Maths is Fun at Burpham

The answer is what is the question?

Progression of Mathematical Understanding 12 + 19 Active/concrete Building visual images Abstract 13 - 8 Communicating Mathematically Pattern Spotting Children must have concrete experiences that enable them to create visual images. They should be encouraged to articulate their learning and to become pattern spotters. Numicon software example 3

0.1 1 bead string count stick Multilink place value apparatus Sliders 0.1 place value counters 1 0 1 10 0.1 100 1 Cuisenaire Numicon What have you got on your table? Have a look at everything – what would you do with these apparatus? What are they called? Which year group would use these apparatus? Go through each in turn and explain uses Mulitlink – subtraction is the same as finding the difference. KM Numicon – Guess my shape – I have two numicon shapes in my bag that total 9. What could they be? PB Percentages (KM) Sliders and place value cards – KM Counters – counting in 5’s etc Cuisenaire track – KM Numberlines and 100 squares – PB Counting sticks – KM Carpet numbers - PB counters number grids 100 and 200 number line 4

What numbers mean What does number 3 mean Take number 3 and show in all its forms What do you think we mean by the number 3? Take answers Children need to shift from thinking about 3 as an adjective telling how many? To a value – with a label – a 3.

Now we are ready to count! How do we count? Use our fingers? Count anything – apples, pencils, people etc Put in a row to count so you are accurate. Count in 2’s 5’s 10’s – think about counting money. Not always counting in 1’a Counting from 0. Counting on and back from any number. What about negative numbers? Counting fractions and decimals. Greater than and less than Which number comes before and after.

Which is the biggest number? 1,2,3,4,5,6,7,8,9,10 Egyptian numbers first – KM – our decimal system Place value – how many tens, hundreds etc. – place value hats Which is the biggest number? Or which has the highest value? Need an order and know a position – need a structure – numbers run from 0- infinity – use numberlines to help.

Place Value Th H T U 6 5 3 2

Calculations and operations. What are these? 4 operations addition, subtraction, multiplication and division – relationships between them. Commutative law – what does that mean? Vocabulary – You have all got an operation – write down all the other words, language for this. Bomb timer – 1 minute.

The four stages Mental Informal Expanded Efficient Note that mental and informal methods will continue all the way through primary maths.

Addition 76 + 47 = 86 +10 96 +10 106 +10 116 +10 123 +7 76 116 76 + 40 123 + 7 Now say you are going to demonstrate the recording methods used for each of the operations in turn. (animated slide) Addition The number line models the counting on that children may be doing in their heads. It supports their thinking. You will see this type of recording in children’s books from KS1 onwards. The second example illustrates moving towards a more efficient method. Something that the parents may have done in their calculations earlier. To fit in with your school’s policy you need to chose one of the next 2 slides and delete the other: Addition using the vertical expansion Addition using the horizontal expansion

Partitioning 48 + 33 40 8 30 3 70 + 11 = 81

Column Method 358 358 + 33 + 33 11 391 80 300 391 Leading to Compact Expanded Compact 358 + 33 11 80 300 391 358 + 33 1 Leading to 391

Subtraction Imran has 43 conkers; he gives 24 away to his friends. How many does he have left? 43 – 24 = 43 -1 19 20 -3 23 -10 33 -10 (Animated slide) This slide demonstrates to parents the process of using an empty number line to support children’s thinking in subtraction. It might well be how they (the parents) would work this mentally using an imaginary number line. Children will experience this type of recording from Y2. The jumps are below the line to show ‘counting back’. 19 conkers

Subtraction as finding the difference 5 12 Difference

Subtraction - Finding the difference on a number line Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy? 93 – 55 = 60 +5 90 +30 93 +3 55 (Animated slide) Another subtraction calculation, this time involving difference. Here the child has counted on from 55 to 93, recording the jumps on a number line. Having a visual image like this supports the child with what is going on in their head. The big jump of 30 may initially be made with three jumps of 10. 38p more

Subtraction 8.23 – 4.55 = 3.68 +0.23 +0.45 +3 The same method but using decimals. Counting on or complementary addition is used. This is one of the reasons that children work on complements, as mentioned earlier. Putting one number underneath the other would result in many children giving an answer of 4.12. 4.55 5.00 8.00 8.23

Number line 4 x 2 +2 +2 +2 +2 2 4 6 8 4 x 2 = 2 + 2 + 2 + 2 Multiplication as repeated addition 4 x 2 +2 +2 +2 +2 2 4 6 8 4 x 2 = 2 + 2 + 2 + 2 So, 2 x 4 = 8

Arrays 3 x 6 Or Add the dots

Arrays 5x6 4x5 3x2

Partitioning 24 x 5 20 x 5 = 100 4 x 5 = 20 100 + 20 = 120

Grid Method 25 x 35= 20 + 5 30 + 5 X 20 5 30

Now multiply – watch the zeros! 25 x 35= X 20 5 30 600 6 150 15 100 10 25

What next? 25 x 35= X 20 5 30 600 150 100 25 6 1 5 +   2 8 7 5

Try this one… Use the Grid Method of multiplication to work out this question… 71 x 43 =

71 x 43 = X 70 1 40 3 2800 28 40 210 21 3

71 x 43 = X 70 1 40 3 2 8   1 4 + 3 5 28 2800 40 210 21 3

Expanded Multiplication 38 x 7 210 56 (30 x 7) (8 x 7) 266

Division Sharing Grouping

Arrays 12 ÷ 3 = 4

Repeated subtraction 3 6 9 12 12 - 3 – 3 – 3 – 3 ÷ 3 = 4 - 3 - 3 - 3 ÷ 3 = 4 - 3 - 3 - 3 - 3 3 6 9 12 12 - 3 – 3 – 3 – 3

Counting in steps 3 6 9 12 ÷ 3 = 4 Add the jumps + 3 + 3 + 3 + 3 3 6 9 12 + 3 + 3 + 3 + 3 Fingers “6 “9 “12” “3”

Chunking 75 ÷ 5 75 10 x 5 5 x 5 25 75 - 50 (10 x 5) 25 - 25 (5 x 5) Need to know tables! 75 ÷ 5 = 15 BBC News Video Link

72 ÷ 4 = 18 18 4 72 we know 10 x 4 40 - 32 we know 8 x 4 32 - .

New Curriculum Aims FLUENCY REASONING PROBLEM SOLVING

Introducing the Bar Model Relationships within the

Problems to solve Tom has a bag of 34 marbles. His friend gives him 28 more. How many does he have now? 34 28 Ask participants to use the bar(s) to solve the problems, allow them to record in their own way and then compare how they drew the bars For problem 2 you might discuss whether 1 or 2 bars were drawn to illustrate the concept of difference 62

Kelsey was running a 26 mile marathon Kelsey was running a 26 mile marathon. After 18 miles she felt very tired. How many more miles did she have to run? 26 18 8

Multiplication The sum of 2 numbers is 60. One number is 3 times as big as the other. What is the bigger number? 45 15 15 15 15 Participants draw bars/blocks and calculate the answers to the problems 60

Ratio Tim 12 12 Sally 12 12 12 36 Additional slides, explore ratio if time Tim and Sally share marbles in the ratio of 2:3 If Sally has 36 marbles, how many are there altogether? 60

KS2 2012 Ask participants to solve this problem and ask how hard Y6 children found this? The majority of children found this difficult – even those at L5! Explain that we will explore representations that might help children to more easily access the structure of the mathematics and solve the problem.

GCSE higher paper 2012! Ralph posts 40 letters, some of which are first class, and some are second. He posts four times as many second class letters as first. How many of each class of letter does he post?

Make sure maths is fun! How can you help? Use school methods Talk about how you do maths Be positive Ask your child to explain Give praise and encouragement (Animated slide) Final slide and how parents can help at home. Encourage parents to talk to the teachers. LEA publications: Sums and things for parents Helping your child with maths Useful websites for parents: www.leics.gov.uk/education/ngfl/numeracy www.standards.dfes.gov.uk Make sure maths is fun!

Helping at home KS1/ EYFS Play board games Cook – measuring and weighing Look at numbers in the environment e.g. telephone keys, number plates, door numbers, book pages, sleeps until Christmas! Money Comparing heights Birthdays, Months of the year, Days of the week Time  

Props around the house KS2 A prominent clock A traditional wall calendar Board games that involve dice or spinners A pack of playing cards A calculator Measuring Jug Dried beans, Macaroni or Smarties A tape measure and a ruler A large bar of chocolate Fridge magnets with numbers on Indoor/outdoor Thermometer Unusual dice A dartboard with velcro darts )

Homework! Related to classwork Use method shown in class Check with teacher if unsure! It’s the child’s responsibility to complete their homework!

ICT games Crickweb Top marks Woodland juniors Maths Zone