Woodcote Primary School Learning Ladder Maths Milestone 1 Autumn

Transcription

1 Maths Milestone 1 tumn count to ten twenty, forwards backwards, beginning with 0 or 1, or from any given count, read write to in numerals words show s using objects pictures the words; equals to, more than, less than (fewer), most, least bonds to to add subtract subtract one-digit twodigit s to 20, zero (0) read, write underst equations with +, - = signs one step adding subtracting using objects pictures count in multiples of 2 5 language to put events in order; before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening, recognise name days of the week, months years (i.e 2015) name common 2D shapes rectangles ( squares), circles, triangles name common 3D shapes cuboids ( cubes), pyramids spheres describe position movement whole, half, quarter three quarter turns

2 Maths Milestone 1 ring say one more one less than a given count in twos fives to 40 count to 40, forwards backwards, beginning with 0 or 1, or from a given name recognise tens ones one-digit adding subtracting missing subtract within 40, a two-digit ones subtract within 40, a two-digit tens subtract within 40, two twodigit s subtract within 40, adding three one-digit s the weight, length, height capacity of objects, i.e. longer, lighter than, less than, full measure begin to record lengths, heights, mass/weight, capacity volume in nonstard units tell the time to o clock half past, draw the hs on a clock solve for time; quicker, slower, earlier, later recognise & use language relating to dates, days, weeks, months & years sequence events in chronological order

3 Maths Milestone 1 mmer count to across 100, forwards backwards, beginning with 0 or 1, or from any given find estimate s to 100 using pictures objects read write s to at least 100 in numerals words subtract within 100, a two-digit ones subtract within 100, a two-digit tens subtract within 100, two twodigit s one-step multiplicati on division use objects, pictures arrays with the support of an adult recognise, find name half as one of two equal parts of an object, shape or amount recognise, find name a quarter as one of four equal parts of an object, shape or amount recognise money name the different coins notes

4 Maths Milestone 1 Working at Greater Depth In addition to the Year 1 Programmes of Study I underst regularly use the following correctly. Place Value. Division & show fluency notice patterns in counting forwards backwards across 100 sometimes in larger steps I show understing about facts to solve more difficult recall use addition subtraction facts to 20 fluently division in different topics measures more tricky (these may be practical), money other measures, time show understing about more difficult practical money other measures sort common 2-D & 3-D shapes & common objects show fluency in mental addition & subtraction of onedigit & two-digit s to 20 explain solve more difficult half & quarter of shapes amounts show understing & solve more difficult shapes their properties more complex whole, half three-quarter turns addition subtraction facts to solve more tricky Next Steps for Depth look at an answer decide what the question could have been with empty boxes explain what is wrong with an example correct the error draw a picture to explain or demonstrate what I have worked out explain to a partner how I know something using key/star words say what would have come before what would come next, explain how I know find the odd one out explain why it doesn t fit spot explain patterns make up a reallife story using my maths convince someone else that I am right

5 Maths Milestone 2 tumn place value facts to solve order s from 0 up to 100 using <, > = count in steps of 2, 3, 5 from 0, in tens from any, forward & backward find 10 or 100 more or less than a given recall use addition subtraction facts to 20 to find facts up to 100 show that addition can be done in any order that subtraction cannot recognise use the inverse relationship between addition & subtraction & subtract within 100, adding three onedigit s calculate & write division equations using x, & = & division using objects, arrays, repeated +, mentally, known facts show that can be done in any order that division cannot recall x & facts for the 2, 5 10 tables, recognising odd even s choose use appropriate stard units to estimate measure length/ height in any direction (m/cm) to the nearest appropriate unit, using rulers scales order length record the results using >, < = interpret construct simple pictograms, tally charts, block diagrams simple tables ask answer simple questions by counti9ng the of objects in each category sorting categories by quantity ask answer questions about totalling comparing data in groups

6 Maths Milestone 2 ring order length mass record the results using <, > = recognise the hundreds, tens ones in a 3- digit count from 0 in multiples of 4, with + & - s, quantities & measures my knowledge of mental written methods with + & - of money, giving change show that addition can be done in any order subtraction of one from another cannot recognise, find, name & write 1 fractions of a 4 4 length, shape, set of objects or amount write simple fractions for example 1 2 of 6 = 3 recognise the equivalence of recognise & use symbols for pounds ( ) & pence (p) combine coins to make different amounts find different combinations of coins that equal the same amount describe the properties of 2D shapes (sides line of symmetry) describe the properties of 3D shapes (edges, vertices & faces) find 2D shapes on the surface of 3D shapes. describe position, direction movement, movement in a straight line, rotation through right angles (clockwise anticlockwise) order arrange patterns sequences sort common 2D 3D shapes

7 Maths Milestone 2 mmer order capacity temperature record the results using <, > = estimate s to 1000 using pictures or objects order s up to 1000 read write s up to 1000 in numerals words + & - s mentally, a 3- digit ones + & - s mentally, a 3- digit tens + & - s mentally, a 3- digit hundreds + & - with up to 3- digits using column method estimate the answer use the inverse to check my answers recall use x facts for the 3 & 4 tables show that of two s can be done in any order division of one by another cannot choose use units to estimate measure capacity (l/ml) & temperature ( C) to the nearest unit order mass, volume capacity record the results using >, < = tell & write the time to 5 minutes, quarter past/ to the hour draw the hs on a clock face I know the of minutes in an hour & the of hours in a day sequence intervals of time underst draw simple pictograms, tally charts, block diagrams simple tables ask answer simple questions by counting the data ask answer questions about totalling comparing data

8 Maths Milestone 2 Working at Greater Depth In addition to the Year 2 Programmes of Study I underst regularly use the following correctly. Calculation Number Facts. Division & work out mental calculations when regrouping is required (e.g ) more complex missing (e.g. 14 +? 3 = 17) word that involve more than one step reason about addition (e.g. reason that the sum of 3 odd s will always be odd) facts to make deductions outside known facts (e.g. 18 x 5 cannot be 92) read the time on the clock to the nearest 5 minutes describe similarities differences of shape properties. recognise the relationships between addition & subtraction can rewrite addition statements as simplified statements find fractions of amounts determine remainders given known facts (e.g = 5 with no remainder so 16 3 will have a remainder of 1 ) read scales in divisions of ones, twos, fives tens in a practical situation where not all s on the scale are given Next Steps for Depth look at an answer decide what the question could have been with empty boxes explain what is wrong with an example correct the error draw a picture to explain or demonstrate what I have worked out explain to a partner how I know something using key/star words say what would have come before what would come next, explain how I know find the odd one out explain why it doesn t fit spot explain patterns make up a reallife story using my maths convince someone else that I am right

9 Maths Milestone 3 tumn recognise the place value of each digit`, order s up to 100 find 10 or 100 more or less than a given read write s up to 1000 in numerals words + & -, missing, using facts, place value subtract 2-digit & 3-digit s mentally a 3- digit ones, tens or hundreds + & - with up to 3-digits using column methods + & - amounts of money to give change continue to measure using the appropriate tools units measure the perimeter of simple 2D shapes interpret present data using bar charts, pictograms tables one-step two-step questions using information presented in scaled bar charts, pictograms tables a line. estimate the answer use the inverse to check measure lengths (m/cm/mm)

10 Maths Milestone 3 ring (Including Decimals) count up down in tenths subtract fractions with the same denominator within one whole subtract lengths within the same unit of measure (m/cm/mm) write calculate statements for x & using the tables for 2, 3, 4, 5 10 times tables multiply a 2-digit by 2, 3, 4, 5 or 10 mentally using a formal written method. x &, missing, & such as n x 3 = m showing understing that the two missing s will change in relation to each other find write fractions of s, unit fractions non-unit fractions with small denominators I underst tenths arise from dividing an object into 10 equal parts & in dividing 1- digit s or quantities by 10 recognise show equivalent fractions with small denominators order unit fractions, fractions with the same denominators tell & write the time from an analogue clock, using Roman numerals 12 hour 24 hour clocks. estimate read time to the nearest minute read time in sec, min, hr I know the of seconds in a minute, days in each month, year. the duration of events

11 Maths Milestone 3 mmer (Including Decimals) find 1000 more or less than a given recognise the place value of each digit in a 4-digit order s beyond 1000 round any to the nearest 10 or 100 write calculate statements for x & using the tables for 6 8 times tables multiply a 2-digit by any 1-digit mentally using a formal written method. measure mass (kg/g) measure volume/ capacity (l/ml) use mixed units of measures i.e. 3m 45cm use simple equivalent of measure recognise angles as a property of shape or a description of turn identify right angles recognise that two right angles make a half-turn, three makes three quarters of a turn four a complete turn. identify whether angles are greater than or less than a right angle draw 2D shapes make 3D shapes using modelling materials identify horizontal vertical lines pairs of perpendicular parallel lines recognise 3D shapes in different orientations

12 In addition to the Year 3 Programmes of Study I underst regularly use the following correctly. Place Value Calculations Decimals & demonstrate fluency reasoning in counting in multiples of 4, 8, to 1000 demonstrate fluency reasoning in comparing ordering s up demonstrate reasoning about facts to solve more complex Maths Milestone 3 Working at Greater Depth demonstrate reason about more reason about & fluency in mental addition & subtraction solve more complex unit complex, money solve more complex of 1- & 2-digit s to 20 addition fractions, tenths equivalent fractions with small denominators other measures, duration of time. reason about shapes right angles & turns more subtraction facts to more complex practical complex solve more complex horizontal, money other vertical, perpendicular measures. parallel lines, rounding recall use interpret s with accuracy construct with accuracy to draw measure division facts for pictograms more straight lines s tables complex tables using from 2 to 10 scales e.g. 2,5,10 units per cm ask answer questions presented in division in a range many contexts about of contexts data presented in measures different forms look at an answer decide what the question could have been with empty boxes Next Steps for Depth explain what is draw a picture to explain to a say what would wrong with an example explain or demonstrate partner how I know have come before correct the error what I have worked out something using what would come next, key/star words explain how I know spot explain make up a real-life convince someone find the odd one patterns story using my maths else that I am right out explain why it doesn t fit

13 Maths Milestone 4 tumn (Including Decimals) find 1000 more or less than a given recognise the place value of each digit in a 4-digit order & s beyond 1000 round any to the nearest 10, 100 or 1000 read Roman numerals to 100 ( I to C ) count in multiples of 6, 7, 9, subtract s with up to 4- digits using column methods estimate use the inverse operations to check the answers to calculations addition subtraction two-step deciding which operations methods to use why recall x & facts for times tables up to 12 x 12 x &, correspondence in which n objects are connected to m objects place value known facts to multiply divide by 0 & 1 multiply together 3 s up to 12 x 12 multiply 2-digit 3- digit s by a 1-digit using a formal written method converting hours to minutes; minutes to seconds; years to months; weeks to days write convert time between analogue digital hour clocks comparison, sum difference using information presented in bar charts, pictograms, tables other graphs interpret present discrete continuous data using appropriate graphical methods, bar charts time graphs

14 Maths Milestone 4 ring (Including Decimals) count up down in hundredths I recognise that hundredths arise when dividing an object by one hundred dividing tenths by 10 round s with one place to the nearest whole s with the same of places to the nearest whole subtract fractions with the same denominator find the effect of dividing 1- or 2-digit s by , identifying the value of the digits in the answer as ones, tenths hundredths recognise show, using diagrams, families of equivalent fractions increasingly harder fractions to calculate divide quantities, nonunit fractions where the answer is a whole recognise write equivalence of any of tenths or hundredths recognise write equivalence to simple measure money fractions s to two places. estimate, calculate different measures, money in pounds pence measure calculate the perimeter of rectangles in cm m convert different units of measure find the area of rectangles by counting squares

15 Maths Milestone 4 mmer (Including Decimals) count backwards through zero to include negative s my prior learning of + & - in a range of consolidati on, reasoning problem solving activities recognise & use factor pairs that can be done in any order in mental calculations my prior learning of x & in a range of consolidation, reasoning problem solving activities write & calculate mathematical statements for x & using tables I know, twodigit s time one-digit s, using mental & progressing to written methods describe positions on a 2-D grid as coordinates in the 1st quadrant describe movements between positions as translations plot specified points draw sides to complete a given polygon complete a simple symmetric figure with a specific line of symmetry identify, order acute obtuse angles up to 2 right angles classify quadrilater als triangles based on their properties.

16 Maths Milestone 4 Working at Greater Depth In addition to the Year 4 Programmes of Study I underst regularly use the following correctly. Place Calculations & Value Decimals demonstrate demonstrate reason about more reason about & fluency fluency in mental solve more complex solve more complex reasoning in counting addition & complex, money in multiples of 6,7,9,25 subtraction of onedigit & two-digit other measures, shapes 1000 in equivalents of duration of SP different triangles, comparing s to 20 s (tenths time using acute obtuse ordering s hundredths) hour clock. angles beyond 1000 addition families of equivalent subtraction facts fractions to solve more complex demonstrate reasoning about facts to solve more complex. look at an answer decide what the question could have been with empty boxes recall use fluently division facts for facts up to 12x12 ask division in a range of contexts measures. answer questions using data presented in a range of graphs demonstrate an understing of graphical representation of data to record change over time. reasoning about shapes their positions on a 2- D grid using coordinates in the first quadrant Next Steps for Depth explain what is draw a picture explain to a say what would wrong with an to explain or partner how I know have come before example correct demonstrate what I something using what would the error have worked out key/star words come next, explain how I know spot make up a reallife convince find the odd one story using my explain patterns someone else that I out explain why maths am right it doesn t fit

17 Maths Milestone 5 tumn Division read, write, order s to at least determine the value of each digit count forwards or backwards in steps of powers of 10 negative s in context, count forwards backwards with positive negative whole s, through zero. round any up to to the nearest 10, 100, 1000, read Roman Numerals to 1000 (M) recognise years written in Roman numerals subtract s mentally with increasingly large s + & - whole s with more than 4-digits, using column method rounding to check answers to calculations determine, in the context of a problem, levels of accuracy addition subtraction multi-step in contexts, deciding which operations methods to use why x & s mentally drawing upon known facts x & whole s by 10, 100 & 1000 x & s mentally drawing upon known facts x s up to 4-digits by a 1- digit or 2-digit using grid method long s up to 4-digits by a 1- digit using a formal written method interpret remainders appropriately for the context identify multiples factors, finding all factor pairs of a, common factors of two s recognise use square s cube s the correct notation identify multiples factors, finding all factor pairs of a, common factors of two s I know use the vocabulary of prime s, prime factors composite s measure & calculate the perimeter of composite rectangular shapes in cm & m convert between different units of metric measure underst use approximate equivalences between metric common imperial units such as inches, pounds & pints converting between units of time calculate the area of rectangles using square centimetres square metres. estimate the area of irregular shapes estimate volume (i.e. using 1cm³ blocks to build cuboids) capacity (i.e. using water)

18 Maths Milestone 5 ring (Including Decimals Percentages) establish whether a up to 100 is prime recall prime s up to 19 round s with two places to the nearest whole to one place addition, subtraction, division a combination of these, understing the meaning of the equals sign subtract fractions with the same denominator denominators that are multiples of the same addition, subtraction, division a combination of these, understing the meaning of the equals sign multiply proper fractions mixed s by whole s, supported by materials diagrams division, scaling by simple fractions i.e. recipes for different s of people. & order fractions whose denominators are multiples of the same recognise mixed s improper fractions convert from one form to the other write mathematical statements >1 as a mixed identify, name write equivalent fractions of a given fraction, represented visually, tenths hundredths read, write, order s with up to 3 places recognise use thousths relate them to tenths, hundredths equivalents up to three places x & whole s by 10, 100 & 1000 write percentage, fraction equivalents all 4 operations to solve measure using notation recognise the per cent symbol (%) & underst that per cent relates to of parts per hundred which require knowing percentage, equivalents fractions with a denominator of 10 or 25 comparison, sum difference using information presented in a line graph complete, read interpret information in tables, timetables

19 Maths Milestone 5 mmer (Including Decimals Percentages) round s with two places to the nearest whole to one place demonstrate my prior fluency in learning of mental addition + & - in a & subtraction range of of consolidati one-digit & on, two-digit s reasoning to 20 problem solving activities addition, subtraction, division a combination of these, understing the meaning of the equals sign use my prior addition, learning of subtraction, x & in a range of consolidation division a, reasoning combination of these, problem understing solving the meaning of activities the equals sign up to three places x & whole s by 10, 100 & 1000 all 4 operations to solve measure using notation I know a whole turn is a turn is 180 find angles on a straight line the properties of rectangles to find missing lengths & angles draw angles, measure them in degrees ( ) identify 3D shapes, cubes other cuboids, from 2D representations reflect translate shapes using appropriate language, knowing the shape has not changed distinguish between regular irregular polygons based on reasoning about equal sides angles

20 In addition to the Year 5 Programmes of Study I underst regularly use the following correctly. Place Value Calculations, Decimals Percentages & demonstrate demonstrate reason about demonstrate fluency fluency flexibility in solve more fluency in converting reasoning in counting solving multi-step complex between different in steps of powers of equivalent units of measure to 10 for any given addition & subtraction fractions, solve, using up to of larger s all four operations demonstrate reasoning about facts to solve more complex look at an answer decide what the question could have been with empty boxes Maths Milestone 5 Working at Greater Depth demonstrate fluency in mental addition subtraction of large s demonstrate fluency in multiplying & dividing whole s & those s by 10, 100 & 1000 reason about solve more complex, for example, square s & cube s s percentages reason about more complex calculation of area volume interpret & construct with accuracy table, timetables line graphs decide which representations of data are most appropriate why reason about make deductions when solving more complex angles more complex reflection translation of shapes Next Steps for Depth explain what is draw a picture explain to a say what would wrong with an to explain or partner how I know have come before example correct demonstrate what I something using what would the error have worked out key/star words come next, explain how I know spot make up a reallife convince find the odd one story using my explain patterns someone else that I out explain why maths am right it doesn t fit

21 Maths Milestone 6; Year 6 Programmes of Study read, write, order s up to & determine the value of each digit round any whole to a required degree of accuracy negative s in context, calculate intervals across zero practical that involve all of the above Addition,, Division x using Grid, Column & long using short & long division, & interpret remainders as whole s, fractions, or by rounding perform mental calculations with mixed operations identify common factors, common multiples & prime s I use my knowledge of the order of operations +/- multi-step deciding which operation method to use why I use estimation to check answers & determine, in the context an appropriate degree of accuracy (Including Decimals Percentages) I use common factors to simplify fractions, common factors to express fractions in the same denomination & order fractions, >1 +/- fractions with different denominators & mixed s multiply simple pairs of proper fractions writing the answer in its simplest form proper fractions by whole s I associate a fraction with division calculate fraction equivalents for a simple fraction x & with s answers recall & use simple fraction, & % equivalences Ratio Proportion the relative sizes of 2 quantities where missing values can be found by using x & facts the calculation of % & the use of % comparisons similar shapes where the scale factor is known/found unequal sharing & grouping using knowledge of fractions multiples Algebra simple formulae generate describe linear sequences express missing algebraically find pairs of s that satisfy an equation with two unknowns enumerate possibilities of combinations from two variables interpret construct pie charts line graphs use these to solve calculate interpret mean as an average the calculation & conversion of units of measure, using notation to 3dp, read, write & convert between stard units of measure using notation to 3dp convert between m & km I recognise that shapes with the same area can have different perimeters I recognise when it is possible to use formulae for area & volume calculate the area of parallelograms & triangles calculate, estimate & volume of cubes & cuboids using stard units ( cubic cm, m, mm, km) draw 2D shapes using from dimensions & angles I recognise, describe & build simple 3D shapes & nets & classify shapes find unknown angles in any triangles, quads & regular polygons illustrate & name radius, diameter & circumference, & know diameter is 2x radius I recognise angles where they meet at a point, are on a straight line, or are vertically opposite, & find missing angles describe position in all four quadrants draw & translate simple shapes on the coordinate plane reflect them in axes

22 In addition to the Year 6 Programmes of Study I underst regularly use the following correctly. Place Calculations FDRP Algebra & & Value explain solve say whether an order generate explain what is that require answer to an addition a set of sequences from rules, the same or different me to read, write, /or subtraction mixed s, write my own rules using a deeper order problem is correct fractions, percentages explain why understing of s up to whether the method is ratios, common patterns 000 determine the explain my decisions geometry occur value of each digit say whether I agree or disagree with a statement by rounding any whole to a required degree of accuracy Maths Milestone 6 Working at Greater Depth effective, with fractions s estimation to answers & explain my reasoning calculations that involve mixed fractions, s, percentages ratios, explain my reasoning answer a range of questions starting What happens if? using a range of measures estimation to explain my reasoning with angles that involve calculations with negative s look at an answer decide what the question could have been with empty boxes confidently use long answer true or false statements division to solve a fractions, range of s, percentages those with /or ratios s calculate the area perimeter of a range of shapes, compound shapes made of different shapes my knowledge order mixed, of the order of fractions, s operations to carry out percentages on a calculations line justify the four operations my choices Next Steps for Depth explain what is draw a picture explain to a say what would wrong with an to explain or partner how I know have come before example correct demonstrate what I something using what would the error have worked out key/star words come next, explain how I know spot make up a reallife convince find the odd one story using my explain patterns someone else that I out explain why maths am right it doesn t fit