Welcome to Primary Mathematics at Canterbury Christ Church University

1. Welcome toPrimary Mathematicsat Canterbury Christ Church University The Pre-Programme Mathematics Task

2. Introduction The Primary Maths tutor team are looking forward to meeting you on our programme. We hope that you will enjoy learning how to teach mathematics to children so that they become confident, motivated and enthusiastic mathematicians. We recommend that you refresh your knowledge of the mathematics taught in primary school before you join the programme. This is because you will be working with children in school very early on in your programme. If your offer on this programme was accompanied with a requirement to work on your mathematics, be prepared to talk to your maths tutor about the work you have done when you arrive in University. It may be some time since you studied mathematics, and it is important that you have a secure knowledge of the mathematics in the current curriculum up to at least the end of Key Stage 2 (even if you are focusing on the Early Years.). During the programme we will develop your understanding of the mathematics in the primary curriculum, and beyond, and prepare you to teach it to children so that they understand it too. If you have any queries do contact Gina on gina.donaldson@canterbury.ac.uk

3. You can access the curriculum on: Early Years: https://www.gov.uk/government/publications/early-years-foundation-stage-framework--2 Key Stages 1 and 2: https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study

4. For your independent study, we recommend: The BBC Bitesize website http://www.bbc.co.uk/education Or you can log on to the following website, where you will need to register by choosing a user name and password: http://www.ncetm.org.uk Under the Self Evaluation Tab, choose Mathematical content knowledge. The self-evaluation tool allows you to open examples for each part of the curriculum in order to check your understanding.

5. How to use this power point • In each area of mathematics, we have listed the aspects we would like you to be accurate in. • Read the list and if you are unsure of any aspect, open the link to look at the content in more detail. • To navigate: Use the home button to return to the list of areas of mathematics. Use the back button to take you back to the contents for the area you were focusing on.

6. Areas of mathematics Click on an arrow to take you to the contents of each aspect. Number Geometry Statistics Measurement Algebra End task

7. Number In particular ensure that you are secure in: • Rapid recall of number bonds, i.e. pairs of numbers which total 10, 20, 100, 1000, and 1. • Rapid recall of multiplication facts up to 12 x 12. • Addition and subtraction of larger numbers using a written method. Make sure you can use quick and accurate formal methods to work with numbers of up to four digits, and numbers with digits after the decimal point. • Multiplication and division of larger numbers using a written method. Make sure you can use quick and accurate formal methods to work with numbers of up to four digits, and numbers with digits after the decimal point. • Your knowledge of the place value of our number system e.g. the way our numbers are written in columns, with each column having a value ten times larger than the one on its right. • Your knowledge of the order in which to calculate operations. • Your knowledge of fractions and mixed numbers, what they are called and what they mean. Make sure that you are familiar with and can solve problems with the key equivalent fractions, decimals, and percentages for example ½, ⅓, ¼, ⅔, ¾, 1/10. Ensure you are able to order, add and subtract fractions with different denominators, multiply two fractions and divide a fraction by a whole number. • Your knowledge of negative numbers and how to calculate intervals across zero. • Reading Roman numerals to 1000 and recognising years written in Roman numerals.

8. Rapid recall of number bonds Ensure that you have a very quick memory of the number bond facts to increase your speed with harder calculations and your confidence in the classroom. For example, make sure you can remember all the pairs of numbers which add up to 10, 20, 100, 1000, and 1. • Try to remember the related subtraction facts • For example, 34 + 66 = 100 so 100 – 34 = 66 and 0.7 + 0.3 = 1 so 1 - 0.7 = 0.3 • Use the patterns in the facts to help you • Try to play games regularly where you add and subtract numbers quickly such as darts.

9. Rapid recall of multiplication facts up to 12 x 12 • Make sure that you can remember the multiples of every number up to 12 (e.g. the multiples of 4 are 4, 8, 12, 16…), in order, and that you can multiply quickly any two numbers up to twelve. Look for strategies to learn these table facts. Explore the patterns in the tables by writing down the multiples of each number. Which have odd and even multiples? Use the fact that multiplication is commutative, i.e. 3 x 4 = 4 x 3 • Make up games to increase your speed of recall such as times table snap. • Make sure you learn all the doubles of numbers up to 20 e.g. double 7 is 14 and all the halves of even numbers up to 40 e.g. half of 16 is 8. • It is also important that for any multiplication fact that you can state the corresponding division facts e.g. 3 x4 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 • Also, make sure you can multiply any two digit number by one digit number e.g. 24 x 3 by working out 20 x 3 and adding it to 4 x 3 • Make sure you can easily recognise the square numbers e.g. 1x1, 2x2, 3x3, 4x4… • Be able to state the factors of any number (for example the factors of 12 are 1, 2, 3, 4, 6 and 12 as they divide 12 with no remainder)

10. Addition and subtraction • Addition of two larger numbers together using a formal written method Make sure you have a quick and accurate method to add two numbers of up to four digits, and numbers with decimals e.g. • Subtraction of larger numbers using a formal written method Make sure you have a quick and accurate method to subtract two numbers of up to four digits, and numbers with decimals e.g.

11. Multiplication and division • Multiplication of larger numbers together using a formal written method Make sure you have a quick and accurate method of long multiplication to multiply two numbers of up to four digits, and numbers with decimals e.g. • Division of two larger numbers together using a formal written method Make sure you have a quick and accurate method of short and long division to divide two numbers of up to four digits by up to a two digit number, and numbers with decimals e.g.

12. Place Value • For example, the way our numbers are written in columns, with each column having a value ten times larger than the one on its right H T O . • Make sure you can round a number such as 3.456 to the nearest whole number or to one or two decimal places • Order numbers such as 3.7, 3.24, 3.04, 3.4, 0.34, 3.09 according to their size • Ensure your can multiply and divide by 10, 100, 1000 by moving digits rather than moving the decimal point

13. The Order of Operations • Your knowledge of how to use the order of operations when calculating with more than one operation to solve a problem For example solving problems such as 2 + 3 x 7 • Remind yourself of BIDMAS (brackets, indices, division, multiplication, addition, subtraction)

14. Your knowledge of fractions, what they are called and what they mean For example make sure that you know: • How to read and write fractions, and what each number in the fraction means • How to read and write a mixed number such as 3 ½ • How to find a fraction of a number e.g. ¾ of 24 • How to simplify a fraction like 35/49 to write it in its simplest terms • How to find a percentage of a number such as 30% of 120 • What the equivalent decimals and percentages are for key fractions: ½, ¼, ¾, ⅓, 2/6, 1/20, 2/10 • How to change a fraction to its equivalent decimal and percentage e.g. ⅛ = 0.125 = 12.5% • How to find common denominators • How to order fractions with different denominators by changing them into equivalent fractions with common denominators  • How to add and subtract fractions with different denominators by changing them into equivalent fractions with common denominators. • How to multiply two fractions • How to divide a fraction by a whole number.

15. Negative numbers Practise counting backwards from zero, using the term negative. Ensure that you are able to calculate intervals across zero. For example, find the difference between temperatures of -5° C and 7° C. Record positive and negative numbers on a number line.

16. Roman Numerals Check your ability to read Roman numerals to 1000 and recognise years written in Roman numerals: • What are the seven basic symbols used and what are their values? • What are the rules for combining symbols to build new amounts? • Can you write your age, your house number and your year of birth in Roman numerals? • Where might you find Roman numerals in use today?

17. Geometry In particular ensure that you are secure in: • The names of 2D and 3D shapes. • The properties of 2D and 3D shapes.

18. 2D and 3D shape names For example: Ensure that you can recognise these 2D shapes - rectangle, square, parallelogram, rhombus, trapezium, octagon, pentagon, hexagon, circle, semicircle and these 3D shapes - cube, cone, cuboid, sphere, cylinder, triangular- based pyramid, tetrahedron, square-based pyramid, triangular prism, hexagonal prism

19. Properties of 2D and 3D shapes Make sure you can describe shapes using their properties, for example: • For 2D shapes – Number of sides, number and size of angles, vertices, lines of reflectional symmetry, orders of rotational symmetry, tessellation, number of right angles, parallel sides Parts of a circle (the radius, diameter and circumference) • For 3D shapes – Number of faces, edges and corners/vertices, parallel planes and symmetry

20. Statistics In particular try to ensure that you are secure in: • Calculating the mean of a set of data • Understanding bar charts, pictograms, line graphs, pie charts • Your ability to use tables, charts and graphs to solve problems

21. Calculating the mean Ensure that you can solve these types of problems: “The wages of 10 workers in a factory are £40,000, £32,000, £9000, £9000, £9000, £9000, £9000, £9000, £9000 and £9000. What is the mean?”

22. Understanding charts, tables and graphs Ensure that you can identify the following and understand when they might be used:

23. Using tables and charts to solve problems Ensure that you can interpret tables and charts, for example, what could have happened here?: Make sure that you can set and answer questions from a range of tables, graphs and charts.

24. Measurement In particular ensure that you are secure in: • The key units of measurements and their related conversions. • How to calculate measurements for example the area of a parallelogram and triangle, and the volume of a cuboid.

25. Units of measurement Ensure you are familiar with the key units of measurements and their related conversions, for example: Make sure you can state the key units used to measure length, mass, capacity, time, volume, angle and area.  Remember the conversions between metric units of measurement e.g. 10mm = 1cm 100 cm = 1m 1000 m = 1km 1000g = 1kg 1000ml = 1l Remind yourself of how to convert between miles and kilometres for example using a line graph.

26. Calculating measurements • What are the formulae for finding the area of: • a rectangle? • a triangle? • a parallelogram? • a circle? • How would you use these to find the volume of: • a cuboid? • a cylinder? • Which units of measurement would you use?

27. Algebra In particular ensure that you are secure in: • Using simple formulae. • Generating and describing linear number sequences. • Expressing missing number problems algebraically. • Finding pairs of numbers that satisfy an equation with two unknowns eg x + y = 1. • Listing the possibilities of combinations of two variables.

28. Using simple formulae For example • Use the formulae written in words for finding the area of a rectangle, or its perimeter • Consider why these sort of ‘Think of a number’ games work: Think of a number, add two to it, double it, add two, half it, take away the number you first thought of and your answer is… 3.

29. Generating and describing linear number sequences For example: • Counting in different steps, exploring the patterns in the multiplication tables • Explore the Fibonacci sequence 1,1,2,3,5,8,13… • 1,4,7,10… will it ever reach 300?

30. Expressing missing number problems algebraically Find the values and then make up some of your own: d + 1 = 4, s – 6 = 14, 4t = 50, 2x – 4 = 8 Write some known rules algebraically: • How to find the perimeter of a rectangle with length a and width b • How to find the perimeter of a square side s • How to find the area of a rectangle

31. Finding pairs of numbers that satisfy an equation with two unknowns For example, can you find pairs of numbers to make these calculations correct? • x+y= 10 • a+b= 0 • c–d= 10 • s+t= 1

32. Listing the possibilities of combinations of two variables For example: • What are the number of possibilities when you throw two 6-sided dice? • How many ways can three children line up for assembly? • Four children? • Ten children?

33. Thank you for completing this task We hope that you are now feeling more secure in the areas of mathematics you will be teaching. During your programme we will cover with you the best ways to teach mathematics. Remember that if your offer on this programme was accompanied with a requirement to work on your mathematics, you should be prepared to talk to your maths tutor about the work you have done when you arrive in University. We look forward to meeting you when you begin your programme. The Maths Team