ࡱ> Y bjbjWW %==]< !Fp"""EEEEEEE$FHF F"/""" F?+ p???"jE"E??1DrETEt-{%E Pre- R Year R Year 1 Year 2 Year 3 Year 4Teaching Programme: COUNTING AND RECOGNISING NUMBERS COUNTING 1-5 Say and use the number names in order in familiar contexts such as number rhymes e.g. 5 Little Ducks. Recite the number names in order, continuing the count forwards and backwards to 5 and from 5. EQUIVALENCE Demonstrate relationships between objects e.g. glove for hand, shoe for foot etc. Recognise when 2 small sets are equivalent. Create a set equivalent to a given set by matching experiences of situations where 1:1 matching is important. Describe situations where 1:1 matching is important.  Pre- R CARDINAL NUMBERS 1 5 Can pile concrete apparatus e.g. cubes, cotton reels etc. Distinguish between a single item and many items. Recognise the numeral 1, the spoken word one and associate them with 1 item. Recognise 2 items and use the word two or pair to describe them. Recognise the numeral two, the spoken word two and associate them with two items. Recognise 3 items and use the word three to describe them. Recognise the numeral 3, the spoken word three and associate them with 3 items. Recognise 4 items and use the word 4 to describe them. Recognise the numeral 4 and spoken word four and associate them with 4 items. Recognise five items and use the word five to describe them. Recognise the numeral 5, the spoken word five and associate them with 5 items.  Pre- R  Pre- R READING AND WRITING NUMBERS Recognise any number of items from 1 5 and use words to describe them. Draw the numerals 1 5.  Pre- R Begin to record numbers by making marks. Use language such as more or less or fewer or the same as in the context of sets of objects. Recognise which sets contain more than, fewer than less than or the same as by matching. Discuss situations where more than, less than occur. Construct sets containing more than, fewer than less than or the same as Draw sets containing more than, less than or the same as Place sets of objects in order according to the number in the set. Write the numerals 1 5 in order. Order numeral cards so as to make a number track from 1 5. Associate the correct number of objects with each numeral on a number track. Count out any number from 1 5. Understand that the last number counted gives the size of the set. Pre-R Count objects and pictures from 1 5 presented in a variety of ways. In the context of counting up to 5 objects, begin to realise that the number of objects is not affected by their size, shape, type or position; In the context of counting up to 5 objects, begin to realise that the purpose of counting is to tell how many there are. In the context of counting up to 5 objects, know that the last number name spoken is the answer to how many questions and tells you how many there are. In the context of counting up to 5 objects, begin to realise that no matter in which order the collection is counted the number remains the same; In the context of counting up to 5 objects, know that if two different counts of a collection give different answers, then something is wrong. Begin to recognise small numbers of objects without counting e.g. collections up to three objects, number of fingers held up on one hand; dot patterns to 5 on dice, cards, dominoes. Name the first, second and last object in an ordered set. Follow instructions to order objects first, second and so on. Be introduced to ways of counting systematically to keep a track of the count e.g. by touching them one by one. Be introduced to ways of counting randomly arranged objects arranged, e.g. by moving them into a straight line or by moving them across one by one when counting. Begin to recognise counting errors e.g. made by a puppet. Begin to discuss ways of counting so that it is easier to count accurately. Pre-R ESTIMATION Estimate numbers of objects up to three.  Pre-R  Pre-R  Pre-R  Pre-R  Pre-R Pre-R Pre-R Pre-R Pre-R  Pre-R  Pre-R SOLVING PROBLEMS REASONING ABOUT NUMBERS OR SHAPES Talk about, recognise and experience simple pattern Experience pattern through threading beads, arranging building blocks in repeating sequences of colour etc. Copy a model of a simple repeating pattern. Be introduced to pattern in everyday life e.g in clothing, wallpaper, the environment Be encouraged to solve simple problems or puzzles in a practical context and respond to What could we try next? Experience sorting by shape, texture, size, function etc. Sort things as part of classroom routines. Pre-R Name the common colours and sort accordingly PROBLEMS INVOLVING REAL LIFE OR MONEY Be encouraged to use developing mathematical ideas to solve practical problems involving counting and comparing in a real or role play context.  Pre-R MONEY Be introduced to the names of the different coins, penny and pence. Match coins and use them in role play. identify and name 1p coin. Count 1p coins to 5p. Use 1p coins to correspond to prices to 5p.  Pre-R MEASURES, SHAPE AND SPACE COMPARING AND ORDERING MEASURES Introduce terms such as Large / small in the context of objects Introduce vocabulary such as long, short, tall. Introduce vocabulary such as thick, thin, wide, narrow. Experiment with sand and water and other materials, pouring from one container to another etc. Be introduced to the terms full, empty, part full in the context of their pouring activities. Experience a range of activities whereby objects are sorted using the criteria heavy, light, the same when weighing with hands. Be introduced to the terms heavy, light, the same Use the terms heavy, light, the same appropriately. Be introduced to the terms heavier and lighter in the context of comparing 2 objects. Experience practical activities that involve area e.g. putting bed-clothes on dolls, covering paper with paint, colouring in outline etc. Pre-R TIME Be made aware of patterns such as the sequence of the day, night, day, night etc. Be introduced to the pattern of the days of the week.  Pre-R EXPLORING PATTERN, SHAPE AND SPACE Match objects to holes (sorting box) Matching objects to holes (inset puzzle) Use tools to create shapes e.g. playdoh, pastry and cutters etc. Introduce common 2D shape names: circle, square, rectangle, triangle. Create 2D shapes by drawing around a template or inside a stencil Experiment with 2D shapes, placing them in different positions etc. Begin to sort 2D shapes by grouping similar shapes together. Experimentation with 3D shapes in a range of contexts to develop an understanding of their properties. Free play with a variety of spheres to develop an understanding of their properties. Experimentation with a range of construction toys. Use reclaimed materials to make models. Begin to sort 3D shapes by placing similar shapes together. Experience pattern using 2D and 3D shapes.  Pre-R POSITION AND MOVEMENT Use everyday words to describe position Understand inside and outside, up and down, first, second and last, high and low to describe position. Experiment with a programmable toy to create movement. Begin to use the instruction forward (Fd) and backward (Bk) in the context of moving the toy.  Pre-R Begin to follow simple instruction to create movement e.g. in PE. Teaching Programme: Reception COUNTING AND RECOGNISING NUMBERS COUNTING AND PROPERTIES OF NUMBER Say and use the number names in order In familiar contexts such as number rhymes, songs, stories, counting games and activities ( to ten, then twenty and beyond). Recite the number names in order, continuing the count forwards or backwards from a given number. Say the number name that goes after a given number. Start from a given number and stop at another. Count on several numbers from a given number. Recognise that somethingtynine signals a change in the decade. Say the number name that goes before a given number name. Start to use zero as an extension of the counting sequence when counting backwards. Recite the number sequence consistently back to zero from 51020 a number such as 16 Start from a given number name and count back to another. Count back several numbers from a given number. . Year R Count reliably up to 10 everyday objects (first to 10, then beyond), using a wide variety of opportunities. Give just one number name In one to one correspondence with an object. Begin to realise when counting that the number of objects is nor affected by their size, shape or position. Count out a specified number of things from a collection of objects. Recognise small numbers without counting, number of fingers held up on one hand and then two, dot patterns on dice, dominoes, playing cards. Begin to realise that there is no need to count when the number can be recognised without counting. Know the purpose of counting is to tell how many there are. Know the last number name spoken is the answer to how many questions and tells you how many there are. Know that, no matter in which order a collection is counted the number remains the same. Know that if two different counts of a collection give different answers, then something is wrong. Count systematically to keep a track of the count. Count a collection of objects in different arrangements, organising the count by using a strategy for keeping track of where the count begins and ends. Count objects in a line first touching them one by one, then without touching them. Count objects arranged randomly by moving them into a straight line. Year R Count objects arranged randomly by moving them across one by one when counted. Count objects arranged randomly by leaving them in position but touching them. Count objects arranged randomly by counting systematically without touching them. Recognise counting errors e.g. made by a puppet. Discuss ways of counting so that it is easier to count accurately Begin to recognise none and zero in stories, rhymes and when counting. Count reliably in other contexts, such as clapping sounds hopping movements strides across a room etc. . Count pairs of claps or drum beats. Count a collection of up to 10 objects in more difficult formations using a strategy for keeping a track of where the count begins. Count objects that are out of reach. Count objects in a ring marking the starting point in some way. Count some mixed objects that vary markedly in size. Count some moving objects. Begin a count with a named object. Count along and back a blank number track. Count the jumps on a blank number line using objects. Count the jumps on a blank number line quietly using fingers. Count the jumps on a blank number line mentally. Recite the sequence: ten, twenty.one hundred, forwards. Recite the sequence: ten, twenty.one hundred backwards Year R Count on in tens, starting from a given tens number. Count back in tens, starting from a given tens number. Say the tens number that goes after a given one. Say the tens number that goes before a given one. Count along a number track numbered only in tens. Count from a given tens number and stop at another. Count in twos. Begin to understand and use in practical contexts: odd, even, every other Recite number rhymes that involve counting in twos. Count pairs e.g. pairs of animals, socks, children. Using a number track say aloud every other number starting at one. Say aloud every other number starting at two. On a number track numbered only 1 and 10 suggest the position of the numbers in between and discuss. Extend to a number track beyond 10. READING AND WRITING NUMBERS Recognise numerals 1 to 9, then 0, 10, beyond 10. Recognise numerals familiar to them e.g age, house number, bus number. Recognise numerals on number tracks, number cards, grids, numbers around school, clocks, computer. Match collections of real objects then pictures of collections of things to numerals. Match numbers to dot patterns. Use number cards as labels. Begin to recognise 0 as the numeral associated with none or the space before 1 on the number track. Year R Begin to read the first few number names, including zero. Read these words: zero, one two, three, four, five. Begin to record numbers, initially by making marks. Begin to record numbers by simple tallying. Begin to record numbers by writing numerals. Make own marks or tallies to record numbers or quantities arising in or resulting from practical activities. Begin to write numerals correctly at least to 10. Reinforce the writing of numerals through activities such as tracing on a variety of textures, air writing etc Use language such as more or less, greater or smaller, to compare two numbers saying which is more or less. Say a number or numbers lying between two given numbers. Begin to understand and use in practical contexts: the same number as, bigger, larger, smaller, biggest, largest, smallest, more, less, fewer, most, least, fewest, order, first, last, before, after, next, between. Find out by counting which of two collections has more/less, checking if necessary by lining up and matching 1: 1. Know that a number following another number in the counting sequence is bigger. Say a number that is one more than a given number. Say a number that is one less than a given number. Discuss unpriced and then priced items in a class shop. Say which might cost more/ less. Year R Order a given set of numbers: for example, the set of numbers 1 to 6 given in random order. Arrange in order a complete set of numbers ( first objects, then dot patterns, then numerals) progressing to 10 or more. Order a given set of selected numbers: for example, the set 2, 5, 1, 8,4 starting with the smallest number. Order a given set of selected numbers: for example, the set 2, 5, 1, 8,4 starting with the largest number... Begin to understand and use ordinal numbers in different context. Begin to understand and use ordinal numbers to denote position: first, second, third, fourth, last, last but one. Begin to understand the relationship between cardinal and ordinal numbers up to 10th , that is a number allocated six in a count is the sixth object counted. Begin to understand for example, that if you are fifth in a race, four runners beat you. Year R ESTIMATION Begin to understand and use in practical contexts- guess how many, estimate, nearly, close, about the same as, just over, just under, too many, too few, enough, not enough Estimate a number in the range that can be counted reliably, then check by counting. Year R Year R ADDING AND SUBTRACTING ADDING AND SUBTRACTING In practical activities and discussion, begin to use the vocabulary used in adding and subtracting eg In practical contexts using objects, by modelling with apparatus and by modelling with fingers- Year R More, and add, make, sum, total, altogether, score, take away, leave, how many are left? How many are gone? One more, two more, one less, two less, how many more to make ? how many more is than .? How many less is . than .? difference between Find one more than a given number in a range of contexts. Find one less than a given number in a range of contexts. Begin to relate addition to combining two groups of objects; extend to three groups, saying how many there are altogether by counting all the objects. Begin to relate addition to counting on. Begin to relate the addition of doubles to counting on. Find a total by counting on when one group of objects is hidden. Separate ( partition ) a given number of objects into two groups eg say how up to 10 objects can be separated into two groups and find different ways of doing it. Talk about outcomes and find own ways of recording. Select two groups of objects to make a given total Begin to relate subtraction to taking away and counting how many are left. Remove a smaller number from a larger one and find how many are left by counting back from the larger number. Begin to find out how many have been removed from a larger group of objects by counting up from a number. Work out by counting how many more are needed to make a larger number i.e. by counting up. Year R Year R Year R Year R Year R Year R Year R Year R SOLVING PROBLEMS REASONING ABOUT NUMBERS OR SHAPES Talk about, recognise and recreate simple patterns eg simple repeating or symmetrical patterns from different cultures. Use shapes, printing, weaving, bead threading, computer programs etc. to make own repeating patterns such as: cotton reel, sponge, cotton reel, sponge or thumb, palm, palm, thumb, palm, palm. Talk about, copy and continue repeating patterns of sounds or movements in music or dance e.g. hop, hop, jump or tap, tap, pause, tap Solve simple problems or puzzles in a practical context, and respond to What could we try next? Year R Talk about and record in own way how problem was resolved. Make simple estimates eg of the number of cubes that will fit in a box or strides across the room. Check by counting. Predict in a range of activities e.g. a hidden part of a pattern, a shape in a bag, who will be number 8 when counting around a ring. Sort and match objects, pictures or children themselves, justifying the decisions made. Begin to understand and use the terms: sort, match, count.. Sort and display objects according to their characteristics eg shiny / dull, hard / soft, rough / smooth Sort and count the children themselves using one criterion. Sort, match or order flat or solid shapes and explain what has been done. PROBLEMS INVOLVING REAL LIFE OR MONEY Use developing mathematical ideas and methods to solve practical problems involving counting and comparing in a real or role play context eg do we have enough biscuits for everyone? Counting doubling and halving. Use vocabulary such as: double, half and pair e.g. slices of bread needed for 4 sandwiches, colour half red half blue, how many pairs of socks? Counting: repeated addition, grouping or sharing. Use vocabulary such as: share, group, left over, how many times? Solve story-based problems. Year R MONEY Begin to understand and use vocabulary related to money: coin, penny, pence, pound, price, costs, costs more, costs less, total, pay, change, how much? how many? Use coins to pay for things or to buy things in the class shop etc. recognising that coins are used to pay and give change. Play money games using 1p coins to the value of 10p and 1 coins to the value of 10. Distinguish coins: 1p, 2p, 5p, 10p, 20p, 50p, 1, 2 and use in sorting activities( P.21) Choose and use the appropriate number operation to solve story problems involving money. Explain orally and where appropriate, record in own way how problem was solved. Begin to recognise that some coins have greater value than others and will buy more. Be aware that two 1p coins are equivalent to a 2p piece. Begin to count together a 2p and a 1p coin. Work out the total cost of a basket of items (up to about 6) Work out what to buy and how to pay, considering the coins that could be used. Consider what coins could be used to make 5p. Begin to read and write prices such as 8p or 4 and count penny and pound coins to match. Match penny coins to prices in a class shop extending to a combination of 1p and 2p coins. Year R MEASURES, SHAPE AND SPACE COMPARING AND ORDERING MEASURES Use language such as more or less, longer or shorter, heavier or lighter to compare two quantities, then more than two, by making direct comparisons of lengths or masses, and by filling and emptying containers. Begin to understand and use in practical contexts: size, length and distance, long/er, short/er , tall/er, high/er, low/er, wide/r, narrow/er, deep/er, shallow/er, thick/er, thin/ner, far /further, near/er, close/r Mass :weight, weigh, heavy/heavier, light/er. Capacity: full, half empty, empty and compare, more, less, Compare length, width etc. of two and then three or more objects. Find objects that are taller, shorter, wider etc. than an example. Use hands to say which of two objects is heavier / lighter or about the same. Find objects that are heavier, lighter or about the same as a given one. Use a balance to find out which of two and then three objects is lighter or heavier. Understand that if A is heavier than B, then B is lighter than A. Fill and empty containers describing them as full, half full, empty or as having more / less in them after filling / emptying. Find containers that hold more / less than a given example. Year R Begin to understand and use in practical contexts: estimate.. enough, not enough, too much, too little, nearly, close, about the same as, just over, just under. TIME Begin to understand and use the vocabulary of time in practical contexts: day, week, morning, afternoon, night, today, yesterday, tomorrow, birthday, holiday, oclock, bedtime, dinnertime, playtime, now, soon, before, after, next, last, quickly, slowly. Begin to know the days of the week and talk about them in familiar activities. Sequence familiar events e.g. events in their day or in a well-known story. Listen to and discuss stories that cover the passing of time. Begin to be aware of the duration of time e.g. what can they do before the sand runs through a timer? Be aware of the language of clock time in rhymes and stories. Begin to know key times of the day. Begin to read oclock time. Year R EXPLORING PATTERN, SHAPE AND SPACE Use language such as circle or bigger to describe the shape and size of solids and flat shapes. Understand and use in practical contexts the words: shape, pattern, flat, curved, round, straight, solid, hollow, corner, face, side, end, sort, make, build, draw. Use a variety of shapes to make models, pictures and patterns. Begin to name solids such as a cube, cone, sphere and flat shapes such as a circle, triangle, square, rectangle 3D shapes Identify solid shapes that can be seen around the school and the classroom. Start to become aware of some properties of solid shapes eg all flat surfaces, can roll / slide etc. Make models that vary in shape, size and texture, describing it and saying what shapes have been used. Make shapes from modelling materials and describe them. Make a copy of a simple model as accurately as possible. Fit solid shapes together and investigate which ones stack, which fit the best inside another container etc. 2D shapes Find similar shapes on faces of objects. Year R Find solid shapes with faces that match a 2D outline. Describe and sort 2D shapes using appropriate vocabulary. Find shapes which are not square etc. Begin to sketch 2D shapes. Put sets of objects in order of size. Discuss the fact that the shapes are the same although the size might change. Understand and use in practical contexts: size, bigger, larger, smaller. Listen to and talk about stories related to size. Talk about, recognise and recreate patterns: eg simple repeating or symmetrical patterns in the environment. SYMMETRY Find halves of paper shapes by folding them. Discuss matching pairs etc. in symmetrical models POSITION AND MOVEMENT Use everyday words to describe position, direction and movement eg follow and give instructions about positions, directions and movements in PE and other activities. Understand and use in a range of practical contexts: Position:, over, under, above, below, on, in, outside, inside, behind, beside, before, after, next to, opposite, between, close, far apart Year R Middle, corner, top, bottom, front, back, side. Direction: left, right, up, down, forward, backwards, sideways, across, along, around, through, to from, towards, away from, Listen to and discuss stories such as Rosies Walk, Bear Hunt, Wheres Spot.. Make own books. Talk about positions in a range of contexts. Talk about movements and direction in a range of contexts. Follow simple instructions to create movement. Give instructions to other children. Begin to control a programmable toy. Use Fd with distance and numberline. Begin to use right and left with distance. Begin to sequence instructions to control movement. Describe movements taken on a simple route. Understand and use in a range of practical contexts: movement: roll, slide, turn, stretch, bend. Explore and talk about things that turn. Collect and sort objects that will roll, slide, roll and slide. Teaching Programme: Year 1 NUMBERS AND THE NUMBER SYSTEM COUNTING, PROPERTIES OF NUMBERS & NUMBER SEQUENCES Know the number names and recite them in order, from and back to zero. Join in rhymes like Ten Green Bottles Recognise zero and none in stories and other contexts, including the counting sequence. Say the sequence ten, twenty, thirty,.. one hundred. Respond to questions such as What number comes before / after a particular number? Year 1 Count reliably at least 20 objects. Understand and use in practical contexts: count, how many? Count reliably at least 20 objects, recognising that the size of the set is given by the last number in the count. Count objects in a variety of arrangements and understand that the number of objects is still the same. Count objects without touching them. Describe and extend number one sequences counting on or back in steps of ones. Counting in ones Start at any small number count on in ones to 30 or more, then back in ones to zero. Count on or back a set number from a given number e.g. count on 4 from 3. Count on or back from a given number to another one and say how many has been counted. E.g Count from 7 10, counted 3. Describe and extend number sequences count on or back in steps of 10 or 100 from any number. Counting in tens Using a number square, respond to questions such as: Count on in tens, from zero, from any number. Count back in tens from 100, from any number. Count in tens from zero until told to stop. Say the number of tens counted. Count on or back several tens, starting from a given number. Describe and continue a pattern e.g. 80, 70, 60, 50, . Year 1 Describe and extend number sequences count on or back in steps of 100 from any number Count in twos to 20 or more and back again. Count in twos from one and back again. Join in rhymes that involve counting in twos. Recognise numbers to about 20 as every other number Count on in steps of 5 from zero to 20 or more and back again. Begin to count on in steps of three from zero. Year 1 Understand and use in practical contexts: odd, even, every other PLACE VALUE AND ORDERING Read and write numerals from 0 to at least 20 in a range of contexts. Write in words numerals to 20. Know what each digit represents in numbers from 10 20. Begin to partition larger numbers.into a multiple of ten and ones (TU) Represent a number on an abacus. . Understand and use in practical contexts: units or ones, tens, digit Solve problems such as : make 6 into 16, 14 into 4. What number needs to go in each box? 14 = * + 4, 12 = 10 + * Exchange up to 20 pennies for 10p and 1p coins Year 1 Understand and use the vocabulary of comparing and ordering numbers, including ordinal numbers to at least 20 and: how many, as many as, the same number as, equal to, more than, less than, fewer than, greater than, smaller than, larger than, most, least, smallest, largest, order, first, last, before, after, next, between, half way between. Use the = sign to represent equality. Compare two familiar numbers, say which is more or less, and give a number which lies between them. Within the range 0 to 30, say the number that is one or ten less than any given number. Year 1 Order numbers in real contexts in other curriculum areas. Order numbers to at least 20 and position them on a number track. Year 1 ESTIMATION Understand and use in practical contexts: guess how many, estimate, roughly, nearly, about the same as, close to, too many, too few, enough, not enough. Give a sensible estimate of a number of objects that can be checked by counting( e.g. up to about 30 objects) Year 1 Year 1 CALCULATIONS UNDERSTANDING ADDITION AND SUBTRACTION Understand the operation of addition and use the related vocabulary. Understand and use in practical contexts: more, add, sum, total, altogether, equals, sign and read and write the plus(+) and equals (=) sign. Year 1 Understand addition as combining sets to make a total, steps along a number track (counting on) Begin to understand that adding zero leaves a number unchanged. Respond rapidly to oral questions phrased in a variety of ways: 3 add 1, add 2 to 4, 6 plus 3, what is the sum / total of 2 and 8, How many are 3 and 5 altogether, which 2 / 3 numbers could make 9 altogether, what must I add to 4 to make 10.. Record simple mental additions in a number sentence , using the + and = signs. Recognise the use of symbols to stand for unknown numbers. Complete these style of questions with rapid recall, based on number facts to 5. Complete these style of questions using counters on a number line or 10p and 1p coins, then mental strategies, explaining method to 20 and beyond. Recognise that addition can be done in any order, but not subtraction. Begin to recognise that more than two numbers can be added together. With the aid of apparatus add three numbers., explore three hops on numberline etc. Mentally add mentally three small numbers within the range 1 to about 12. Respond to oral questions explaining the strategy used; e.g. what different totals can you make from the set 1 to 5? Record simple mental additions in a number sentence using + and = signs. Year 1 Understand the operation of subtraction and related vocabulary. Understand and use in practical contexts: take away, subtract, how many are left, how much less is.. than .. difference between, how much more is than how many more to make and read and write the minus sign. Understand subtraction as taking away, finding the difference between, how many more to make (complementary addition.) Begin to understand that subtracting zero leaves a number unchanged. Respond rapidly to oral questions phrased in a variety of ways such as: 4 take away 2, take 2 from 7, 7 subtract 3, what number must I take from 14 to leave 10?, how many more than 3 is 9? 6 taken from a number leaves 3, what is the number? find pairs of numbers with a difference of 2. Record simple mental subtractions in a number sentence using the and = signs. Recognise the use of symbols to stand for numbers and complete with rapid mental recall, examples based on facts to 5. Complete examples to 20 and beyond using rods, counters, numberline , 10p and 1p coins, Then mental strategies, explaining method. RAPID RECALL OF ADDITION AND SUBTRACTION FACTS Know by heart all addition and subtraction facts for all numbers up to/ including 5. Understand and use in practical contexts: double, half, halve. Year 1 Know by heart all addition doubles from 1+ 1 to at least 5+ 5. Begin to know doubles from 6+6 to 10 +10. Respond rapidly to oral questions such as: Double 4, half of 6, two fives, How many socks in two pairs? Know by heart all pairs of numbers that total 10. MENTAL CALCULATION STRATEGIES (+ AND -) Use knowledge that addition can be done in any order to do mental calculations efficiently. For example: Put the larger number first and count on in ones, including beyond 10 (e.g. 7 + 5); Begin to partition and recombine by breaking units of 6, 7, 8, 9, into 5 and a bit E.g. work out mentally that; 5+8 = 5 plus (5+3) = 10+3 =13 Identify near doubles, using doubles already known (e.g. 6+5) Add 9 to single digit numbers by adding 10 then subtracting 1. Use patterns of similar calculations (e.g. 10 0 = 10, 10 1 = 9, 10 8 = 2 ) Use known number facts and place value to add or subtract a pair of numbers mentally. Add or subtract a single digit to or from a single digit without crossing 10. Add or subtract a single digit from a teens number without crossing 20 or 10. Begin to add a teens number to a teens number without crossing the tens boundary e.g. 14 add 11. Year 1 Add 10 to a single digit number and subtract 10 from a teens number. Begin to add a pair of single digit numbers, crossing 10. Use two steps and cross 10 as a middle stage. E.g. 6 + 7 =13 = 6 + 4+ 3 = 10 + 3 =13. Begin to add a single digit to a teens number crossing 20 as a middle stage. Use and apply these skills in a variety of contexts and curriculum areas. Year 1 Year 1 Year 1 Year 1 Year 1 SOLVING PROBLEMS MAKING DECISIONS Understand and use in practical contexts: operation, sign, number sentence. Choose and use appropriate number operations and mental strategies to solve problems in a wide variety of contexts. Decide whether the calculation can be done mentally or needs the use of apparatus. Explain and record how the problem was solved. (For examples see p. 62 71) REASONING ABOUT SHAPES OR NUMBERS Solve simple mathematical problems or puzzles; recognise and predict from simple patterns and relationships. Suggest extensions by asking What if.? Or What could I try next? Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. (P.64) Explain methods and reasoning orally. Year 1 PROBLEMS INVOLVING REAL LIFE, MONEY OR MEASURES Use mental strategies to solve simple problems. Use own mental strategies to solve story problems about numbers in real life, choosing an appropriate operation (counting, addition, subtraction, halving or doubling) Explain methods and reasoning orally and record way in which the problem was solved using a number sentence and signs (+ - =) where appropriate. Year 1 MONEY Recognise all coins. Exchange coins up to 10p for an equivalent number in smaller coins. Extend to 20p. Understand and use in practical contexts: coin, penny, pence, pound, price, cost, costs more / less, change, total, pay, how much. Use own mental strategies to solve problems involving money in contexts such as the classroom shop. Explain methods and reasoning orally and record in own way how the problem was solved. Find totals and give change. Decide what to buy and how to pay. Year 1 MEASURES, SHAPE AND SPACE MEASURES Understand and use in practical contexts, the vocabulary related to length, mass and capacity: Length and distance: long, short, tall, high, low, wide, narrow, deep, shallow, thick, thin, far, near, close Mass: weight, weighs, heavy, light, balances Capacity: full, empty, holds And comparative words such as longer, longest. Compare two lengths, masses or capacities by direct comparison; extend to more than two. Measure using uniform non-standard units (e.g. straws, wooden cubes, yogurt pots) and standard units (e.g. metre sticks, kilograms and litre jugs). Estimate before measuring and discuss results. Suggest suitable standard or uniform non standard units and measuring equipment to estimate, then measure, a length, mass or capacity, recording estimates and measurements as about 3 beakers full or about as heavy as 20 cubes. Make simple measuring devices. Understand and use in practical contexts- guess, roughly, nearly, close to, about the same as, too many, too few, enough, not enough. Year 1 TIME Understand and use in context the vocabulary related to time- names of days of the week, seasons, hour, day, week, month, year, season, morning, afternoon, evening, night, midnight, weekend, today, yesterday, tomorrow, now, soon, early, late, before, after, first, second, next, quick, fast, slow, How long ago, how long will it be to, how long will it take to, how often, always, never, often, sometimes, usually, once, twice, And comparatives such as faster, slower, takes longer. Know that: 1 week = 7 days 1 day = 24 hours. Know in order the days of the week. Order familiar events in a day, week or story. Read the time to the hour or half hour on an analogue clock. Make estimates and check using a simple timer in PE, Science etc. Year 1 SHAPE AND SPACE Use everyday language to describe features of familiar 3D and 2D shapes. Understand and use in practical contexts: shape, pattern, flat, hollow, side, edge, face, straight, curved, round, point, pointed, corner, sort, build, make, draw. Name, sort and describe some features and properties of familiar 2D and 3D shapes such as: cube, cuboid, sphere, cone, cylinder, circle, triangle, rectangle, square. E.g. number or type of faces, sides, edges, corners. Talk about the shapes and patterns in curtains, clothes etc. Make models, shapes and patterns with increasing accuracy and describe their features. Use construction kits, everyday materials and malleable materials e.g. plasticine. Begin to relate 3D shapes to pictures of them. Use bricks to build models from pictures. Make pictures and patterns using a range of 2D shapes and describe. Year 1 SYMMETRY Make halves of paper shapes by folding them. Make them into symmetrical patterns by cutting out small pieces or by ink blot painting. POSITION AND MOVEMENT Describe positions and directions Understand and use in practical contexts: position, over, under,underneath, above, below, on,in, outside, inside, in front, behind, beside, before, after, next to, opposite, between, close, far apart, middle, centre, edge, corner, top, bottom, side, direction, left, right, up, down, forwards, backwards, sideways, across, along, around, through, to, from, Year 1 towards, away from, journey. Use everyday language to describe and talk about position, direction and movement in a range of contexts. Understand and use in practical contexts: slide, roll, turn, whole, half. Recognise whole turns and half turns. Talk about, make and continue repeating patterns using a variety of media, describing what is happening. Year 1 ORGANISING AND USING DATA Solve a given problem by collecting, sorting, and organising information in simple ways such as using objects or pictures. Discuss and explain results. Solve a given problem by collecting, sorting, and organising information in simple ways such as in a list. Discuss and explain results Solve a given problem by collecting, sorting, and organising information in simple ways such as in a simple table. Discuss and explain results.Teaching Programme: Year 2 NUMBERS AND THE NUMBER SYSTEM COUNTING, PROPERTIES OF NUMBERS & NUMBER SEQUENCES .Say the number names in order from zero to at least 30. Say the number names in order from 30 back to zero. Say the number names in order from zero to at least 50. Say the number names in order from 50 back to zero. Say the number names in order from zero to at least 100. Say the number names in order to from at least 100. back to zero. Fill in gaps on a number track less than 30 with some numbers already entered. Fill in gaps on a number track less than 50 with some numbers already entered. Fill in gaps on a number track less than 100 with some numbers already entered. Place numbers a specified interval in front of a given number on a number track. Place numbers a specified interval behind a given number on a number track. Counting forwards on a number track, give the interval between two specified numbers. Counting backwards on a number track, give the interval between two specified numbers. Year 2 Count reliably up to 100 objects by grouping them: for example, in tens, then in fives or twos. Use, understand and begin to read count, tally and how many? Understand that if you tally in different groupings, the answer will still be the same. Suggest appropriate tally groupings for different counting scenarios eg children in a class, sugar lumps in a box, eggs in a carton. Describe and extend simple number sequences: count on or back in ones, starting from any two digit number; count on or back in tens, starting from any two digit number; From zero and then from any small number, count on in 2s to at least 30. From zero and then from any small number, count on in 3s to at least 30. From zero and then from any small number, count on in 4s to at least 30. From zero and then from any small number, count on in 5s to at least 30. Investigate the patterns when Count on in 2s on a 4x4 grid and colour the squares you land on. Repeat on a 5x5 and then predict 6x6. Describe the rule, and extend, sequences to 30 which are multiples of 2. Describe the rule, and extend, ascending and descending sequences to 30 which are multiples of 3. Create sequences with a given constraint eg includes the numbers 6 and 12. Year 2 Respond to questions such as Which tens number comes before/after 30? Know how many tens it takes to get from one number to another eg 20 to 70, 54 to 94. Count in hundreds from and back to zero; Respond to questions such as Which hundreds number comes before/after 400? Know how many hundreds it takes to get from one number to another eg 120 to 270, 354 to 594. Count on in twos from and back to zero or any small number. Begin to recognise two- digit multiples of 2 as numbers ending in 0, 2, 4, 6, 8. Begin to recognise two-digit multiples of 5 as numbers ending in 0 or 5. Begin to recognise two-digit multiples of 10 as numbers ending in 0. Understand, use and begin to read multiple. Recognise odd and even numbers to at least 30 Know which odd/even number comes before/ after a specified number to at least 30. Know that an even number is divisible exactly by 2 and there is 1 left over when an odd number is divided. Count on in steps of 3, 4 or 5 to at least 30, from and back to zero, then from and back to any given small number. Year 2 Describe sequences and extend them. Understand, use and begin to read odd, even, sequence, predict, continue and rule. PLACE VALUE AND ORDERING Read whole numbers to at least 100 in figures. Read whole numbers to at least 100 in words. Write whole numbers to at least 100 in figures. Write whole numbers to at least 100 in words. Know what each digit in a two-digit number represents, including 0 as a place holder. Partition two-digit numbers into a multiple of ten and ones (TU). Show two-digit numbers on an abacus. Understand, use and begin to read units or ones, tens, hundreds, digits, one-digit number, two-digit number, three-digit number, place value. In one step (operation) Make 5 into 45 etc Change 49 into 9 etc. Explain what number needs to go in each box- 64 = ( + 4, 53 = 50 + ( Make the biggest and smallest numbers with two provided digits. Exchange up to 100 pennies for 10p and 1p coins. Year 2 Understand, use and begin to read write the vocabulary of comparing and ordering numbers eg ordinal numbers in words, how many, the same number as, equal to, more than, less than, fewer than, greater than, smaller than, Larger than, most, least, smallest, largest, order, first, last, before, after, next, between, halfway between. Use the = sign to represent equality. Compare two given two-digit numbers, say which is more or less, and give a number which lies between them. Say the number that is 1 more or less than any given two-digit number. Say the number that is 10 more or less than any given two-digit number Year 2 Order whole numbers to at least 100. Position numbers to 100 on a number line. Position numbers to 100 in 100 square. Position numbers to 100 in a number square fragment containing some numbers. Use a number line with its ends labelled in multiples of 10 ( 50 to find the halfway number eg halfway between 30 and 50. Year 2 ESTIMATION AND ROUNDING Use and begin to read guess how many, estimate, round, nearest, roughly, nearly, close to, about the same as, too many, too few, enough, not enough. Give a sensible estimate of at least 50 objects. Record estimates on a number line and use it to find the difference between it and the actual number. Estimate the position of an undivided number line whose ends are numbered and ( 10. Begin to round numbers less than 100 to the nearest 10 by saying which number it is nearer to (a number ending in 5 rounds up because it is halfway). Year 2 FRACTIONS Understand, use and begin to read part, fraction, one whole, one half, one quarter. Recognise and write , as one half, one quarter. Begin to recognise and find one half of shapes. Recognise not-halves. Begin to recognise and find one quarter of shapes. Recognise not-quarters. Begin to recognise and find one half of small numbers of objects. Begin to recognise and find one half of objects such as a cake or a jar of water. Begin to recognise and find one quarter of small numbers of objects. Begin to recognise and find One quarter of objects such as a cake or a jar of water. Begin to recognise that two halves or four quarters make one whole and that two quarters and one half are equivalent. Recognise that two quarters and one half make one whole. Begin to position halves on a number line eg 5 is between 5 and 6 Say half of an even number ( 20. Year 2 CALCULATIONS UNDERSTANDING ADDITION AND SUBTRACTION Use and begin to read and begin to write more, add, sum, total, altogether, equals, sign. Use the +, and = signs to record mental additions and subtractions in a number sentence. Year 2 Recognise the use of a symbol such as symbol 110 \f "Monotype Sorts" \s 10 or symbol 115 \f "Monotype Sorts" \s 10 to stand for an unknown number, and complete using rapid recall for facts to 10. Recognise that addition can be done in any order, but not subtraction: for example, 3 + 21 = 21 + 3, but 21 3 does not equal 3 21. Understand that more than two numbers can be added. Add two-digit numbers with the help of 10p and 1p coins or 10-sticks and unit bricks.(totals up to 100). Add two-digit numbers with the help of a number line (totals up to 100). Add two-digit numbers with the help of 100 square (totals up to 100). Add two-digit numbers (totals up to 100) using and explaining mental strategies. Understand that subtraction is the inverse of addition (subtraction reverses addition). Begin to add three single-digit numbers mentally (totals up to about 20). Add three or more one- or two-digit numbers with the help of 10p and 1p coins or 10-sticks and unit bricks.(totals up to 100). Add three or more one- or two-digit numbers with the help of a number line (totals up to 100). Add three or more one- or two-digit numbers with the help of 100 square (totals up to 100). Add three or more one- or two-digit numbers (totals up to 100) using and explaining mental strategies. Investigate 3 hops on a number line from a given start to a specified end ( 100 and record in the form 32 + ( + ( = 100 Year 2 Find the missing number in equations of the forms- 1 + ( + 5 = 35 1 + 29 + ( = 35 ( + 29 + 5 = 35 Explore the different totals which can be made by adding different combinations of provided numbers eg three out of 14,15,16,19. Using coins if necessary, add bills containing 3 or more two-digit numbers of pennies. RAPID RECALL OF ADDITION AND SUBTRACTION FACTS Know by heart all addition and subtraction facts for each number to at least 10; Know all pairs of numbers with a total of 20 (e.g. 13 + 7, 6 +14); Year 2 Know by heart all pairs of multiples of 10 with a total of 100 (e.g. 30 + 70). MENTAL CALCULATION STRATEGIES (+ AND -) Use knowledge that addition can be done in any order to do mental calculations more efficiently. For example: Put the larger number first and count on in tens or ones. Add three small numbers by putting the largest number first and/or find a pair totalling 10. Partition into 5 and a bit when adding 6, 7, 8 or 9, then recombine (e.g. 16 + 8 = 15 + 1 + 5 + 3 = 20 + 4 = 24); partition additions into tens and units, then recombine. Find a small difference by counting up from the smaller to the larger number e.g. 42 39, and know that it is easier than counting back. Identify near doubles, using doubles already known (e.g. 8 + 9, 40 + 41). Add/subtract 9 or 11:add/ subtract 10 and adjust by1. Begin to add/subtract 19 or 21: add/subtract 20 and adjust by 1. Use patterns of similar calculations eg 7+0 = 7, 6+1=7 etc to derive 3+4= . State the subtraction corresponding to a given addition, and vice versa. Year 2 Use known number facts and place value to add/subtract mentally eg different number sentences linking 2,7,9. Add or subtract a single digit to or from any two-digit number without crossing the tens boundary eg 32+5. Add or subtract a single digit to/from a multiple of ten. Subtract a single digit from a multiple of ten. Begin to add a two-digit number to a multiple of ten without crossing the tens boundary or 100. Add/subtract a teens number to/from a two-digit number without crossing the tens boundary or 100. Add or subtract 10 from or to any two-digit number, without crossing 100. Add or subtract a pair of multiples of 10 without crossing 100. Find what must be added to a two-digit multiple of 10 to make 100. Add or subtract a multiple of 10 to or from a two-digit number without crossing 100. Add or subtract a pair of multiples of 100 without crossing 1000. Bridge through 10 or 20, then adjust. Add a pair of single-digit numbers, or subtract a single digit from a teens number, crossing 10. Add a single digit to a teens number, or subtract a single digit from a twenties number, crossing 20. Find a small difference between a pair of numbers lying each side of 20, or another multiple of 10. Year 2 Year 2 UNDERSTANDING MULTIPLICATION AND DIVISION Use and begin to read double, times, multiply, multiplied by, multiple of, lots of, groups of, times as (big, long, wide) and read and write the x sign; one each, two each etc, share, halve, divide, left over, divided by, equal groups of, and read and write the division sign . Understand the operation of multiplication as repeated addition or as describing an array. Begin to understand that multiplication can be done in any order. Begin to understand division as grouping (repeated subtraction) or sharing. Use counters for sharing, then a number line for repeated subtraction and then mental strategies for dividing one- and two-digit numbers by one digit or 10. Use the x, and = signs to record mental calculations in a number sentence. Recognise the use of a symbol such as symbol 142 \f "Monotype Sorts" \s 10 or symbol 115 \f "Monotype Sorts" \s 10 to stand for an unknown number in number sentences involving x or . Know and use halving as the inverse of doubling. RAPID RECALL OF MULTIPLICATION AND DIVISION FACTS Understand, use and begin to read double, twice, half, halve, whole, divide by two, divide into two etc. Year 2 Know by heart: multiplication facts for the 2 and 10 times-tables; Know doubles of numbers to 10 and the corresponding halves. Begin to know: multiplication facts for the 5 times-table. Derive quickly: division facts corresponding to the 2 and 10 times-tables; doubles of all numbers to at least 15 (e.g. 11 + 11 or 11 x 2); doubles of multiples of 5 to 50 (e.g. 20 x 2 or 35 x 2); halves of multiples of 10 to 100 (e.g. half of 70). MENTAL CALCULATION STRATEGIES (x and ) Use known number facts and place value to mentally carry out simple multiplications and divisions. Multiply a single digit by 1 or 10. Divide a two-digit multiple of 10 by 1 or 10. Begin to double any multiple of 5 up to 50. Begin to halve any multiple of 10 to 100. Multiply a single digit up to 5 by 2,3,4,5. Year 2 CHECKING THE RESULTS OF CALCULATIONS Repeat addition in a different order. Check with an equivalent calculation. Year 2 SOLVING PROBLEMS MAKING DECISIONS Understand, use and begin to read operation, sign, symbol, number sentence. Choose and use appropriate operations and efficient calculation strategies (e.g. mental, mental with jottings) to solve problems. Decide what equipment will be needed eg cubes, squared paper, 100 square, coins etc. Explain how the problem was solved. REASONING ABOUT NUMBERS OR SHAPES Solve mathematical problems or puzzles, recognise simple patterns and relationships, generalise and predict. Suggest extensions by asking What if? or What could I try next? Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. Explain how a problem was solved orally and, where appropriate, in writing. Year 2 PROBLEMS INVOLVING REAL LIFE, MONEY OR MEASURES Use mental addition, subtraction, simple multiplication and division to solve simple word problems involving numbers in real life, money or measures, using one or two steps. Explain how the problem was solved. Year 2 MONEY Understand and begin to read coin, pound, , pence, price, cost, pay, costs more/less, change, total, how much? Recognise all coins. Exchange coins for their equivalent value of two or three smaller coins. Total coins to a pound or less Begin to use .p notation for money eg know that 4.65 indicates 4 and 65p). Find totals, give change, and work out which coins to pay. Year 2 MEASURES, SHAPE AND SPACE MEASURES Use and begin to read- long, short, tall, high, low, wide, narrow, deep, shallow, thick, thin, far, near, close, weight, weighs, heavy, light, balances, full, empty, holds, roughly, nearly, about, close to. Know that- 1 metre = 100 centimeters 1 kilogram = 1000 grams 1 litre = 1000 millilitres Estimate, measure and compare lengths in m. Estimate, measure and compare lengths in cm. Estimate, measure and compare masses using kg. Estimate, measure and compare capacities, using litres. For a variety of practical situations, correctly select m, cm, kg or l. For m, cm, l or kg, read a simple scale to the nearest labeled divisions. Record estimates and measurements as 3 and a bit metres long or about 8 centimetres or nearly 3 kilograms heavy. Use a ruler to draw and measure lines to the nearest centimetre Solve simple problems incorporating Year 2 units, using one or two steps, explaining reasoning and, where appropriate, writing a number sentence. using one or two steps Year 2 TIME Use and begin to read names of the days of the week, names of the months, seasons of the year, second, minute, hour, day, week, fortnight, month, year, season, morning, afternoon, evening, night, midnight, weekend, today, yesterday, tomorrow,now, soon, early, late, before, after, first, second, next, quick, fast, slow, how long ago?, how long will it be to?, how long will it take to?, how often?, always, never, often, sometimes, usually, once, twice, and comparatives such as faster, slower, takes longer etc, Suggest suitable Year 2 units to estimate or measure time and use them in practical contexts. Order the months of the year. Order the seasons. Know 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes, 1 minute = 60 seconds. Use metal strategies to solve simple problems incorporating these units. Read the time to the hour, on a digital clock. Read the time to half hour on a digital clock. Read the time to a quarter past on a digital clock. Read the time to a quarter to on a digital clock Read the time to the hour on a 12-hour analogue clock. Read the time to half hour on a 12-hour analogue clock. Year 2 Read the time to a quarter past on a 12-hour analogue clock. Read the time to a quarter to on a 12-hour analogue clock. SHAPE AND SPACE Understand, use and begin to read shape, pattern, flat, solid, hollow, side, edge, face, straight, curved, round, point, pointed, corner, sort, draw, make, build, circular, triangular, rectangular, surface. Use the mathematical names for common 3-D and 2-D shapes, including the pyramid, cylinder, pentagon, hexagon, octagon. Sort shapes and describe some of their features, such as the number of sides and corners, symmetry (2-D shapes), or the shapes of faces and number of faces, edges and corners (3-D shapes). Make and describe shapes, models, pictures and patterns using, for example, solid shapes, templates, pinboard and elastic bands, squared paper, straws, cubes, a programmable robot. Relate solid shapes to pictures of them. Year 2 SYMMETRY Understand, use and begin to read fold, match, mirror line, reflection, symmetrical. Use reflecting objects and surfaces to make and describe reflections. Create symmetrical patterns eg ink devils, pegboard, cubes etc Begin to recognise line symmetry in pictures and patterns, testing with a mirror. POSITION AND MOVEMENT Use mathematical vocabulary to describe position, direction and movement. Understand, use and begin to read position, over, under, underneath, above, below, on, in, outside, inside in front, behind, beside, before, after, next to, opposite, between, close, far apart, middle, edge, corner, centre, top, bottom, side, direction, left, right, up, down, forwards, backwards, sideways, across, along, Year 2 around, through, to, from, towards, away from, journey. higher, lower, clockwise, anti- clockwise, route. Describe, place, tick, draw or visualise objects in given positions using the Year 2 language. eg using squared paper, describe the movement of a counter in terms of how many squares along/up. eg using squared paper, describe the movement of a counter in terms of how many squares up/down/left/right. Understand, use and begin to read slide, roll, turn, whole turn, half turn, quarter turn, right angle, straight line. Recognise whole, half and quarter turns, to the left or right. Recognise whole, half and quarter turns, clockwise or anti-clockwise. Know that a right angle is a measure of a quarter turn. Recognise right angles in squares and rectangles. Give instructions for moving along a route in straight lines and round right-angled corners: for example, to pass through a simple maze. Describe repeating patterns in terms of the shape sliding along and turning through.. Year 2 ORGANISING AND USING DATA Understand, use and begin to read sort, set, represent, graph, table, list, count, label, most,/least common/ popular. Solve a given problem by sorting, classifying and organising information in simple ways, such as: in a list eg odd numbers from15 to 35; a simple table eg names with 3,4,5,6letters; in a 4-branch decision tree; in a pictogram where a symbol represents one unit eg faces for children going to bed at different times; in a block graph where a block represents one. Discuss and explain results. Teaching Programme: Year 3 NUMBERS AND THE NUMBER SYSTEM COUNTING, PROPERTIES OF NUMBERS & NUMBER SEQUENCES Fill in gaps on a number track less than 1000 with some numbers already entered. Place numbers a specified interval in front of or behind a given number on a number track to 1000. Counting forwards/backwards on a number track to 1000, give the interval between two specified numbers. Year 3 Count larger collections by grouping them: eg in tens, then other numbers. Use, read and begin to write count, tally and how many? Suggest appropriate tally groupings counting scenarios in the hundreds. Describe and extend number sequences: count on or back in twos starting from any two-digit number. count on in steps of 3 from any small number to at least 50, then back again. count on in steps of 4 from any small number to at least 50, then back again count on in steps of 5 from any small number to at least 50, then back again count on or back in tens, starting from any two- or three-digit number. Investigate the patterns when You count on in 3s on a 4x4 grid and colour the squares you land on. Repeat on a 5x5 and then predict 6x6. For each square, predict numbers not on it which would be coloured/not coloured. Describe the rule, and extend, Ascending and descending sequences to 100 which are increments of 2, 3, 4 or 5, starting from zero or any small number. Year 3 Create sequences with a given constraint eg includes the numbers 7 and 12. Know how many tens were counted on or back to get from one specified number to another. count on or back in hundreds, starting from any two- or three-digit number. know how many hundreds were counted on or back to get from one specified number to another. Count on or back in multiples of 50, starting at zero. Recognise two-digit and three- digit multiples of 2 as numbers ending in 0, 2, 4, 6, 8. Recognise two-digit and three-digit multiples of 5 as numbers ending in 0 or 5. Recognise two-digit and three-digit multiples of 10 as numbers ending in 0. Recognise three-digit multiples of 50 as numbers ending in 00 or 50. Recognise three-digit multiples of 100 as numbers ending in 00. Be able to give multiples of 10, 50 or 100 before or after a specified number. Use, read and begin to write multiple. Know how to recognise odd and even numbers to at least 100. Know which odd/even number comes before/ after a specified number to at least 30. Know an even number ends in 0, 2, 4, 6 or 8 and an odd numbers ends in 1, 3, 5, 7, 9. Know if you add two odd or even numbers, the answer is even, and if you add an odd and even, the answer is odd. Year 3 Use, read and begin to write odd, even, sequence, predict, continue, rule and relationship PLACE VALUE AND ORDERING Read whole numbers to at least 1000 in figures. Read whole numbers to at least 1000 in words. Write whole numbers to at least 1000 in figures. Write whole numbers to at least 1000 in words. Know what each digit in a three-digit number represents, including zero as a place holder. Partition three-digit numbers into a multiple of 100, a multiple of ten and one (HTU). Show three-digit numbers on an abacus. Use, read and begin to write units or ones, tens, hundreds, digits, one-digit number, two-digit number, three-digit number, place value. In one step (operation) Make 478 into 978 etc Make 326 into 396 etc Change 707 into 507 etc Change 263 into 203 etc Explain what number needs to go in each box- 364 = ( + 60 + 4, 472 = 400 + ( + 2 Make the biggest and smallest numbers with three provided digits. Exchange pennies for 1, 10p and 1p coins. Year 3 Use, read and begin to write write the vocabulary of comparing and ordering numbers eg ordinal numbers in words, how many, the same number as, equal to, more than, less than, fewer than, greater than, smaller than, Larger than, most, least, smallest, largest, order, first, last, before, after, next, between, halfway between Use the = sign to represent equality. Compare two given three-digit numbers, say which is more or less, and give a number which lies between them. Say the number that is 1 more or less than any given two- or three-digit number. Say the number that is 10 more or less than any given two- or three-digit number. Say the number that is 100 more or less than any given two- or three-digit number. Year 3 Order whole numbers to at least 1000. Position numbers to 1000 on a number line. Position numbers to 100 in a number square fragment containing fewer numbers than in Year 2. Use a number line with its ends labelled in multiples of 10 ( 100 to find the halfway number eg halfway between 30 and 90. Year 3 ESTIMATION AND ROUNDING Use, read and begin to write guess how many, estimate, round, nearest, roughly, nearly, close to, approximately, too many, too few, enough, not enough. Give a sensible estimate of up to about 100 objects. Explain how estimates were made and justify why they are reasonable. Estimate the position of an undivided number line whose ends are numbered and ( 100. Round any two-digit number to the nearest 10. Round any three-digit number to the nearest 100. Round numbers which are units of measurement eg , g, m, cm etc. Year 3 FRACTIONS Use, read and begin to write part, fraction, one whole, one half, one quarter, three quarters, one third, two thirds, one tenth etc Recognise unit fractions Up to 1/n where n ( 10 Shade fractions of the form 1/n on shapes which have been subdivided, including into parts (n. Recognise shapes shaded in ways which are not equal fractions eg not 1/5. Identify the fraction of a shape not shaded. Identify the fraction (1/n)of a set which has been ringed or collected Identify the fraction of a set of objects which have not been ringed or collected. Complete shading partly shaded, subdivided shapes to make a specified fraction. Begin to recognise simple fractions that are several parts of a whole. Begin to recognise simple equivalent fractions: for example, five tenths and one half, five fifths and one whole. Place halves, quarters, three quarters on a number line. Compare familiar fractions: for example, know that on the number line one half lies between one quarter and three quarters, a half is less than three quarters etc. Year 3 Use a number line to find half of any number to 100. Estimate a simple fraction eg it is nearly half past, a jar of 100 sweets is nearly half empty, so it has about 50 sweets. CALCULATIONS UNDERSTANDING ADDITION AND SUBTRACTION Read and begin to write more, add, sum, total, altogether, equals, sign. Use the +, and = signs. Extend understanding of the operations of addition and subtraction. Year 3 Recognise the use of a symbol such as symbol 110 \f "Monotype Sorts" \s 10 or symbol 115 \f "Monotype Sorts" \s 10 to stand for an unknown number, and complete using rapid recall for facts to 20 Continue to recognise that addition can be done in any order. Extend understanding that more than two numbers can be added Add two-digit and three-digit numbers with the help of apparatus or pencil and paper Extend understanding that subtraction is the inverse of addition .Add three or four single-digit numbers mentally. Add three or more one-, two-or thee-digit numbers with the help of 10p and 1p coins or 10-sticks and unit bricks. (totals up to 1000). Add three or more one-, two-or three-digit numbers with the help of a number line (totals up to 1000). Add three or more one-, two-or three-digit numbers with the help of 100 square (totals up to 1000). Add three or more one-, two or three-digit numbers (totals up to 1000) using and explaining mental strategies Investigate 3 hops on a number line from a given start to a specified end ( 1000 and record in the form 132 + ( + ( = 100 Find the missing number in equations of the forms- 190 + ( + 5 = 300 190 + 105 + ( = 300 ( + 105 + 5 = 35 Explore the different totals which can be made by adding different combinations of provided numbers eg three out of 19,63,54,106,97. Using coins if necessary, add bills containing 3 or more two- digit numbers of pennies. Year 3 Using coins if necessary, add bills containing 3 or more figures of the form 4.50. RAPID RECALL OF ADDITION AND SUBTRACTION FACTS Know by heart: all addition and subtraction facts for each number to 20; all pairs of multiples of 100 with a total of 1000 (e.g. 300 + 700). Year 3 Derive quickly: all pairs of multiples of 5 with a total of 100 (e.g. 35 + 65). MENTAL CALCULATION STRATEGIES (+ AND -) Use knowledge that addition can be done in any order to do mental calculations more efficiently. For example: put the larger number first and count on; add three or four small numbers by putting the largest number first and/or by finding pairs totalling 9, 10 or 11; Partition into 5 and a bit when adding 6, 7, 8 or 9 (e.g. 47 + 8 = 45 + 2 + 5 + 3 = 50 + 5 = 55) partition into tens and units, then recombine (e.g. 34 + 53 = 30 + 50 + 4 + 3). Find a small difference by counting up from the smaller to the larger number (e.g. 102 97). Identify near doubles, using doubles already known (e.g. 80 + 81). Add and subtract mentally a near multiple of 10 to or from a two-digit number by adding or subtracting 10, 20, 30 and adjusting. Use patterns of similar Calculations eg 4-3=, 14-3= to derive 84-3. Say or write a subtraction statement corresponding to a given addition statement, and vice versa. Year 3 Use known number facts and place value to add/subtract mentally eg different number sentences linking 5,8,13. Add or subtract a single digit to or from any three-digit number without crossing the tens boundary eg 532+5. Add a two-digit number to a multiple of hundred. Subtract a single digit from a multiple of hundred. Begin to add a two-digit number to a multiple of ten, crossing 100. Add/subtract a pair of teens numbers without crossing the tens boundary or 100. Add or subtract 10 to or from any two-or three-digit number including crossing the hundreds boundary. Begin to subtract or add a pair of multiples of 10, crossing 100. Find what must be added to a three-digit multiple of 10 to make the next higher multiple of 100. Add or subtract a multiple of 10 to or from a two-digit number, crossing 100. Add or subtract a pair of multiples of 100, crossing 1000 Bridge through a multiple of 10, then adjust. Consolidate subtracting a single digit from a teens number, crossing 10. Add or subtract a single digit to/from a two-digit number, crossing the tens boundary. Find a small difference between a pair of numbers lying each side of a multiple of 100 from 100 to 1000. Begin to add or subtract any pair of two-digit numbers. Year 3 PENCIL AND PAPER PROCEDURES (+ AND -) Use informal pencil and paper methods to support, record or explain partial mental jottings. Discuss and compare methods and explain how they work. Start with TU + TU, then HTU+TU or HTU + HTU using jumps of 100, 10 or 1, then by adding the most (or least) significant number first. Begin to use column addition and subtraction for HTU TU where the calculation cannot easily be done mentally. Use informal pencil and paper methods to support, record or explain partial mental jottings. Discuss and compare methods and explain how they work. Star with TU-TU, developing to HTU-TU or HTU-HTU. Do this first not crossing the tens or hundreds boundary, then crossing either the tens or the hundreds. Do first by counting up from the smaller to the bigger (complementary addition), then by compensation (take too much off, add back), then by decomposition Year 3 UNDERSTANDING MULTIPLICATION AND DIVISION Read and begin to write double, times, multiply, multiplied by, multiple of, lots of, groups of, times as (big, long, wide) and read and write the x sign; share, halve, divide, divided by, equal groups of, left over, remainder, the sign and understand that means one divided into two parts. Understand multiplication as repeated addition. Extend understanding that multiplication can be done in any order. Understand division as grouping (repeated subtraction) or sharing. Recognise that division is the inverse of multiplication. Use counters for sharing, then a number line for repeated subtraction and then mental strategies for dividing larger two-digit numbers by 1-12. Use the x, and = signs to record mental calculations in a number sentence. Recognise the use of a symbol such as symbol 142 \f "Monotype Sorts" \s 10 or symbol 115 \f "Monotype Sorts" \s 10 to stand for an unknown number involving x or . Begin to find remainders after simple division, expressing them in whole numbers. Round up or down after division, depending on the context. RAPID RECALL OF MULTIPLICATION AND DIVISION FACTS Use, read ad begin to write read double, twice, half, halve, whole, divide by two, divide into two etc and know that is one half. Year 3 Know by heart: multiplication facts for the 2, 5 and 10 times-tables. Begin to know the 3 and 4 times-tables. Derive quickly division facts corresponding to the 2, 5 and 10 times-tables. Derive quickly doubles of all whole numbers to at least 20 (e.g. 17 + 17 or 17 x 2). Derive quickly doubles of multiples of 5 to 100 (e.g. 75 x 2, 90 x 2). Derive quickly doubles of multiples of 50 to 500 (e.g. 450 x 2); Derive halves quickly eg 36 2, half of 130, 900 2). MENTAL CALCULATION STRATEGIES (x and ) To multiply by 10/100, shift the digits one/two places to the left, observing the patterns made by successive multiplying by 10 eg 3x10, 3x10x10 etc. Use doubling or halving, starting from known facts (e.g. 8 x 4 is double 4 x 4). Find a quarter of a number as a half of a half. Say or write a division statement corresponding to a given multiplication statement. Use known number facts and place value to carry out mentally simple multiplications and divisions. Multiply a single digit by 1,10 or 100. Divide a three-digit multiple of 100 by 10 or 100. Double any multiple of 5 up to 50. Halve any multiple of 10 to 100. Multiply a two-digit multiple of 10 up to 50 by 2,3,4,5 or 10. Year 3 Multiply a two-digit number by 2,3,4 or 5 without crossing the tens boundary. CHECKING THE RESULTS OF CALCULATIONS Check subtraction with addition, halving with doubling and division with multiplication. Repeat addition or multiplication in a different order. Check with an equivalent calculation. Year 3 SOLVING PROBLEMS MAKING DECISIONS Use, read and begin to write operation, sign, symbol, number sentence, equation. Choose and use appropriate operations (including multiplication and division) to solve word problems, and appropriate ways of calculating: mental, mental with jottings, pencil and paper. Decide what equipment will be needed eg cubes, squared paper, 100 square, coins etc. Explain how the problem was solved. REASONING ABOUT NUMBERS OR SHAPES Solve mathematical problems or puzzles, recognise simple patterns and relationships, generalise and predict. Suggest extensions by asking What if? or What could I try next? Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. Explain methods and reasoning orally and, where appropriate, in writing. Year 3 PROBLEMS INVOLVING REAL LIFE, MONEY OR MEASURES. Use mental addition and subtraction, simple multiplication and division, to solve simple word problems involving money in real life, money or measures using one or two steps and explaining how the problem was solved. Year 3 MONEY . Use, read and begin to write coin, pound, , pence, note, price, cost, cheaper, more/less expensive, pay, change, total, how much? Recognise all coins and 20, 10 and 5 notes. Exchange a note for its equivalent value in smaller notes or in 2 and 1 coins. Understand and use .p notation (for example, know that 3.06 is 3 and 6p. Find totals, give change, and work out which coins to pay. Year 3 MEASURES, SHAPE AND SPACE MEASURES Read and begin to write- long, short, tall, high, low, wide, narrow, deep, shallow, thick, thin, far, near, close, weight, weighs, heavy, light, balances, full, empty, holds , distance, roughly, nearly, about, approximately. Know that- 1 kilometre = 1000 metres 1 metre = 1000 centimeters 1 kilogram = 1000 grams 1 litre = 1000 millilitres Begin to use decimal notation for metres and centimetres. Estimate, measure and compare lengths in km. Estimate, measure and compare masses using g. Estimate, measure and compare capacities, using millilitres. For a variety of practical situations, correctly select km, m, cm, kg, g, ml or l. Read scales to the nearest division (labeled or unlabelled). Record estimates and measurements to the nearest whole or half unit (e.g. about 3.5kg), or in mixed units (e.g. 3m and 20cm). Use a ruler to draw and measure lines to the nearest half centimetre. Solve simple problems incorporating these units, using one or two steps, explaining reasoning and, where appropriate, writing a number sentence. Year 3 TIME Read and begin to write names of the days of the week, names of the months, seasons of the year, second, minute, hour, day, week, fortnight, month, year, date, century, calendar, season, morning, afternoon, evening, night, midnight, weekend, today, yesterday, a.m., p.m., tomorrow,now, soon, early, late, before, after, first, second, next, quick, fast, slow, how long ago?, how long will it be to?, how long will it take to?, how often?, always, never, often, sometimes, usually, once, twice, and comparatives such as faster, slower, takes longer etc,. Suggest suitable Year 3 units to estimate or measure time and use them in practical contexts. Use a calendar to find the date. Write the date correctly. Know birthdate (d/m/y). Know 1 year = 365 days 1 year = 52 weeks 1 year = 12 months 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 secs. Use metal strategies to solve simple problems incorporating these units. Read the time to 5 minutes on an analogue . Read the time to 5 minutes on a 12-hour digital clock Year 3 SHAPE AND SPACE Use, read and begin to write shape, pattern, flat, solid, hollow, side, edge, face, straight, curved, round, point, pointed, corner, sort, draw, make, build, circular, triangular, rectangular, surface, circular, triangular, rectangular, surface. Use the mathematical names for hemisphere, prism, semi- circle, quadrilateral. Classify and describe 3-D and 2-D shapes, including the hemisphere, prism, semi-circle, quadrilateral referring to properties such as reflective symmetry (2-D), the number or shapes of faces, the number of sides/edges and vertices, whether sides/edges are the same length, whether or not angles are right angles Make and describe shapes and patterns: for example, explore the different shapes that can be made from four cubes; fold and cut paper to make squares, octagons and stars; put 2 identical 2D shapes together and describe the new shape. Use a programmable robot to draw rectilinear shapes. Relate solid shapes to pictures of them. Make 3D shapes from provided nets. Year 3 SYMMETRY Use, read and begin to write fold, match, mirror line, reflection, symmetrical . Identify and sketch lines of symmetry in simple shapes with more than one line. Recognise shapes with no lines of symmetry. Sketch the reflection of a simple shape in a mirror line along one edge. POSITION AND MOVEMENT Read and begin to write the vocabulary related to position, direction and movement: for example, use, read and begin to write position, over, under, underneath, above, below, on, in, outside, inside in front, behind, beside, before, after, next to, opposite, between, close, far apart, middle, edge, corner, centre, top, bottom, side, direction, left, right, up, down, forwards, backwards, sideways, across, along, Year 3 around, through, to, from, towards, away from, journey. higher, lower, clockwise, anti- clockwise, route, grid, row, column, map, plan, compass point, north, south, east, west, horizontal, vertical, diagonal, descend, ascend. Describe and find the position of a square on a grid of squares with the rows labeled in numbers and columns labeled in letters. Recognise and use the four compass directions N, S, E, W. Describe movement on squared paper in terms of number of squares and N/S/E/W direction. Use, read and begin to write slide, roll, turn, whole turn, half turn, quarter turn, right angle, straight line , and be able to say that an angle is greater/smaller than Make and describe right- angled turns clockwise and anti-clockwise. Make and describe right-angled turns, including turns between the four compass points. Know a straight line is two right angles. Identify right angles in 2-D shapes and the environment. Sort shapes according to their right angles. Recognise that a straight line is equivalent to two right angles. Year 3 Compare angles with a right angle ie bigger/same/smaller. Use a tiling computer programme to create a pattern which is repeated along a line. Reflect the tile in one axis, and describe how the pattern changes. ORGANISING AND USING DATA Use, read and begin to write sort, set, graph, represent, chart, pictogram, diagram, table, list, count, tally, axis, label, title, most/least common/popular. Solve a given problem by organising and interpreting numerical data in simple lists, tables and graphs, for example: a 8-branch decision tree; simple frequency tables eg number of votes for different TV programmes; pictograms symbol representing two units; bar charts intervals labeled in ones then twos; Venn diagram eg loop for squares inside a rectangle for all shapes. Carroll diagrams eg even/not even (no horizontal criteria) Teaching Programme: Year 4 NUMBERS AND THE NUMBER SYSTEM Year 4 Properties of numbers and number sequences: Recognise and extend number sequences formed by counting from any number in steps of constant size, extending beyond zero when counting back: for example, count on in steps of 25 to 500, and then back to, say, 100. Year 4 Recognise multiples of 2, 3, 4, 5 and 10, up to the tenth multiple Mentally multiply or divide any integer up to 1000 by 10 (whole-number answers), and understand the effect ie when you multiply a number by 10, the digits move one place to the left, and when you divide by 10, the digits move one place to the right. It is useful to demonstrate this on a ThHTU board. Respond to questions such as How many times larger is 260 than 26?, How many coins are there in 1500?, How much is a ten-pack of dog food if one tin is 42p? Begin to multiply by 100. Recognise odd and even numbers up to 1000, and some of their properties, including the outcome of sums or differences of pairs of odd/even numbers. Year 4 PLACE VALUE, ORDERING AND ROUNDING (WHOLE NUMBERS) Read whole numbers to at least 10000 in figures. Read whole numbers to at least 10000 in words. Write whole numbers to at least 10000 in figures. Write whole numbers to at least 10000 in words. Know what each digit in a four-digit number represents, including zero as a place holder. Partition numbers into thousands, hundreds, tens and ones. Use, read and writ units or ones, tens, thousands, ten thousand, hundred thousand, million, digit, one-digit number, two-digit number, three-digit number, four-digit number etc, numeral, place value. Know what is 1, 10, 100, 1000 more/less than specified number, including those with units such as p, ml, g, m. Count on or back in tens, hundreds or thousands from any whole number up to 10000. Know how many tens you count on to 23 to get just past 100, how many hundreds you count on to 374 to get more than 1000. Year 4 Multiply whole numbers by 10, understanding that the digits move one place to the left. Divide whole numbers by 10, understanding that the digits move one place to the right. Use, read and write the vocabulary of comparing and ordering numbers eg how many, as many as, the same number as, equal to, more than, fewer than, greater than,less than, smaller than, larger than, more, least, largest, smallest, order, first, last, before, after, next, between, half way between, ordinal numbers as words and in the form nth. Use symbols correctly, including less than (<), greater than (>), equals (=). Give one or more numbers lying between two given numbers Year 4 Order a set of whole numbers less than 10000. Year 4 ESTIMATION AND ROUNDING Use, read and write guess, estimate, approximate, round, nearest, roughly, nearly, approximately, too many, too few, enough, not enough. Make and justify estimates up to about 250, and estimate a proportion. Estimate the position of a number on a line whose ends only are numbered, and explain how the decision was made. Estimate and use simple proportions eg if there is half a jar of sweets which originally contained 200, how many are there? Compare contents of containers eg half as much in that one as this, or one and a half times as much in that one. Round any positive integer less than 1000 to the nearest 10 or 100. Round measurements in seconds, minutes, hours, metres, kilometres, miles, kilograms, litres, to the nearest 10 or 100 units. calculations by approximations. Use, read and write in context integer, positive, negative, minus, above/below zero. Recognise negative numbers in context (e.g. on a number line, on a ladder, on a temperature scale). Order positive and negative numbers. Use, read and write next, consecutive, sequence, predict, continue, rule, relationship, sort, classify, property. Describe, extend and explain number sequences and patterns. Year 4 Make general statements about odd and even numbers and/or give examples that match them. Use, read and write multiple, digit. Recognise multiples in the 2,3,4,5 &10 times tables. Solve problems which involve multiples. Investigate the patterns produced by multiples on different-sized grids. FRACTIONS Use, read and write fraction, half, quarter, eighth, sixth, third etc. Use fraction notation. Recognise simple fractions that are several parts of a whole, such as 2/3 or 5/8 Recognise mixed numbers. Recognise the equivalence of simple fractions (e.g. fractions equivalent to . Identify two simple fractions with a total of 1 (e.g 3/10 and 7/10. Recognise one whole is equivalent to two halves, three thirds, n nths. Order simple fractions: for example, decide whether fractions such as 3/8 or 7/10 are greater or less than one half. Begin to relate fractions to division and find simple fractions of form 1/n of shapes, numbers or quantities. Find fractions of form m/n of shapes. PROPORTION Use, read and write in every, for every. Begin to use ideas of simple proportion: for example, one for every and one in every Year 4 DECIMALS Understand decimal notation and place value for tenths and hundredths. Place decimal numbers on a line where only the whole numbers are labelled and the decimal places indicated by marker lines. Use decimal notation to order amounts of money. Use decimal notation to convert a sum of money such as 13.25 to pence. Work out calculations with mixed units eg and p, m and cm. Use decimal notation to convert lengths such as 125cm to metres. Use decimal notation to round a sum of money to the nearest pound. In one step (operation) change one number to another separated by more than 0.1 eg 4.7 to 4.9; 6.9 to 6.1. Recognise the equivalence between the decimal and fraction forms of one half and one quarter, and tenths such as 0.3. CALCULATIONS UNDERSTANDING ADDITION AND SUBTRACTION Use, read and write take away, subtract, how many are left, how much less, difference between, how much more, how many more to make, decrease, inverse and the minus sign Year 4 Consolidate understanding of relationship between + and . Understand the principle (not the names) commutative and associative laws as they apply to addition and subtraction. Understand that the sum of two positive numbers is greater than either number. Understand that addition and subtraction are the inverses of each other, and use this to check results. Consolidate subtraction as taking away. Consolidate subtraction as finding the difference between. Consolidate subtraction as complementary addition. Understand that subtraction is non-commutative. Understand that subtracting zero leaves a number unchanged. Understand that subtraction is the inverse of addition, and use this to check results. Year 4 RAPID RECALL OF ADDITION AND SUBTRACTION FACTS Consolidate knowing by Heart addition facts for all numbers to 20. Consolidate knowing by heart subtraction facts for all numbers to 20. Year 4 Derive quickly all number pairs that total 100 (e.g. 62 + 38, 75 + 25, 40+ 60). Derive quickly addition doubles from 1+1 to 50+50. Derive quickly all addition doubles which are multiples of 10 eg 290+290/ Derive quickly all addition doubles which are multiples of 100 eg 1900+1900. Derive quickly all pairs of multiples of 50 with a total of 1000 (e.g. 850 + 150). MENTAL CALCULATION STRATEGIES (+ AND -) Find a small difference by counting up (e.g. 5003 4996). Count on or back in repeated steps of 1, 10, 100 or 1000. Partition into tens and units, adding the tens first. Partition into hundreds, tens and units, adding the hundreds first Identify near doubles, using known doubles (e.g. 150 + 160). Add or subtract the nearest multiple of 10, 100 or 1000, then adjust. Continue to use the relationship between addition and subtraction eg if you know 36+19=55, you know 19+36, 55-19, 55-36. Add 3 or 4 small numbers, finding pairs totalling 10, or 9 or 11. Recognise that a set of numbers like 5+5+6+4 is equivalent to 5x4. Add three two-digit multiples of 10, such as 40 + 70 + 50. Use known number facts and place value to add or subtract mentally, including any pair of two-digit whole numbers. Continue to add or subtract two-digit multiples of 10. Year 4 Add or subtract a pair of multiples of 100, crossing the 1000 boundary. Revise adding or subtracting a multiple of 10 to/from a two- or three- digit number, without crossing the hundreds boundary. Revise adding a two-or three- digit number to a multiple of 10, 100 or 1000. Find what to add to a two- or three- digit number to make 100 or the next higher multiple of 100. Find what to add to a four- digit multiple of 100 to make the next higher multiple of 1000. Add a single digit to any three- or four-digit number, crossing the tens boundary. Subtract a single digit from a multiple of 100 or 1000. Subtract a single digit from a three- or four-digit number, crossing the tens boundary. Find a small difference between a pair of numbers lying each side of a multiple of 1000. Add or subtract any pair of two-digit numbers, including crossing the tens boundary. Year 4 PENCIL AND PAPER PROCEDURES (+ AND -) Using informal pencil and paper methods, and adding the most significant digit first, add HTU + TU, then HTU + HTU, crossing the tens or the hundred boundary or both. Using informal pencil and paper methods, and using compensation (add too much, take some off), add HTU + TU, then HTU + HTU, crossing the tens or the hundred boundary or both. Use standard written method, adding the units first and carrying where necessary. Using methods similar to the above, extend addition to money as decimals, adding two or more three-digit sums of money, with or without adjustment to the pounds, and lining up decimal points. Using informal pencil and paper methods subtract HTU TU, then HTU -HTU, using counting up (complementary addition), crossing the tens or the hundred boundary or both. Using informal pencil and paper methods, and using compensation (take off too much,add some on), subtract HTU - TU, then HTU - HTU, crossing the tens or the hundred boundary or both. Use standard written method, subtract using decomposition. Using methods similar to the above, extend subtraction to money as decimals, adding two or more three-digit sums of money, with or without adjustment from the pence to the pounds, and lining up decimal points. Year 4 UNDERSTANDING MULTIPLICATION AND DIVISION Use, read and write times, multiply, multiplied by, product, multiple, inverse and the x sign; share, group, divide, divided by, divided into, divisible by, factor, quotient, remainder, inverse and the x and / signs; Share,group, divide, divided by, divided into, divsible by, factor, quotient, remainder, inverse and the dividing signs and // Extend understanding of the operations of x and , and their relationship to each other and to + and . Understand the principles (not the names) of the commutative, associative and distributive laws as they apply to multiplication. Commutative- 8x15=15x8. Associative- 6x15=6x(5x3) = (6x5)x3=30x3=90 Distributive- 18x5= (10+8)x5= (10x5)+(8x5)=50+40=90 Understand that multiplication and division are the inverse of each other, and use this to check results. Understand division either as grouping or as repeated subtraction. Begin to relate division and fractions. Find remainders after division. Divide a whole number of pounds by 2, 4, 5 or 10 to give .p. Round up or down after division, depending on the context. RAPID RECALL OF MULTIPLICATION AND DIVISION FACTS Use, read and write double, twice,half, halves, whole, divide by 2, divide into 2, and as a half. Year 4 Know by heart: multiplication facts for 2, 3, 4, 5 and 10 times-tables. Begin to know: multiplication facts for 6, 7, 8 and 9 times-tables. Derive quickly:division facts corresponding to 2, 3, 4, 5 and 10 times-tables. Derive quickly doubles of all whole numbers to 50 (e.g. 38 + 38, or 38 x 2); Derive quickly doubles of multiples of 10 to 500 (e.g. 460 x 2); Derive quickly doubles of multiples of 100 to 5000 (e.g. 3400 x 2); Derive halves quickly (e.g. 74 2, half of 420, half of 3800). MENTAL CALCULATION STRATEGIES (x and ) Use doubling or halving, starting from known facts. For example: double/halve two-digit numbers by doubling/halving the tens first; to multiply by 4, double, then double again; to multiply by 5, multiply by 10 then halve; to multiply by 20, multiply by 10 then double; find the 8 times-table facts by doubling the 4 times-table; find quarters by halving halves. Use closely related facts (e.g. to multiply by 9 or 11, multiply by 10 and adjust; develop the x6 table from the x4 and x2 tables). Partition and use the distributive law (e.g. 23 x 4 = (20 x 4) + (3 x 4)). Use the relationship between multiplication and division eg knowing 12x9 means you know 9x12, 9, 108(12, 25x4=25+25+25+25. Year 4 Use known number facts and place value to multiply and divide integers, including by 10 and then 100 (whole-number answers) eg multiply a two- or three- digit number by 10 or 100. Divide a four-digit multiple of 1000 by 10 or 100. Double any multiple of 5 up to 100. Halve any multiple of 10 to 200. Consolidate multiplying a two- digit multiple of 10 by 2,3,4,5 or 10, and begin to multiply by 6,7,8 or 9. Multiply a two-digit number by 2,3,4 or 5, crossing the tens boundary. PENCIL AND PAPER PROCEDURES (x and ) Use informal pencil and paper methods to support, record or explain short multiplications and divisions eg the grid method and partitioning. Approximate first so children can check if actual answer makes sense. Use informal pencil and paper methods for division eg using multiples of the divisor and then moving into standard short division form. Approximate first so children can check if actual answer makes sense. CHECKING THE RESULTS OF CALCULATIONS Check with the inverse operation. Check the sum of several numbers by adding in reverse order. Check with an equivalent calculation ie by using a different calculation pathway. Year 4 Estimate and check by approximating (round to nearest 10 or 100). Use knowledge of sums or differences of odd/even numbers eg adding odd+odd=even, e+e=e, o+e=o, e-e=e,o-o=e,o-e=o,e-o=o. SOLVING PROBLEMS MAKING DECISIONS Use, read and write operation, sign, symbol, number sentence, equation. Choose and use appropriate number operations and appropriate ways of calculating (mental, mental with jottings, pencil and paper) to solve problems. REASONING ABOUT NUMBERS OR SHAPES Explain methods and reasoning about numbers orally and in writing. Begin to use conventional notation and vocabulary to record the explanation. This should be extended to calculations which cannot be done wholly mentally. Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking What if? Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. Year 4 PROBLEMS INVOLVING REAL LIFE, MONEY OR MEASURES. Use all four operations to solve word problems involving numbers in real life, money and measures, using one or more steps, including converting pounds to pence and v.v. Year 4 MONEY Use, read and write money, coin, pound, , pence, note, price, cost, cheaper, more expensive, pay, change, total, value, amount. Change pounds to pence and vice versa. Find simple fractions of whole numbers of pounds. Year 4 MEASURES, SHAPE AND SPACE MEASURES Use, read and write unit, standard unit, metric unit, imperial unit, standard metric units (km, m, cm, mm, kg, g, l, ml), including their abbreviations, and imperial units (mile, pint).; length and distance words like long, short, tall, high, low, wide, narrow, shallow, deep, thick, thin etc; far, near, distance, circumference, perimeter; mass words like big, bigger, small, smaller, balances; weight words like heavy, light, weighs; capacity words like full, empty, holds; comparative words like longer, longest. Know and use-the equivalent of one half, one quarter, three quarters and one tenth of 1km, 1m, 1kg, 1litre in m, cm, g, ml. Convert up to 1000 centimetres to metres, and vice versa. Begin to use decimal forms eg 1.6m in cm. Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity. Record estimates and readings from scales to a suitable degree of accuracy. Measure and calculate the perimeter and area of rectangles and other simple shapes, using counting methods and standard units (cm, cm squared) Solve story problems using km, m, cm, kg, g, ml or l. Year 4 TIME Use, read and write names of the days of the week, months and seasons; day, week, fortnight, month, season, year, leap year, century, millenium, morning, afternoon, evening, night, midnight, noon, hour, minute, second, today, tomorrow, weekend, a.m., p.m., how long ago, how long will it be to, arrive, depart, faster, fastest, slowest, takes longer, takes less time, earliest, latest. Know and use the rhyme 30 days hath September and/or teach knuckles. Suggest suitable Year 3 units to estimate or measure time and use them in practical contexts. Read simple timetables. Use this years calendar. Know- 1 millenium = 1000 years 1 century = 100 years 1 year = 365 days 1 year = 52 weeks 1 year = 12 months 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 secs Use all four operations to solve word problems involving time. Estimate/check times using seconds, minutes, hours. Read the time from an analogue clock to the nearest minute. Read the time to the nearest minute from a 12-hour digital clock. Use am and pm and the notation 9:53. Year 4 SHAPE AND SPACE Use, read and begin to write pattern, shape, 2-D, two-dimensional, 3-D, three- dimensional, line, edge, side, face, surface, base, point, angle, vertex, vertices, centre, radius, diameter, net, make, build, construct, draw, sketch, curved, straight, regular, irregular, concave, convex, closed, open, circular, triangular, hexagonal, cylindrical, spherical, square- based, right-angled. Name, describe, classify and Visualise 3-D and 2-D shapes including circle, semi-circle, triangle, equilateral triangle, isosceles triangle, quadrilateral, rectangle, oblong, pentagon, hexagon, heptagon, octagon, polygon, cube, cuboid, pyramid, sphere, hemisphere, cylinder, cone, prism, tetrahedron, polyhedron. Classify polygons using criteria such as number of right angles, whether or not they are regular, symmetry properties. Make shapes: for example, construct polygons by paper folding or using pinboard, and discuss properties such as lines of symmetry. Visualise 3-D shapes from 2- D drawings and identify simple nets of solid shapes. Year 4 SYMMETRY Use, read and write mirror line, line of symmetry, line symmetry, symmetrical, reflect, reflection, translation. Sketch the reflection of a simple shape in a mirror line parallel to one side (all sides parallel or perpendicular to the mirror line). Know that equivalent points of an object and its reflection are the same (shortest) distance from the line of symmetry. POSITION AND MOVEMENT Use, read and write prepositions and everyday words to describe position and movement, position, direction, ascend, descend, journey, route, map, plan, grid, row, column, origin, co- ordinates, compass point, north, south, east, west, north-east, north-west, south- east, south-west, horizontal, vertical, diagonal. Recognise simple examples of horizontal and vertical lines. Year 4 Recognise positions and directions: for example, describe and find the position of a point on a grid of squares where the lines are numbered, using terms of the form 4 along, 2 up. Begin to understand the convention (4,2) Use the eight compass directions N, S, E, W, NE, NW, SE, SW. Make and measure clockwise and anti-clockwise turns: for example, from SW to N, or from 4 to 10 on a clock face. Use, read and write turn, rotate, whole turn, half turn, quarter turn, angle, right angle, straight line, degree, ruler, set square, angle measurer. Begin to know that angles are measured in degrees and that: one whole turn is 360 or 4 right angles; a quarter turn is 90 or one right angle; half a right angle is 45. Relate the angles between points of the compass to degrees. Start to order a set of angles less than 180. Year 4 PROBABILITY Use the language associated with probability to discuss events, including those with equally likely outcomes- likely, unlikely, certain, impossible, possible, probable. ORGANISING AND USING DATA Use, read and write vote, survey, questionnaire, data, count, tally, sort, set, represent, table, list, graph, chart, diagram, axes, label, title, most least common or popular. Solve a problem by collecting quickly, organising, representing and interpreting data in tables, charts, graphs and diagrams. 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