What is numeracy?
Numeracy is a proficiency which is developed mainly in mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables.
At Debden Park High School we believe that numeracy is a fundamental life skill. It is our aim to develop an ethos in which numeracy is upheld as a key to success at school, further education or training and in society. Numeracy helps students to make sense of the world in which they live and make wise financial decisions in the future. Building on experiences, it encourages thinking and reasoning skills to develop and helps to improve confidence to tackle situations that arise. The mathematics curriculum requires a deeper understanding to allow students to be able to use and apply skills and concepts. This improves students’ ability to solve problems and progress to harder skills that rely on the students’ understanding of prior learning. It is important to consider the impact of students’ mathematical knowledge, understanding and skills on outcomes across the curriculum.
Aims of the DPHS numeracy policy:
To raise the profile of numeracy across the school.
To support the transfer of pupils’ knowledge, skills and understanding between subjects by ensuring consistency of practice including methods, vocabulary and notation.
Make numeracy teaching an overt part of every curriculum area where it naturally arises
Roles and responsibilities
As a department:
Create a positive and attractive environment which celebrates numeracy.
To ensure pupils meet the expectations of a year 6 pupil when they enter in year 7 and meet or exceed the expectations of a year 9 pupil when they complete KS3 according to teacher and summative assessments.
Run the Numeracy 10410 (Maths mastery questions) to fill gaps in pupils’ basic mental calculation strategies and also to empower them with the numeracy skills and fluency required to fully access GCSE Maths concepts when they move to Key Stage 4 study.
Identify pupils who require additional intervention to plug numeracy gaps, including those who are eligible for numeracy catch-up funding. Intervention is delivered to students through an intervention programme led by maths teachers. (the intervention list is compiled by the KS3 maths lead)
Run the Times Tables Rock Stars programme in Year 7 (and in other year groups where necessary) to improve pupils’ speed and accuracy in recalling their times tables, an essential skill to free up working memory to solve other problems.
Identify pupils who require additional support to learn their times tables effectively and promote these in lessons
Seek opportunities to use topics and examination questions from other subjects in mathematics lessons.
Be aware of the mathematical techniques used in other subjects and provide guidance and training to other departments so that a sound, coherent and consistent approach is used in all subjects, using preferred methods.
Provide information about common misconceptions and errors which may occur during teaching of specific topics.
Provide guidance to other departments on what numeracy skills pupils are expected to have acquired by any given stage, so that teachers know whether a skill needs teaching for the first time or reinforcing. For example, Science teachers teach graph skills in Year 7so, as a department, we have also adapted our SOW so that students are exposed to graphs in maths first so this can then be applied in science..
Class Teachers
All staff have high expectations that all children can achieve their full potential. Provide opportunities for using cross curricular mathematical techniques. Provide examples of numeracy in everyday situations. Schemes of Work to have a numeracy focus where relevant.
KS3 Coordinator (Madam Everard - louisa.everard@dphs-tkat.org)
Any queries regarding KS3 will be the responsibility of Madam Everard who leads any SOW changes, assessments and set changes. In regards to numeracy her aims are:
To ensure that the KS3 scheme of work exploits opportunities to improve mathematical understanding.
To develop numeracy events for Year 7 and Year 8; cross curricular days, activities with external companies (e.g. puzzle company)
To develop a clear programme of numerical activities for students.
To work with the primary liaison in mathematics to ensure that the primary mathematics curriculum is used to ensure progress and continuity is maintained during transition.
To be a champion for numeracy; assemblies, displays, maths days and parents’ consultation evenings.
To provide professional development for staff for mathematics to ensure confident delivery of mathematical skills and concepts across the curriculum.
To identify mathematical techniques which can be used across the school (e.g. in Science)
To ensure that the mathematical department has a calculator policy for numeracy, which all staff can use consistently across the curriculum.
To ensure that a strategic action plan to improve numeracy is included within the mathematics action plan.
To coordinate the implementation of numeracy activities at times outside of lessons.
Primary liaison & transition co-ordinator
(Madam Stoller - mia.stoller@dphs-tkat.org)
Our primary liaison & transition co-ordinator’s main role will be to ensure the smooth transition of primary mathematics to secondary by ensuring all Y6 students are able to access their maths learning from Y5/6 and also make connections with our KS3 curriculum so they have the best chance of success in maths from September. As well as working alongside Madam Eveard she also works with our feeder schools to see how we can further develop our curriculum in line with changes at KS2 to further ensure a smooth transition from Y6 to Y7. Similar to Madam Everards role she will ensure that:
To plan and deliver numeracy events for Year 6 during the summer term
To develop a clear programme of numerical activities for students.
To work with the KS3 maths co-ordinator to ensure that the primary mathematics curriculum is used to ensure progress and continuity is maintained during transition.
To be a champion for numeracy; assemblies, displays, maths days and parents’ consultation evenings.
To provide professional development for staff in secondary to show how mathematical skills and concepts are transferred across the curriculum (from KS2 to KS3).
To coordinate the implementation of numeracy activities at times outside of lessons.
Vocabulary
All vocabulary is included as part of the VCM’s which are accessible to teachers. Teachers will ensure students are able to confidently use, develop and explain understanding of both tier 2 and 3 vocabulary. The following are all important aspects of helping pupils with the technical vocabulary of Mathematics:
Using a variety of words that have the same meaning e.g. add, plus, sum
Encouraging pupils to be less dependent on simple words e.g. exposing them to the word multiply as a replacement for times
Discussion about words that have different meanings in Mathematics from everyday life e.g. take away, volume, product etc.
Highlighting word sources e.g. quad means 4, lateral means side so that pupils can use them to help remember meanings.
What will we as teachers ensure?
1. Be aware of the mathematical techniques used in other subjects and provide assistance and advice to other departments, so that a correct and consistent approach is used in all subjects.
2. Provide information and training to other subject teachers on appropriate expectations of students and difficulties likely to be experienced in various age and attainment groups.
3. Through liaison with other teachers, attempt to ensure that students have appropriate numeracy skills by the time they are needed for work in other subject areas.
4. Seek opportunities to use topics and examination questions from other subjects in mathematics lessons.
Maths across the curriculum
Mathematical skills can be consolidated and enhanced when pupils have the opportunity to apply and develop them across the curriculum. Poor skills, in particular, hold back pupil’s progress and lower their self-esteem. All teachers should consider pupil’s ability to cope with the numerical demands of everyday life and provide opportunities for pupils to:
Handle number and measurement competently, mentally, orally and in writing.
Use calculators accurately and appropriately.
Interpret and use numerical and statistical data represented in a variety of forms.
Specific mathematical links with other subjects:
Department
Mathematical content
Art
Symmetry; other transformations; paint mixtures as a ratio
History
Timelines; sequencing events
Geography
Representing data; finding averages; use of spreadsheets History Timelines; sequencing events
Digital Literacy
Collecting and representing data
MFL
Dates; counting in other languages
PE
Collecting real data; timing; measuring
Science
Formulae; calculating means and percentages; calculating with positive, negative and decimals; substitution; rearranging formulae; collecting and representing data.
DT
Measurement; properties of shape; scaling and ratio.
English
Identifying important information in a text will help them to better understand problem solving questions.
Music
Sequencing
Calculators
In order to improve numeracy skills, it is essential that pupils should be encouraged to use non-calculator methods whenever possible. All students should have a calculator when necessary; this should be a scientific calculator. Calculators are made available to students through parent pay and are encouraged to buy here as it is at a discounted rate (£10). Students studying maths at A level must have the casio classwiz X-991Ex from September (students at GCSE who are thinking about A level should also consider this calculator as an option).
Method
It is important that all teachers in department are consistent with methods used for calculations to avoid confusion. This does not disallow the possibility of introducing a new method in order to improve understanding or part of a lesson designed to investigate alternative methods. Weekly/bi-weekly subject knowledge sessions led by the lead practitioner for maths will ensure teachers use and set out methods correctly for students to ensure consistency across the department.
Working out
Students should be encouraged to work down the page where necessary. In all arithmetic, the importance of place value and neat column keeping should be stressed.
E.g £3.50 x 0.85 + £3.50
This is poor practice: £3.50 x 0.85 = 2.975 + 3.50 = 6.475 = £6.48
This is good practice: 3.50 x 0.85 + 3.50 = 2.975 + 3.50
= 6.475
= £6.48
Language
We must be consist using the correct mathematical language at all times
When referring to decimals say “three point one four” rather than “three point fourteen”.
Units of area and volume:
○ cm 2 is read as ‘square centimetres’ (not ‘centimetres squared’ or ‘squared centimetres’)
m 3 is read as ‘cubic metres’ (not ‘metres cubed’)
Read numbers out in full, so for 3400 say “three thousand, four hundred” rather than “three, four, zero, zero”
It is important to use the correct mathematical term for the types of average being used, i.e. mean, mode or median
When referring to a number rather than an operation, use the terminology negative 7, not minus 7, unless talking about temperature
Encourage pupils to be less dependent on simple words e.g exposing them to the word “multiplied by” as a replacement for “times”.
Highlighting word sources e.g. quad means 4, lateral means side so that pupils can use them to help remember meanings. This applies to both prefixes and suffixes.
Discussion about words that have different meanings in Mathematics from everyday life e.g. take away, product, similar etc.
Reading and writing numbers
Pupils must be encouraged to write numbers simply and clearly. Most pupils are able to read, write and say numbers up to a thousand, but often have difficulty with larger numbers. It is now common practice to use spaces rather than commas between each group of three figures, for example: 34 000 not 34,000 though the latter will still be found in many textbooks and cannot be considered incorrect. In reading large figures pupils should know that the final three figures are read as they are written as hundreds, tens and units. Reading from the left, the next three figures are thousands and the next group of three are millions, for example: 3 027 251 is three million, twenty seven thousand and fifty one.
BIDMAS
It is important that pupils follow the correct order of operations for arithmetic calculations. Most will be familiar with the mnemonic BIDMAS:
Brackets
Indices
Division & Multiplication (equal priority - where both exist, you go from left to right)
Addition & Subtraction (equal priority - where both exist, you go from left to right)
This shows the order in which calculations should be completed, for example:
5 + 3 x 4 = 5 + 12
= 17
5 + 3 x 4 = 8 x 4
= 32 (incorrect)
The important facts to remember are that the Brackets are done first, then Indices, Multiplication and Division and finally, Addition and Subtraction, for example:
(i) ( 5 + 3 ) x 4 = 8 x 4
= 32
(ii) 5 + 6 x 2 – 4 = 5 + 12 – 4
= 17 – 4
= 13
Care must be taken with Subtraction, for example:
(i) 15 - 7 + 4 = 8 + 4 but 15 - 7 + 4 = 15 - 11
= 12 = 4 (wrong)
Mental calculations
Most pupils should be able to carry out the following processes mentally though the speed with which they do it will vary considerably.
recall addition and subtraction facts up to 20
recall multiplication and division facts for tables up to 10 x 10.
Pupils should be encouraged to carry out other calculations mentally using a variety of strategies but there will be significant differences in their ability to do so. It is helpful if teachers discuss with pupils how they have made a calculation. Any method which produces the correct answer is acceptable, for example:
53 + 19 = 53 + 20 – 1
284 – 56 = 284 – 60 + 4
32 x 8 = 32 x 2 x 2 x 2
76 ÷ 4 = (76 ÷ 2) ÷ 2
Use of the equals sign
Pupils often use the ‘ = ‘ sign incorrectly. When doing a series of operations they sometimes write mathematical sentences which are untrue, for example:
5 x 4 = 20 + 3 = 23 – 8 = 15 5 x 4 =/ 15
It is important that all teachers encourage pupils to write such calculations correctly:
5 x 4 = 20
20 + 3 = 23
23 – 8 = 15
The ‘ = ‘ sign should only be used when both sides of an operation have the same value. There is no problem with a calculation such as:
43 + 57 = 40 + 3 + 50 + 7 = 90 + 10 = 100
since each part of the calculation has the same value. The ‘ ≈ ‘ (approximately equal to) sign should be used when estimating answers.
eg 2 378 – 412 ≈ 2 400 – 400
2 400 – 400 = 2 000
Calculating percentages of quantities
Methods for calculating percentages of a quantity vary depending upon the percentage required. Pupils should be aware that fractions, decimals and percentages are different ways of representing part of a whole and know the simple equivalents, for example:
10% = 1 /10 12% = 0.12
Where percentages have simple fraction equivalents, fractions of the amount can be calculated, for example:
i) To find 50% of an amount, halve the amount.
ii)To find 75% of an amount, find a quarter by dividing by four and then multiply it by three.
Most other percentages can be found by finding 10%, by dividing by 10, and then finding multiples or fractions of that amount, for example:
To find 30% of an amount first find 10% by dividing the amount by 10 and then multiply this by three. 30% = 3x10%
Similarly: 5% = half of 10% and 15% = 10% + 5%
Most other percentages can be calculated in this way. When using the calculator it is usual to think of the percentage as a decimal (multiplier). Pupils should be encouraged to convert the question to a sentence containing mathematical symbols. (‘of’ means ×), for example: Find 27% of £350 becomes 0.27 × 350 =
and this is how it should be entered into the calculator.
Calculating one number as a percentage of another
This is one of the most essential numeracy techniques pupils need to be able to do effortlessly, for example, converting a test score of 43 out of 70 to a percentage, pupils should know and understand the following steps:
1. Write ‘47 out of 70’ as a fraction 43/70
2. Convert the fraction to a decimal 43 ÷ 70 = 0.61428…
3. ×100 to convert the decimal to a percentage 0.6142… × 100 = 61.428…%
4. Round the percentage to an appropriate degree of accuracy 61.4% to 1 decimal place In practice, this can entered on a calculator simply as 43 ÷ 70 × 100 and written as 70 x 100% = 61.4%
Years 12-13 Wider Reading List
The books below are a selection of our favourite reads and we have given an indication of the accessibility of each book by putting a number before the title. This is a guide only and some students will be able to access texts outside of these guidelines.
A prefix of a 3 indicates the book is an interesting read which is accessible to all students in Years 12-13 and a 4 indicates the book is more conceptually demanding and is accessible to able, well motivated students in the 6th form
Many of these books are available from the LRC. If you are having problems finding a book/is not in the library please speak to Mde Fonda or Mde Longman.
The History of Mathematics Podcasts and Videos
3 The Story of Maths - The history of mathematics from ancient times to the present day. Narrated by Oxford mathematics professor Marcus du Sautoy, the series covers the seminal moments and people in the development of maths.
Episode 1 Episode 2 Episode 3 Episode 4 Book
3 A Brief History of Mathematics - Ten fifteen minute podcasts that reveal the personalities behind the calculations from Newton to the present day. How do these masters of abstraction find a role in the real world? - Free BBC Podcast
4 A Tribute to Euler (You tube) by William Dunham - Click here
3 Black Heroes of Mathematics - An Inspirational Talk
4 3blue1brown - A selection of fun animated clips exploring different concepts of high level maths e.g. how does Bitcoin actually work?
Mathematical Puzzles and Problems
3 The Most Beautiful Mathematical Formulas – 49 Short, thoroughly entertaining chapters that makes Maths accessible
3 Ten Years of Mathematical Challenges - Junior, Intermediate and Senior Maths Challenge Papers with worked solutions
3 The Moscow Puzzles - a marvellously varied assortment of brain-teasers by Boris Kordemsky
4 Journey through Genius - An exploration of some of the great theorems of mathematics by William Dunham.
4 The Millennium Problems - The 7 greatest unsolved mathematical problems of our time by Keith Devlin.
The Man Who Counted
3 The Man Who Counted is a collection of famous mathematical puzzles, taken from a popular newspaper column, features the ""writings"" of the fictional author, Malba Tahan, who describes different mathematical puzzles and solutions applied to real situations.
Ian Stewart
3 Does God Play Dice? by Ian Stewart. An excellent introduction to Chaos. The title is a quotation from Einstein, who believed the answer was no!
3 Game, Set and Math.
Chaos & Fractals
3 Chaos, The amazing Sciences of the unpredictable by James Gleick.
3 Fractal, Images of Chaos by Hans Lauwerier. A look at the use of fractals in computer art, modelling population growth and the movements of the planets in the solar system.
Rob Eastaway
3 Why do Buses Come in Threes?
3 How Long is a Piece of String?
Matt Parker
3 Humble Pi. What makes a bridge wobble when it's not meant to? Billions of dollars mysteriously vanish into thin air? ...
3 The Maths Book - Big Ideas Simply Explained.
4 Things to make and do in the fourth dimension.
The Magical Maze
3 The Magical Maze is structured on the image of a maze representing the network of connected mathematical ideas. It covers topics such as numbers, probability, game theory, patterns and oscillators, as well as knots, computability, chaos and other topics chosen to communicate the intellectual excitement and beauty of mathematics as a subject.
Mathematicians
3 A Tribute to Euler (You tube) by William Dunham - Click here
3 A Beautiful Mind - The Life of Mathematical Genius and Nobel Laureate John Nash by Sylvia Nasar .
3 Einstein's Heroes - Blending Science, History and Biography a look at the beauty of Mathematics and those that inspired Einstein by R Arianrhod
3 Isaac Newton - The people who mattered to him, the influences which played on him and the contexts of his achievements by James Gleick
3 Newton - The Making of a Genius - A biography of the great man.
3 Prisoner's Dilemma - Game theory plus bring to life the mathematician Von Neumann by William Poundstone.
3 The Man Who Loved Only Numbers - A biography of a mathematical genius. Paul Erdos was the most prolific pure mathematician in history and, arguably, the strangest too.
3 In Code - The story of an unknow teenager Sarah Flannery and her journey to create a new coding system by Sarah Flannery
The Development of Maths
3 e = mc2 - A biography of the World's most famous equation by David Bodanis.
3 Einstein's Universe - An exploration into the key ideas regarding relativity and their implications by Nigel Calder
4 Taming the Infinite - The Story of Mathematics from the first numbers to Chaos Theory by Ian Stewart
Martin Gardner
3 The Unexpected Hanging
3 Further Mathematical Diversions
3 Fractal Music
3 Mathematical Carnival
Application of Mathematics
3 About the Size of It - The common sense approach to measuring things by Warwick Cains
3 Longitude - The True Story of the solving of the Greatest Scientific Problem of the time by Dava Sobel.
3 A Short History of Nearly Everything - My favourite book of all time, taking you on a journey from the Big Bang to modern day in an engaging accessible manner by Bill Bryson
3 Measuring the Universe - This is the story of the questions that have been asked about the universe and our place in it by intelligent minds, combining History and Science by Kitty Ferguson
3 The Lunar Men - The dreams and determination of the engineers of the 18th century by Jenny Uglow
3 The Neptune File - Tom tells the story of John Couch Adams and the quest to find the planet Neptune using mathematics to locate it's position.
3 The Magic of Mathematics - explores the mathematics of nature, literature and art. This fascinating look at the surprising ways mathematics influences the everyday world takes an abstract universe and anchors it to the "real" worlds of science, history and the arts in an intriguing way.
4 It must be beautiful - An exploration of some of the great equations of modern science presented for the non-mathematician by a range of experts.
Simon Singh
3 The Code Book.
3 The Cracking Code Book.
3 Fermat’s Last Theorem.
Alex Bellos
3 Alex's Adventures in Numberland - Alex explains the surprising geometry of the 50p piece, and the strategy of how best to gamble it in a casino. He shines a light on the mathematical patterns in nature, and on the peculiar predictability of random behaviour.
3 So You Think You've Got Problems
3 Can You Solve My Problems
3 Alex Through The Looking Glass
Interesting Reads
3 Images of Infinity - A collection of images, writings and cartoons revolving around the ideas and paradoxes associated with the infinite and infinitesimal. Can a drawing of a hand drawing itself and the thing it is drawing ever be finished? by Tarquin Press.
3 Proofs Without Words by Roger B. Nelson. A look at the use of pictures and diagrams that enable us to see why a particular mathematical statement is true. Visual clues to stimulate mathematical thought.
3 Once Upon a Number - An exploration as to how logicians are inventing ways to deal with real world situations by mathematical means by J.A. Paulos
More Challenging Reads
4 The Music of the Primes - A look at Riemann's hypothesis and the relevance of a formula to generate primes by Marcus Du Sautoy
4 Finding Moonshine - A book full of insight into the nature of symmetry and the people who study it by by Marcus Du Sautoy
4 Dr Riemann's Zeros - The search for the $1,000,000 solution to the greatest problem in Mathematics by Karl Sabbagh
4 How Big is Infinity - An exploration into the most perplexing, stimulating and surprising questions in Mathematics by Tony Crilly
4 A Brief History of Time - From the Big Bang to Black Holes by Stephen Hawking
4 The Best Writing on Mathematics - Memorable pieces of writing on Mathematics from 2011
4 An Imaginary Tale: The Story of the square root of -1 by Paul Nahin
4 e The Story of a Number - What is e, it's origins and applications by E Maor
4 Six Easy Pieces - The fundamentals of Physics explained by Richard Feynman.