

I can estimate how many times an event will happen by multiplying the probability of the event by the number of trials e.g. if I roll a dice 60 times I expect 10 sixes (L7)

I can use relative frequency to compare the outcomes of experiments (C)

Distance – Time graphs and proof

I can interpret distance-time graphs and solve simple speed problems (6)

I can find time or distance using the formula S = D/T (6)

I can complete a distance-time graph from given information (6)

I can calculate complex average speeds from distance-time graphs (7)

I can understand the difference between demonstration and proof (7)

I can discuss and interpret graphs modelling real situations (8)

Project 3 - … in the middle

A Functional skills activity that allows students to investigate a mathematical problem. This allows students to puts they’re learning, skills and understanding of Term 4 modules into practice to enable them to answer the problem.

**Term 6 - Assessment**

Students sit their final end of year assessment which compromises of a calculator paper, non-calculator paper and a mental arithmetic test. These tests cover all the work taught during the course of Year 9. An accurate level is then calculated which reflects a students overall mathematical ability. The results from this are also recorded on their student progress sheet and show the progress made over the course of the year.

The results for this test along with other teacher assessments carried throughout the course of the year help determine which GCSE set would be most appropriate for each individual students in Year 10.

**Key Stage 4**

Course Title: Mathematics

Qualification: GCSE

Awarding Body: Edexcel

Description of Course

The course will:

- Develop mathematical skills using a variety of techniques, including practical and investigational methods;
- Use and apply skills and knowledge relating to number, algebra, shape, space and measures and handling data.

**Key Stage 5**

Course Title: Mathematics

Qualification: AS/A2

Awarding Body: Edexcel http://www.edexcel.com/quals/gce/gce08/maths/Pages/default.aspx

Examination– 100% Coursework – 0%

Pre-requisite Recommendations:

- GCSE Mathematics grade B or above.
- Students must have a passion for Mathematics and have a degree of perseverance and an ability to work well independently.