progress in mathematics scheme of work for year 5 web viewthis draws together those key aspects of...

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Securing Progress in Mathematics Scheme of Work for Year 5

Scheme of Work: Mathematics Year 5

Contents and the intended use of each section within the Scheme of WorkEssential Learning in MathematicsThis draws together those key aspects of mathematics pupils need to secure so that they can make good progress over the year and are ready to move onto the work set out in the following year. When planning the year’s work keep these aspects of mathematics in mind. Return to them at regular intervals and provide pupils with the opportunity to refresh and rehearse them through practice, consolidating and deepening their knowledge, skills and understanding.

Problem Solving, Reasoning, CommunicatingThis provides a short summary of the problem solving and reasoning activities pupils should engage in and the communication skills expected of them.

Language and MathematicsThis section emphasises the importance of spoken language in the teaching and learning of mathematics and the need for pupils to acquire a range of appropriate mathematical vocabulary. It highlights and exemplifies five functions language plays in the learning of mathematics.

Learning the Language of MathematicsTwo simple-to-remember principles are identified, that seek to promote the incorporation of language into mathematics planning and teaching.

Key Mathematical VocabularyThis table lists key mathematical vocabulary organised under seven strands of mathematical content which reflect the headings used in the National Curriculum. The table provides a checklist you can refer to when planning. There is some overlap across the year groups to consolidate pupils’ learning.

Learning OutcomesThis table lists the learning outcomes for the year and reflects the National Curriculum Programme of Study. You can select and refer to the learning outcomes, choosing those that will be your focus for a teaching week. This way you can monitor the balance in curriculum coverage over the year.

Assessment Recording SheetThe sheet provides a way of maintaining a termly record of pupils’ attainment and progress in mathematics. The seven headings reflect those in the table of learning outcomes. This is to help you to cross-reference teaching coverage against your assessment of learning, and to identify future learning targets against need. The ‘see-at-a-glace’ profile of progress and attainment can be used to monitor pupils’ progress over time.

Week-by-week PlannerThis sets out weekly teaching programmes, covering 36 teaching weeks. This programme is organised into 6 half terms with 6 teaching weeks within each half term. The weekly teaching programmes offer a guide to support your medium-term and long-term planning. There is sufficient flexibility in the programme to make adjustments to meet changes in lengths of terms. The mathematics for each week is described as bullets. These bullets are not equally weighted and one bullet does not represent a day’s teaching. Use the bullets listed to map out the whole week. Planning based on the weekly teaching programmes should also take account of your day-to-day assessment of pupils’ progress. If more or less time is required to teach a particular aspect of mathematics set out in the programme, review your plans and adjust the coverage of the content in the programme accordingly. It is important that your planning reflects the speed and security of your pupils’ learning. The accompanying notes and examples offer some ideas about how to teach aspects of the content set out in the week. They may inform planning in other weeks too when content is revisited. They are not exhaustive and the resources alluded to in the text are not provided in these documents. The programme reflects the content in the National Curriculum, with the highest proportion of time being devoted to Number.

©Nigel Bufton MATHSEDUCATIONAL LTD 2


Essential Learning in Mathematics

Summary of Essential Learning in Year 5 Count forwards and backwards from any number in powers of ten including through zero; interpret negative numbers

and Roman numerals in context; determine prime, square and cube numbers Identify the value of digits in whole and decimal numbers; round numbers to the nearest power of ten and decimals to

nearest whole number and to one decimal place; write decimals and percentages as fractions Add and subtract mentally pairs of numbers with up to four digits; use formal written methods to add and subtract

whole numbers and decimal numbers in context; add and subtract fractions with related denominators Recall and use multiplication facts to 12 x 12 to multiply and divide mentally and identify factors and multiples; use

formal methods to multiply numbers with up to four digits by 1- or 2-digit numbers, and to divide numbers with up to four digits by 1- or 2-digit numbers; multiply whole numbers by proper fractions to get whole number answers

Convert between units of measure and time; calculate the perimeter and area of rectangles and composite shapes and volumes of cuboids; read, interpret and use data presented in tables, line and time graphs

Recognise and name 3-D shapes from 2-D drawings; draw straight lines accurately and draw and measure angles in degrees; apply the properties of triangles and rectangles and identify regular polygons; reflect and translate shapes on grids including the coordinates in the first quadrant

Problem Solving, Reasoning, Communicating Pupils solve problems that involve two or more steps and a range of measures and decimal numbers. They use and convert between standard metric

units and begin to use approximate equivalents for the most common imperial units of measure where the context makes it appropriate. Pupils apply the four operations and combinations of these operations to logic problems that involve finding missing values or optimum solutions that meet given conditions. They apply scaling to given measurements to calculate the increases or decreases between a scale drawing and its realisation. Pupils read and interpret information presented in tables, including timetables, and graphs, including line graphs that show a relationship between two continuous variables such as temperature and time. They solve problems that require the calculation of simple fractional and percentage parts of quantities in order to compare the size of the proportional parts.

Pupils use their knowledge of factors and multiples to sort and test relationships between numbers. They determine whether a number is prime, square or a cube and offer reasons for their decisions. Pupils generate linear sequences and describe in words the term-to-term rule. They use properties of angles at a point or on a straight line to calculate missing angles, explaining how they arrived at their answers. Pupils explore the properties of familiar shapes and begin to make and test deduction about lengths of sides and the angles.

Pupils read positive and negative numbers accurately, convert between decimal numbers and fractions and translate percentages into fractions. They explain how to order, add and subtract fractions that are multiples of the same number and read and interpret improper fractions and mixed numbers. Pupils describe the effect of multiplying and dividing whole numbers by 10, 100, or 1000. Pupils read angles in degrees and name angles by their size. They describe reflections and relate a reflection to lines of symmetry, find the position of points following a reflection or translation.

Language and Mathematics©Nigel Bufton MATHSEDUCATIONAL LTD 3


The National Curriculum (Section 6: September 2013 Reference DFE-00180-2013) declares that:“Teachers should develop pupils’ spoken language, reading, writing and vocabulary as integral aspects of the teaching of every subject. Pupils should be taught to speak clearly and convey ideas confidently ... They should learn to justify ideas with reasons; ask questions to check understanding; develop vocabulary and build knowledge; negotiate; evaluate and build on the ideas of others ...They should be taught to give well-structured descriptions and explanations and develop their understanding through speculating, hypothesising and exploring ideas. This will enable them to clarify their thinking as well as organise their ideas ... Teachers should develop pupils’ reading and writing in all subjects to support their acquisition of knowledge ... with accurate spelling and punctuation.” When we think mathematically we may use pictures, diagrams, symbols and words. We communicate our ideas, reasons, solutions and strategies to others using the spoken and written word. We listen to how others explain their methods using mathematical language and read what they have written so we can interpret their ideas and solutions. Language is a fundamental tool of learning and this is as true for learning mathematics as it is for any other subject.Having a good command of the spoken language of mathematics is an essential part of learning, and for developing confidence in mathematics. Children who say little are usually those who are fearful about saying the wrong thing, or giving an incorrect answer. Very often the quiet children are those who may lack knowledge of, or confidence in using the necessary vocabulary to express their ideas and thoughts to themselves and consequently to others.Mathematics has its own vocabulary which children need to acquire and use. They need to be taught how to pronounce, write and spell the mathematical words they are to use, and to know when they apply and to what they apply. Learning the vocabulary and language of mathematics involves: associating objects, shapes and events with their names (e.g. M is 1000, CM is 900; 4³ = 4 × 4 × 4; cm² represents square cm; this makes it a reflex angle) stating, repeating and recalling facts aloud, and explaining how they can be used and applied (e.g. one tenth is 10% so three tenths is 30%; 15 030 is 15

thousand and 30 so take away 9 020 will leave 6 thousand and 10; the diagonals of a rectangle cross to make four triangle which are all isosceles) describing the relationship between two or more items, shapes, events or sets (e.g. only this fraction is bigger than one as the denominator is bigger than

the numerator; 37 must be prime as I cannot find any factors but 27 is not prime as 3 × 9 = 27; the 16:48 train is after the 4.25pm train) identifying properties and describing them (e.g. a right angle is 90º and this reflex angle is 3 right angles so is 3 × 90º; when I reflect the shape it does not

change shape only position and now it points in a down; the numbers in this sequence are getting bigger as I add a quarter each time) framing an explanation, reasoning and making deductions (e.g. I know the polygon I made has equal sides but this angle is bigger than this one so it is not

regular; 48 is not a square number as 7² = 7 × 7 = 49; 63 divided by 5 has remainder 3, I think numbers with 3 units will have remainder 3 if I divide by 5)

Learning the Language of MathematicsLearning to use the language of mathematics requires carefully prepared opportunity and continued experience and practice. When planning consider when and how your children will be taught to:

See the words – Hear them – Say them – Use and apply them – Spell them – Record them

It is important that children memorise and manipulate the language of mathematics. When planning consider when and how your children will learn to:

Visualise and manipulate mathematical pictures, diagrams, symbols and words in their heads



Key Mathematical Vocabulary: Year 5

Number

Count in multiples of, count forward, count backwards through zero, consecutive; positive number, below zero, negative number, integer; negative one, negative two ..., minus one, minus two ..., number line; one thousand, ten thousand, ten thousand and one ..., one hundred thousand, one hundred thousand and one ..., one hundred thousand one hundred and one ... one hundred and one thousand one hundred and one ... million; place value, digit, units, ones, tens, ... ten thousands, hundred thousands, millions; single-digit number ... seven-digit number; Roman numerals, I ... IV, V, VI ... IX, X, XI ... XXXIX, XL, XLI ... XLIX, L, LI, LII ... LX, LXI ...C ... CDXCIX, D... CMXCIX, M ... MMXIV; partition, exchange, exchange for one thousand, exchange for ten hundreds; numerals, place holder; greater than (>), less than (<); fewer, fewest, least; estimate, round up/down, approximate, check, round to nearest ten, nearest hundred ... nearest hundred thousand; prime, prime number, square, cube

Calculation (mental and

written)

Addition, increase, sum, total; subtract, subtraction, take away, decrease, fewer, less, difference between; add sign (+), subtraction sign (-), equals sign (=), equivalence; calculate, calculation, mental calculation, formal written method, columnar method; double, scale up; halve; share out equally, equal groups of, left, left over, remainder; divide, divide by, divide into, divisible by, quotient, remainder after division; factor, factor pair, prime factor, composite number, division fact, short division, scale down; count in twos ..., count in tens, count in hundreds, repeated addition, array, rows, columns; number of equal groups; multiply, multiple, product, multiplication, short multiplication, multiplication fact, multiplication table; multiplication sign (×), division sign (÷); commutative rule, commutative operation, associative, associative law, distributive law; inverse, inverse operation

Fractions

Whole, proper fraction, improper fraction, mixed number, denominator, numerator, unit fraction, non-unit fraction, equivalent fractions, simplify, cancel; fraction of, proportion, equal parts, share equally; halves; quarters, four quarters make a whole; two quarters make a half; thirds, one third, one third of ... three thirds make a whole ... fifths, sixths, sevenths, eights, ninths, tenths, hundredths, thousandths; one eight, two eights ... eight eighths, one whole, one and one eight, one and two eights ...; decimal numbers, decimal point, decimal place, one decimal place ... three decimal places; whole number boundary, bridging zero; ones, tenths, hundredths; round to nearest whole number, percentage (%), parts per hundred

Measurement

Units of measure, metric unit, imperial unit, yard, pound, pint; measurement, scale, scale drawing; equivalent units, convert, conversion, mixed units, intervals, value of interval; length, perimeter; standard units of length, kilometre, metre, centimetre, millimetre; weight, mass, scales; standard units of weight, kilogram, gram; standard units of capacity, volume, litre, millilitre; temperature, degree Centigrade (ºC), thermometer; cold colder, freezing, freezing point, boiling; calendar, leap year, seven days, week, fortnight, twelve months, (one year), 24 hours, (one day), 60 minutes (one hour), 60 seconds (one minute); duration, sequence of events; analogue clock, digital clock, 12-hour clock, 24-hour clock; a.m., p.m., noon, midnight; thirteen fifty, fifty minutes past one p.m., ten to two in the afternoon; area of 2-D shape, square cm (cm²), square m (m²); volume cubic cm (cm³)

Geometry

Point; plane, 2-D shape, perimeter, area; straight, triangular, rectangular, rectilinear, composite, circle, circular; corner, side; 3-D shape, surface, flat surface, face, edge, vertex, vertices; cube, cuboid, sphere, cylinder, cone, pyramid, prism; triangle, isosceles, equilateral; quadrilateral, square, rectangle, parallelogram, rhombus, trapezium, kite; polygon, pentagon ... decagon, regular, irregular; symmetric, line of symmetry, vertical, horizontal; orientation; rotate, clockwise, anti-clockwise, degrees, protractor, right-angle turn (90º); acute (< 90º) acute (> 90º, < 180º), reflex (> 180º) reflex angle; half turn (180º), angles about a point (360º); perpendicular, parallel lines; coordinates, plot, axes, quadrant; translation, reflect, reflection

StatisticsCount, frequency, discrete data, category; measure, continuous data, time, changes over time, trend; table, group, sort, organise, arrange, present, interpret, information; tally chart, frequency table; pictogram, blocks, block graph, bars, bar graph, time graph, line graph; title, label; number fewer, least number, total number, maximum number; scale, unit size, number of units represented, units per interval, units per picture

Problem solving,

Reasoning, Communicating

Explore, investigate, use, apply, analyse, interpret; solution, method, strategy; rearrange, organise, maximum, minimum; combine, separate, join, link; build, draw, represent, sketch, measure, record, show your working; sign, symbol, notation, resource; show how, show why, represent, identify; recite, repeat, recall; explain why, what, how, when; give a reason, justify, if, so, as, because, and, not, cannot; same, same as, different, example, counter-example; visualise, imagine, see in your head, pattern, relationship; sequence, term, position, generate, predict, rule, rule, test

End-of-Year Learning Objectives for Year 5 Record of coverage©Nigel Bufton MATHSEDUCATIONAL LTD 5


A. Number – rounding and place valueA1. Can read, write and order whole numbers with 6 or more digits and identify the values of the digits A2. Can read, write and order decimal numbers with up to 3 places and identify the values of the digitsA3. Can count forwards and backwards in powers of 10, round to nearest power of 10, round decimals to whole numbers and tenthsA4. Can read, write and interpret negative numbers and count through zeroA5. Can read numbers written using Roman numerals: I, V, X, L, C, D, M

B. Number – calculation (mental and written)B1. Can add and subtract mentally 1- and 2-digit numbers and multiples of 10, 100, 1000 to and from given whole numbersB2. Can use formal written methods to add and subtract whole 4-digit numbers and decimal numbers with up to 3 placesB3. Can recall the multiplication tables to 12 x 12 and use to identify factor pairs and common factors of two numbersB4. Can use known facts to multiply and divide mentally including multiplying and dividing by 10, 100 and 1000B5. Can use efficient formal written methods to multiply numbers with up to 4-digits by a 1- or 2-digit numberB6. Can use efficient formal written methods to divide numbers with up to 4-digits by a 1- or 2-digit numberB7. Can use rounding to give approximate solutions to calculations and check answersB8. Can record the remainder after division in different ways and interpret remainders in the context of the problemB9. Can identify, recognise and use common prime numbers, square numbers and cube numbers

C. Number – fractions, including decimal and percentagesC1. Can order, name, write and convert between mixed numbers and improper fractions and generate equivalent fractionsC2. Can compare, add and subtract fractions whose denominator are multiples of the same numberC3. Can express fractions whose denominators are multiples of 100, 10, 5 and 2 as percentages and decimal equivalents

D. MeasurementD1. Can measure accurately using metric units for length, weight, capacity and convert between common metric unitsD2. Can calculate the perimeter of composite rectilinear shapes and the area of simple rectangular shapes in cm²D3. Can estimate volume and capacity using practical resourcesD4. Can convert between units of time, read and use 12-hour and 24-hour notation, and calculate time intervals

E. Geometry – properties of shapes, position and directionE1. Can draw angles in degrees, estimate, compare and name angles E2. Can identify and use the sums of angles at a point, on a straight line and other 90º multiples to calculate missing anglesE3. Can describe and use the properties of rectangles and regular polygons to determine related facts E4. Can translate and reflect shapes, use coordinates in the first quadrant to describe position and movement of shapes

F. Statistics – read, interpret tables and line, time graphsF1. Can read, interpret and represent data in tables, including timetables, and use information presented in a line graph

G. Problem solving, reasoning, communicatingG1. Can solve problems involving time, money, measures, use links to fractions, decimals and percentages in calculationsG2. Can determine term-to-term rules for sequences, use known facts to make deductions about numbers, shapes, anglesG3. Can represent problems and solutions using symbols and diagrams and share explanations and reasons for choices

Assessment Recording Sheet



Mathematics in Year 5 Autumn term Spring term Summer termName:

Class:Key: 5.1 – Working towards expectations 5.2 – Meeting expectations 5.3 – Exceeding expectations

A. Number – rounding and place value 5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

B. Number – calculation (mental and written) 5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

C. Number – fractions, including decimal and percentages 5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

D. Measurement 5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

E. Geometry – properties of shapes, position and direction 5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

F. Statistics – read, interpret tables and line, time graphs 5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

G. Problem solving, reasoning, communicating

5.1 5.2 5.3 5.1 5.2 5.3 5.1 5.2 5.3

End-of-year assessment of progress and attainment in mathematics Summary report:

Overall end-of-year assessment in mathematics: Working towards Year 5 expectations Meeting Year 5 expectations Exceeding Year 5 expectations

Teacher: Date of final assessment:

Week-by week Planner Year 5Autumn Term (First half term)©Nigel Bufton MATHSEDUCATIONAL LTD 7


Week 1 Week 2 Week 3Number Number/Measurement Geometry/MeasurementMain Teaching: Recognise and read

the powers of 10; 10,100...1 000 000; use to partition and combine numbers

Read and write whole numbers with 6 or more digits; identify the place values of the digits

Read scales with whole and decimal number intervals and identify mid points

Round whole numbers to the nearest power of 10

Read and write numbers with up to 3 decimal places

Identify the value of decimal digits as 10ths,100ths,1000ths

Round numbers with 2 decimal places to the nearest whole number and to 1 decimal place

Apply rounding when solving problems

Notes/examplesRead these numbers and give the value of the 6 digits: 63 678; 623 451; 616 006; 6 600 060...

down up 300 400What number is in the middle? Is 329 closer to 300 or 400? What is 329 to the nearest 100? We round down to 300 the 300s numbers up to and including the middle number 350. The rest we round up to 400. Round 6740 to the nearest 1000.

down Up 6000 6500 7000This line helps us see if 6740 is closer to 6000 or 7000. We round to 7000. Round 3.54 to the nearest whole number.

down up 3 3.5 4We round to 4. Round 3.54 to 1 decimal place.

down up 3.50 3.55 3.60It’s below 3.55 so we round to 3.5. What value is the 7 in: 2.17, 1.72, 0.117

Main Teaching: Count forward and

back in steps of powers of 10 from any given number

Recognise the impact on digits and their place value when adding or subtracting pairs of multiples of powers of 10

Count up from 0 in steps of single-digit numbers; apply to counts in multiples of 10, 100, 1000...

Use formal column methods for addition and subtraction of 3-, 4-digit whole numbers

Apply counts in 60s to conversion of time between seconds, minutes and hours

Solve problems involving the conversion between units of time

Solve missing number problems involving one unknown number

Notes/examplesCount up in steps of 100 from 407. Stop. We have reached 907; how many 100s have we added to 407? As we cross from the 900s to 1000s what changes? Which digits remain unchanged; why? Count back in 1000s from 11 026. What boundaries did we cross this time? At what number did we stop; why? How many 1000s have we subtracted from 11 026? Read my number: 7 301 582. What must I add/subtract to change the digit 3 to 4; the 5 to 2; 7 to 1; 0 to 8...? Count forward from 0 in 6s; now in 60s. Recite the 60 times table. How many minutes in 4 hours...? How many seconds in 8 minutes...? Count in 3s; in 30s. Count in 9s; in 90s. If we can count in 1-digit steps we can count in 10s, 100s, 1000s... Count in 4s, 400s, 4000s....

Main Teaching: Know that angles are

measured in degrees, a right angle is 90º, a whole turn is 360º

Use º symbol, estimate and compare the size of an angle and its complement to 360º

Draw and measure angles using a protractor, including acute, obtuse and reflex angles

Measure angles in triangles; draw triangles, measure and sum its angles, conjecture and test

Confirm that angles about a point sum to 360º and angles on a straight line to 180º

Convert multiple right angles to degrees

Calculate the complement of angles

Solve missing angle problems involving 1 unknown angle on a straight line or about a point

Notes/examples

I can use my 2 plates to make angles about the centre point. If I turn it a quarter of the way around, what red angle do I make? A right angle... Angles are measured in degrees. 1 right angle is 90 degrees, which we write as 90º. Count in 9s and now in 90s. If I turn and make an angle of 2 right angles, how many degrees is this angle; and 3 right angles; and a complete turn. So there are 360º in one complete turn. If I make ½, ¾, 2, 1½ turns how many degrees is that...? Is this angle acute? Is it obtuse? What is your estimate? If my red angle is 120º, what size is the blue angle? My red angle is 60º what’s its complement to 90º, 180º, 360º? Show me a reflex angle. Is the complement to 360º of an acute angle always a reflex angle?

Mental Work: Recall multiplication facts to 12x12 Read large whole numbers and decimal numbers Round numbers to required accuracy

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Apply x, ÷ facts to calculations with powers of 10 Use x, ÷ by 60 to convert between sec, min and hrs

Mental Work: Add and subtract numbers to make 90, 180, 360 Compare, estimate angles in 2-D and 3-D shapes Use x, ÷ by 90 to convert right angles to degrees

Extension Work: Explore prefixes mega, giga, tera in number & ICT

Extension Work: Solve missing number problems in context of time

Extension Work: Draw, measure and sum angles in quadrilaterals

Autumn Term (First half term)Week 4 Week 5 Week 6Measurement/Number Geometry/Measurement Number



Main Teaching: Measure, compare

and sort lengths using the metric units m, cm, mm

Measure, compare and sort weights using the metric units kg, g

Measure, compare and sort capacities using the metric units l, ml

Estimate lengths, weights, capacities

Know equivalences between metric measures and use to convert between the units km to m; l to ml; kg to g

Multiply and divide whole numbers by 10, 100, 1000 with a whole number answer

Convert units of time involving hours, days, weeks, years

Solve practical problems that involve estimating and taking measurements, calculating and rounding

Notes/examplesI walk 7km how many m do I walk; how many cm, mm? Each week I drive 85km. How many m is that? The distance to the moon is 384 400 km. How many m is that? 384 400 000m. How do we convert between km and m? How many km in 1 million m? Step ½m. How many steps would you take to walk a 1km? Everyone walk around the playground in ½m steps for 3 minutes. How far did you walk? How can we get a good estimate of how far the class walked in 3 minutes? What units do we use to measure capacity? What is a kilolitre. I drink 2l of liquid per school day. How many school weeks will it take to drink 1 kl? How many 250ml bottles can be filled from 1kl? Estimate the capacity of these bottles in ml. Use water to find their capacities. How can we find the capacity of this room?

Main Teaching: Identify familiar 3-D

shapes from 2-D representations and state their properties

Interpret simple isometric drawings of 3-D shapes and build the shapes using interlocking cubes

Draw on an isometric grid representations of 3-D shapes made from cubes

With a ruler, measure and draw accurately lines of given length

With a protractor, measure and draw accurately angles of given size

Draw a triangle accurately given information on its angles and its sides; find additional information by measuring

Solve missing angle problems involving unknown angles on a straight line or about a point

Notes/examples. . . . . . A . . . B . . . . . . . . . . . . . . C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . These shapes are drawn on an isometric grid. What 3 shapes can you see? How many cubes can you see in shape C? Use the grid to draw A, which is 1 cube. Now draw 2 connected cubes like B but in all possible orientations. Do the same for 3 connected cubes. Here are pictures of connected cubes. Work out how many cubes you need to build the shape then build it. All shapes will stand up as shown.To shape C I want you to remove 1 base cube and add 2 cubes above the base. Draw your shape. To shape B I want you to add 5 cubes. Draw your shape. Ask someone to use it to make your shape.

Main Teaching: Practise formal column

methods for addition/subtraction of 4-digit whole numbers

Recognise numbers either side of 0 are positive or negative; count back through 0 and forward from a negative number in steps of any size

Read scales with positive and negative numbers

Interpret negative numbers in context; carry out addition and subtraction calculations where the answer may be positive or negative

Generate and extend number sequences including those with negative numbers

Describe in words and symbols the term-to-tem rule for a linear sequence

Solve word problems involving negative numbers in context such as temperature

Notes/examplesImagine a hot air balloon. You pull a red cord for hot air; it goes up 1m per pull. Pull a blue cord and it goes down 1m per pull. The balloon is in the air. The pilot sets his levelling gauge to zero. He gives 9 tugs on the red cord. Later he gives 3 tugs on the blue cord. We calculate 9-3=6, to work out that the gauge shows 6. He gives the blue 8 tugs; later he tugs the red cord twice. Write down the calculation (6-8+2) and work out the number on the gauge. Back at 0m.The pilot pulls the blue 5 times and then the blue 4 more times before he tugs the red 6 times. What’s on the gauge now? Work out the gauge numbers for these calculations. Each time start at 0. 4-7; 7-4; 4+6-8; 4-8+6; 5-7-3; 5-3-7; 10-6-4 List calculations with 3 numbers that give answers: 4, 0, -5, -2, 2...What numbers are hidden: -5+█=1;4-█+2=-3;█-8+4=1

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Add and subtract sequences of 1-digit numbers Add and subtract sequences of multiples of 10, 100

Mental Work: Identify 2-D and 3-D shapes from given properties Work out complements of angles to 90º, 180º, 360º Estimate length in cm, weight in g, capacity in ml

Mental Work: Recall x facts to 12x12 use to derive ÷ facts + and - pairs of 1-digit numbers with + or - answers Complete number sentences with + or - answers

Extension Work: Explore relationship between 1l and 1kg of water

Extension Work: Draw cuboids to scale given their dimensions

Extension Work: Describe sequence rules algebraically: tn=tn-1 - 4...

Autumn Term (Second half term)Week 1 Week 2 Week 3Number Number Number/Geometry/Measurement



Main Teaching: Add and subtract

mentally numbers in the 1000s

Practise formal column methods for addition and subtraction of 4-digit whole numbers

Use and apply mental and written methods of division and multiplication to solve problems involving money and measures

Multiply and divide whole numbers by 10, 100, 1000 with a whole number answer

Multiply 2-, 3- and 4-digit numbers by a 1-digit number using a formal written method

Read, write and order large numbers and decimal numbers with up to 3 decimal places

Solve missing digit problems involving multiplication

Notes/examplesMy sheet of addition and subtraction calculations has errors. Correct the errors. What errors did I make; what target would you set me?Recite the 3 times table to 3x12. Now recite the 3 times table with multipliers 10, 20, 30... Now use multipliers 100, 200... and then 1000s.What is 360÷3; 1800÷3...? Use another times table... When we multiply a 2-digit number by 1-digit number we multiply the 1s then the 10s and add. For a 3-digit number we multiply the 1s, 10s then 100s and add. For 4-digit numbers we have 1000s too. Describe the patterns in these calculations? Explain the method; use it to multiply by a 1-digit number. 6 8 2 6 8 3 2 6 8 x 4 x 4 x 4 3 2 3 2 3 2 2 4 0 2 4 0 2 4 0 2 7 2 8 0 0 8 0 0 1 0 7 2 1 2 0 0 0 1 1 3 0 7 2 Find the four 1 missing digits: █ 4x█=█ █4

Main Teaching: Estimate answers to

multiplication and division calculations using rounding

Apply knowledge of table facts to compare the size of answers to calculations

Recall and use the inverse relationships to check answers

Use the symbols <, >, = to record comparisons between numbers and calculations

Divide 2-digit numbers by a 1-digit number using a formal written method

Use and apply written methods of multiplication and division to solve problems involving whole numbers

Solve missing digit problems involving multiplication

Notes/examplesEstimate 48x6. What did you multiply? Estimate 88÷6What did you divide? Work out 25x3. What is 75÷3; 75÷25? Remember x and ÷ are inverse operations. Will 87÷3 be bigger or smaller than 25? Bigger as 87 gives us more to share between 3. To work out 87÷3 we start with the 80. Count out the 10s of 3:10x3=30; 20x3=60; 30x3=90. Stop too big. We can only get 20 3s out of 80. We write the 2 in the tens column, as 20 is 2 tens, and write the 60 below the 87 and subtract. This leaves 27

T U T U2 9 2 4

3 8 7 4 9 66 0 8 02 7 1 62 7 1 6

0 0Now we find the 3s in 27 which is 9. This means 87÷3=29. Work out 29x3 to check. Explain how to use this method for 96÷4. Practise this method for 2-digits divided by 1-digit numbers. Find the missing digits: █4÷█=█1

Main Teaching: Know that a right

angle has 90º; use º symbol and convert multiples of right angles to º and vice versa

Identify the sum of the interior angles in 2-D shapes where corners are 1 or 3 right angles

Draw 2-D shapes, whose corners are either 1 or 3 right angles, given the sum of its interior angles

Make and test a generalisation about the sum of interior angles of 2-D shapes whose corners are 1 or 3 right angles; explain thinking and reasoning

Extend the 9 times table to 90, 99 and 999 times tables; identify patterns in the numbers and use to x and ÷ large numbers

Generate and extend number sequences that involve decimals

Notes/examplesRecite the 9 and 90 times tables. Turn through 3...8 right angles, how many degrees is that? A square has how many right angles; in degrees? What are the interior angles at the corners of my green shape? 8 angles are right angles. 4 angles have 3 right angles. How many right angles is that? What is the sum of the angles in º? In º find the sum of the angles in these shapes?

Make a shape with right-angled corners that sum to 720º. Can you make a shape with right-angled corners that sum to 900º? Ethan says “99x4 is easy: 100x4=400; 400-4=396.” Is he right? Work out the 99 times table. Describe any patterns you find. He says: “501÷99 is easy too, it’s 5 with remainder 6.” Work out the 999 times table. How can you use these 2 tables to calculate: 408÷99 and 8998÷999...?

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Solve simple missing number or digit problems

Count from a whole numbers in steps of 12

, 13

, 14

or

110

Mental Work: Use rounding to estimate x and ÷ calculations Multiply multiples of 1 and 10 by 25, 50, 75 & 100 Use known facts to estimate x and ÷ calculations

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Read & add numbers to 100 in Roman numerals Count from any whole numbers in decimal steps

Extension Work: Solve multiplication problems with missing digits

Extension Work: Solve division problems with missing digits

Extension Work: Describe sequence rules algebraically: tn=tn-1 +1.5...



Autumn Term (Second half term)Week 4 Week 5 Week 6Number/Statistics Geometry/Measurement NumberMain Teaching: Multiply and divide

whole and decimal numbers by 10, 100 and 1000 where answers have up to 3 decimal places

Explain the effect of x and ÷ of whole and decimal numbers by 10, 100 and 1000

Construct, read and interpret information in a table

Convert fractions with denominators 10, 100 or 1000 to decimal equivalent and vice versa

Write 10ths as 100ths and 1000ths etc

Add and subtract 10ths, 100ths, 1000ths and convert the answers to decimals

Read scales with fraction or decimal number intervals

Notes/examplesDividing by powers of 10 moves digits right. Look at this pattern: 1÷10=0.1;2÷100=0.02;3÷1000=0.003 Multiplying by powers of 10 moves digits left. Look at the pattern: 0.001x10=0.01; 0.002x100=0.2; 0.003x1000=3 Explain the rule for the moving digits. Present this in a table we can refer to.

÷ move right x move left1 ÷10 0.1 0.01 x1000 101 ÷100 0.01 0.01 x100 11 ÷1000 0.001 0.01 x10 0.1

When dividing or multiplying by 10, 100, 100, decide if the answer will get smaller or bigger, which way the digits must move and how far they are to move. Remember, division can be represented as a fraction:

1÷10 is 1

10 and

110

=0.1; 2÷100 is

2100 and

2100=0.02; 3÷1000 is

31000

=0.003. 0.1 0.12 0.1231

1012100

1231000

The number of decimal digits is the same as the number of zeros in the 10ths, 100ths or 1000ths. What is 0.307 as a fraction? There are 3 decimal digits so we use 1000ths and

write: 307

1000 . What is 9

100as a

decimal? 100 has 2 zeros so 2 decimal digits. We write 0.09. We must put the 0 in front of the 9.

Main Teaching: Use mathematical

language to name and describe 3-D shapes, prisms, pyramids, cylinders, cones, spheres etc

Identify properties of 3-D shapes and sort by their properties; using tree, Venn or Carroll diagrams

Plot points on a coordinate grid in the first quadrant

Draw 2-D shapes on coordinate grids; identify the lines of symmetry and coordinates of missing corners or points on sides

Build cubes and cuboids from interlocking cubes and recognise that the number of cubes used describes the volume

Make trays from card and find the volume using cm cubes; calculate volume in cm³

Notes/examples

My rectangular card is 16cm by 12cm. What size is each small square? 2cm by 2cm. If I cut the card along the red lines I can fold my card into an open box or tray like this. How long, how high, how wide, is my tray? If I unfold my tray can you see how to work these measurements out before I fold it? I pack the tray with 1cm by 1cm cubes. How many layers of cubes will I have? How many cubes in each layer? How many cubes will I need to fill the tray? The answer is the volume of my tray in 1cm by 1cm cubes, which we write as cm³. Make a tray 16cm by 10cm by 5cm. What size card do you need to start with? Find out how many centimetre cubes will fit into your tray so it is full.

Main Teaching: Read and write a

decimal as a fraction 10ths 100ths or 1000ths

Understand how and use mixed numbers to describe whole and part shapes

Express quantities as mixed numbers and improper fractions

Convert improper fractions to mixed numbers and vice versa

Recognise that improper fractions represent whole numbers when the numerator is a multiple of its denominator

Understand that per cent % means per 100 and know 100% represent a whole; write %ages as fractions with denominator 100 and as decimals

Notes/examples

If the blue rectangle is one whole rectangle, how many whole rectangles are there? 2 1 blue + 1 green. What part of the whole rectangle is the red shape? It has 8 squares or 2 columns of 4. A whole shape has 12 squares or 3

columns of 4. It is 8

12 or 23 so

we have 2⅔ whole rectangles. How many ⅓ rectangles in total? Yes 8. It means we have 8 thirds. We

write: 2 23 =

83 . How many

small squares in a whole rectangle; in the part shape; and altogether? 12, 8 and 32.

We write: 2 812

= 3212

.

If the large square is now the whole shape, what fraction of large squares can you see?

Convert these improper fractions to mixed numbers:

65

, 75

, 85

, 95

, 105

, 115

,... What

is the pattern? Convert: 505 ,



Remember 9

10= 90

100=900

1000606 ...

10010 ?

Mental Work: Identify the value of decimal digits in 10ths,100ths,1000ths Add and subtract decimals < 10 with 1 decimal place Give complements to 1 of decimals with 2 decimal places

Mental Work: Imagine, name 3-D shapes given properties Identify the squares to 12² and cubes to 10³ x 3 1-digit numbers, solve missing digit problems

Mental Work: Give complements of fractions to a whole number Multiply simple mixed numbers by whole numbers Divide simple improper fractions by whole numbers

Extension Work: Generate, explore and apply the 49 and 499 times tables

Extension Work: Measure volume and capacity of trays in cm³, ml

Extension Work: Explore the value of the 4th decimal number

Spring Term (First half term)Week 1 Week 2 Week 3Number/Measurement/Statistics Number NumberMain Teaching: Convert between units

of time including years, months, weeks, days, hr, min, sec

Work out fraction of hr or min, answer in whole units

Calculate fractions of a period of time such as a sixth of a minute

Read, write and interpret times, and passages of time using analogue and digital 12- and 24-hour clocks

Read and interpret timetables and use to plan events such as visits or journeys

Add and subtract times in hr and min that cross the 60 boundary

Multiply and divide times by whole numbers and give answers in hr, min or as a fraction of a unit

Solve problems involving time, convert answer to most appropriate units

Notes/examplesWhat is 4hr 36min + 2hr 48min? We add the hrs then min: 6hr (36+48)min. As there are 60 min in 1hr we write: 36+48=70+14 =60+24=1hr 24min. The answer is 7hr 24min. We can record in a table:

hr min + hr min4 36 + 2 486 70 + 0 147 10 + 0 147 24 + 0 0

When subtracting we can subtract the hrs. Subtract min we must decide if we exchange 1hr into 60 min

hr min - hr min4 36 - 2 482 36 - 0 481 60+36 - 0 481 12+36 - 0 01 48 - 0 0

I travel for 48min each day. Over 5 days how long am I travelling? 5x48=10x24=240min240÷60=24÷6=4 so 4 hrs. I swim 40 lengths in 1hr 10min. How long does it take me to swim 1 length? 1hr 10min = 70min

Main Teaching: Use multiplication

and division facts to find factors of 2- and 3-digit numbers and multiples of 10 and 100; find factor pairs and common factors

Know and use the priority of operations; construct equivalent number sentences to support mental calculations e.g. 1824÷6=912÷3=304; 788÷7=700÷7+70÷7+ 18÷7=100+10+2 r 4 =112 r 4

Understand that a prime number has only 2 factors; determine 1- and 2-digit prime numbers; recall first 10 primes and use to generate composite numbers

Divide 2- and 3-digit numbers by a 1-digit number using formal written methods of long and short division; apply to

Notes/examples When we divide by a 1-digit number we work out multiples of 100s, 10s, 1s, write them down and subtract. This is a method of long division method.

T U H T U1 4 1 4 2

7 9 8 7 9 9 47 0 7 0 02 8 2 9 42 8 2 8 0

0 1 41 4

0We can use the short method of division. Instead of writing down each step we do an extra calculation in our heads.

T U H T U1 4 1 4 2

7 9 28 7 9 29 14We work out how many 7s will go into the 9; a short cut to working out how many 10s of 7 go into 90. The answer is 1. The 2 left over we carry over to the 8 to make 28. 7s into 28? 4, we put the 4 in the 1s column. Explain and use the method

Main Teaching: Use multiplication

and division facts to find multiples of 2-digit numbers and of multiples of 10 and 100; find common multiples and lowest common multiples

Know and use the priority of operations to writeequivalent number sentences and to support mental calculations e.g. 8x45=4x2x45= 4x90=360; 7x89=7x90-7x1= 630-7=623

Calculate square and cube numbers and use ², ³ signs

Multiply 2-, 3- and 4-digit numbers by a 1-digit number using formal written methods of long and short multiplication; apply to solve

Notes/examplesWhen we multiply by a 1-digit number we multiply the 1s, 10s, 100s, 1000s, write them down and add. This is a method of long multiplication. T U H TU ThH TU 8 7 3 8 7 4 3 8 7 x 6 x 6 x 6 4 2 4 2 4 2 4 8 0 4 8 0 4 8 0 5 2 2 1 8 0 0 1 8 0 0 1 2 3 2 2 2 4 0 0 0 1 1 2 6 3 2 2 1 1We can use the short method of multiplication. Instead of writing down each step we do an extra calculation in our heads. T U H TU ThH TU 8 7 3 8 7 4 3 8 7 x 6 x 6 x 6 5 2 2 2 3 2 2 2 6 3 2 2 4 5 4 2 5 4We know 7x6=42 so we write the 2 in the 1s column, and carry the 4 into the 10s. We now deal with 10s. We know 8x6=48 and add 4 to get 52 to get the 10s. We write the 2 in the 10s column and 5 in the answer, or we carry the 5 into the 100s column. Explain and use the method



70÷40=7040 =

74 =1

34 min

solve problems to ÷ by1-digit numbers. problems to x by1-digit numbers.

Mental Work: Use x, ÷ by 60 to convert hr to min; min to sec Convert 24hr times to 12hr times using am, pm Round times to nearest hr or min

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Determine factors of given number; identify primes Convert %age to fraction in 100th and to decimals

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Determine multiples of 2 given numbers Work out squares and cubes of numbers to 10

Extension Work: Add and subtract times in min and sec and 24hr

times in hr and min and in hr, min and sec

Extension Work: Explore tests of divisibility for 2, 3, 4, 5, 6 and 9; look

for any patterns in the multiples of 11

Extension Work: A square number is the sum of consecutive odd

numbers. True or false?

Spring Term (First half term)Week 4 Week 5 Week 6Measurement/Geometry Number/Measurement Number/MeasurementMain Teaching: Use mathematical

language to describe properties and name prisms and pyramids by referring to the shape of the base as appropriate; identify and sort 3-D shapes by their properties including the shapes of faces

Recognise volume is measured in cubic units cm³, m³; relate this to cube numbers

Measure and calculate in cm³ or m³ the volumes of square- and rectangular-based prisms or cuboids

Express in words the rule for calculating the volume of cubes and cuboids

Work out the dimensions of a rectangle given its perimeter and the ratio of the sides or

Notes/examplesStar has 9 identical sticks of 6 linked 1cm cubes. She says: “The volume of a stick is 6 cubic centimetres.” She pushes the 9 sticks together to form a shape with square ends. She says: “This is a square-based prism.” Is she right? What is the volume of her shape? Draw Star’s shape on an isometric grid. Draw the faces of Star’s shape. With 12 sticks of cubes what prisms could Star make? What is the volume of each prism? Varsha builds a layer of blue and

red blocks. He adds on three more

identical layers. How many blocks has he used? What is the volume of his shape if each block is a 4cm cube? Si’s rectangle is 6cm by 4cm. What’s its perimeter? Jo’s

Main Teaching: Read and identify the

values of points on scales that have whole number, decimal and fraction intervals

Calculate the size of intervals on partially numbered scales

Construct, extend and describe sequences involving fractions or decimals

Calculate lengths and use a ruler to draw accurately lines and intervals in cm and mm

Represent families of fractions visually and use to identify pairs of equivalent fractions and to compare fractions

Work out unit and proper fractions of measures and other quantities by identifying the value of one part in the

Notes/examplesDraw a 4 rectangles each 12cm by 1cm. Divide the strips into 12, 6, 4 and 3.

What fractions can we write in each section of these strips? How many 12ths is equivalent

to one third? We write 13

=4

12.

Identify as many pairs of equivalent fractions as you can. How can we divide our unit strip into 5ths, 8ths and 10ths? What is 12cm in mm? Work out 120÷5... Draw the 3 strips divided into 5ths, 8ths and 10ths. Identify new pairs of equivalent fractions. What fractions are missing? 7ths and 9ths and 11ths. Draw the 3 fractions strips accurately. Use your fraction strips to

decide if 58

> 34

; 49

< 56

; 37

=

Main Teaching: Find perimeters and

areas of rectilinear shapes drawn on square grids

Estimate the areas of irregular rectilinear shapes

Recognise perimeter is measured in linear units and area in square units cm², m²

Describe in words and symbols the rules for finding perimeter and area of squares and rectangles and apply to simple composite rectilinear shapes

Using square grids draw sequences of rectilinear shapes; identify and describe growth patterns in areas and perimeters of these shapes

Test generalisations about relationships between perimeters of rectilinear shapes;

Notes/examples

Jan and Dan have made this pattern of shapes on a cm grid. “We add the next size of square to make our new shape and fill in the yellow squares to make a big rectangle. We have used 1, 2, 3 and 4 cm squares. We then find the perimeters of the rectangle and the yellow shape.” Jan says: “I think the perimeter of the shape made up of just blue and green squares is always the same as the big rectangle.” Dan says: “I think the yellow shape has the same perimeter as the perimeter of the previous rectangle.” Are they right? Test their claim to see if you



the perimeter or area and one of its sides

rectangle is twice as long as it high. The perimeter is 36cm, what’s its length?

appropriate strip and then scaling up

511;...? Which strip would we

use to work out ninths? If a strip represents 56ml, in m

what is the value of 19 of 56ml

and 49

of 56ml? Use strips to

work out fractions of measures

make generalisations test, explain, reason

agree or not. Explain your thinking and reasoning.

Mental Work: Calculate the square and cube of a number Calculate volume of cuboids area of base & height Estimate volume of cuboid against known volume

Mental Work:

Count in steps of 15

, 25

, 35

, 45

; 1

10,

310

, 710

, 9

10 &

100ths Generate equivalent fractions to a given fraction Calculate unit fractions of quantities (exact answers)

Mental Work:

Count in steps of 15

, 25

, 35

, 45

; 1

10,

310

, 710

, 9

10 &

100ths Given dimensions, find area/perimeter of rectangle Visualise shape made from cut or folded rectangle

Extension Work: Find volume & capacity of plastic cuboid container

Extension Work:

Describe sequence rules algebraically: tn=tn-1 - 14

...

Extension Work: Draw rectilinear shape with given perimeter or area

Spring Term (Second half term)Week 1 Week 2 Week 3Number Geometry/Measurement Statistics Main Teaching: Multiply and divide

whole and decimal numbers by 10, 100 and 1000 where answers have up to 3 decimal places

Carry out mental calculations with/without jottings that involve the four operations

Know and use brackets, the rules and priority of operations to write equivalent number sentences and to support mental calculations e.g.

Notes/examplesWe have used short multiplication to multiply by a 1-digit number. We use long multiplication to multiply by a 2-digit number. We still do calculations in our heads. To multiply by 34 we multiply by the 4 just as we’ve been doing then multiply by the 30 in a similar way. ThH T U ThH T U 8 7 3 8 7 x 3 4 x 3 4 2 3 2 3 4 8 1 5 4 8 2 2 2 2 6 1 0 1 1 6 1 0 2 9 5 8 1 3 1 5 8 1

We know 7x4= 28 so we put the 8 in the 1s column, and

Main Teaching: Estimate the size of

an angle about a point and in a shape

Name angles as acute, obtuse, reflex and right angled; recognise convex and concave angles in shapes

Measure and draw angles in degrees using a protractor

Measure sides and angles in triangles and quadrilaterals

Recognise the angles of a triangle sum to 2 right angles or 180º

Notes/examples

Estimate the size of each angle made by the 2 lines What must the 4 angles sum to? What must the 2 angles on the straight line sum to? Which angles are equal? If one of the angles is 130º what size are the other 3 angles? Draw and cut out 3 identical triangles. Mark the angles a, b and c. Can you put them together to make a straight line? Which of the angles meet on a straight line? What do you think the 3 angles of a triangle sum to? (180º or 2

Main Teaching: Read scales, with

and without, numbered intervals; use given information to calculate the size of intervals and to label the scales on a line graph

Read and interpret data presented in tables and convert this to a time or line graph

Annotate a graph with vertical and horizontal straight lines to read values

Notes/examples

The line graph shows the temperature of an oven. It was switched on at 4:30pm. The horizontal axis is in minutes and the vertical axis is temperature in ºC. At 4:50pm it reached 160ºC to



13x8+13x12=13x(8+12)=13x20=2601.2x6-0.7x6=(1.2-0.7)x6 =0.5x6=3

Multiply 2-, 3- and 4-digit numbers by a 1-or 2-digit number using formal written methods of long and short multiplication

Solve problems that involve scaling measurements up or down from and to make scale drawings

carry the 2 into the 10s column. This time we write 2 close to 8. 8x4=32 and add the 2 so we have 34 10s. We write 4 in the 10s and 3 in the 100s. Now we multiply by 30. As this is a 10s number we can write a 0 in the 1s column and multiply by 3. 7x3=28 so 8 in the 10s and carry 2 into the 100s ready to add. 8x3=24, add the 2 we carried and write 26. Add up the products for the answer.

Use angle properties of triangles to find sums of angles in quadrilaterals and other polygons expressed as right angles and degrees

Explore the properties of rectangles and squares by folding and measuring; use the properties to deduce related facts about the shapes

right angles). Draw a quadrilateral. Mark a point inside. Join it to each of the quadrilateral’s corners. How many triangles are inside the quadrilateral? How many right angles, º do the quadrilateral’s angles sum to? Now try a pentagon, hexagon... Can you see a pattern? Explain.Cut out a rectangle. Fold it, measure angles, sides and describe what you notice.

Tell the story of data from a bar chart, and time or line graphs

Solve problems involving sums, differences, time intervals etc using information presented in a line or time graph

Solve problems by gathering information from tables and charts, including timetables

heat food. Later at 200 ºC a chicken was put in the oven. Label the axes and use the graph to tell a story. The table below shows the temperature in an office. On the day the heating broke down. Use the data to draw a line graph with time along the horizontal axis. When temperature is below 18 ºC the office is closed. For how long was it closed? When were temperatures between 21 ºC and 23 ºC?

Time Temp Time Temp08:00 19ºC 15:30 16 ºC09:30 22 ºC 17:00 24 ºC11:00 25 ºC 18:30 22ºC12:30 19 ºC 20:00 19 ºC14:00 16 ºC

Mental Work: Recall x facts to 12x12 use to derive ÷ facts Add and subtract sequences of 1-digit numbers + and - sequences of multiples of 10, 100

Mental Work: Calculate complements to 90, 180, 360 Calculate missing angles about points & in triangles Use mathematical language to describe 2-D shapes

Mental Work: Identify points on partially numbered scales + and - pairs of 1-digit numbers with + or - answers + and - 2-digit decimals with 1 or 2 decimal places

Extension Work:

Count back from whole numbers in steps of 12

, 13

, 14

,

110

Extension Work: Explore regular & irregular polygons with ICT tools

Extension Work: Use ICT to evaluate different graphs for a data set

Spring Term (Second half term)Week 4 Week 5 Week 6Number Number Geometry



Main Teaching: Carry out mental

calculations with/without jottings that involve the four operations

Know and use brackets, the rules and priority of operations to write equivalent number sentences and to support mental calculations e.g. 55÷13+10÷13=(55+10)÷13=65÷13=586÷7-51÷7=(86-51)÷7=35÷7=5

Use mental calculations to generate times tables for 2-digit number

Divide 2- and 3-digit numbers by a 1-or 2-digit number using formal written methods of long and short division

Solve problems that involve scaling quantities and measurements up by multiplying and down by dividing

Notes/examplesWe have used the short division to divide by a 1-digit number. We use long division to divide by a 2-digit number. Will 875÷16 have a remainder? Explain why 16 is not a divisor of 875.

H T U5 4 r 11

1 6 8 7 58 0

7 56 41 1

Since we are dividing by 16 it is useful to derive the 16 times table we can refer to as we do the division.We cannot divide the 8 by 16 so we work out how many 16s will go into 87. There are 5 as 5x16=80 so we write 5 in the 10s and subtract to get 7. Now we involve the 5 and use 75. There are 4 16s in 75 as 4x16=64 and 5x16=80 is too big. We write 4 in the 1s column and subtract; the remainder is 11, we write:

874÷16 = 54 r 11, or 54 1116

.

Main Teaching: Multiply and divide

whole numbers, and those involving decimals with up to 3 decimal places, by 10, 100 and 1000

Find factor pairs of numbers; use the vocabulary of product, composite number, prime number and prime factor

Express numbers to 100 as a product of its prime factors

Solve multi-step word problems involving + and - representing the problem in a picture to annotate and interpret and to identify the calculations

Solve puzzles involving missing numbers given information about its factors

Test conjectures about numbers and explain reasoning

Notes/examplesTom and Pam buy pens. They spend £5.50. Tom pays 94p more than Pam. How much do each pay? Start with a picture to represent the problem.

550p

Which bar is Tom/Pam? Who paid more for the pen? How much more? Annotate our picture. They paid 550p but if Pam had paid the same as Tom the total would increase by 94p to 644p.

Tom? 644pPam? 94pTom spent half of this £3.22 and Pam £2.28p. Ali and Ram share £2.12 in 2p coins. Ali ends up with 40p less than Ram. How many 2p coins do each end up with? Draw and annotate a picture.What 2-digit number whose digits sum to 9 has factors 5 and 6?What 3-digit number has factors 6 and 8 if its digits sum to 15?Do square numbers have an odd number of factors?

Main Teaching: Plot and identify points

on coordinate grid in the first quadrant

Draw shapes by plotting the corners given their coordinates and label the corners

Translate shapes; describe a translation, giving the direction and distance of the change in position

Recognise that for a translation the size and orientation of the shape is unaltered and only position is affected

Reflect shapes; describe a reflection by describing the mirror line (line of reflection) as horizontal or vertical and a point through which it passes

Recognise that for a reflection the size of the shape is unaltered but position and orientation is affected

Generate patterns using repeated reflections or translations of a simple shape

Notes/examples

What are the coordinates of the corners of the green shape? I reflected this shape twice and translated it once. Describe the reflections and translation. Identify the coordinates of the corners of the shapes in their new positions.On another grid of the same size, a triangle has corners at A(5,7), B(8,6) and C(6,5). I reflect it in the horizontal line and the vertical line that both pass through the point (4,4). I also translate the triangle down 4 and left 4 units. Draw the shapes, label its corners and record the coordinates of the corners of the new triangles. Has any triangle changed its shape or size or orientation?

Mental Work: Recall x facts to 12x12; derive related x, ÷ facts Say if and why a given fraction is <, > or = 1/2 Round mixed, decimal numbers to required accuracy

Mental Work: Convert %age to fraction in 100th and to decimals Calculate unit fractions of quantities, exact answers Calculate 10, 25 & 50% of quantities, exact answers

Mental Work: Identify points and movement on a coordinate grid Visualise a translation & identify changes to a shape Visualise a reflection & identify changes to a shape

Extension Work: ÷ powers of 10 by 3, 6.. look at pattern in remainders

Extension Work: Use ICT to explore the factors of p²-1 (p is prime>2)

Extension Work: Explore how Rangoli designs are constructed

Summer Term (First half term)


1x16 162x16 323x16 484x16 645x16 806x16 96

: :


Week 1 Week 2 Week 3Number Number/Measurement GeometryMain Teaching: Use formal written

column methods to add and subtract up to 4-digit whole numbers and decimals with up to 3 decimal places

Practise formal written methods to multiply 3- and 4-digit whole numbers by 1-, 2-digit numbers and divide 3- and 4-digit whole numbers by 1-digit numbers

Solve problems multiplication and division problems; record remainders as whole numbers or fractions in the context of the problem

Solve missing digit problems involving multiplication and division

Know and use the prime, square and cube numbers

Identify and describe patterns; conjecture and test; explain reasoning

Notes/examplesWork out: 8.9+5.725 and 8.9-5.725. We include zeros to set out decimals so the points are lined up. 8 9 10

8.900 8. 9 0 0 + 5.725 - 5. 7 2 5 14.625 3. 1 7 5 1

For a Year 5 party I need 7 loaves (£1.35 each); 3 packets of ham (£2.19 each) and 2 blocks of cheese (£3.48 each). How much will it all cost? Work out the covered up numbers to make these statements correct: 88█÷7=1█7; █57x6=15█2 324÷█=█6; 16█÷6=2█ My 2 numbers sum to 16. One number is prime the other is a square number. What are my 2 numbers?My number a is double my number b; a+b is 21. What are my 2 numbers?My number is cubed to give an odd number with 3 digits. What 3-digit numbers are possible? Are 4³-1³; 5³-2³; 6³-3³; 7³-4³...all multiples of 9?

Main Teaching: Read and write

decimals with up to 3 decimal places; identify the value of the digits after the decimal point

Represent decimals with up to 3 decimal places as fractions with denominators 1000, 100 or 10

Recognise the relationship between the units of metric measure and convert between them

Measure capacity, weigh, length; read and record measurements using mixed units or as a decimal of the larger units

Add and subtract measurements that use decimal notation and apply to problems including those involving perimeters of composite rectilinear shapes

Notes/examplesRead these numbers: 4.5; 8.65; 3.905... Identify the value of 5 in each number. What is 8.105 as a fraction? There are 3 decimal digits so

we have 1000ths: 8105

1000=

81051000The table shows how units of metric measure relate

Metric units1km 1000m

1m 1000mm1m 100cm

1cm 10mm1kl 1000l

1l 1000ml1kg 1000g

1g 1000mgRemember: kilo means 1000 units; centi means one 100th and milli one 1000th of a unit. We multiply and divide by 1000, 100 or 10 to convert between these units. What is 1.25km in m? x1000: write 1250m. What is 50g in kg? We ÷ by 1000. 50÷1000=

501000 so 0.050kg or 0.05kg.

What is 5075ml in l? We ÷ by

1000 to get 50751000 we have 3

zeros so 3 decimal digits: 5.075l. What is 3500ml in l? ÷1000 gives 3l 500ml or 3.5l. What is 5080g in kg? ÷1000 5kg80g 5.080kg.

Main Teaching: Compare, measure

and draw acute, obtuse and reflex angles in degrees using a protractor

Know that the angles at a point sum to 360ºand adjacent angles on a straight line sum to 180º

Measure the interior and exterior angles in triangles; conjecture and test generalisations about the sums of these angles

Draw triangles, using a ruler and protractor, given information on the lengths of sides and size of angles

Recognise 3-D shapes from their 2-D representations

Name faces on 3-D shapes including prisms and pyramids; combine cut-outs of the faces of 3-D shapes to make simple nets and check the fit

Notes/examplesThe exterior angles a, b, c of a triangle are marked below. a b cDraw triangles of your own. Measure their exterior angles and find the sum a+b+c. What do you notice? Can you make a general statement about the sum of the exterior angles of a triangle?

Draw a large triangle you can walk around. Start at the corner with the star. Walk in the direction of the arrow. At each corner turn through the exterior angle so you face along the next side. Repeat until you are back at and ready to move along the red arrow. How many degrees did you turn as you went once around the triangle? Draw a large quadrilateral. Measure the exterior angles and sum. Walk around it once. Explain what you notice.

Mental Work: Read, order large numbers in words & numerals

Mental Work: State equivalences between fractions and decimals

Mental Work: Recognise 3-D shapes from 2-D representations



Recall x facts to 12x12; derive related x, ÷ facts Calculate squares, cubes; recall primes to 19

Convert measurements to kilo, centi or milli units Calculate complement to a given unit eg 350 ml to1 l

Name the angles in 2-D and 3-D shapes Visualise & name shapes from their descriptions

Extension Work: Explore the factors of square & cube numbers

Extension Work:

Count back from whole numbers in steps of 12

, 14

, 15

,

110

Extension Work: Explore the properties of quadrilaterals using ICT

Summer Term (First half term)Week 4 Week 5 Week 6Number/Measurement Number/Measurement NumberMain Teaching: Read accurately linear

and circular scales that involve partially labelled and unlabelled intervals

Work out intervals on scales with whole, decimal and positive and negative numbers, including intervals of time on a clock

Recognise per cent, % means per 100 and to find 1% of a quantity involves dividing by 100

Scale up 1% to find larger percentages of quantities

Convert percentages to decimal and fractional equivalents and vice versa

Solve problems involving calculating a fraction of a quantity

Solve problems involving calculating a percentage of a quantity including a reduction in cost

Notes/examplesRemember % means parts

per hundred. 1% is 1

100

What is 65% as a fraction?What does 100% tell us?To work out 1% we divide by 100. Once we know 1% we can scale up to find other %ages. £1 has 100 pence. It means 1% is 1p. What is 10% of £1; 20% of £1...A supermarket sale offers 30% off all clothes. What does this mean? Jeans cost £25, what will I pay? £25 is 2500p and 1% of

2500p is 1

100 so we get

25p.10% is 25px10=£2.50 and 30% is 3x£2.50 = £7.50. Put this is a table:

100% Whole 2500p

1% ÷100 25p10% x10 250p30% x3 750p=£7.50

Cost £25 - £7.50£17.50

What would I pay for:a jumper costing £36socks costing £8

Main Teaching: Practise and use the

formal written method to multiply 3- and 4-digit whole numbers and decimals with up to 2 decimal places, by 1- and 2-digit numbers

Measure length, weight and capacity, using metric units, m, cm, mm; kg, g; l, cl, ml

Convert between different units of metric measures; express measures in mixed units or as a decimal of the larger units

Recognise and use approximate equivalents to convert between metric and common imperial units

Solve problems involving converting between units of time: weeks, days, hours...

Solve problems involving decimal notation with up to 3 decimal places, in the context of measures and money

Notes/examplesWe can use the formal method to multiply decimal numbers by 1- and 2-digit numbers. We carry out the division as usual. In the answer we must place the point so there are the same decimal places as in the number we multiply. H T U .t H T U .t h 9 .5 3 8. 7 6 x 2 7 x 3 4 3 3 3 2 6 6. 5 1 5 5. 0 4 1 2 2 1 1 9 0. 0 1 1 6 2. 8 0 2 5 6. 5 1 3 1 7. 8 4 1 1

Road signs give distances

in miles. 1km is about 58

of a mile The distance by road to a town is 24 miles, how many km it that?We used to buy petrol in gallons. My converter says 1gallon = 3.78541178litres.How many litres would a 5,500 gallon tanker hold?The USA still weighs items in pounds (lbs). A pound is about 0.45kg. A rare fish called an opah weighed 180lbs. What was the

Main Teaching: Practise and use the

formal written method to divide 3- and 4-digit whole numbers and decimals with up to 2 decimal places, by 1- and 2-digit numbers

Add and subtract simple fractions with the same denominator and with related denominators

Convert improper fractions to a mixed fraction

Multiply simple fractions by a whole number

Recognise the equivalence of common fractions to decimals and percentages

Solve problems and puzzles involving missing numbers and quantities

Solve problems involving totals made up of combinations of up to 3 multiples of 1-digit numbers

Notes/examplesWe can use the formal method to divide decimal numbers by 1- and 2-digit numbers. We line up the decimal point in the answer to the decimal point in the dividend. We do the division as usual.

H T U4 5 . 3

1 5 6 7 9 . 56 0

7 97 5

4 54 5

0The answer has 1 decimal place: 679.5÷15=45.3.Letters represent decimal number < 1. Totals for 4 of the rows and columns are shown. Find the missing numbers and totals?

A B C B 1.5A C D B 1.4C C C C 2.0D A C C 1.5

1.3 1.7 1.7 1.8Pentagons, squares and triangles in a box share a total of 49 sides. How many of each shape are in the



a coat costing £44Which is more 50% of £20 or 20% of £50?

weight of the fish in kg? box?

Mental Work: Convert %age to fraction in 100th and to decimals Calculate unit fractions of quantities, exact answers Calculate 10, 25 & 50% of quantities, exact answers

Mental Work: Convert between units by x and ÷ by 10, 100, 1000 Recall units of time and convert between units + and - decimals with 1 non-zero decimal place

Mental Work: Recall and use multiplication and division facts Calculate complements of fractions to whole numbers Compare fractions with equal & related denominators

Extension Work: Interpret sequence rules expressed algebraically to

count on, back from whole numbers in fraction steps

Extension Work: Explore imperial and metric units of measure: litres

and pints; grams and ounces; yards and metres

Extension Work: 315 divisible by 7 as 2x3+15=21 and 21 is divisible by

7. Does this work for other numbers?

Summer Term (Second half term)Week 1 Week 2 Week 3Number/Measurement Number GeometryMain Teaching: Estimate weight,

capacity and volumes of objects, scale up and measure to compare approximations against exact values

Know that 1 cubic centimetre displaces 1ml of water and use to measure volumes of irregular shapes

Work out a fraction that is equivalent to another fraction given its numerator or its denominator

Convert improper to mixed fractions and vice versa

Add and subtract fractions with denominators that are multiples of one another

Multiply proper fractions and mixed numbers by whole numbers in the

Notes/examplesEstimate the weight of an orange, plum and grape? Use your estimate to work out approximately how many pieces of each fruit there be in 0.25kg? Weigh each piece of fruit and scale up to 0.25kg. Is your estimating precise?Estimate the volume of each piece of fruit in cm³.Identify the numerator or the denominator in these equivalent fractions:

25

= █10

; 35

= █25

; 34

=

6█ ;

23 =

8█

What is one third of 45g?What is ¾ of 1l in ml?What is 1⅛ of 4m in cm?What is 23/5 of 500g?Hanna counts out her stickers. If I had 3 more I would have ¼ of all 60 stickers. How many stickers has she?Tim eats ⅔ of his chews.

Main Teaching: Read, write and order

whole and decimal numbers including those with placeholder zeros

Round decimal numbers to the nearest whole number and tenth

Read negative numbers in context, from scales and calculate intervals between two integers

Read and use Roman numerals l, V, X, L, C, D and M; record and identify years written using Roman numerals

Generate and extend number sequences that cross zero, and with decimal or fractional steps

Convert percentages to decimal and fractional equivalents and vice versa

Notes/examplesThe Roman numerals for the numbers 1 to 10 are:

I ll lll lV V1 2 3 4 5Vl Vll Vlll lX X6 7 8 9 10

Remember the l, V and X are 1, 5 and 10, and L and C are 50 and 100.

X XX XXX XL L10 20 30 40 50LX LXX LXXX XC C60 70 80 90 100

The next 2 symbols are D and M. They are 500 and 1000. We can now write large numbers using Roman numerals.

C CC CCC CD D100 200 300 400 500

DC DCC DCCC CM M600 700 800 900 1000

Can you see the underlying rules apply again this time with the 100, 500 and 1000? The C behaves like the X and l; the D like the L and V. We write the year 2010 as MMX. A grave stone had the year of a death CMLXXXll on it? What year

Main Teaching: Compare, measure

and draw acute, obtuse and reflex angles in degrees using a protractor

Know that the angles at a point sum to 360ºand adjacent angles on a straight line sum to 180º

Interpret and use the conventional markings for parallel lines and right angles

Measure the angles about parallel lines and interior angles of quadrilaterals; conjecture and test generalisations about the relationship between angles

Use the properties of angle sums to find missing angles

Know that regular polygons have equal sides and equal angle and a square is

Notes/examples

What are these 2 shapes called? What do the arrows and little squares tell us? What are the lines inside the shapes called? List the properties of a rectangle. And of the trapezium. Draw similar trapeziums and rectangles with their diagonals and cut them out. Measure the angles and cut along the diagonals and look for any properties. Conjecture and test them out with other shapes.Alice has drawn 4 identical quadrilaterals. She says “I can always fit my 4 quadrilaterals around a point with no spare space. Rectangles and squares are easy, but other shapes



context of measures Solve multi-step

problems involving fractions

He gives ¼ of what he has left to Clea who eats these 3 chews. How many chews did Tim have at the start?What are the answers to:25 +

710 ;

56 +

12 ; 1

34 -

78 ;

23 -

19?

Solve problems involving simple percentages of quantities

was it? Write other years using Roman numerals. What does the 11 times table look like in Roman numerals?

regular quadrilateral Make simple

deductions and explain reasoning

work too.” Test her conjecture. What does it tell us about the angles in a quadrilateral?

Mental Work: Recall and use multiplication and division facts Extend sequences of multiples of 2s to 12s Calculate fractions of quantities, exact answers

Mental Work: Round number to required degree of accuracy Calculate multiples of 10% and 5% of given quantities Complete number sentences with + or - answers

Mental Work: Estimate the size of acute, obtuse & reflex angles Calculate angles about point, on straight lines Visualise quadrilaterals from their descriptions

Extension Work: Measure volume and capacity and convert units

Extension Work: Explore how the Mayan’s number system used . and ̶

Extension Work: Explore practically angles around parallel lines

Summer Term (Second half term)Week 4 Week 5 Week 6Number Number Number/Measurement/GeometryMain Teaching: Practise and use

formal written column methods to add and subtract up to 4-digit whole numbers and decimals with up to 3 decimal places

Practise and use formal written methods to multiply and divide 3- and 4-digit whole numbers and decimals with up to 2 decimal places, by 1- and 2-digit numbers

Add, subtract and

Notes/examplesIn the 14 times table tell me any facts you know? Yes 1x14 and 10x14. We will add, subtract, double and halve facts we have to work out all the facts?

1 x 14 142 x14 283 x14 424 x14 565 x14 706 x 14 847 x 14 988 x 14 1129 x 14 12610 x14 14011x14 15412x14 168

How can we find 3x14? Add the 2x14 and 1x14. What do we do to get 6x14? Double to get 4x14; 8x14... add or subtract to work out 7x14...

Main Teaching: Solve multi-step word

problems involving the four operations; represent the problem in a picture to annotate and interpret and to identify the required calculations

Solve problems where two unequal quantities are to be scaled up or down while keeping the relative sizes fixed

Solve simple ratio problems in context by scaling up or down

Solve missing digit problems involving the four operations

Generate number sequences that involve

Notes/examplesFor every 2 cups of flour add half a spoon of salt. How much salt in 8 cups? At a large party, every plate has 3 sandwiches; 2 cakes and 1 piece of fruit. In one room there are 14 plates, how many cakes are there? Another room has 36 sandwiches; how many plates are there? The third room the total number of cakes, sandwiches and fruit comes to 120. How many plates are in that room?Fill in this x table:

x 1 2 3 ... 121 1 2 32 2 4 63 3 6 9:

12

Main Teaching: Measure and work

out the perimeter of composite rectilinear shapes

Identify and apply the symmetry and structure of rectilinear shapes to calculate areas and perimeters

Use a rectangle as a template to generate sequences that follows a pattern and rule; describe in words the rule used to generate the sequence

Calculate the area and perimeter of a sequence that is constructed from

Notes/examples

Describe the structure and symmetry of each shape. Explain how you use this to work out the area and perimeter of the shapes so you don’t count each individual squares? Marlie makes shape sequences using blue and red 6cm by 4cm rectangles. Find the areas and perimeters of her 3 shape sequences. She continues her pattern of



double facts to construct the 14, 16, 18 multiplication tables

Identify and describe patterns in the unit digits in the 12, 14, 16 and 18 times tables and relationships between the digits

Can you see any patterns? What unit digit is in 17x14? What multiples of 14 will have a 6 digit in the units? Is 1347 divisible by 14? Why not? Could 734 by a multiple of 14? Is it? Why not? Work out the 16, 18 times tables. Write out the 12 times table too. Look for patterns and relationships. Describe them. Explain how they inform mental calculation.

fractions and decimals; identify and describe sequences using term-to-term rules

Identify, generate and describe patterns in tables of numbers; generalise and test and explain thinking and reasoning

Find the sum of the numbers in the 3 by 3 square. Now work out the sums of other squares of numbers which have 1 in the left-hand corner. What do you notice? Can you explain why the answers follow a pattern? What are the sums of the rows and columns? What does the 12 by 12 square add up to?

rectangles; predict the area and perimeters for sequences of a given number of rectangles and check by calculation

Calculate missing lengths of sides in rectangles and simple composite rectilinear shapes

shapes. Describe how to calculate the area and perimeter of her shapes sequences. What is the area and perimeter of a 4, 5...10... shape sequence?

Mental Work: Recall and use multiplication and division facts Calculate simple fractions & %ages of quantities

Mental Work: Recall and use multiplication and division facts Scale 2 quantities up or down retaining relative size

Mental Work: Visualise & describe composite rectangular shapes Calculate simple areas & volumes given dimensions

Extension Work: Extend to construct 22, 24, 26, 28 times tables;

identify patterns in the digits and use to calculate

Extension Work: Count on, back from whole numbers in fraction steps

predict the number of steps to reach a target number

Extension Work: Femi uses 3cm by 2cm rectangles to build a shape

5cm by 6cm. How? What rectangles can he make?


progress in mathematics scheme of work for year 5 web viewthis draws together those key aspects of...

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