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©MATHSEDUCATIONAL LTD Securing Progress in Mathematics Scheme of Work for Year 4 Securing Progress in Mathematics: Scheme of Work for Year 4 Contents and the intended use of each section within the Scheme of Work Essential Learning in Mathematics This 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, Communicating This provides a short summary of the problem solving and reasoning activities pupils should engage in and the communication skills expected of them. Language and Mathematics This 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 Mathematics Two simple-to-remember principles are identified, that seek to promote the incorporation of language into mathematics planning and teaching. Key Mathematical Vocabulary This 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 Outcomes This 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 Sheet The 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 Planner This 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. 2 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Essential Learning in Mathematics Summary of Essential Learning in Year 4 Count in single-digit multiples, and in 10s, 100s, 1000s from any number; use negative numbers to count backwards through zero Compare and order numbers beyond 1000; identify the place value of the digits in four-digit numbers and partition and recombine; round to nearest 10, 100 or 1000; in context, read, write and compare decimals up to hundredths Add and subtract mentally combinations of multiples of 1, 10, 100, 1000; use formal written methods to add and subtract numbers with up to four digits Recall multiplication facts to 12 x 12; use to derive division facts, and to multiply and divide multiples of 10 and 100 by single-digit numbers; use formal methods to record multiplication of two-digit and three-digit numbers by one-digit numbers; find unit and non-unit fractions of quantities; recognise equivalents Measure and convert between common standard units of measure including money and time; find and compare the perimeters and areas of rectangles; present small data sets as bar charts or time graphs and interpret and interrogate results Name, classify angles up to two right angles, and triangles and quadrilaterals with special properties; identify and use line symmetry; plot points in the first quadrant of coordinate grids and describe translations Problem Solving, Reasoning, Communicating Pupils solve problems that involve more than one step. They determine which operations to use and the order in which they are to carry them out. Pupils interpret and use information from tables and graphs that show discrete data, and compare and manipulate the frequencies or the quantities displayed. They interpret continuous data in time graphs and describe the changes that have taken place over the period of time represented by the graph. Pupils solve measure and money problems that involve the interpretation of decimal numbers and problems that require the manipulation of simple fractions. They convert between common units of measure to simplify or to set the solution in an appropriate context. Pupils extend their knowledge of the four operations and their understanding of the relationships between them. They use the associative and distributive laws to re-write and carry out mental and written calculations drawing on their knowledge of place value and partitioning to explain their reasons for applying these methods. Pupils use unit and non-unit fractions to describe and determine parts of a shape or a quantity and relate the fractions to equal parts of a whole, quantities or sets of items. Pupils recognise that an angle is formed by turning about a point and is a property of a 2-D shape. They use this knowledge to reason and to decide whether a shape does or does not belong to particular and special classes of shapes. Pupils read increasingly large numbers, recognise the value of the digits, and begin to interpret tenths and hundredths in decimal numbers. They identify positive and negative numbers as they count forwards and backwards. Pupils name an increasing number of 2-D and 3-D shapes and identify and describe their angular properties and any lines of symmetry. They find the perimeters and areas of rectangles and simple rectilinear shapes. Pupils use coordinates in the first quadrant to describe the position of points on a plane and the movement of points as translations. 3 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Language and Mathematics 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. L is 50 and C is 100; 4 and 5 are a factor pair of 20; any quadrilateral has 4 straight sides) stating, repeating and recalling facts aloud, and explaining how they can be used and applied (e.g. 234 - 44 is 234 - 34 - 10, which makes the answer 200 - 10 = 190; 53 is 50 + 3, I can write 53 x 8 as 50 x 8 plus 3 x 8; a rhombus has 4 sides the same length like a square but the angles are not right angles) describing the relationship between two or more items, shapes, events or sets (e.g. 15:15 is half an hour after 14:45; the fraction ½ is in the middle of the 0 to 1 number line and ¾ is half way between ½ and 1; these three rectangles are each 20 square cm but their lengths,10cm, 5cm, and 20cm, are not equal) identifying properties and describing them (e.g. when you divide 100 by 1 you get 100 as 100 is 100 ones; this point on the grid is 3 along and 7 up so the coordinates are (3, 7); the 50 times table is like the 5 times table with an extra zero; this isosceles trapezium is like an isosceles triangle with its top cut off) framing an explanation, reasoning and making deductions (e.g. I knew that 2 x 4 x 5 is 40 as 2 x 5 is 10 and 10 x 4 is 40; this rectangle must have 2 lines of symmetry as all rectangle do; 60 minutes in 1 hour means if I sleep for 10 hours this is 600 minutes; 548 rounds to 500 because 48 is less than 50, half way between 500 and 600) Learning the Language of Mathematics Learning 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 4 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Key Mathematical Vocabulary: Year 4 Number Count in multiples of, count forward, count backwards through zero, consecutive; positive number, above zero, 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; place value, digit, units, ones, tens, teens, hundreds, thousands, ten thousands, hundred thousands; single-digit number ... four-digit number ... sixdigit number; Roman numerals, I ... IV, V, VI ... IX, X, XI ... XXXIX, XL, XLI ... XLIX, L, LI, LII ... LX, LXI ... XCVIII, XCIX, C; partition, exchange, exchange for one thousand, exchange for ten hundreds; numerals, place holder; hundred more/less, thousand more/less; greater than (>), less than (<); fewer, fewest, least; estimate, round up/down, approximate, check, round to nearest ten, nearest hundred ... nearest thousand Calculation Addition, increase, sum, total; subtraction, take away, decrease, fewer, less, difference between; add sign (+), subtraction sign (-), equals sign (=); calculate, calculation, mental calculation, formal written method, columnar method; double, scale up; halve; share out equally, equal groups of, left, left over, remaining; divide, divide by, divide into, divisible by, quotient, factor, factor pair, 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; scale up, scale down, 4 times as heavy, holds 3 times the amount, twice as tall Fractions Whole, one whole, fraction, denominator, numerator, unit fraction, non-unit fraction, equivalent fractions, simplify; fraction of, proportion, equal parts, share equally, equal parts of the whole; halves, two halves make a whole; 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; 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, two decimal places; whole number boundary, ones, tenths, hundredths; round to nearest whole number; £.p Measurement Units of measure, metric unit, measurement, quantity, scale, equivalent units, convert, conversion, mixed units, intervals, value of interval; length, perimeter; standard units of length, kilometre, metre, centimetre, millimetre; metre stick, measuring tape, ruler; weight, mass, scales; standard units of weight, kilogram, gram; measuring jug, 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 centimetres Geometry Point; shape, flat, 2-D shape, perimeter, distance around, area, space inside; 3-D shape, surface, flat surface, straight, triangular, rectangular, circle, circular; corner, side; face, edge, vertex, vertices; cube, cuboids, sphere, cylinder, cone, pyramid, prism; triangle, isosceles, equilateral; quadrilateral, square, rectangle, parallelogram, rhombus, trapezium, kite; polygon, pentagon ... decagon, regular, irregular; symmetric, line of symmetry, reflect, reflection, vertical line, horizontal line; orientation; turn, rotate, clockwise, anti-clockwise, quarter turn, right-angle turn; smaller than one right angle, acute angle, between one and two right angles, obtuse angle; perpendicular lines, parallel lines; coordinates, plot, axes, quadrant; shift, translation Statistics Count, 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; title, label; number fewer, least number, total number, maximum number; scale, unit size, number of units represented, units per interval, units per picture Reasoning and solving problems 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 5 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 End-of-Year Learning Objectives for Year 4 Record of coverage A. Number – counting and place value A1. Can count in single-digit multiples and multiples of 25, 50, 100, 1000; count backwards to include negative numbers A2. Can read, write and order whole numbers with four or more digits; read numbers using Roman numerals: I, V, X, L, C A3. Can use place value to compare and partition 4-digit whole numbers and decimal numbers with 1 or 2 decimal places A4. Can round numbers to the nearest 10, 100 and 1000 and round decimals with 1 decimal place to nearest whole number B. Number – calculation (mental and written) B1. Can add and subtract mentally 2-digit numbers and multiples of 10, 100 and 1000 B2. Can add and subtract mentally quantities of money in £s and pence and measurements that involve different units B3. Can recall the multiplication tables to 12 x 12, derive related multiplication and division facts and identify factor pairs B4. Can use the formal written column methods to add and subtract numbers with up to four digits B5. Can use number facts and the rules of arithmetic to re-write number expressions and carry out calculations B6. Can use a formal written method to multiply 2-digit and 3-digit numbers by a single-digit number C. Number – fractions (including decimals) C1. Can construct practically families of equivalent fractions and add and subtract fractions with the same denominators C2. Can find unit and non-unit fractional parts of quantities where the answer is a whole number C3. Can count up and down in hundredths, recognise and record halves, quarters, tenths, hundredths as decimals C4. Can interpret answers to division of 1-digit and 2-digit whole numbers by 10 or 100 as tenths and hundredths C5. Can recognise that as the numerator of a fraction with fixed denominator increases the fraction gets bigger D. Measurement D1. Can measure accurately using metric units for length, weight, capacity, and convert between different common units D2. Can measure and calculate the perimeter of rectangles and composite rectilinear shapes using metric units D3. Can find the areas of rectangles and composite rectilinear shapes drawn on grids or by counting squares D3. Can read and interpret times presented in 12-hour and 24-hour notation, convert units and calculate time intervals E. Geometry – properties of shapes, position and direction E1. Can draw lines and 2-D shapes accurately; use properties to classify and name triangles and quadrilaterals by type E3. Can plot points on a coordinate grid in the first quadrant and draw and complete shapes in different orientations E4. Can describe relative positions of points and shapes as translations to left/right and up/down E5. Can name and compare acute and obtuse angles by size; recognise equal lengths and angles in regular polygons E7. Can identify lines of symmetry in 2-D shapes and complete 2-D shapes given a line of symmetry F. Statistics – interpret discrete and continuous data F1. Can organise, present and interpret discrete data in frequency tables, pictograms and bar charts using non-unit scales F2. Can organise, present and interpret continuous data in tables and time graphs; explain changes over time G. Problem solving, reasoning, communicating G1. Can solve 2-step problems involving money, measures, time, fractions; use multiplication/division to scale up and down G2. Can provide reasons for choosing operations to solve problems and for using particular properties to classify shapes G3. Can use the language of fractions, decimals and negative numbers when counting, comparing and sorting numbers 6 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Assessment Recording Sheet Mathematics in Year 4 Autumn term Name: Spring term Summer term 4.1 – Working towards expectations 4.2 – Meeting expectations 4.3 – Exceeding expectations Key: Class: A. Number – counting and place value 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 B. Number – calculation (mental and written) 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 C. Number – fractions (including decimals) 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 D. Measurement 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 E. Geometry – properties of shapes, position and direction 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 F. Statistics – interpret discrete and continuous data 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 G. Problem solving, reasoning, communicating 4.1 4.2 4.3 4.4 4.1 4.2 4.3 4.4 4.1 End-of-year assessment of progress and attainment in mathematics Summary report: Overall end-of-year assessment in mathematics: Working towards Year 4 expectations Meeting Year 4 expectations Teacher: Exceeding Year 4 expectations Date of final assessment: 7 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Week-by-week Planner Year 4 Autumn Term (First half term) Week 1 Number Main Teaching: Notes/examples Read the numbers: 2, 23, Read and write whole 234, 2 345. Which is the numbers, including biggest number? As the 1000s, in words and number of digits increases numerals the values of the digits Recognise and apply change. Read the words the underlying triplet and numbers in the table: structure of numbers: 1 One read the HTUs of 10 Ten 1000s first and then 100 One hundred the HTUs 1 000 One thousand Indentify and use 10 000 Ten thousand One hundred zeros as place holders 100 000 thousand Compare and order Zeros are important as numbers beyond they fix the value of the 1. 1000; start with the Read the numbers with 6 1000s then HTUs replacing 1. A comma can Recognise and replace the space: read identify the place 25,000. How many 1000s value of the digits in do we have? What are the up to 6-digit numbers values of the 2 and the 5? Add and subtract Read 626,468... Read the mentally multiples of number as HTU of 1000s 10, 100, 1000 and then the HTUs. What Identify complements is the value of each 6? to 100 and 1000 What is: 3+8; 30+80; Solve problems that 300+800; 3,000+8,000..? involve the mental What is 12-5; 120-50; addition or subtraction 1200-500; 12,000-5000..? of whole numbers and And 400+700-500-300..? inverse relationships And 24,000-6,000-6,000..? Week 2 Number Main Teaching: Read and write whole numbers, including 1000s, in words and numerals Partition 3-digit numbers into 100s, 10s and 1s in alternative ways to use in the subtraction by decomposition method of calculation Use a formal written column method to add and subtract pairs of 2-digit and 3-digit numbers Add and subtract mentally multiples of 10, 100, 1000 Determine when a written method or a mental method of addition or subtraction is required and explain why Solve problems that involve the mental or written methods of addition or subtraction of whole numbers Mental Work: Recall and apply + & - number bonds to 18 Recall the 2, 3, 4, 5, 6, 8 and 10 times tables State the value of the digits in up to 6-digit numbers Extension Work: Solve missing number problems using + & - facts Mental Work: Recall and apply + & - number bonds to 18 Recall the 2, 3, 4, 5, 6, 8 and 10 times tables Use x facts to derive related division facts Extension Work: Apply multiplication facts to multiples of 10, 100 Notes/examples Read the numbers out as I point to the words. Then write down the numbers in words and numerals. One Two : Eight Nine Zero Eleven Twelve : Eighteen Nineteen Hundred Thousand Ten Twenty : Eighty Ninety Use the written column method to work out 512467. What do we do first? Partition. 512=500+10+2. As we cannot subtract 7 from 2 nor 6 from 0 we partition 512=400+100+12 and write 41012 into the subtraction calculation. - HTU 41012 467 45 + HTU 658 176 834 1 1 Use the column method to work out 658+176. We add the digits in the 1s, 10s and 100s, and when the additions are 10 or more write a 1 for the 10 below the line in the next column. Week 3 Geometry/Measurement Main Teaching: Use a ruler to measure accurately in cm and mm Make and draw triangles of different types; name and classify them Make and test a generalisation on the relationship between 3 lengths if they are to form the sides of a triangle Make and draw quadrilaterals of different types and name them Identify lines of symmetry in triangles and quadrilaterals presented in different orientations and sizes Sort triangles and quadrilaterals using criteria related to their properties, including their symmetries Notes/examples Cut strips of card of lengths shown in the table. Your group needs 3 strips of each length. Length 4cm 6cm 8cm 10cm 12cm 14cm Strips of card Pick any 3 strips. Can you always use the 3 you pick to make a triangle? Which don’t work? Explain why. Pick two 6cm strips and one 8cm strip; make a triangle. What is it called? If all my strips are the same length what type of triangle do I make? Which triangles have a line of symmetry? Make a triangle with 6cm, 8cm, and 10cm strips. What type of angle is at 1 of its corners? How can we check this? Make 2 of the triangles. Put them together. What shape do they make? What are its 4 angles? What quadrilaterals can you make with 4 strips? Mental Work: Recognise symmetry in shapes in the environment Name triangles & quadrilaterals from information Visualise shapes made from 2 overlapping shapes Extension Work: Using strips make & explore pentagons/hexagons 8 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Autumn Term (First half term) Week 4 Number/Measurement Main Teaching: Notes/examples Count up from 0 and Use this array to count in 3s and in 4s. back in multiples of 3s 4s 2, 3, 4, 5 and 6 o o o o o o o Count up from 0 and o o o o o o o : : : : : : : back in 7s; construct o o o o o o o and recite the 7 How can counting in 3s and times tables 4s help us to count in 7s? Use the 7x table to Add the 3s and 4s to get 7s convert weeks to 3s 4s 7s days and vice versa 3 4 7 6 8 Know that a : : : multiplication fact 30 40 can be written in 2 33 44 ways (multiplication 36 48 is commutative) and Fill in our table. Count in each corresponds to 3s, 4s and 7s. Recite the 3, a division fact (its 4, 7 times tables. inverse) What other counts could we Write the related use? 2s and 5s; 1s and 6s. multiplication and 2s 5s 7s division facts given 2 5 7 4 10 1 multiplication fact : : : Apply the associate 20 50 and commutative 22 55 laws to multiply 3 24 60 numbers mentally Which table was easier to e.g. 4x7x5=4x5x7 use? Why? Hide the tables; =20x7=140 recite the 3, 4, 7 times Solve problems that tables and now the 2, 5, 7 involve missing times tables. What is 8x7? numbers in x, ÷ 8x2=16 and 8x5=40 so it’s number sentences 56. Try 6x7; 4x7; 7x7... Mental Work: Recall the 2, 3, 4, 5, 6, 7, 8 and 10 times tables Derive division facts from these times tables Read, compare & order numbers with up to 6 digits Extension Work: Make 6x,7x,8x tables by subtracting from 10x table Week 5 Number Main Teaching: Notes/examples Read aloud the first 4 rows in Practise using a this table. Explain what is formal written 10 000 ÷10 = 1000.1 column method to 1000 ÷10 = 100.1 add and subtract 100 ÷10 = 10.1 pairs of 2-digit and 10 ÷10 = 1.1 3-digit numbers 1 ÷10 = ?.1 Recognise, when happening. dividing 1000s, Each time we ÷ by 10: the 100s, 10s and 1s by first digit 1 moves one place 10, how the number right; and we lose a 0. The gets smaller numbers get smaller. What is Understand that the answer to 1÷10? As the tenths arise when numbers get smaller, it must dividing 1s by 10 be less than 1. The answer is and hundredths one tenth. We write it as 0.1. when dividing 1s by This is a decimal and the . is 100 or by 10 and 10 called the decimal point. The Understand that the first number after the decimal decimal point point is a tenth. For 1÷10 we separates whole write 0.1 which is 1 tenth. and part numbers 2÷10=0.2 or 2 tenths Carry Read, write, order this on to 9÷10. What is decimals with 1 or 2 10÷10? It is 10 tenths and decimal places that is one whole or 1. What Count up and down 1 ÷10 = 0.1 0.1 ÷10 = 0.01 in tenths and if we divide 0.1 by 10? It will hundredths, as fractions or decimals be 0.01 or one hundredth. Can you predict how we write Solve practical 1÷100? Say: “1÷100 is 0.01 problems involving or one hundredth.” And say: tenths and 2÷100=0.02=2 hundredths... hundredths Mental Work: State numbers above/below given decimal number State number above/below given tenth or hundredth Read, compare & order decimals with up to 2 places Extension Work: Count in non-unit fractional or decimal steps Week 6 Geometry/Measurement Main Teaching: Notes/examples Read scales with My horizontal stick starts at 0. integer-valued The intervals are in 7s. What is intervals this number..? And the number Recognise that two perpendicular scales at this end? I turn my stick vertically. 0 is at the bottom can be used to identify movement in and intervals are size 6. What are these values..? I have a two directions and a position on 2-D grids horizontal and a vertical stick with scales 0 to 10. They are Describe positions as coordinates in the on the sides of a grid like this. first quadrant Plot points in the first quadrant of a grid for given coordinates Plot corners of a shape and draw the sides to complete the shape Draw familiar triangles and quadrilaterals in the A star is on the grid. The star is first quadrant and at 0 on both sticks. This point give the coordinates is called the origin. I move the of the corners star along my horizontal stick Use left, right, up, and up my vertical stick. It down to describe a moves to here. What were my movement between two moves along the 2 sticks? positions on grids Where is the star on the grid? Draw rectangles on We write its position in a grid and count the brackets: (9,3), (along,up). squares inside it What is this position..? Mental Work: Identify points on scales with integer intervals Read scales 0 to 1 with decimal, fractional intervals State coordinates of points on grids with simple scales Extension Work: Describe & simplify composite movements on grids 9 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Autumn Term (Second half term) Week 1 Number/Measurement Main Teaching: Notes/examples Recite the 4 times table. Use multiplication What is 10x4? What is 20 tables to generate x4, 30x4, 40x4...? the tables for Remember 30 is 3 10s so multiples of 10 and 30x4 is 3 10sx4 or 12 10s 100 Derive division facts and 12 10s are 120. Knowing our 4 times tables from multiplication makes this easy. Recite the facts involving 3 times table. Use it to multiples of 10 and work out 10x3, 20x3, 100 30x3... What is 100x3, Know the effect of 200x3, 300x3...? multiplying any Can you remember how to number by 0 or 1 work out 57x3 using a grid? and dividing by 1 We partition 57 into 10s Multiply 2-digit and and 1s and multiply 50 and 3-digit numbers by 7 by 3 and add: a 1-digit number 57x3 50x3 150 using a grid method 7x3 21 of long 57x3 = 171 multiplication How can we use the table Recognise the to work out 257x3? We effect on a grid partition 257 into 100s, 10s multiplication of and 1s, multiply each part changes to 1 of the 257x3 200x3 600 digits in the 3-digit 50x3 150 number 7x3 21 Solve problems 257x3 = 771 that involve x and ÷ by 3 and add the answers. multiples of 10 and What is the same/different 100 in context such about the 57x3 and 257x3 as large sums of grids? What is 287x3...how money in £s does the table change? Mental Work: Recall the 2, 3, 4, 5, 6, 7, 8 and 10 times tables Count from 0 in 50s & 25s, describe patterns Use x tables & x10s to x ‘teens’ by 1-digit number Extension Work: Identify patterns in the digit sums of multiples of 3 Week 2 Number/Measurement Main Teaching: Notes/examples The Roman numerals for Read and write the numbers 1 to 10 are: Roman numerals to I ll lll lV V 100 using: l, V, X, L 1 2 3 4 5 and C Vl Vll Vlll lX X Recognise the 6 7 8 9 10 underlying structure The l, V and X are 1, 5 and involves working with 10. The next symbols are L and around the 50 and C 100. This is how numbers 1, 5, 10, 50 we write the 10s to 100. and 100 X XX XXX XL L Understand that there 10 20 30 40 50 is no symbol to LX LXX LXXX XC C represent zero in this 60 70 80 90 100 system, while our Can you see a pattern? Can number system has 0 you explain how Roman and the position of numerals work? The rules the symbols do not we used for 1 to 10 are signify their value, X similar to those for 10 to is 10 no matter where 100. We used 10, 50 and it appears 100 rather than 1, 5 and 10. Read time to the Convert 43 and 87... XLlll nearest minute on and LXXXVll... Write the analogue clocks with 100 square 1 to 100 in Roman and Arabic Roman numerals. What numerals patterns can you see in the Convert between 12columns? How do you know hour am, pm times if a Roman number is a and 24-hour times multiple of 5, or a multiple of Solve problems 10? Use the 100 square to involving 24-hour work out LXlV + Xll; LVl time and calculation XlX. What is V1xX, Xlll x lV; of time intervals LXXX÷X, C÷XXV...? Mental Work: Recall the 2, 3, 4, 5, 6, 7, 8 and 10 times tables State number before/after given Roman number Use x tables & x10s to x ‘teens’ by 1-digit number Extension Work: Explore time zones and times in different countries Week 3 Number Main Teaching: Notes/examples Here are 4 problems: Count out, read and 1. Paula has 3 50p coins. Ali holds record quantities of 4 times as many, how much money using £.p money has Ali? notation; recognise 2. Class 4 has 18 boys; twice as many as Class 1. How many that the . separates £ boys in Class1? from p and links to 3. Dad buys each of his 3 children decimal numbers a £1.50 ice cream. Altogether Compare and order how much money does he spend? quantities of money 4. £3.20 is shared out equally in £, p or mixed £.p between 4 children. How much units; convert units money in pence will each get? Add and subtract Read each problem. What do sums of money; give we know? What we are we to change and scale up find out? Draw pictures to amounts of money by help us to solve the problems. multiplying Lead pupils to these pictures: Solve problems Problem 1 Paula 3 involving the addition Ali and subtraction of Problem 2 sums of money Class 4 18 Represent problems Class 1 using box pictures; Problem 3 Children £1.50 £1.50 £1.50 annotate the boxes to Dad solve the problem Problem 4 Solve problems that Cubes £3.20=320p involve calculation of Pupils parts or the whole, by What numbers can we write identifying what is in the boxes? In Ali’s 4 boxes given information, we write 3s; so he has 12 what information is 50ps or £6. Write numbers in missing and what is the other boxes. Can you to be found solve the problems? How? Mental Work: Identify bigger/smaller amounts of money in £, p, £.p Add & subtract pence; cross the £ boundary & convert Use x tables & x10s to x 2-digit by 1-digit number Extension Work: Solve mentally 1, 2-step +, - missing number problems 10 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Autumn Term (Second half term) Week 4 Number Main Teaching: Notes/examples Use this array to count in 3s Count up from 0 and in 6s. How can counting and back in in 3s and 6s help us count in multiples of 2, 3, 4, 9s? Add 3s and 6s to get 9s. 5, 6 and 7 3s 6s Count up and back o o o o o o o o o in 9s; construct and o o o o o o o o o : : : : : : : : : recite the 9 times o o o o o o o o o tables Fill in our table. Count in 3s, Derive division 6s and 9s. Recite the 3, 6, 9 facts from known times tables. Hide the table. multiplication facts Recite 3, 6, 9 times tables Practise using a again. grid method of 3s 6s 9s 3 6 9 multiplication to 6 12 multiply 2-digit and : : : 3-digit numbers by 30 60 a 1-digit number 33 66 Read and write 36 72 10ths and 100ths Describe the pattern in the 9 as fractions and times table to 10x9. The 10s decimals increase by 10, 0 up to 90. Divide 1- or 2-digit The 1s decrease by 1, 9 to 0 numbers by 10, by List the numbers 1 to 10. 10 and 10 again, There are 9 gaps shown by and by 100; identify ☺. The arrow points to 4. the values of the How many faces to the left decimal digits and the right of the arrow? It means 4x9=36. Work out 8x9. Solve money or 1 2 3 4 5 6 7 8 9 10 measure problems ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ that involve scaling 3 6 quantities down by Explain the rule. Smile as you 10 and 100 recite the 9 times tables! Week 5 Geometry Main Teaching: Describe, identify, annotate and draw parallel and perpendicular lines Draw accurately common 2-D shapes including trapezium rhombus, parallelogram Draw, fold, cut up and measure common 2-D shapes to investigate and check their properties Use reasoning to make a general statement about the properties of and relationships between the sides and angles of 2-D shapes including those of the parallelogram Recognise which properties of a shape are independent of its orientation or size and explain why Identify lines of symmetry in shapes Begin to identify the properties of symmetry shapes, the equal sides and equal angles Mental Work: State the value of the digits in up to 6-digit numbers Give fraction/decimal equivalents of 10ths & 100ths Compare & order decimals with up to 2 places Extension Work: Construct a decimal ruler with 10ths and 100ths Mental Work: Recall the 2 to 10 times tables and division facts Identify parallel & perpendicular lines in shapes/objects Identify & compare properties in sets of 2-D, 3-D shapes Extension Work: Make & explore pentagons/hexagons with parallel sides Notes/examples These 2 lines are always the same distance apart no matter how long they become. What do we call these lines? Parallel. To show they are parallel we draw arrows on them. The opposite sides in this shape are parallel. It is called a parallelogram. With your ruler draw parallelograms. Make sure the sides are parallel. In your group, find out what you can about the sides and angles of parallelograms. Fold or cut them up to compare angles; measure the sides etc. Now complete these sentences: I think the sides of a parallelogram... I think the angles of a parallelogram... Do any of the parallelograms have a line of symmetry? What additional properties would make it symmetrical? Week 6 Number/Measurement Main Teaching: Notes/examples Here are 4 problems. Convert 1. Rik pours 450ml of water out of a between 12jug leaving him with 680ml. How hour am, pm much water was in the jug? times and 242. Together 2 bags weigh 1kg. One weighs 340g more than the other, hour times; what does each bag weigh? calculate times 3. Cans of juice hold 200ml and are at start or end in packs of 6. A box has 9 packs of an interval in it how much juice is in a box? 4. 5 shelves hold box files 8cm wide. Estimate and Each shelf holds the same compare the number of files. If there are 150 weigh, length files, how wide is each shelf? and capacity of Read the problems. What objects or information are we given? containers What do we have to work out? against known Draw pictures to help us. Lead quantities pupils to these pictures: Read partially Problem 1 Jug full numbered Jug after scales Problem 2 Convert Bag 1 between Bag 2 common units Problem 3 Can of measure Pack Solve 1- and 2Box ..... step part/whole Problem 4 measure 5 Shelves problems; draw 150 Files and annotate What numbers can we write in box pictures the boxes? Which problems and identify the need more than 1 calculation? required What must we work out first? calculations What are the calculations? Mental Work: Recall the 2 to 10 times tables and division facts State end/start time given intervals start/end time Use x tables & x10s to x 2-digit by 1-digit number Extension Work: Solve 1 & 2-step x, ÷ missing number problems 11 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Spring Term (First half term) Week 1 Measurement/Number/Statistics Main Teaching: Notes/examples Practise using mental The daily intake of salt for Y4 methods and a formal children is up to 4g. Weigh out 4g. Does this look a lot? written column A 200g pack of tortilla chips method to add and has 2.2g of salt. If you ate subtract pairs of 2half the pack how much salt digit and 3-digit would you eat? The table numbers Read, write and order shows the salt content in some popular foods. decimals with 1 or 2 Food Salt decimal places 1 Chicken nugget 0.1g Add and subtract Cheeseburger 1.5g mentally decimal Fried chicken 2.1g numbers with 1 Portion of chips 0.4g 1 Sausage 1.5g decimal place 2 Bacon rashers 1.9g Measure using metric Slice of white bread 0.5g units; recognise how Coke 0.1g the units used reflect Milkshake 0.4g scale and context Muffin 1.6g Baked beans 0.5g Know that measuring Fruit & vegetables 0g accurately requires Over a day I had 3 Muffins interpreting the value and 2 milkshakes, how much and size of intervals salt did I eat? Work out how and comparing much salt you’d eat with Read and interpret meals made up of this type of measurement data food. Look at food labels to that involves decimal make tables of how much fat, numbers set out in protein, fibre, salt and sugar tables and charts Solve problems using is in food. Your intake should published information be no more than: fat 64g; protein 24g; fibre 15g; sugar involving scaling sums and differences 85g. Plan meals with little salt or sugar; low fat content... Mental Work: Add & subtract pairs of whole numbers in 100s, 1000s Add pairs of decimal numbers <10 with 1 dec place x & ÷ numbers by 10, 100; answers up to 2 dec places Extension Work: Explore calories and protein content of foods Week 2 Number Main Teaching: Use multiplication facts to recall division facts Represent and calculate unit fractions of a quantity using equal sharing and division Recognise that nonunit proper fractions are scaled up unit fraction Calculate non-unit fractions of quantities by scaling up or multiplying the unit fraction value Use strips divided into equal parts to generate fraction sentences for fractions with the same denominator Add and subtract fractions with the same denominator, answers < 1 Solve problems that involve calculating non-unit fractional parts with whole number answer Notes/examples What’s 16÷4; 48÷8; 36÷4..? Our strip represents £24. Fold it in half. What amount of the £24 do the 2 equal parts or halves represent? £12. Fold into quarters. What amounts do the 4 equal parts or quarters represent? £6. Now fold into eighths. What amounts do the 8 equal parts or eights represent? £3. Dividing £24 gives us 1 of the equal parts or unit fraction part 1 1 2 4 of £24 = £24÷2 of £24 = £24÷4 1 of £24 8 = £24÷8 If we know one quarter find: 2 4 = of £24 3 4 = of £24 4 4 of £24 = Explain how you did this. Why is: 24 of £24 equal to 12 of £24? Why is 44 equal to £24? Now work out: 28; 38; 48 ; 58 ; 68 ; 78; 88 of £24. What other fractions of £24 are equal to the eighths? Our new strip represents £60. Draw it on a grid. What is each equal part worth? Work out all the tenths of £60. Explain how to work out all the fifths of £60. Mental Work: Recall the 2 to 10 times tables and division facts ÷ 100s, 1000s by 1-digit number, whole number ans Calculate fractions of measure, whole number answer Extension Work: Work out all the thirds, sixths, ninths of quantities Week 3 Measurement Main Teaching: Know that 1km is 1000m, 1kg is 1000g and 1l is 1000ml and convert multiples of the larger units to smaller units Calculate halves, quarters, tenths and hundredths of multiples of the larger unit and express in the smaller units Read values on scales that involve intervals of 25, 50, 100 Recognise that one half is equivalent to five tenths and fifty hundredths of 1 whole Use ‘by-eye’ halving and other division strategies to estimate where to place values within intervals Solve problems that involve estimating, comparing and taking measurements, and converting to smaller units Notes/examples Our empty bottles can hold 2 litres. You are going to make a measuring bottle to measure capacity up to 2l, in l and ml? Stick a strip of paper down the empty bottle. We will draw a scale on it. Mark where you think 2l will come up to. Where will we mark 1 litre? How many millilitres in a litre? Where would we put half a litre? How many ml is that? Mark 500ml. Now mark 1l 500ml. What is half way between 500ml and 0ml? Mark a quarter litre or 250ml... Explain how we estimate where to mark 100ml. Is it closer to 250ml or 0ml? Where do we mark 50ml? Now mark 50ml and 25ml intervals on your strip of paper. Count in 25ml from 0ml. Point to the markers as you count. Stop at 1l. Keep counting past 1l say 1l 25ml... How much liquid will 1 tenth of the bottle hold..? Now check your estimates using the bottles and jars whose capacities we know. Mental Work: Count in 1000s, 500s, 250s, 100s, 50s and 25s Convert milli units by ÷ 1000, whole number answer Read scales, identify size or end-points of intervals Extension Work: Draw capacity scales on non-uniform bottles 12 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Spring Term (First half term) Week 4 Number/Measurement Main Teaching: Notes/examples How much do I need to Practise using mental methods and a formal add to £3.65 to make it up to £4? What is £6 minus written column £5.65? Why do these method to add and questions have the same subtract pairs of 2answer? We are making a and 3-digit numbers sum of money up to whole Convert between 12£s. Ask different questions hour am, pm times that give the same answer. and 24-hour times Add and subtract money Use the 6 times table by partitioning: to generate £2.85 + 40p multiplication and 15p 25p division facts involving £3.00 + 25p 60; convert hours to Partition 40p into 15p and minutes and minutes 25p. Then add 15p to to seconds £2.85 to get £3. Add and subtract £2.35 80p amounts of money £1.35 100p £1.35 + 20p using methods that Partition £2.35 into £1.35 involve partitioning and £1 or 100p. Then take and adjustments 80p from 100p to get 20p. Identify the numbers Add and subtract money and values of coins by making up to whole £s and notes needed to and adjusting the pence: make up given £1.34 + £2.98 amounts of money £1.34 + £3.00 2p Solve 2-step problems £6.50 £4.89 involving the addition £6.50 £5.00 + 11p and subtraction of How many 5p coins will money and time, and make £2.85 up to £3.20? the conversion How do we solve this? between units Mental Work: Recall the 2 to 10 times tables and division facts Give complements to £1 of amounts in pence Calculate sums of multiple quantities of coins/notes Extension Work: Plan journey from timetable; use 12-hr am/pm time Week 5 Number/Measurement/Geometry Main Teaching: Notes/examples Use strips divided into Measure out a square 1m by 1m. This is a square equal parts to metre. We call the amount generate fraction sentences for fractions of space in a flat shape like our floor, its area. How with the same many square metres will denominator cover our carpet area? Add and subtract fractions with the same denominator, with answers <1 Practise calculating non-unit fractions of quantities by scaling up or multiplying the The grid shows a garden. unit fraction value A square is 1m by 1m. Understand that area What size is the garden in is measured in square metres? It has a squares; find simple fish pond, a flower bed areas by counting and a grassy area. There squares in units of are paths around the pond square metres or and flower bed. The path square centimetres uses 1m square slabs. Find the area of What are the areas of the rectangular shapes 2 paths? And the fish drawn on cm grids by pond, the flower bed and counting the squares grassy area? Building this inside the shape garden cost £65 per Plot corners of simple square metre. How much rectilinear shapes; was the pond..? On a grid draw the sides to design a garden. Include complete the shape 1m wide paths. Give all and find its area the areas and the costs. Mental Work: Complete fraction sentences and complements to 1 Estimate areas of everyday rectangular shapes Identify points and positions on a coordinate grid Extension Work: Extend the design to include rectilinear shapes Week 6 Number Main Teaching: Identify the place value of digits in whole numbers and decimals with 1 and 2 places Identify the midpoint in intervals of pairs of whole numbers and decimals in the context of money Compare and order whole and decimal numbers in the context of measures, and money in pounds and pence Round whole numbers to the nearest 10, 100 or 1000, and decimals with up to 2 decimal places to the nearest whole number, in the context of money Use rounding to estimate/check answers to problems Notes/examples A hand span is 13cm, is it closer to 10cm or to 20cm? Look at your ruler. Of 18cm, 14cm and 15cm which are closer to 10cm than 20cm? How did you decide? What about 15cm? It’s in the middle so we go up to 20cm. Give me lengths closer to: 20cm than 30cm; 80cm than 70cm; 400m than 500m; 9000km than 8000km...We have been rounding our numbers to the nearest 10, 100 and 1000. These 4 sums of money: £3.40; £3.99; £3.01; £3.56 are all £3 and some pence. Which sum is the biggest? And the smallest? Which sums are greater than £3.50? And smaller? £3 £3.50 £4 Where on our money line will we place each sum of money? Is £3.40 closer to £3 or £4? Which sums are closer to £4? Which sum is closest to £3? We use this method when we round a decimal to the nearest whole number. Rounding 3.01 and 3.40 to the nearest whole number the answer is 3; for 3.56 and 3.99 the answer is 4. Mental Work: Estimate positions of the tenths along an interval Round in context decimals to nearest whole number Round pairs of whole numbers and + & - results Extension Work: Round time & measures to the nearest whole unit 13 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Spring Term (Second half term) Week 1 Number Main Teaching: Notes/examples How do we use our column Practise using mental methods and method to calculate 7,2624,538? What do we do first? formal written Decide how we are going to column methods to partition. Start: add and subtract 7,262=7000+200+60+2 and pairs of 2- and 3check what we can or digit numbers cannot subtract. We cannot Partition 4-digit subtract 8 from 2; we can numbers in various subtract 3 from 6, but not 5 ways from 2. We partition 7,262 Extend the formal as 6000+1200+50+12 and written column write: 612 512 in the top line method to add and Th H T U Th H T U subtract 4-digit 7 2 62 6 12 512 numbers 4 5 38 4 5 38 Use inverse 2 7 24 operations to check Use the column method to answers work out 6,058+1,846. As Solve problems that before, we add the digits in involve the the 1s, 10s, 100s and now calculation of nonthe 1000s. When the unit fractions of additions are 10 or more we quantities by scaling write 10 as a 1 below the up or multiplying the line in the next column. unit fraction value Th H T U Represent tenths 6 0 5 8 + and hundredths as 1 8 4 6 7 9 0 4 decimals/fractions 1 1 Solve missing digit Check your answers using number problems the inverse operation. that involve +, - of What digits are hidden: whole numbers 2█3+█45=70█;103-█5=6█ Mental Work: Recall the 2 to 10 times tables and division facts State the value of digits in up to 6-digit numbers Estimate answers to + & - calculations by rounding Extension Work: Use alternative strategies to + & - whole numbers Week 2 Measurement/Geometry Main Teaching: Notes/examples Understand that area is measured in square cm or square m and perimeter is a length measured in cm or m Walk round and measure perimeters of The grid is made up of 1cm rectilinear figures in squares. What units are we cm or m using to measure the area? Find perimeters of What is the area of each rectilinear shapes shape? All are 10 square drawn on cm square centimetres. We want to grids give the answer work out how far it is in cm around each shape. This is Find areas of called the perimeter of the rectilinear shapes shape. Do you think drawn on cm square shapes with equal area grids by counting the have equal perimeters? squares inside the Start with the green shape. shape and give the Mark a blob on a corner to answer in square cm On square grids, draw remind you where you start rectilinear shapes with the count. What is its perimeter? It’s 12cm as given area and find perimeter is a length their perimeters around the shape. Are the Recognise that any change in position of a perimeters of the shapes the same length? Make shape does not alter your own shapes on the its perimeter or area grid and work out areas Compare and order and perimeters. Find the grid shapes by the areas of shapes with areas size of their areas or 12 square cm... their perimeters Mental Work: Recall the 2 to 10 times tables and division facts Identify & compare properties of 2-D or 3-D shapes Calculate perimeters of simple rectilinear shapes Extension Work: Explore size of perimeters of shapes with same area Week 3 Statistics/Geometry Main Teaching: Notes/examples We collect data by counting Interpret and objects or the times an event present discrete happens. This counting data is data in tables and called discrete data. A survey bar charts asked people to say which Read scales and shape they liked most: select sensible Shape People interval sizes for Triangle //// //// //// //// //// // scales on bar charts Square //// //// //// //// //// /// Rectangle //// //// //// / Associate discrete Parallelogram //// //// // data with counts of Rhombus //// /// occurrences and Trapezium //// / Pentagon //// //// //// items in categories Hexagon //// //// //// //// //// Read values from What graph/chart can we use to tables and bar display this data? Draw a bar charts to answer chart. What scale should we questions relating to use? Should we use 2s? Which sums, differences shape was least/most popular? and comparisons How many more liked squares Draw, make and than rhombuses? How many name acute and people were surveyed? What obtuse angles; type of triangles could have order angles up to 2 been drawn? Draw all these right angles shapes accurately include the Design symmetrical different triangles. Take your patterns on a grid drawings home. Ask everyone using practical which shapes they like/dislike. resources such as Bring your results back to use counters, blocks in class. On the coordinate grid and mirrors the vertical line is a line of Remove or add symmetry. If I put a counter items to a pattern to here, where must this counter retain or secure its go so we have symmetry? symmetry Mental Work: Calculate sums & differences from tables & charts Calculate fractions of measure, whole number answer Make & identify combinations of ½ , ¼ right angles Extension Work: Plan and carry out a survey; present findings to class 14 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Spring Term (Second half term) Week 4 Number Main Teaching: Notes/examples Understand and use Count up in 7s and 70s. Circle all the multiples of 7 on the 100 the terms multiple, square. Are 28, 42, 77...circled? Is divisible, factor and there a pattern? What was the remainder largest multiple? 98. To check 98 List multiples of single-digit numbers is a multiple of 7, partition 98 into multiples of 7: 98=70+28. We can up to 100; identify patterns and extend then divide each number by 7 and add: 98÷7 = 70÷7+28÷7 multiples beyond = 10 + 4 = 14 100 and check It means 98÷7=14 and 14x7=98 Generate division Is 107 a multiple of 7? Partition facts from multiples 107 into 70 and 37: 107=70+37. of a given number What multiple of 7 is closest to 37? Recognise that 5x7=35. 37=35 + 2 so 107 = 70 + division can lead to 35 + 2. We divide by 7: remainders 107÷7=10+5, but we cannot divide Apply the 2 by 7. It’s the remainder. We write distributive law for division over + and - 107÷7=15 r 2. In our division table we write 115÷7 as 7 into 115. Our Partition 2- and 3method is partition 115 into 70s digit numbers into multiples of a divisor and other multiples of 7. Then divide, writing the answers on the with priority to 10x top line. the divisor; use in a division table to divide 3-digit numbers by 1-digit numbers Solve problems that involve division and multiplication by 1digit in context 115÷7 7 7 7 115÷7=16 r 3 10 115 70 70 + 6 r + + 45 42 + 152÷6 6 6 6 6 10 152 60 60 60 3 3 152÷6=25 r 2 + 10 + 5 r 2 + + + 92 60 60 + + 32 30 + 2 Mental Work: Recall the 2 to 10 times tables and division facts Carry out simple division calculations with remainders Give highest multiple of 1-digit number < given number Extension Work: For 1-digit divisor list numbers<100 with same remainder Week 5 Number Main Teaching: Use commutative and associative laws for multiplication to rearrange and work out multiplication calculations with up to 3 numbers Apply the distributive law for multiplication over + and –; multiply 1-digit numbers mentally with jottings, by 19, 29...; 21, 31... by multiplying by 20, 30...and adjusting Use multiplication tables to generate tables for multiples of 10 and 100 Multiply 2- and 3digit numbers by a 1digit number using a grid method multiplication; convert the grid method to a formal column method of long multiplication Solve missing digit number problems that involve x, ÷ Notes/examples What is 4x7x5? If we rearrange it, what is 4x5x7? 20x7=140. And 9x6x5..? Explain how we work out 76x4 and 376x4 using a grid. What is the first step? 76x4 76x4 376x4 354x4 70x4 6x4 = 280 24 304 300x4 70x4 6x4 = 1200 280 24 1504 1 We don’t need to write the middle column each time. TU 76 0x 4 24 280 304 1 HTU 376 x 4 24 280 1200 1504 1 We use the place value of each digit as we multiply by 4. We work along from the 1s digit to the 10s and then 100s. 6 is a unit digit; 6x4 is 24 which we write down. 7 is 70 so will have 0 in the units; 7x4 is 28 so we write 280. The 3 is 300 and has 2 0s; 3x4 is 12 so we write 1200. Now we can add up. Mental Work: Recall the 2 to 10 times tables and division facts Multiply together 3 whole numbers after reordering Generate x & ÷ number sentences for 10s & 100s Extension Work: Use distributive law to x 99, 199..; 201, 301... by 1s Week 6 Measurement/Geometry/Statistics Main Teaching: Notes/examples Practise using the written methods to multiply and divide by a 1-digit number and use to solve problems Find perimeters of This centimetre grid has green rectilinear shapes rectangles. What size are the drawn on cm rectangles in cm, smallest to square grids, give biggest? Explain how this answers in cm sequence of rectangles grows. Find areas of What’s the area of each rectilinear shapes rectangle? What are the units drawn on cm for the area? Centimetre square grids by squares. What’s the perimeter counting the of the rectangles? What units squares inside the do we use for the perimeter? shape, and give Cm. Make a table to collect the answer in the areas and perimeters. square cm Explain how these grow and Describe and build use this to predict the size, the sequences of area and the perimeter of the rectangular next 5 rectangles? Explain shapes; tabulate what you did. Now check your their size, area and predictions. Start with a 3 by 1 perimeters; use to rectangle and make a predict next values sequence of rectangles. Find Describe rules to their areas, perimeters and find the areas and predict. Now make sequences perimeters of from a 4 by 1 rectangle. Find rectangles in a rules for working out areas sequence and perimeters of rectangles. Mental Work: Identify & compare properties of 2-D or 3-D shapes Calculate perimeter & area of any n by 1 rectangle Calculate fractions of lengths, whole number answer Extension Work: Explore perimeters/areas of L-shapes on cm grids 15 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Summer Term (First half term) Week 1 Number Main Teaching: Notes/examples Count up from 0 and Count in 10s, 1s and 2s. Fill in the first 3 columns of the table. back in multiples of 10s 1s 2s 11s 12s 2 to 10 10 1 2 11 12 Construct, recite and 20 2 4 recall the 11 and 12 30 3 6 times tables : : : 100 10 20 Identify, describe 110 11 22 and apply patterns in 120 12 24 the 11 and 12 times Which 2 columns can we use tables to support to work out the 11s? 10s and mental division; use 1s. And for the 12s column? multiplication facts to 10s and 2s. Fill them in. What identify remainders pattern can you see in the 11s Work out the factor column? Does this make the pairs for numbers to 11s easy to remember? Recite 100 that are in the the 10, 11, 12 times tables. multiplication tables Hide the table. Recite these Use the distributive times tables again. Look at the and associative laws 1s digits in the 12 times to rewrite arithmetic tables. What do you notice? expressions and to Why do they have the same carry out mental pattern as those in the 2 times calculations table? And why are the 11s involving 1- and 2digits the same as in the 1s? digit numbers Is 88 divisible by 11? What is Practise using the remainder when you divide mental and written 89 by 11? And 92..? Is 12 a methods to multiply factor of 89? No. Multiples of and divide whole 12 cannot end in 9. What is numbers by a 1-digit the remainder when you divide number and use to 89 by 12...? And 109÷12..? solve problems Week 2 Number Main Teaching: Practise using mental methods and formal written column methods to add and subtract pairs of numbers with up to 4 digits Use diagrams to identify fractions of a whole and write fractions in symbols and words Recognise and generate sets of equivalent fractions Add and subtract fractions with the same denominator Generate fraction sentences for fractions with equal denominators, and complements to 1 Practise calculating non-unit fractions of quantities by scaling up or multiplying the unit fraction value Solve problems that involve applying fractions in context Mental Work: Recall and use 12x12 multiplication & division facts Multiply and divide by 10 and multiples of 10 Identify remainders for 2-digit numbers ÷ by 3,4,5 Extension Work: Explore patterns in units digit in other times tables Mental Work: Recall and use 12x12 multiplication & division facts Multiply and divide by multiples of 10 and 100 Count in thirds, quarters, fifths, tenths, hundredths Extension Work: Make 0 to1 rulers to record equivalent fractions Notes/examples How many small rectangles are there in the big rectangle? What fraction of the rectangle is: blue; yellow; red; green? We can write this in words. Blue Yellow Red Green Half of the shape Quarter of the shape Eighth of the shape Sixteenth of the shape How many sixteenths make up the red, yellow and blue rectangles? How many eighths make up the yellow and blue rectangles? How many quarters make up the blue rectangles? This means 1 2 4 8 Blue = = = 2 Yellow 4 1 4 = 8 2 8 1 = 16 4 16 2 = 8 16 These are equivalent fractions They represent the same part of the whole rectangle. Can you see a pattern? How have numerator and denominators been changed in each row? Use a rectangle with 9 rows and 6 columns to generate equivalent thirds, sixths, ninths Red Week 3 Geometry Main Teaching: Construct triangles using practical resources; calculate the perimeters of triangles by adding lengths of sides Name and compare properties of 2-D shapes; use their properties including perimeters, the size of angles, to sort and classify shapes Name common 3-D shapes; identify the number of faces, edges and vertices and the shape of the faces Build symmetrical shapes on a grid using practical resources such as strips of card, squares, triangles and mirrors Recognise that a line of symmetry cuts a shape in half; identify the equal sides and angles in symmetry shapes Notes/examples Length 4cm 5cm 7cm Strips of card Use 3 of the strips of card to make a triangle. What is the perimeter of a triangle? It’s the distance around the triangle so add together the lengths of the 3 strips. With 3 strips make the triangle with the smallest perimeter. And the largest perimeter. What type of triangles are these? The smallest has perimeter of 12cm and the biggest is 21cm. Use the strips to make all in-between triangles with perimeters: 13cm, 14cm up to 20cm. Which are symmetric? Name the triangles and their angles. Explain why you could not make all of the triangles with the strips? A cube has how many faces, edges and vertices? A cube has 1 vertex sliced off to make a new face. What shape is the new face? How many faces, edges, vertices has our new shape? Now cut off another vertex...Describe what changes/stays the same Mental Work: Identify possible triangles with given perimeter Identify & compare properties of 2-D or 3-D shapes Give coordinates of points in symmetric grid pattern Extension Work: Cut vertex off prisms/pyramids & explore new shape 16 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Summer Term (First half term) Week 4 Numbers/Measurement Main Teaching: Notes/examples 26 Read and write in 12 14 words and numerals 7 5 9 4 7 3 whole numbers The 3-row Sum Triangle is beyond 1000 and made of sums of the pairs of decimal numbers numbers in the row below: with up to 2 places 7+5=12 and 5+9=14; Round whole 12+14=26. Fill in the blue numbers to the Sum Triangle. What is the nearest 10, 100 or top number? Try some base 1000, and decimals numbers of your own. Can with up to 2 decimal you make the top number places to the nearest 35? Does only 1 set of 3 whole number numbers give you 35? Can Practise using you use 3 odd base numbers mental methods and to make 35? Or 3 even base formal written column numbers? Explore the top methods to add and number when the base subtract pairs of numbers are equal. Can you numbers with up to 4 see patterns in the 3-row digits Sum Triangle numbers? Can Read and write the you predict the top number Roman numerals given 3 base numbers? Now using: l, V, X, L and use a 4-row Sum Triangle C; use to construct and explore patterns in the Sum Triangles triangle’s numbers. Use only Solve problems that odd or even base numbers. involve identifying Can you predict top numbers describing and with 4, 3 or 2 equal base applying patterns; numbers, 2 pairs equal, or 4 conjecture and test; different base numbers? and follow a line of Make and test conjectures enquiry and follow a line of enquiry. Mental Work: State the value of the digits in up to 6-digit numbers Add and subtract sequences of 1-digit numbers Identify remainders for 2-digit numbers ÷ by 4,5,6 Extension Work: Explore number patterns in Multiplication Triangles Week 5 Number Main Teaching: Practise using mental methods and formal written column methods to add and subtract pairs of 4-digit numbers Practise using mental methods and formal written methods to multiply and divide whole numbers by a 1digit number Understand and use the language of simple ratio or scaling e.g. 5 times as wide; a third as full; twice as heavy Generate tables of numbers that satisfy and show the multiplicative relationship between the numbers Represent in pictures problems which involve a multiplicative relationship between two quantities Solve problems that involve scaling up or down by multiplying and dividing Notes/examples Over time, Anna buys 4 times the number of apples to pears. She makes a table to show the numbers: Pears 1 2 : Apples 4 8 : If she buys 12 pears, how many apples did she buy? Put numbers in our box picture. Why do we x by 4? Apples Pears She buys 36 apples; how many pears? Draw a box picture. Why do we ÷ by 4? Anna buys 30 apples and 6 pears, how many times more apples than pears did she eat? We have to work out how many boxes. Apples Pears ... We divide apples by pears. These problems all involve scaling up or down, x or ÷. We can put this in a table: Given Smaller Bigger Smaller and Bigger To find Bigger Smaller How many times more We Multiply Divide Divide bigger by smaller Mental Work: Recall and use 12x12 multiplication & division facts Identify remainders for 2-digit numbers ÷ by 5,6,7 Identify rule for and continue number sequences Extension Work: Explore examples of multiplicative relationships Week 6 Statistics/Measurement Main Teaching: Associate continuous data with taking measurements Interpret discrete data presented in pictograms and bar charts and continuous data presented in time graphs Interpret the vertical scale on a bar chart as a frequency count and solve problems involving sums and differences Interpret the vertical scale on a time graph showing a measure and the horizontal axis showing time; use to estimate and measure changes over time Generate a time graph to present change in a measure over a given period of time Tell the story of data shown as a time graph Estimate, compare and calculate using different measures including time, money Notes/examples At 8:30am Sam sits on a park bench so his dog can run around for 20 minutes. The graph shows how far the dog is away from Sam. The vertical axis is the distance the dog is from the bench; the scale is in 5m intervals. Time in 2 minute intervals is on the horizontal axis. When was the dog farthest away from Sam? When did the dog first start running back? How far did the dog run in the first 2 minutes? And in the last 4 minutes? Estimate how far the dog ran altogether? When did Sam whistle for his dog to return? Measurement data like this is called continuous data. Make up your dog-walking graph on these axes. Tell your story of one man and his dog. Mental Work: Compare and order measures including money in £.p Read and convert times on 12- & 24-hours clocks Interpret simple pictograms, bar charts & time graphs Extension Work: Use ICT packages to interpret similar time graphs 17 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Summer Term (Second half term) Week 1 Number Main Teaching: Notes/examples Recognise and write decimal equivalents to: ¼; ½ ; ¾ In this fraction wall there are 5 Recognise and use diagrams to generate whole strips. Into what fraction has each strip been divided? sets of equivalent Use the equivalent lengths of fractions sections of the strips to identify Add and subtract equivalent fractions. ½ = ...; fractions with the ⅓=...¼=... same denominator Jayla says: ‘If I multiply any Generate fraction fraction’s numerator and sentences for denominator by 2 the two fractions with equal fractions will be equivalent.’ Is denominators, and she right? Test this with identify complements diagrams using the unit to 1 fractions: ⅓; ⅕; ⅙.. And the non Practise calculating unit fractions: ⅔; ⅘... non-unit fractions of ⅟10 ⅟10 ... quantities by scaling 0.1 ... 0.1 up or multiplying the 50 50 ... 100 100 unit fraction value The strips are in 10 equal parts. Convert and write as decimals any number The yellow strip is marked in tenths as fractions; blue as of tenths or decimals, green as hundredths. hundredths and vice What is 0.4 as tenths, as versa hundredths? What is ½ in Order decimals with tenths, hundredths, as a up to 2 decimal 50 decimal? If ½ is what is ¼ in places 100 Solve fraction and hundredths? How do we write ¼ decimal measure and as a decimal? And ¾? money problems Mental Work: Recall and use 12x12 multiplication & division facts Count in thirds, quarters, fifths, tenths & hundredths Add and subtract tenths or hundredths to decimals Extension Work: Write 5ths, 20ths & 25ths as hundredths and decimals Week 2 Number Main Teaching: Notes/examples Routine problem Practise using -How many 30cm lengths of ribbon mental methods can be cut from a ribbon of 4m? and formal written How much ribbon remains? -A blue Jug holds 350ml, 85ml column methods to more than the red jug. How much add and subtract does the red jug hold? pairs of numbers Non-routine problem with up to 4 digits - Mr Sims buys a cup of tea and a cake and spent £1.60. The cake Practise using was 3 times the cost of the tea. mental methods How much was the cake? and formal written -Al has 17 stickers; Bo has 10 and methods to multiply Ci has 6. How many stickers does Al give Bo and Ci so they have and divide whole equal numbers of stickers? numbers by a 1Correspondence problem digit number - A menu offers me choices for my Solve different meal: fish or chicken; rice, chips or mashed potatoes; peas, beans, types of word carrots or spinach. How many problems; decide different meals can I have? when and how to -Twelve money boxes contain draw and annotate only10p, 20p and 50p coins. They each contain: 7 10p, 6 20p and 5 box pictures to 50p coins. In total, how much interpret and solve money is in all twelve boxes? the problem Logic problem Solve logic -My 3-digit number is less than 300. It’s odd and its digits sum to problems that 13. What numbers could it be? It’s involve using the also a multiple of 7 what is it? given information to -Place the digits 2, 2, 3, 3, 4, 4 in discard and refine the TU sum to make a total of 90? Use the digits 1, 1, 1, 3, 3, 3, 4, 4, possible solutions; 600? use place value and 4 in theT HTUUsum to make H T U recall of number + + facts to test and isolate cases Mental Work: Recall & use 12x12 multiplication & division facts Identify remainders for 2-digit numbers ÷ by 6,7,8 Identify missing numbers from given information Extension Work: Explore if other number sets make TU, HTU totals Week 3 Geometry Main Teaching: Notes/examples Label a 2-D grid with a vertical and horizontal axis with unit intervals Use coordinates in the first quadrant to identify the position of points on a 2-D grid Plot points for given coordinates and There are 10 coloured complete and identify squares on my grid. I move shapes with these from the light red square to points as corners the dark red square. Describe movement Describe my move: 6 right, about a grid by 8 down. I move between 2 giving the change in squares by going 2 left, 4 position in units left down. Which 2 squares did or right, up or down I move between? Blue to Describe translations grey. Make a journey from given the movements square to square and write between points down the moves you make. Give it to a partner who Identify lines of has to give you, in order, symmetry of shapes presented in different the colours of the squares you visited. What are the orientations coordinates of the points at Make symmetrical the bottom left-hand shapes on a corners of the squares? coordinate grid by What are my translations translating squares across and around a from (3,2) to (9,5) to (2,8)? Which squares did I visit? line of symmetry Mental Work: Identify shapes from descriptions or partial views Identify coordinates of points along straight lines Identify coordinates of corners of 2-D shapes Extension Work: Explore ICT coordinate plotting tools & translations 18 ©Nigel Bufton MATHSEDUCATIONAL LTD Securing Progress in Mathematics: Scheme of Work for Year 4 Summer Term (Second half term) Week 4 Number Main Teaching: Notes/examples Suki says: ‘If I put a zero at Recognise and write decimal equivalents to: the end of any number it always gets bigger.’ Is she ¼; ½ ; ¾ Compare fractions and right? Test this with whole and decimal numbers. decimals to ¼; ½ ; ¾; use this method to sort What happens to 12 and 1.2 when you put a zero on fractions and position the end of each number? them on the 0 to 1 Can you make a statement number line that is more accurate than Express decimals as Suki’s? tenths or hundredths Gary says: “0.25 is bigger and vice versa than 0.8 as 25 is bigger Describe the effect of than 8.” Why is he wrong? dividing 1- and 2-digit What picture could you use whole numbers by 10 and 100 and record the to explain to Garry that 0.8 is the bigger? What are the results as decimals Order decimals with up place values of the digits 2, 5 and the 8? to 2 places and apply 2 to measure and money Ali says: “ 3 is bigger than 5 2 1 5 contexts as is over and 12 3 2 12 Make a conjecture: “I think that...”, test it and isn’t” Draw a picture to help us see if Ali is right or describe and explain not? List fractions you think observations and thinking with examples are bigger than a half or smaller than a half. Explain and pictures how you decided. What Test whether a fractions do you know that statement is true, are bigger/smaller than a sometimes true, or quarter? Which is smaller false; give reasons for three quarters or 0.8? decisions Mental Work: Count in thirds, quarters, fifths, tenths & hundredths Add & subtract fractions, decimals with 1 or 2 places Identify remainders for 2-digit numbers ÷ by 7,8,9 Extension Work: Follow lines of enquiry by asking: “What if...” Week 5 Statistics/Measurement Main Teaching: Notes/examples Depth cm Tallies Stream Recognise that for >00; =<20 //// //// measurement data Low >20; =<40 //// / you use scales to >40; =<60 // Full compare and is >60; =<80 //// continuous; count >80; =<100 //// High data is in whole The table shows the depth in numbers and is cm of water in a stream. The discrete depth was measured every fortnight over a year. The Interpret discrete water is described as low, full, data presented in or high. A high stream can tables, pictograms flood the land. Write each row and bar charts, and in a sentence e.g. The stream continuous data was full twice when the water presented in tables was 40cm to 60cm deep. and time graphs Write a story describing the Answer and pose year. Explain why you think questions from data rainfall caused the change in presented in tables, the stream’s depth. When did charts and graphs it flood? Interpret and label the scales on a time graph and use to identify and measure This graph shows the cost of changes over time a heating an office over 12 Tell the time-based from data presented hours. It was switched on at 06.30. The horizontal axis is in a table or as a time. The vertical axis is cost. time graph Each interval is worth £3.50. Estimate, compare Draw the graph. When was it and calculate using switched off? When did the different measures, cost exceed £10..? time and money Mental Work: Read & interpret scales showing time & measures Interpret simple pictograms, bar charts & time graphs Add & subtract fractions, decimals with 1 or 2 places Extension Work: Tell a time-based story; draw its time graph Week 6 Number/Measurement Main Teaching: Read, write and convert time between analogue and digital 12- and 24 hour clocks and convert hours to minutes and minutes to seconds Read and use a calendar to calculate intervals and to convert years to months, months to weeks and weeks to days Explore relationships between the numbers set out in a calendar month; conjecture and test on other months Generate sequences of numbers that involve one or two operations; describe the term-toterm rule in words e.g. double the number and add 1 to get the next term, use the rule to predict future values Solve missing number problems that involve one or two operations using box pictures Notes/examples It is my birthday in 8 weeks and 2 days from today. How many days is that? Use the calendar to find the first Sunday in May and the last Saturday in June. Count the weeks does this include? How many schools days does this cover - do not count the half term week? What do we multiply by to convert full weeks to days and school weeks to days? Our dog has been with us since November last year. How many months has he been with us? How many weeks have we had him? On the calendar find January the 12th. What day is that? Find these 4 dates in January. They form a grid of 4 numbers: 12 19 13 20 Work out the diagonal sums 12+20 and 13+19. What do you notice? Now choose other sets of 4 calendar grid numbers to explore diagonal sums. Mental Work: Recall & use 12x12 multiplication & division facts Identify remainders for 2-digit numbers ÷ by 3 to 9 Solve missing number or missing digit problems Extension Work: Explore diagonal differences and other relationships 19 ©Nigel Bufton MATHSEDUCATIONAL LTD