2. Welcome to our Maths Workshop for parents – thank you so much for coming! There is a selection of maths resources arranged on the tables around the edge of the hall – please feel free to have a look and have a ‘play’! Using models and images in maths is essential in helping the children understand underlying patterns and principles of maths.

3. Learning, Growing and Succeeding Together

5. Oh no!!!

10. etc.

12. add plus more than increase total sum altogether double How many more? and

13. The Downley Staff – and guests!

14. Mental Recall of Number Bonds … This is REALLY IMPORTANT!!!

15. Doubles and near doubles 6 + 6 = 12, 6 + 7 = 13, 6 + 5 = 11 35 + 35 = 70, 35 + 36 = 71 etc Multiples of 10 and multiples of 5 which add up to 100… 70 + 30, 45 + 55 etc Number bonds to 10 eg, 10 + 0 = 10, 9+ 1 = 10…. Addition facts for numbers up to 10 6+0=6; 5+1=6; 4+2=6… Numbers bonds to 20  19+1; 18+2; 17 + 3 All addition facts to 11, 12, 13 …20

16. ‘Sums!!!’

18. 17 + 5 = ? Writing operations and solving problems using ‘informal methods’ Firstly, encourage mental strategies (starting with the higher number, counting on, looking for pairs which make 10, verbal discussion about the method used to get an answer, checking!) On Monday morning, Beech get 4 housepoints, Chestnut get 3, Oak get 6 and Willow get 7. What is the total number of housepoints given?

19. 7 8 8 3 Double 8 =16 7 and 3 are bonds to 10 Total is 16+10 = 26 Use knowledge of place value and adding on 10 to a number Find the total

20. Simple, informal jottings… use of a number line 17 + 5 = ? 1718192021222324 X If another way has been used, encourage discussion about the method and talk about how effective it is.

21. The importance of understanding PLACE VALUE

22. 25 2 Tens and 5 Units PLACE VALUE – Tens and Units… What is the value of each underlined digit in the following numbers? 293 2 Hundreds, 9 Tens and 3 Units 2849846028498460 158 317 708 965 Can you add single units to any number? Can you add multiples of 10 to any number Can you add multiples of 100 to any number?

24. What would 10 more than this number be? What about 1 more? 10 less? Explain how you know. What numbers are covered? How do you know?

25. 63 This is a section from a hundred square. What are the missing numbers? Explain how you know.

26. 45 This is a section from a hundred square. What are the missing numbers?

27. 48 + 1 = 48 + 10 = 48 + 100 = 139 + 1 = 139 + 10 = 139 + 100 = 299 + 1 = 299 + 10 = 299 + 100 = 48 + 3 = 48 + 30 = 48 + 300 = 139 + 6 = 139 + 60 = 139 + 600 = 299 + 9 = 299 + 90 = 299 + 900 =

28. Being able to split a number into Hundreds, Tens and Units is VERY IMPORTANT! This is called ‘partitioning’ and ‘recombining’ 28  2 tens and 8 units 28 = 20 + 8 49  4 tens and 9 units 49 = 40 + 9 384  616  902  7 tens and 3 units = 6 tens and 2 units 3 hundreds and 7 units = 200 + 50 + 6 = 500 + 10 + 9 =

29. Different ways of adding up – mentally and with jottings…

30. Using a ‘mental’ or empty numberline 24 + 47= 47 + 24 = 47 + (20 + 4) = 47 5768 X 67697071 +10 +1

31. Getting quicker… 24 + 47= 47 + 24 = 47 + (20 + 4) = 47 X 67 +20 +4 71

32. And more difficult… 38 + 74 = 74 + 38 = 74 + (30 + 8) = 74 X 104 +30 +8 112

33. A different strategy… 26 + 42 = Add the tens together and then add the units together 26+42 (20 + 40) + (6 + 2) = 60 + 8 = 68

34. Larger numbers – crossing the hundreds boundary… 97 + 76 = Add the tens together and then add the units together 97+76 (90 + 70) + (7 + 6) = 160 + 13 = 173

35. Vertical Layouts – Formal Written Methods (Year 4 ish)

36. Only starting this when confident with stages so far! Wherever possible, children should be encouraged solve problems mentally. Vertical addition should be used as the problems become too complicated to solve mentally… 500 + 123 Easy! - a MENTAL calculation! 367 + 256 Tricky! A written calculation! But I still need MENTAL skills!!!

37. First steps (using partitioning) 236 + 421 = ? 2 0 +300+64 0 +200+16 0 0 + 50 +7 657 =

38. The ‘Expanded’ method 4 6 +38 9 5 70085441401

39. The Compact Method – ‘Carrying’ 4 6 +38 9 5 84 1 5 1

40. Harder numbers, decimals etc Years 5 & 6

41. Adding Decimals… When using a vertical layout, ALWAYS, ALWAYS make sure the decimal points are lined up.

42. Adding Decimals (compact method)… £42.45 + £3.85 + £135.45 + 6p = £181.81 £135.45 £42.45 £3.85 +£0.06 £181.81 112

44. subtract take away decrease leave How much less is..? reduce difference between How many fewer is…..than….? minus

45. Multiples of 10 up to 100… 70 - 30, 100 – 20 = 80 etc Number bonds up to 10 Eg, 3 - 0 = 3, 5 - 1 = 4…. 10 - 0 = 10, 9 - 1 = 8 Numbers bonds up to 20 All bonds to 11, 12, 13 …20 It is important that children move away from the language of ‘take away’ in Key Stage 2 and move towards ‘subtraction’.

47. Counting back… …on a numberline

48. Simple, informal jottings… use of a number line 7 - 5 = ? At Key Stage 1, children will count back on the numberline to find the answer. - 5 27

49. Counting on… …with a numberline

50. You buy an item for £8. You give a £20 note to the shopkeeper. What is the change? You buy an item for £15.56 You give a £50 note to the shopkeeper. What is the change?

51. Subtraction – Think of it as ‘finding the difference’ 20 – 8 = 20 8

52. 20 – 8 = 20 8

53. 20 – 8 =12 20 8 Count on… From 8 to 20… 12 steps It’s really easy to jot a numberline to count on…

54. 20 – 8 = 810 20 2 10 12 8 20

55. What is the difference between 74 and 47? 4750 7074 3 20 4 27 4727 74

56. You buy an item for £15.56 You give a £50 note to the shopkeeper. What is the change? 15.5615.6016.0050.0020.00 4p £4 40p£30 Then total all the jumps  4p + 40p + £4 + £30 = £34.44 Jumps can be labelled with pounds and pence notation, or with decimal notation, leading to 0.04 + 0.40 + 4.00 + 30.00 = 34.44 = £34.44 15.56

57. 100 -43 341 Decrease 100 by 43 SUBTRACTION MISCONCEPTIONS

58. Decrease 100 by 43 4350 100 7 50 57 4357 100

59. 775 -292 325 775 – 292 =

60. 292300 700 775 8400 75 483 292483 775

61. The link between addition and subtraction

62. + = - = - + -

63. 5 + 4 = 9 4 + 5 = 9 9 - 5 = 4 9 – 4 = 5 9 4 5 ___ + ___ = ___ ___ - ___ = ___ ___ – ___ = ___ 8 6 ___ + ___ = ___ ___ - ___ = ___ ___ – ___ = ___ ___ + ___ = ___ ___ - ___ = ___ ___ – ___ = ___ 15 11 Number triangles are BRILLIANT. Know 1 FACT, know 4 FACTS! They will help you a lot with addition and subtraction… Example Complete… 14 10

64. Can I solve this mentally? Yes! CHECK!

65. Can I solve this mentally? NO 1. Estimate 2. Numberline 3. Add jumps 4. CHECK!

66. 119 127 120 +30 127 – 119 = +7+1 8 127 8 119 + - -

67. 156 – 88 = 88 90 +2 68 +60 150 +6 156 8868 - - +

68. £10.00 – £3.56 = £3.56 £3.60 +£0.04 £6.44 +£0.40 £4.00 +£6 £10.00 £3.56£6.44 - - +

69. Mrs Webb took 5 hours to run a marathon and Paula Radcliffe took 2 hours and 16 minutes. How much faster was Paula? 2h 16 min 5h 2h 20 min 3h +4 min +40 min + 2h 5h – 2h 16 min = 2h 44 min

70. More challenging calculations

71. Subtracting Decimals (numberline)… + 0.5 +0.7 2.5 3 3.7 3.7 – 2.5 = 1.2 0.5 + 0.7 = 1.2

72. 3.81 6.24 4.00 +2.00 6.00 +0.19+0.24 6.24 – 3.81 = 2.43 Number lines with more complex calculations

73. Vertical Subtraction? High level 4

74. Only start this when confident with stages so far! Wherever possible, children should be encouraged to solve problems mentally. Vertical subtraction should only be used when your child is fully confident with being able to subtract using a numberline. 500 - 4 Easy! - a MENTAL calculation! 367 - 256 Tricky! A written calculation! But I still need MENTAL skills!!!

75. Beginning decomposition 754 - 86 700 50 4 + + 80 6 + - + 70040 14 + + 80 6 + - 600 140 14 + + 80 6 + - 600 60 8 + += 668

76. Formal decomposition 7 5 4 8 6 - 4 1 6 1 8 66

78. multiply lots of multiples double scale up product repeated addition double arrays times

79. Can you draw an image to show … 4 x 2

80. 4 sets of 2

81. 4 x 2 4 lots of 2 2 + 2 + 2 + 2

82. 4 x 2 4 lots of 2 20648 2 + 2 + 2 + 2

83. 4 x 2 4 times 2

84. 4 x 2 4 two times 4 + 4

85. 4 x 2 4 multiplied by 2 ARRAYS

86. Fast, mental recall of times tables is really, really IMPORTANT!

87. Back to the importance of PLACE VALUE and NUMBERLINES!

88. Use ‘Partitioning’ to help… 18 x 8 = (10 x 8) + (8 x 8) = 80 + 64 = 144 080 +80 +64 10 x 8 8x8 144

89. 10 8 8 The beginning of the ‘GRID’ method 18 x 8 =144 80 64

90. 10 8 8 80 64 18 x 8

92. 38 x 27 308 7 20600 56210 160 760 + 266 1026 810 + 216

93. 365 x 24 605 4 20 1200 20240 100 7300 + 1460 8760 7200 + 1440 + 120 Problem: How many hours are there in a year? 300 6000 1200

94. For upper KS2 high fliers… How about multiplying decimals? Let’s try 2.3 x 4.59 The grid method should still be used… and a really good understanding of place value is essential!! 2 0.3 0.09 0.54 9.18 1.377 10.557 8 0.027 0.18 1.0 0.15 1.2

95. Skills needed Skills needed to be able to carry out the grid method of multiplication when multiplying 2 two- digit numbers. partition numbers into tens and units/ones recall multiplication facts multiply by ten multiply by multiples of ten add together two and three-digit numbers decide whether the answer is sensible

96. Multiplying by 10 It is important that multiplying by 10 is not thought of as a case of ‘adding zeros’. It isn’t an inappropriate expression because adding zero actually leaves a number unchanged and the ‘add a zero rule’ fails when, for example, 0.2 is multiplied by 10 (‘adding a zero’ results in 0.20). Children need to understand that when you multiply by 10 the digits move one place to the left, leaving an empty space which is filled by zero (a place holder).

97. Multiplication facts Children will struggle with multiplication if they can’t recall multiplication facts. Knowing a multiplication table is much more than being able to recite it in order. It also means children should be able to respond quickly to oral or written questions phrased in a variety of ways, e.g. What are seven fives? What is 7 times five? 5 multiplied by 7 is… How many fives in 35? What would I multiply by five to get 35? What are the factors of 35?

98. Sensible answers Encourage children to approximate/estimate (a sensible guess) before calculating Approximately what is 4.92 x 3? You might decide to use 5 x 3 = 15 as an approximation/estimation. How might you approximate 23 x 8? You might use 20 x 10 = 200

99. 197 X 201 29 X 5 8.9 X 12

100. 197 X 201 is about 40000 29 X 5 is about 150 8.9 X 12 is about 108

101. The ‘standard’ written method…. 365 x 24 20 (5 x 4) 24 0 (60 x 4) 200 (300 x 4) 1 00 (5 x 20) 2 00 (60 x 20) 000 (300 x 20) 6 760 8 (365 x 20) 365 x 24 300 7 460 1 760 8 1 1 (365 x 4)

103. divide group divisor quotient remainders share fractions decimals

104. 12  3 = 4 Sharing There are three children and 12 cakes. How many can they each have, if I share them out equally? Sharing 12 things equally into 3 piles. How many in each

105. Grouping There are 12 cakes. How many children can have three each? (How many threes are there in 12?) 12  3 = 4

106. Language and division The  sign represents both the sharing and grouping aspects of division Encourage the children to read this as ‘divided by’ rather than ‘shared by’, Even easier – ‘HOW MANY!’

107. HOW MANY three’s make 12? 4 three’s make 12 4 x 3 = 12 Know 1 fact, know 4 facts!!! 12  3 = ?

108. 4 x 3 = 12 3 x 4 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3

109. 4 x 3 = 12 3 x 4 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 12 4 3 x ÷÷

110. x = ÷ =

111. 2 x 4 = 8 4 x 2 = 8 8 ÷ 2 = 4 8 ÷ 4 = 2 8 4 2 ___ x ___ = ___ ___ ÷ ___ = ___ 8 6 24 4 Number triangles are BRILLIANT. Know 1 FACT, know 4 FACTS! They will help you a lot with multiplication and division Example Complete… 45 9 ___ x ___ = ___ ___ ÷ ___ = ___ ___ x ___ = ___ ___ ÷ ___ = ___

112. 100  50 = 100  2 = 100  5 = 100  20 = 100  10 = 2 50 20 5 10 Look for patterns and relationships too!

114. dividing any number by 0 gives an answer of 0 eg, 6 ÷ 0 = 0 0 ÷ 59 = 0 dividing any number by 1 leaves the number unchanged e.g, 12  1 =12 1,346 ÷ 1 = 1,346 Order does matter 16  2 does not equal 2  16 division is the opposite of multiplication eg, 3 x 4 = 12 so 12 ÷ 4 = 3 there will be remainders for some division calculations eg, 11 ÷ 2 = 5 and a remainder of 1 You’ll be laughing if you remember these simple facts…

115. 18  3 = 6 Division and number lines/repeated subtraction (getting close to ‘chunking’) 0 3 6 9 12 15 18

116. So think of 18  3 As ‘How many 3s are in 18?’ Generally speaking, children are happier and more accurate when counting forwards… 015129318603003069120306309630 96301512963018151296300306309630 9630151296301815129630

117. Problem solving 1. I have 26 eggs. If 6 eggs fit in one box, how many boxes will I need for ALL the eggs? 2. There are 26 children in a P.E lesson. If teams of 6 are needed, how many full teams can be made?

118. The same basic calculation will be needed, but how we deal with the remainder will be different. So we need to calculate 26 ÷ 6 0612182426 r2 So the answer is 4 r 2 If we need to box up all the eggs, this means we need 5 boxes (but only 4 will be full) If we need teams of 6 children in P.E., we can only have 4 teams, with 2 children left out.

119. 70 ÷ 5 = Grouping - How many 5’s are there in 70? Chunking on a number line 40 45 50 55 60 65 70 0 5 10 15 20 25 30 35 14 Start with ‘chunks’ of 10 then see what’s left 10x5 1x5

120. 52 ÷ 4 = Grouping - How many 4’s are there in 52? 13 52 0 40 10x4 44 1x4 48 1x4

121. 37 ÷ 3 = Grouping - How many 3’s are there in 37? 12 r 1 Remainders are easy! 37 0 10x3 1x3 33 1x3 36 r1 30

122. Dividing by chunking – written vertical method 72 - 50 (10x5) 22 - 20 (4x5) 2 Answer: 14 remainder 2 1 x 5 = 5 2 x 5 = 10 5 x 5 = 25 10 x 5 = 50 Good informal jottings 72 ÷5 = 14 r 2

123. Try this… 47 - 30 (10) 17 - 15 (5) 2 Answer: 15 remainder 2 1 x 3 = 3 2 x 3 = 6 5 x 3 = 15 10 x 3 = 30 Good informal jottings 47 ÷3 = 15 r 2

124. Problem solving Four children collected £68 for charity. They each collected the same amount. How much did each one collect? I have 177 cakes. One box holds 8 cakes. How many boxes will I need?

125. 68 ÷ 4 = How many 4’s are there in 68? 7 x 4 or 7 groups of 4 28 17 68 10 x 4 or 10 groups of 4 40 0 68 - 40 (10 x 4) 28 - 28 (7x4) 0 Answer: 17 40

126. 177 ÷ 8 = Grouping - How many 8’s are there in 177? 22r1 177 10 x 8 10 groups of 8 80 r1 0 23 boxes is the correct answer 80 160 10 x 8 10 groups of 8 80 176 2 x 8 2 groups of 8 16

127. EVEN LARGER NUMBERS… 276 - 200 (40 x 5) 76 - 50 (10 x 5) 26 - 25 (5 x 5) 1 Answer: 55 r1 10 x 5 = 50 20 x 5 = 100 40 X 5 = 200 276 ÷ 5 = 55 r1

128. Know that it is possible to divide a smaller number by a larger number Know that the line in the middle of a fraction means ‘divided by’ Know how to work out a fraction as a decimal on a calculator Fractions! A whole session by itself but… 3 4

129. www.amathsdictionaryforkids.com/

131. Example Level 4 problems Non calculator

132. Example Level 4 problems Calculator

133. Example Level 4 problems Calculator

134. 1.157 2. 34 3. a. £14.40 b. 20 badges Let’s check the answers!

135. http://www.woodlands-junior.kent.sch.uk/maths/

136. Very well done everyone! Thank you for your time! A favour please…