Mathematics Workshop 2013 www.chaddlewood-primary.plymouth.sch.uk/maths

and why we’ve changed some things What we’ve learnt, and why we’ve changed some things

As part of our regular assessments within mathematics we identify; How we found out.. As part of our regular assessments within mathematics we identify; - Children making ‘above’ expected progress within a particular mathematical area This helps us to identify how we can stretch their knowledge and understanding (for example, the child might have mastered a concept and be able to apply the skill. We then move the child carefully on to the next step). Children making ‘average’ progress within a particular mathematical area Children making ‘below’ expected progress within a particular mathematical area We can then investigate the cause of this and, as appropriate, alter how these strategies are addressed

How we found out.. To find this out we…. Carry out informal assessments by; - observing what children do without our help - question them to identify how far their understanding reaches - ask ‘how’ they know Through; - what they normally do in class - monitoring by myself and external organisations/people - the recording within their books

We identified... That some children answer questions literally That some children struggle with understanding a lot of different approaches to a problem - That some children were slow at calculating mentally

and what children do too What you do, and what children do too

Question 1 I have 28 apples in one hand and 57 apples in the other. What have I got..? Big hands

Question 2 Find x. Here it is! 4cm 3cm x

Answer 3 Write the number one hundred and two in digits. 1002

Place Value Simply – recognizing that the value of a digit is determined by its place in a number. TH H T U . Tenths Hundredths 1 3 2 5 3 2 5 1 3 2 5 4 . 1

Common mistakes… - Writing ‘one hundred and thirty six’ as 10036. - Thinking that 6,000 is one more than 5099. - Thinking that 3.153 must be larger than 3.35 because it has more digits in it. - Thinking that 0.75 is smaller than 0.203 because 75 is smaller than 203.

Question 4 Sam has £1 in his pocket and apples cost 30p each. How many apples can Sam buy? Show how you got your answer. 3. Sam told me.

What we’ve changed, and what we haven’t

How can you prove to someone that the answer to 9+6 is 15? Some problems... How can you prove to someone that the answer to 9+6 is 15? Which is bigger… 23 or 32? How do you know? What is 149+353?

How things develop across the school

Addition

Addition Counting using objects. Jumping on a number line (of increasing size). Using a hundred square to add 10. … 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Addition Partitioning two digit numbers Adding two digit numbers together (using any equipment, normally hundred squares) Adding two digit numbers together (without equipment) Adding three digit numbers together using above strategy.

Addition Using ‘empty’ number lines. More formal methods of addition. 23 + 12… 20 + 10 = 30 3 + 2 = 5 = 35

Addition Problems which do NOT involve the need to ‘carry’. Problems which do involve ‘carrying’. 358 358 + 31 +138 = 9 (8 + 1) = 16 (8 + 8) 80 (50 + 30) 80 (50 + 30) 300 (300 + 0) 400 (300 + 100) 300 + 80 + 9 = 389 400 + 80 + 16 = 496

Addition Further condensation of method.

Addition Adding decimals. Adding problems including brackets. Algebra. (4 + 7) x 3 =

Addition Condensing algebra. 4f + 7 = f + 16 4f + 7 – 7 = f + 16 – 7 take 7 off both sides 4f = f + 94f – f = f + 9 – f take f off both sides 3f = 9f = 3 divide both sides by 3

Subtraction

Subtraction Using songs and rhymes. Using pictures to take away. Using number lines: ‘11 take away 7 is…’ Finding the difference between quantities. Using number lines: ‘What is the difference between 11 and 7?’

Subtraction Using hundred squares. Subtraction as the inverse to addition. Finding missing numbers, e.g. 2 + 7 = 2 + = 9 2 + 7 = 9 7 + 2 = 9 9 – 7 = 2 9 – 2 = 7

Subtraction Taking away using tens and units. 23 – 12 = Using number lines. 47 – 11 = 22 – 7 = 16 – 9 =

Subtraction More formal representations. 87 – 32 = 55 because 87 – 30 = 57 57 – 2 = 55 Formal written methods. ‘Borrowing’.

Subtraction Decimal numbers 34.8 – 26.4 =

Multiplication

Multiplication Adding groups of equipment. Understanding X as ‘lots of’. 5 + 5 + 5 Arrays.

Multiplication Partitioning numbers. Grid method. 6 x 124 = 124 books were sold. Each book cost £6. How much money was taken?

Multiplication Vertical method 124 x 6 24 (6 x4) 120 (6 x 20) 744 Grid method for larger numbers.

Multiplication ‘Short’ multiplication. 4 6 x 9 4 1 4 4 5

Multiplication ‘Long’ multiplication Making it shorter…

Using multiplication facts ·It is vital that children know their times tables as all the work higher up the school relies on them knowing their tables. ·Tables should be learned at least 2-3 times a week. What is expected Year 2 2 times table 5 times table 10 times table Year 3 2 times table 3 times table 4 times table 6 times table Year 4 Derive and recall all multiplication facts up to 10 x 10 (5 second recall) Years 5 & 6 Derive and recall quickly all multiplication facts up to 10 x 10 (5 second recall)

Division

Division Practical sharing. Counting on in ‘groups’.

Division Introducing sharing.

Division More complex grouping. and sharing.

Division Using number lines. Knowing division as the inverse of multiplication.

Division Remainders. Using number lines confidently.

Division Formal method.

Division Remainders as a fraction. Division of larger numbers.

Division Division including decimals. ‘Bus Shelter’ method.

The models that we use, and why we use them

Partitioning Children need to understand that in 102 there is one lot of one hundred, zero lots of ten and two units. Zero ‘holds’ the place of the tens.

3276 3000+200+70+6 Partitioning So 52 x 3 becomes 50+50+50 and 2+2+2 … Breaking a number up according to its place value. (typically to make addition and multiplication easier). 3276 3000+200+70+6 So 52 x 3 becomes 50+50+50 and 2+2+2 …

How you can support mathematics learning at home

What can I do at home? As well as looking at these strategies at home (in this order), you could… Play number games. Recognise numbers around shops and the environment. Ask for an amount of something. Make number patterns (e.g. one apple, two oranges, three bananas) Use dice – count the dots quickly, predict bottom number on die, difference between two rolls… Which number is missing? Guess the number (it’s one more than 5, it’s between 100 and 150) Share an amount between 2, 3, 4 people. Count backwards and forwards from a given two-digit number. Estimate total of something by rounding to 10, 100, etc. Experiment with shapes through painting, ‘spot the shape’, patterns

What can I do at home? Measures. Cooking! Count up money to find a total. Work out change from shop. Telling the time. What time will it be one hour from now? How long have you spent doing something? What can you do in one minute? Times tables!

What can I do at home? A prominent clock in the kitchen – ideally analogue and digital. Display a traditional calendar, and refer to it. Board games that involve dice and spinners – helps not only with counting but with the concepts of chance. Traditional playing cards – simple games such as snap are a natural way of learning about sorting and chance. Dominoes – to help with number combinations. Using a calculator, for example when shopping. This shouldn’t be seen as a way of ‘cheating’ – just a way to save time. We use these in class to save time to focus on what is really happening. Measuring jugs with scales / kitchen scales. Dried pasta…or Smarties! – useful for counting large collections to investigate remainders etc. Tape measure and ruler – involve your child in ‘real life’ situations. An indoor / outdoor thermometer.

What can I do at home? www.funwithspot.com Great interactive maths games for KS1   www.ladybird.co.uk Counting, matching etc for KS1 www.bobthebuilder.com Challenging activities for KS1 www.teachingtime.co.uk Great site for learning time, includes an interactive clock www.ricksmath.com Learning basic maths skills www.mathsisfun.com Maths games, puzzles and activities General websites: www.mathletics.co.uk www.chaddlewood-primary.plymouth.sch.uk/maths www.mathszone.co.uk www.woodlands-junior.kent.sch.uk/maths www.funbrain.com www.nrich.maths.org Lots of problem solving activities  www.puzzlemaker.com A tool for making and customising maths puzzles    www.coolmath.com Fun maths games   www.4learning.co.uk/numbercrew Good KS1 maths site www.thinkquest.org/25459 Maths games, quizzes ,and problem solving activities

Any questions?