Addition & Subtraction Workshop - Great Missenden

Thursday 25 th April

AdditionStages of progression in Early Years and Key Stage 1• Counting in number rhymes and stories• Finding one more than a number from 1 to 10• Use vocabulary associated with addition• Know by heart all number bonds to 10• Begin to use the + and = signs to record mental calculations• Know that addition can be done in any order to refine mental calculations• Use numbered number lines• Use blank number lines• Use partitioning to reflect mental calculations

Stories can be used as a great starting point for maths work.Here are some example questionsyou could use withThe Very Hungry Caterpillarby Eric Carle.• How many plums did the caterpillar eat ?• How many plums and strawberries did the caterpillar eat altogether ?• How many things did the caterpillar eat on Saturday ?• The caterpillar ate 5 oranges. How many more did he need to eat if he ate 10 orangesaltogether ?• What is the total number of things the caterpillar ate on Tuesday and Wednesday ?• On Monday the caterpillar ate 1 apple. How many would he eat if he ate one more ?• On Thursday the caterpillar ate 4 strawberries. How many would he eat if he ate 1less.• Can you say the days of the week in the correct order ?• Which days are in the “weekend” ?• On which days did the caterpillar eat an odd number of things ?• On which days did the caterpillar eat an even number of things ?• Write your own story about the very hungry caterpillar. What is he going to eat in yourstory ?• Can you write a story where the caterpillar eats a total of 20 things ?• Can you write a story where the caterpillar eats double the amount of things ?

Maths Vocabulary• It is important to vary the vocabulary we use whenwe question children e.g.“7 add 3”Can also be phrased as,7 plus 3What is the sum of 7 and 3 ?What is 7 and 3 altogether ?What is the total of 7 and 3 ?What is 3 more than 7 ?What does 7 and 3 make ?

Learning Number Bonds: Traditional GamesTraditional games are brilliant for early addition• DominoesCan you find the dominoes with a total of 10 ?Can you find all the dominoes that have a total of 7 ? How many combinations didyou find ?• Dice gamesAny dice games like snakes and ladders involve addition.Make your own games on a 100 square• CardsPlay number bond Snap !Instead of looking for identical cards look for cards that add up to a target numbere.g 10 or 20.Play PontoonStick or twist to try and reach a target number e.g. 21• Lady bird AdditionMake ladybird pictures that add up to 10 or 20.• Money SpidersMake each leg of the spider add up to 10p or 20p

• Make number bond bracelets or necklaces with bead stringsUse colour combinations to make totals of 10 or 20.• Make Pasta PicturesMake pasta sums that total 10 or 20• Number Bond Song(sung to the tune of Frere Jacques)1 add 9,1 add 9,9 add 1,9 add 1,Add them all together,Add them all together,That makes 10, that makes 10• DartsDarts helps children practise doubles and trebles.If the numbers are too big, change them for numbers 1 to10 or 1 to 5 spreadrandomly around the board.For addition of higher numbers darts is a great game for developing mental mathsskills

How do children learn ?Different Learning StylesWe all learn in different ways. Psychologists have categorised theway people learn into 4 main learning styles:• Visual Learners• Kinaesthetic Learners• Auditory Learners• Logical LearnersIt is important to remember that our children may not learn in thesame way as ourselves. If we identify how our children prefer tolearn, it can help us, help them.

Visual Learners• Needs and likes to visualise things• Learns through images - can remember the pictures on a page• Enjoys art and drawing• Reads maps, charts and diagrams well• Interested in machines and inventions• Plays with Lego and other construction toys, and likes jigsaw puzzles.• Can be a daydreamer in class.Kinaesthetic Learners• Processes knowledge through physical sensations• Highly active, not able to sit still long• Communicates using body language and gestures• Shows you rather than tells you• Wants to touch and feel the world around them• May be good at mimicking others• Enjoys sports or other activities where they can keep moving.

Auditory Learners• thinks in words and verbalises concepts• spells words accurately and easily, as they can hear the different sounds - sotends to learn phonetically rather than through 'look and say' techniques.• Can be a good reader, though some prefer the spoken word• Has excellent memory for names, dates and trivia• Likes word games• Enjoys using tape recorders and often musically talented• Usually able to learn their times tables with relative ease.Logical Learners• Thinks conceptually, likes to explore patterns and relationships• Enjoys puzzles and seeing how things work• Constantly questions and wonders• Likes routine and consistency• Capable of highly abstract forms of logical thinking at early age• Does mental arithmetic easily• Enjoys strategy games, computers and experiments with a purpose• Creates own designs to build with blocks/Lego• Not so good at the more 'creative' side.

With so many different ways of learning, teachersplan a range of different approaches to teachingmaths.Many children need a visual image of their mathswork to help them understand it. We use a range ofteaching equipment in school to help us.It is very interesting to consider what learning styleyou think you fit into.Do your children learn in the same way ?

Using Number lines for AdditionChildren then move on to drawing their own empty number lines.Here the child starts with56 and has made 3 jumpsof 10 and then a jump of 4to add 34.This child has made the jumpof 4 to get to the multiple of 10and then added the 30 in asingle jump.

Partitioning• Partitioning is a key mental strategy children learn• Children learn to separate out the tens and units• E.g. 47 + 7640 + 70 = 1107 + 6 = 13110 + 13 = 123and later move on to partition hundreds, tens andunits.This mental strategy forms the basis of many ofthe unfamiliar expanded methods.

Stages of progression in Key Stage 2• Informal pencil & paper methods which introduce verticalsetting out of calculation ( most significant digit first )TU + TU• Move on to HTU + HTU with the same strategy• Start to add least significant digit first• Extend to bigger numbers• Formal compact method involving carrying• Extend to decimal numbers

Expanded Method for AdditionCalculate 536 + 242The children are taught to partition the number on paper inexactly the same way as they would do in their heads. Theybegin by adding the largest or most significant numbers first.Stage 1 Stage 2500 + 30 + 6 5 3 6+ 200 + 40 + 2 + 2 4 2700 + 70 + 8 7 0 07 0Answer 778 87 7 8

• This expanded method may feel long winded however itallows children to see the real value of all the numbers.• The language we use is very important to help childrenunderstand the size of the numbers being addedStage 32 7 8+ 1 5 61 4 “eight plus 6 equals fourteen”1 2 0 “seventy plus fifty equals one hundred and twenty”3 0 0 “two hundred plus one hundred equals three hundred”4 3 4*You may also notice that in this example the units are added first, in preparation formoving onto a compact method.

SubtractionStages of progression in early years and Key Stage 1• Counting backwards in number rhymes and stories• Finding one less than a number from 1 to 10• Begin to relate subtraction to “taking away”• Begin to use the – and = signs to record mental calculations• Know by heart all subtraction facts to 10• Know by heart all subtraction facts to 20• Use informal jottings to record calculations e.g. pictures

Maths Vocabulary• It is important to vary the vocabulary we use whenwe question children e.g.“7 take away 3”Can also be phrased as,7 subtract 3What is the difference between 7 and 3 ?What is 7 minus 3 ?What is 3 less than 7 ?If I take 3 from 7, how many are left ?

Using Number Lines for SubtractionNumber lines can help children gradually refine strategies.Child A has made 4 jumps to find the difference between 84 and 197.Child B has made 3 jumps and can jump from 84 to 100 in a single jump

Expanded Method for Subtraction• Use an informal paper and pencil strategy towork out some calculations.• e.g 428 – 174 =300 120400 20 8- 100 70 4200 50 4This method ensures the children understand the realvalue of each digit in the numbers and the real valueof what they “borrow” from the column to the left.

Real Life Problem SolvingA key skill for children to develop is the ability to apply their calculationstrategies to real life problem solving situations.When solving problems children have to:• Read and understand the question• Identify the important information• Identify which operation they need to use to solve the problem• Identify how many calculations are required. Is it a one step problem or amulti-step problem ?• Estimate• Carry out the calculation, showing all working and methods used• Relate their answer to the original problem• Does it answer the problem ?• Is my answer feasible ?• Do I need to write cm, ml, £, p, etc….• Do I need to round my answer up or down to make sense ?

Useful Websites & BooksIn the back of your booklets I have listed somewebsites and books which may be helpful to you athome.