Presentation on theme: "Progression In Calculations at Lyndhurst First School."— Presentation transcript:
1 Progression In Calculations at Lyndhurst First School. Addition and SubtractionMathematical Calculations in School Today.This document is designed to help you to understand the calculation methods your child will be taught in school. When supporting your child at home with Maths work it would be helpful if you could reinforce these methods rather than teach them the way that you were taught. The methods are levelled according to ability and you would need to speak to you child’s teacher to find out which methods would currently be the most appropriate for your child to practice at home.Remember each child progresses at their own pace.
2 Understanding Addition. (EY/1C/1B) ExplanationThe physical act of counting outa set number of objects, and combining two groups, is an important step for children to explore. This is best done in a practical play based context as much as possible.Use a Numicon shape and add on the 1 shape... What number do you have now? Find the new Numicon shape to cover over the top.Understanding addition as combining two groupsChildren need to experience counting out a set of objects and combining them with another set of objects to make a total amount. Initially this needs to be adding 1 more.Eg. 4 plus 1 makes 5.Count out a set of 4 and another set of 1. Then count them altogether to reach a total of 5Explore 1 more through simple songs and rhymes, for example ‘1 man went to mo’ or ‘1, 2, 3, 4, 5, once I caught a fish alive’.Success criteriaI can add one to a small group of objects up to a total of 10 and explain what I am doing.I can count out 1p coins to pay for 2 items totalling up to 10p.Key Questions/VocabularyMore, more than, one more, after, add, plus, count, total, equals, makesWhat is the number after 6?How will you find out how many there are in total?Can you show me how you worked out 1 more than....?
3 Understanding Subtraction. (EY/1C/1B) ExplanationThe physical act of counting outa set number of objects and taking some away is an important step for children to explore. This is best done in a practical play based context as much as possible.Count out a given number of objects and take away 1 of them... How many do you have now?Understanding subtraction as taking awayChildren need to experience counting out a set number of objects and then removing/taking away a certain number from that group. Initially this needs to be taking away 1 from a set.Eg take away 1 leaves 6Count out 7 objects. Then remove 1 from that set and count the objects that are left over.Explore 1 less through simple songs and rhymes, for example ’10 green bottles’ or ‘5 little speckled frogs’.Success criteriaI can use objects to take away 1 from any number up to 10.I can work out how much I have left from an amount up to 10p when I buy a sweet costing 1p (using 1p coins to work practically).Key Questions/VocabularyLess, less than, one less, before, take away, subtract, leaves, equalsWhat is the number before 5?How many different ways can you show me that 8 subtract 1 is 7?Can you show me how you worked out 1 less than.....?
4 Using a Number Track for Addition. (1B/1A) One more than four is fiveExplanationNumber tracks can be used for children to locate a number, learn the order of numbers, and to begin to add one and then more than one to a given number.Children need to be able to understand the order of numbers remains the same and that as we count on the numbers get bigger by 1. They need plenty of practise in counting objects and by rote... Count the stairs as you go up to bed... Count your footsteps as you walk across a room.... Write the numbers to 10 on separate pieces of paper and get your child to put them into order, counting to check., then progress to ordering numbers to 20.Begin to recall all pairs of numbers that total 10.Begin to know doubles up to double 5.Key Questions/VocabularyCount on, add, more, more than, equals, totals,makesFind the number that is one more than...? 4more than...?Count on 3 places from 15, where do you land?How many is 5 more than 8?Order Numicon1 – 10 set, place a shape on top of the next one, noticing how there is a difference of 1.Success criteriaI can use a number track to count on and find the answer to an addition sum up to 10 and then to 20.
5 Simple Jottings/Mark Making for Addition. (1B/1A) =ExplanationSimple mark making is the first stage of children’s independentjottings to help them solve additions. They draw or make theappropriate number of marks under each number then count them upto reach the total. It is not necessary to draw the number of marksunder the answer. Children can also use objects, such as counters,sweets, beads, to create groups to combine to find the total of anaddition.Children need to begin to see that addition produces the same answer which ever way round it is solved eg 8 + 2=10 and 2+8=10.It is COMMUTATIVE. Lay the 8 and 2 Numicon shapes together and place another 2 then 8 on top to see it is the same. Encourage children to see that it is easier and quicker to count on from the largest number.Key Questions/VocabularyCount, count on, more, add, plus, sum,altogether, total, equalsHow many altogether?Find the number that is five morethan...?Count on 6 more from 13, what numberdo you get to?Success criteriaI can use simple jottings to support the addition of two numbers up to a total of 10, then 20.I can begin to select appropriate apparatus to support addition.
6 Using a Number Track for Subtraction. (1B/1A) One less than nine is eightExplanationNumber tracks can be used for children to locate a number, learn the order of numbers, and to begin to find out one less and then a few less than a given number.Children need to be able to understand the order of numbers remains the same and that when counting back the numbers get smaller by 1. They need lots of practice in counting backwards... Count back as you go down the stairs.... Do a countdown from 10 or 20 before you leave the house....Write the numbers to 10 on separate pieces of paper and get your child to order them in reverse, then try from 20.Key Questions/VocabularyCount back, take away, subtract, less than, leaves,equalsFind the number that is one less than ....? Five lessthan....?Count back 4 places from 8, where do you land?How many is 5 less than 9?Order Numicon1 – 10 set, note the difference between two shapes next to each other is 1.Success criteriaI can use a number track to count back and find the answer to a given question starting from numbers up to 10, then up to 20.
7 Simple Jottings/Mark Making for Subtraction (1B/1A) =ExplanationSimple mark making is the first stage of children’sindependent jottings to help them solve subtractions.They draw the initial number of objects and thencross off the number it says to take away andcount the ones left over. Children can also useobjects, such as counters, sweets, beads, to createthe initial group and then physically take away theright number to find the answer to the subtraction.At this level, children need to see that when doing subtraction the biggest number needs to be first and you take away the smaller number.Success criteriaI can use simple jottings to support the subtraction of two numbers starting from numbers up to 10, then 20.I can begin to select appropriate apparatus to support subtraction.Key Question/VocabularyCount, count back, subtract, take away, cross offDifference between, leaves, equalsHow many are left over?Find the number that is 6 less than...?Count back 5 from 16, what number do you get to?
8 Using a Blank Number Line for Addition. (1A/2C) ExplanationBlank number lines are used to enable children to count on and back with more than one jump. Children are taught to draw their own number line and start with the biggest number. There is no need to write +1 in each jump. Children learn to use ones jumps, adding single digit numbers and working within a range up to about 20. It is only necessary to record where they start and where they end up after adding on. They can then progress to using this method of single jumps when adding ‘teen’ numbers and working within numbers to about 30. Remember to jump on from the biggest number!= = 21Rapidly recall all pairs of numbers that have a total of 10.Know doubles to double 5 and begin to know doubles up to double 10.Success criteriaI can use number lines to support the addition of two numbers starting from numbers up to 20, then 30.I can use a number line to help me solve addition problems involving money , up to 30p, and measures, up to a similar amount.Children can use Deines (one blocks) to place in the jumps and support the visual image of how many they need to add on.Key Questions/VocabularyCount on, count on in ones, add, plus, more than, total,equals, makesWhich number are you going to start your line with?How many ones jumps do you need to do?What number have you reached?
9 Using a Blank Number Line for Subtraction. (1A/2C) ExplanationBlank number lines are used to enable children to count on and back with more than one jump. Children are taught to draw their own blank number lines, enabling them to do calculations within any range of numbers. There is no need to write -1 in each jump. Children learn to use ones jumps, subtracting single digit numbers and working within a range up to about 20, then 30. Their recording methods should be the same as for addition, except that with subtraction they start at the right hand end of the line and jump back.9 – 4 = – 6 = 8Success criteriaI can use number lines to support the subtraction of two numbers starting from numbers up to 20, then 30.I can use a number line to help me solve subtraction problems involving money , up to 30p, and measures, up to a similar amount.Children can use Deines (one blocks) to place in the jumps and support the visual image of how many they need to count back.Key Questions/VocabularyCount back, count back in ones, less than, take away,Subtract, leaves, equalsWhere are you going to start your number line?Which number are you starting with?How many jumps back do you need to do?What number have you reached?
10 Developing use of Number Lines, Adding Tens and Ones. (2B) Children need to understand the place value of each digit in order to partition 2-digit numbers into tens and ones.+1026p + 12p = 38pRecall all + and – facts for each number to at least 10.Know doubles up to double 10 and their corresponding halves.26p p p= 54Key Questions/VocabularyAddition, add, plus, more, more than,ten more, count in tens, one more, count inones, total, equals, altogetherHow many tens jumps do you need to do?How many ones jumps?Inverse (children need to know at thisstage that addition and subtraction areinverse operations, they undo each other)ExplanationWhen children understand that 15is made up of one ten and five ones,they can learn a more efficientmethod of using a number line thanjust doing 15 single jumps. Whenconfident adding on ‘teen’ numbers,progress to adding numbers withmore than one ten.Success criteriaI can use number lines more efficiently to add on 2-digit numbers by adding on the tens and then the ones.
11 Developing use of Number Lines, Subtracting Tens and Ones. (2B) Children need to understand the place value of each digit in order to partition 2-digit numbers into tens and ones.-1048g – 13g = 35g35g g g116 – 24 = 92Key Questions/VocabularySubtract, take away, minus, less than,ten less, count back in tens, one less,count back in ones, leaves, equals,Difference between (we find thedifference between when the numbersare close together and it is easier andquicker to count up than back.Eg 53 – 47, it is easier to count on from47 to find the difference between thetwo numbers than count back 47 places.)ExplanationSubtracting tens and ones is the same as foraddition. Jottings are set out as shown, with arecord of where you have reached kept underthe line and the jumps done recorded over theline. There is no need to write +1 or -1 in thesmall jumps, this would be inefficient. Whenconfident adding on ‘teen’ numbers, progress toadding numbers with more than one ten.Success criteriaI can use number lines more efficiently to subtract a 2-digit number by counting back the tens jumps and then the ones jumps.
12 Add or subtract 9 or 11 by Compensation (2B/2A) To add 9, + 10 then -1To subtract 9, -10 and then +1= 34146 – 9 = 137+10-10To subtract 11, -10 then - 1To add 11, + 10 then + 185 – 11 = 74= 128-10+10Practical exploration with money, using 10p and 1p coins can help to support the understanding of which way to compensate.ExplanationWhen adding or taking away 9, childrenare taught that it as quicker to add/subtract ten and then adjust by oneaccordingly. This is why it is importantthat children recognise numberpatterns to count on and back in tensfrom any number.Success CriteriaI can quickly add or subtract 9 from any 2 or 3 digit number by adding or subtracting 10 first and then adjusting by 1.I can quickly add or subtract 11 from any 2 or 3 digit number by adding or subtracting 10 first and then adjusting by 1.Key Questions/VocabularyAdd, plus, more than, sumSubtract, take away,minus, less thanEquals, leaves, totalsadjust
13 Partition and Recombine. (2B/2A) To add 23 and First add the number of tens,so = 50Then add the number of ones, so = 8Finally combine the answers to give the total,so = 58= 58ExplanationSome children find this strategy a quick and easy method for addition, thatthey soon are able to do it mentally. Initially it is important to givecalculations where the ones digits do not total more than 10, (we say theydon’t cross the tens boundary). Once they are confident in this methodthey can progress to partition and recombining 2-digit numbers where theones do cross the tens boundary,eg So 30+20=50, 7+6=13 Then =63Success CriteriaI can do addition more efficiently by partitioning numbers into tens and ones and then recombining them.Key Questions/VocabularyTens digit, ones digit, unitsPartition, split, recombineHow many tens? How many ones?How many altogether?Confidently recall + and – facts to 10 then 20 (eg, 9 + 6, 13 – 7, )Know all + and – facts for multiples of 10 to 100 (eg, , 90 – 20)
14 Develop Efficient Use of Number Lines. (3C/3B) = 117+40+3152 – 68 = 96-6-60-2ExplanationOnce children are confident and accurate in the use of tens and ones jumps, they can progress to usingmultiple of tens jumps. Encourage children to use their knowledge of number bonds to bridge to the nearestmultiple of 10 to make counting easier (as in the second eg). Make sure they keep a record in their jumps ofwhat they are doing so that they can check they have + or – the correct number.Use mental recall of + and – facts to 20 and apply to problems.Know all the + and –facts for multiples of 5 to 100 (eg , 80 – 55).Derive rapidly all number pairs that total 100 (eg , )Success CriteriaI can add and subtract chunks of tens and ones to make my calculations more efficient.I can bridge through the nearest multiple of ten.Key Questions/VocabularyAddition, add, plus, more, more thanSubtract, take away, minus, less thanTen more, ten less, count in tensOne more, one less, count in onesDifference between, inverseEquals, leaves, altogether
15 Partition and Recombine. (3C/3B) Deines can be used to create a clear visual image of the place value of each digit and supports the understanding when the tens or hundreds boundaries are crossed.= 384= 526ExplanationAt this phase. Children canpartition and recombinenumbers that may cross thetens or hundreds boundary.They will also be able to use thismethod with 3-digit numbers.Success CriteriaI can add 3 digit numbers by partitioning them into hundreds, tens and ones, adding them and then recombining to reach the total.Key Questions/VocabularyHundreds digit, tens digit, onesdigit, Partition, split, recombineHow many hundreds? tens? ones?How many altogether?