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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 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.

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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.



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 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 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 ... six-digit 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

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; title, label; number fewer, least number, total number, maximum number; scale, unit size, number of units represented, units per interval, units per picture

Reasoning andsolving

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



End-of-Year Learning Objectives for Year 4 Record of coverageA. Number – counting and place valueA1. Can count in single-digit multiples and multiples of 25, 50, 100, 1000; count backwards to include negative numbersA2. Can read, write and order whole numbers with four or more digits; read numbers using Roman numerals: I, V, X, L, CA3. 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 1000B2. Can add and subtract mentally quantities of money in £s and pence and measurements that involve different unitsB3. Can recall the multiplication tables to 12 x 12, derive related multiplication and division facts and identify factor pairsB4. Can use the formal written column methods to add and subtract numbers with up to four digitsB5. 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 denominatorsC2. 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 decimalsC4. Can interpret answers to division of 1-digit and 2-digit whole numbers by 10 or 100 as tenths and hundredthsC5. Can recognise that as the numerator of a fraction with fixed denominator increases the fraction gets bigger

D. MeasurementD1. Can measure accurately using metric units for length, weight, capacity, and convert between different common unitsD2. Can measure and calculate the perimeter of rectangles and composite rectilinear shapes using metric unitsD3. 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 directionE1. Can draw lines and 2-D shapes accurately; use properties to classify and name triangles and quadrilaterals by typeE3. 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 polygonsE7. 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 dataF1. 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, communicatingG1. Can solve 2-step problems involving money, measures, time, fractions; use multiplication/division to scale up and downG2. Can provide reasons for choosing operations to solve problems and for using particular properties to classify shapesG3. Can use the language of fractions, decimals and negative numbers when counting, comparing and sorting numbers

Assessment Recording Sheet



Mathematics in Year 4 Autumn term Spring term Summer termName:

Class:Key: 4.1 – Working towards expectations 4.2 – Meeting expectations 4.3 – Exceeding expectations

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 Exceeding Year 4 expectations

Teacher: Date of final assessment:

Week-by-week Planner Year 4Autumn Term (First half term)



Week 1 Week 2 Week 3Number Number Geometry/MeasurementMain Teaching: Read and write whole

numbers, including 1000s, in words and numerals

Recognise and apply the underlying triplet structure of numbers: read the HTUs of 1000s first and then the HTUs

Indentify and use zeros as place holders

Compare and order numbers beyond 1000; start with the 1000s then HTUs

Recognise and identify the place value of the digits in up to 6-digit numbers

Add and subtract mentally multiples of 10, 100, 1000

Identify complements to 100 and 1000

Solve problems that involve the mental addition or subtraction of whole numbers and inverse relationships

Notes/examplesRead the numbers: 2, 23, 234, 2 345. Which is the biggest number? As the number of digits increases the values of the digits change. Read the words and numbers in the table:

1 One10 Ten

100 One hundred1 000 One thousand

10 000 Ten thousand

100 000 One hundred thousand

Zeros are important as they fix the value of the 1. Read the numbers with 6 replacing 1. A comma can replace the space: read 25,000. How many 1000s do we have? What are the values of the 2 and the 5? Read 626,468... Read the number as HTU of 1000s and then the HTUs. What is the value of each 6?What is: 3+8; 30+80; 300+800; 3,000+8,000..?What is 12-5; 120-50; 1200-500; 12,000-5000..?And 400+700-500-300..?And 24,000-6,000-6,000..?

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

Notes/examplesRead the numbers out as I point to the words. Then write down the numbers in words and numerals.

ZeroOne Eleven TenTwo Twelve Twenty

: : :Eight Eighteen EightyNine Nineteen Ninety

HundredThousand

Use the written column method to work out 512-467. 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.

H T U H T U

- 41012

+ 6 5 8

4 6 7 1 7 6 4 5 8 3 4

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.

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/examplesCut strips of card of lengths shown in the table. Your group needs 3 strips of each length.

Length Strips of card4cm6cm8cm10cm12cm14cm

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: 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

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

Mental Work: Recognise symmetry in shapes in the environment Name triangles & quadrilaterals from information Visualise shapes made from 2 overlapping shapes

Extension Work: Solve missing number problems using + & - facts

Extension Work: Apply multiplication facts to multiples of 10, 100

Extension Work: Using strips make & explore pentagons/hexagons

Autumn Term (First half term)Week 4 Week 5 Week 6



Number/Measurement Number Geometry/MeasurementMain Teaching: Count up from 0 and

back in multiples of 2, 3, 4, 5 and 6

Count up from 0 and back in 7s; construct and recite the 7 times tables

Use the 7x table to convert weeks to days and vice versa

Know that a multiplication fact can be written in 2 ways (multiplication is commutative) and each corresponds to a division fact (its inverse)

Write the related multiplication and division facts given 1 multiplication fact

Apply the associate and commutative laws to multiply 3 numbers mentally e.g. 4x7x5=4x5x7 =20x7=140

Solve problems that involve missing numbers in x, ÷ number sentences

Notes/examplesUse this array to count in 3s and in 4s.

3s 4so o o o o o oo o o o o o o: : : : : : :o o o o o o o

How can counting in 3s and 4s help us to count in 7s? Add the 3s and 4s to get 7s

3s 4s 7s3 4 76 8: : :

30 4033 4436 48

Fill in our table. Count in 3s, 4s and 7s. Recite the 3, 4, 7 times tables. What other counts could we use? 2s and 5s; 1s and 6s.

2s 5s 7s2 5 74 10: : :

20 5022 5524 60

Which table was easier to use? Why? Hide the tables; recite the 3, 4, 7 times tables and now the 2, 5, 7 times tables. What is 8x7? 8x2=16 and 8x5=40 so it’s 56. Try 6x7; 4x7; 7x7...

Main Teaching: Practise using a

formal written column method to add and subtract pairs of 2-digit and 3-digit numbers

Recognise, when dividing 1000s, 100s, 10s and 1s by 10, how the number gets smaller

Understand that tenths arise when dividing 1s by 10 and hundredths when dividing 1s by 100 or by 10 and 10

Understand that the decimal point separates whole and part numbers

Read, write, order decimals with 1 or 2 decimal places

Count up and down in tenths and hundredths, as fractions or decimals

Solve practical problems involving tenths and hundredths

Notes/examplesRead aloud the first 4 rows in this table. Explain what is

happening.Each time we ÷ by 10: the first digit 1 moves one place right; and we lose a 0. The numbers get smaller. What is the answer to 1÷10? As the numbers get smaller, it must be less than 1. The answer is one tenth. We write it as 0.1. This is a decimal and the . is called the decimal point. The first number after the decimal point is a tenth. For 1÷10 we write 0.1 which is 1 tenth. 2÷10=0.2 or 2 tenths Carry this on to 9÷10. What is 10÷10? It is 10 tenths and that is one whole or 1. What

1 ÷10 = 0.10.1 ÷10 = 0.01

if we divide 0.1 by 10? It will be 0.01 or one hundredth. Can you predict how we write 1÷100? Say: “1÷100 is 0.01 or one hundredth.” And say: 2÷100=0.02=2 hundredths...

Main Teaching: Read scales with

integer-valued intervals

Recognise that two perpendicular scales can be used to identify movement in two directions and a position on 2-D grids

Describe positions as coordinates in the 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 first quadrant and give the coordinates of the corners

Use left, right, up, down to describe a movement between positions on grids

Draw rectangles on a grid and count the squares inside it

Notes/examples

My horizontal stick starts at 0. The intervals are in 7s. What is this number..? And the number at this end? I turn my stick vertically. 0 is at the bottom and intervals are size 6. What are these values..? I have a horizontal and a vertical stick with scales 0 to 10. They are on the sides of a grid like this.

A star is on the grid. The star is at 0 on both sticks. This point is called the origin. I move the star along my horizontal stick and up my vertical stick. It moves to here. What were my two moves along the 2 sticks? Where is the star on the grid? We write its position in brackets: (9,3), (along,up). What is this position..?

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

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

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


10 000 ÷10 = 1000.11000 ÷10 = 100.1100 ÷10 = 10.1

10 ÷10 = 1.11 ÷10 = ?.1


Extension Work: Make 6x,7x,8x tables by subtracting from 10x table

Extension Work: Count in non-unit fractional or decimal steps

Extension Work: Describe & simplify composite movements on grids

Autumn Term (Second half term)Week 1 Week 2 Week 3Number/Measurement Number/Measurement NumberMain Teaching: Use multiplication

tables to generate the tables for multiples of 10 and 100

Derive division facts from multiplication facts involving multiples of 10 and 100

Know the effect of multiplying any number by 0 or 1 and dividing by 1

Multiply 2-digit and 3-digit numbers by a 1-digit number using a grid method of long multiplication

Recognise the effect on a grid multiplication of changes to 1 of the digits in the 3-digit number

Solve problems that involve x and ÷ multiples of 10 and 100 in context such as large sums of money in £s

Notes/examplesRecite the 4 times table. What is 10x4? What is 20 x4, 30x4, 40x4...? Remember 30 is 3 10s so 30x4 is 3 10sx4 or 12 10s and 12 10s are 120. Knowing our 4 times tables makes this easy. Recite the 3 times table. Use it to work out 10x3, 20x3, 30x3... What is 100x3, 200x3, 300x3...?Can you remember how to work out 57x3 using a grid? We partition 57 into 10s and 1s and multiply 50 and 7 by 3 and add:

57x3 50x3 150

7x3 2157x

3 = 171

How can we use the table to work out 257x3? We partition 257 into 100s, 10s and 1s, multiply each part

by 3 and add the answers.What is the same/different about the 57x3 and 257x3 grids? What is 287x3...how does the table change?

Main Teaching: Read and write

Roman numerals to 100 using: l, V, X, L and C

Recognise the underlying structure involves working with and around the numbers 1, 5, 10, 50 and 100

Understand that there is no symbol to represent zero in this system, while our number system has 0and the position of the symbols do not signify their value, X is 10 no matter where it appears

Read time to the nearest minute on analogue clocks with Roman and Arabic numerals

Convert between 12-hour am, pm times and 24-hour times

Solve problems involving 24-hour time and calculation of time intervals

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

The l, V and X are 1, 5 and 10. The next symbols are L 50 and C 100. This is how we write the 10s to 100.

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

Can you see a pattern? Can you explain how Roman numerals work? The rules we used for 1 to 10 are similar to those for 10 to 100. We used 10, 50 and 100 rather than 1, 5 and 10. Convert 43 and 87... XLlll and LXXXVll... Write the 100 square 1 to 100 in Roman numerals. What patterns can you see in the columns? How do you know if a Roman number is a multiple of 5, or a multiple of 10? Use the 100 square to work out LXlV + Xll; LVl -XlX. What is V1xX, Xlll x lV; LXXX÷X, C÷XXV...?

Main Teaching: Count out, read and

record quantities of money using £.p notation; recognise that the . separates £ from p and links to decimal numbers

Compare and order quantities of money in £, p or mixed £.p units; convert units

Add and subtract sums of money; give change and scale up amounts of money by multiplying

Solve problems involving the addition and subtraction of sums of money

Represent problems using box pictures; annotate the boxes to solve the problem

Solve problems that involve calculation of parts or the whole, by identifying what is given information, what information is missing and what is to be found

Notes/examples Here are 4 problems:1. Paula has 3 50p coins. Ali holds

4 times as many, how much money has Ali?

2. Class 4 has 18 boys; twice as many as Class 1. How many boys in Class1?

3. Dad buys each of his 3 children a £1.50 ice cream. Altogether how much money does he spend?

4. £3.20 is shared out equally between 4 children. How much money in pence will each get?

Read each problem. What do we know? What we are we to find out? Draw pictures to help us to solve the problems. Lead pupils to these pictures:Problem 1

Paula 3Ali

Problem 2Class 4 18Class 1

Problem 3Children £1.50 £1.50 £1.50

DadProblem 4

Cubes £3.20=320pPupils

What numbers can we write in the boxes? In Ali’s 4 boxes we write 3s; so he has 12 50ps or £6. Write numbers in the other boxes. Can you solve the problems? How?


257x3 200x3 600

50x3 1507x3 21

257x3 = 771


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

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

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: Identify patterns in the digit sums of multiples of 3

Extension Work: Explore time zones and times in different countries

Extension Work: Solve mentally 1, 2-step +, - missing number problems

Autumn Term (Second half term)Week 4 Week 5 Week 6Number Geometry Number/MeasurementMain Teaching: Count up from 0

and back in multiples of 2, 3, 4, 5, 6 and 7

Count up and back in 9s; construct and recite the 9 times tables

Derive division facts from known multiplication facts

Practise using a grid method of multiplication to multiply 2-digit and 3-digit numbers by a 1-digit number

Read and write 10ths and 100ths as fractions and decimals

Divide 1- or 2-digit numbers by 10, by 10 and 10 again, and by 100; identify the values of the decimal digits

Solve money or measure problems that involve scaling quantities down by 10 and 100

Notes/examplesUse this array to count in 3s and in 6s. How can counting in 3s and 6s help us count in 9s? Add 3s and 6s to get 9s.

3s 6so o o o o o o o o

o o o o o o o o o

: : : : : : : : :

o o o o o o o o o

Fill in our table. Count in 3s, 6s and 9s. Recite the 3, 6, 9 times tables. Hide the table. Recite 3, 6, 9 times tables again.

3s 6s 9s3 6 96 12: : :

30 6033 6636 72

Describe the pattern in the 9 times table to 10x9. The 10s increase by 10, 0 up to 90. The 1s decrease by 1, 9 to 0 List the numbers 1 to 10. There are 9 gaps shown by ☺. The arrow points to 4. How many faces to the left and the right of the arrow? It means 4x9=36. Work out 8x9. 1 2 3 4 5 6 7 8 9 10 ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ 3 6

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

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?

Main Teaching: Convert

between 12-hour am, pm times and 24-hour times; calculate times at start or end of an interval

Estimate and compare the weigh, length and capacity of objects or containers against known quantities

Read partially numbered scales

Convert between common units of measure

Solve 1- and 2-step part/whole measure problems; draw and annotate box pictures and identify the required calculations

Notes/examplesHere are 4 problems. 1. Rik pours 450ml of water out of a

jug leaving him with 680ml. How much water was in the jug?

2. Together 2 bags weigh 1kg. One weighs 340g more than the other, what does each bag weigh?

3. Cans of juice hold 200ml and are in packs of 6. A box has 9 packs in it how much juice is in a box?

4. 5 shelves hold box files 8cm wide. Each shelf holds the same number of files. If there are 150 files, how wide is each shelf?

Read the problems. What information are we given? What do we have to work out? Draw pictures to help us. Lead pupils to these pictures: Problem 1

Jug fullJug after

Problem 2Bag 1Bag 2

Problem 3Can

PackBox .....

Problem 45 Shelves150 Files

What numbers can we write in the boxes? Which problems need more than 1 calculation? What must we work out first?



Explain the rule. Smile as you recite the 9 times tables!

What are the calculations?

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

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

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: Construct a decimal ruler with 10ths and 100ths

Extension Work: Make & explore pentagons/hexagons with parallel sides

Extension Work: Solve 1 & 2-step x, ÷ missing number problems

Spring Term (First half term)Week 1 Week 2 Week 3Measurement/Number/Statistics Number MeasurementMain Teaching: Practise using mental

methods and a formal written column method to add and subtract pairs of 2-digit and 3-digit numbers

Read, write and order decimals with 1 or 2 decimal places

Add and subtract mentally decimal numbers with 1 decimal place

Measure using metric units; recognise how the units used reflect scale and context

Know that measuring accurately requires interpreting the value and size of intervals and comparing

Read and interpret measurement data that involves decimal numbers set out in tables and charts

Solve problems using published information involving scaling

Notes/examplesThe daily intake of salt for Y4 children is up to 4g. Weigh out 4g. Does this look a lot? A 200g pack of tortilla chips has 2.2g of salt. If you ate half the pack how much salt would you eat? The table shows the salt content in some popular foods.

Food Salt1 Chicken nugget 0.1g

Cheeseburger 1.5gFried chicken 2.1g

Portion of chips 0.4g 1 Sausage 1.5g

2 Bacon rashers 1.9gSlice of white bread 0.5g

Coke 0.1gMilkshake 0.4g

Muffin 1.6gBaked beans 0.5g

Fruit & vegetables 0gOver a day I had 3 Muffins and 2 milkshakes, how much salt did I eat? Work out how much salt you’d eat with meals made up of this type of food. Look at food labels to make tables of how much fat, protein, fibre, salt and sugar is in food. Your intake should be no more than: fat 64g; protein 24g; fibre 15g; sugar

Main Teaching: Use multiplication

facts to recall division facts

Represent and calculate unit fractions of a quantity using equal sharing and division

Recognise that non-unit 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

Notes/examplesWhat’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

12 of

£24 = £24÷2

14 of

£24 = £24÷4

18 of

£24 = £24÷8

If we know one quarter find:24 of

£24 =

34 of

£24 =

44 of

£24 = Explain how you did this. Why

is: 24

of £24 equal to 12

of

£24? Why is 44 equal to £24?

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



sums and differences 85g. Plan meals with little salt or sugar; low fat content...

number answerNow work out:

28 ;

38 ;

48; 5

8; 6

8; 7

8; 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.

bottles and jars whose capacities we know.

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

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

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: Explore calories and protein content of foods

Extension Work: Work out all the thirds, sixths, ninths of quantities

Extension Work: Draw capacity scales on non-uniform bottles

Spring Term (First half term)Week 4 Week 5 Week 6Number/Measurement Number/Measurement/Geometry NumberMain Teaching: Practise using mental

methods and a formal written column method to add and subtract pairs of 2- and 3-digit numbers

Convert between 12-hour am, pm times and 24-hour times

Use the 6 times table to generate multiplication and division facts involving 60; convert hours to minutes and minutes to seconds

Add and subtract amounts of money using methods that involve partitioning

Notes/examplesHow much do I need to add to £3.65 to make it up to £4? What is £6 minus £5.65? Why do these questions have the same answer? We are making a sum of money up to whole £s. Ask different questions that give the same answer. Add and subtract money by partitioning:

£2.85

+ 40p

15p 25p£3.0

0 + 25pPartition 40p into 15p and 25p. Then add 15p to £2.85 to get £3.

£2.35 - 80p£1.35 100p

Main Teaching: Use strips divided into

equal parts to generate fraction sentences for fractions with the same denominator

Add and subtract fractions with the same denominator, with answers <1

Practise calculating non-unit fractions of quantities by scaling up or multiplying the unit fraction value

Understand that area is measured in squares; find simple areas by counting squares in units of

Notes/examplesMeasure out a square 1m by 1m. This is a square metre. We call the amount of space in a flat shape like our floor, its area. How many square metres will cover our carpet area?

The grid shows a garden. A square is 1m by 1m. What size is the garden in square metres? It has a fish pond, a flower bed and a grassy area. There are paths around the pond

Main Teaching: Identify the place

value of digits in whole numbers and decimals with 1 and 2 places

Identify the mid-point 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

Notes/examplesA 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?



and adjustments Identify the numbers

and values of coins and notes needed to make up given amounts of money

Solve 2-step problems involving the addition and subtraction of money and time, and the conversion between units

£1.35 + 20pPartition £2.35 into £1.35 and £1 or 100p. Then take 80p from 100p to get 20p. Add and subtract money by making up to whole £s and adjusting the pence:

£1.34 + £2.98£1.34 + £3.00 - 2p

£6.50 - £4.89£6.50 - £5.00 + 11p

How many 5p coins will make £2.85 up to £3.20? How do we solve this?

square metres or square centimetres

Find the area of rectangular shapes drawn on cm grids by counting the squares inside the shape

Plot corners of simple rectilinear shapes; draw the sides to complete the shape and find its area

and flower bed. The path uses 1m square slabs. What are the areas of the 2 paths? And the fish pond, the flower bed and grassy area? Building this garden cost £65 per square metre. How much was the pond..? On a grid design a garden. Include 1m wide paths. Give all the areas and the costs.

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

£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: 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

Mental Work: Complete fraction sentences and complements to 1 Estimate areas of everyday rectangular shapes Identify points and positions on a coordinate grid

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: Plan journey from timetable; use 12-hr am/pm time

Extension Work: Extend the design to include rectilinear shapes

Extension Work: Round time & measures to the nearest whole unit

Spring Term (Second half term)Week 1 Week 2 Week 3Number Measurement/Geometry Statistics/Geometry Main Teaching: Practise using

mental methods and formal written column methods to add and subtract pairs of 2- and 3-digit numbers

Partition 4-digit numbers in various ways

Extend the formal written column method to add and subtract 4-digit numbers

Use inverse operations to check answers

Notes/examplesHow do we use our column method to calculate 7,262- 4,538? What do we do first? Decide how we are going to partition. Start: 7,262=7000+200+60+2 and check what we can or cannot subtract. We cannot subtract 8 from 2; we can subtract 3 from 6, but not 5 from 2. We partition 7,262 as 6000+1200+50+12 and write: 612 512 in the top line

Th H T U Th H T U

- 7 2 6 2

- 6 12 512

4 5 3 8 4 5 3 8

2 7 2 4

Use the column method to

Main Teaching: 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 rectilinear figures in cm or m

Find perimeters of rectilinear shapes drawn on cm square grids give the answer in cm

Find areas of rectilinear shapes drawn on cm square grids by counting the

Notes/examples

The grid is made up of 1cm squares. What units are we using to measure the area? What is the area of each shape? All are 10 square centimetres. We want to work out how far it is around each shape. This is called the perimeter of the shape. Do you think shapes with equal area

Main Teaching: Interpret and

present discrete data in tables and bar charts

Read scales and select sensible interval sizes for scales on bar charts

Associate discrete data with counts of occurrences and items in categories

Read values from tables and bar charts to answer questions relating to sums, differences and comparisons

Notes/examplesWe collect data by counting objects or the times an event happens. This counting data is called discrete data. A survey asked people to say which shape they liked most:

Shape PeopleTriangle //// //// //// //// //// //Square //// //// //// //// //// ///Rectangle //// //// //// /Parallelogram //// //// //Rhombus //// ///Trapezium //// /Pentagon //// //// ////Hexagon //// //// //// //// ////

What graph/chart can we use to display this data? Draw a bar chart. What scale should we use? Should we use 2s? Which shape was least/most popular? How many more liked squares



Solve problems that involve the calculation of non-unit fractions of quantities by scaling up or multiplying the unit fraction value

Represent tenths and hundredths as decimals/fractions

Solve missing digit number problems that involve +, - of whole numbers

work out 6,058+1,846. As before, we add the digits in the 1s, 10s, 100s and now the 1000s. When the additions are 10 or more we write 10 as a 1 below the line in the next column.

+

Th H T U 6 0 5 8 1 8 4 6 7 9 0 4

1 1

Check your answers using the inverse operation. What digits are hidden:2█3+█45=70█;103-█5=6█

squares inside the shape and give the answer in square cm

On square grids, draw rectilinear shapes with given area and find their perimeters

Recognise that any change in position of a shape does not alter its perimeter or area

Compare and order grid shapes by the size of their areas or their perimeters

have equal perimeters? Start with the green shape. Mark a blob on a corner to remind you where you start the count. What is its perimeter? It’s 12cm as perimeter is a length around the shape. Are the perimeters of the shapes the same length? Make your own shapes on the grid and work out areas and perimeters. Find the areas of shapes with areas 12 square cm...

Draw, make and name acute and obtuse angles; order angles up to 2 right angles

Design symmetrical patterns on a grid using practical resources such as counters, blocks and mirrors

Remove or add items to a pattern to retain or secure its symmetry

than rhombuses? How many people were surveyed? What type of triangles could have been drawn? Draw all these shapes accurately include the different triangles. Take your drawings home. Ask everyone which shapes they like/dislike. Bring your results back to use in class. On the coordinate grid the vertical line is a line of symmetry. If I put a counter here, where must this counter go so we have symmetry?

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

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

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: Use alternative strategies to + & - whole numbers

Extension Work: Explore size of perimeters of shapes with same area

Extension Work: Plan and carry out a survey; present findings to class

Spring Term (Second half term)Week 4 Week 5 Week 6Number Number Measurement/Geometry/StatisticsMain Teaching: Understand and use

the terms multiple, divisible, factor and remainder

List multiples of single-digit numbers up to 100; identify patterns and extend multiples beyond 100 and check

Generate division facts from multiples of a given number

Recognise that division can lead to remainders

Apply the

Notes/examplesCount up in 7s and 70s. Circle all the multiples of 7 on the 100 square. Are 28, 42, 77...circled? Is there a pattern? What was the largest multiple? 98. To check 98 is a multiple of 7, partition 98 into multiples of 7: 98=70+28. We can then divide each number by 7 and add: 98÷7 = 70÷7+28÷7 = 10 + 4 = 14 It means 98÷7=14 and 14x7=98Is 107 a multiple of 7? Partition 107 into 70 and 37: 107=70+37. What multiple of 7 is closest to 37? 5x7=35. 37=35 + 2 so 107 = 70 + 35 + 2. We divide by 7: 107÷7=10+5, but we cannot divide

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

Notes/examplesWhat is 4x7x5? If we re-arrange 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 70x4 2806x4 24

76x4 = 304

376x4 300x4 120070x4 2806x4 24

354x4 = 1504 1

We don’t need to write the middle column each time. T U H T U 7 6 3 7 6

Main Teaching: Practise using the

written methods to multiply and divide by a 1-digit number and use to solve problems

Find perimeters of rectilinear shapes drawn on cm square grids, give answers in cm

Find areas of rectilinear shapes drawn on cm square grids by counting the squares inside the

Notes/examples

This centimetre grid has green rectangles. What size are the rectangles in cm, smallest to biggest? Explain how this sequence of rectangles grows. What’s the area of each rectangle? What are the units for the area? Centimetre squares. What’s the perimeter of the rectangles? What units do we use for the perimeter?



distributive law for division over + and -

Partition 2- and 3-digit numbers into multiples of a divisor with priority to 10x the divisor; use in a division table to divide 3-digit numbers by 1-digit numbers

Solve problems that involve division and multiplication by 1-digit in context

2 by 7. It’s the remainder. We write 107÷7=15 r 2. In our division table we write 115÷7 as 7 into 115. Our method is partition 115 into 70s and other multiples of 7. Then divide, writing the answers on the top line.115÷7 115÷7=16 r 3

10 + 6 r 37 1157 70 + 457 70 + 42 + 3

152÷6 152÷6=25 r 210 + 10 + 5 r 2

6 1526 60 + 926 60 + 60 + 326 60 + 60 + 30 + 2

tables to generate tables for multiples of 10 and 100

Multiply 2- and 3-digit numbers by a 1-digit 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, ÷

0 x 4 x 4 2 4 2 4 2 8 0 2 8 0 3 0 4 1 2 0 0

1 1 5 0 4 1We 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.

shape, and give the answer in square cm

Describe and build sequences of rectangular shapes; tabulate their size, area and perimeters; use to predict next values

Describe rules to find the areas and perimeters of rectangles in a sequence

Cm. Make a table to collect the areas and perimeters. Explain how these grow and use this to predict the size, the area and the perimeter of the next 5 rectangles? Explain what you did. Now check your predictions. Start with a 3 by 1 rectangle and make a sequence of rectangles. Find their areas, perimeters and predict. Now make sequences from a 4 by 1 rectangle. Find rules for working out areas and perimeters of rectangles.

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

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

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: For 1-digit divisor list numbers<100 with same remainder

Extension Work: Use distributive law to x 99, 199..; 201, 301... by 1s

Extension Work: Explore perimeters/areas of L-shapes on cm grids

Summer Term (First half term)Week 1 Week 2 Week 3Number Number GeometryMain Teaching: Count up from 0 and

back in multiples of 2 to 10

Construct, recite and recall the 11 and 12 times tables

Identify, describe and apply patterns in the 11 and 12 times tables to support mental division; use multiplication facts to identify remainders

Work out the factor pairs for numbers to 100 that are in the multiplication tables

Notes/examplesCount in 10s, 1s and 2s. Fill in the first 3 columns of the table.

10s 1s 2s 11s 12s10 1 2 11 1220 2 430 3 6

: : :100 10 20110 11 22120 12 24

Which 2 columns can we use to work out the 11s? 10s and 1s. And for the 12s column? 10s and 2s. Fill them in. What pattern can you see in the 11s column? Does this make the 11s easy to remember? Recite the 10, 11, 12 times tables.

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

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 Half of the shapeYellow Quarter of the shapeRed Eighth of the shapeGreen 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

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

Notes/examplesLength Strips of card

4cm5cm7cm

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



Use the distributive and associative laws to rewrite arithmetic expressions and to carry out mental calculations involving 1- and 2-digit numbers

Practise using mental and written methods to multiply and divide whole numbers by a 1-digit number and use to solve problems

Hide the table. Recite these times tables again. Look at the 1s digits in the 12 times tables. What do you notice? Why do they have the same pattern as those in the 2 times table? And why are the 11s digits the same as in the 1s? Is 88 divisible by 11? What is the remainder when you divide 89 by 11? And 92..? Is 12 a factor of 89? No. Multiples of 12 cannot end in 9. What is the remainder when you divide 89 by 12...? And 109÷12..?

same denominator Generate fraction

sentences for fractions with equal denominators, and complements to 1


Solve problems that involve applying fractions in context

blue rectangles? This means

Blue

12 =

24 =

48 =

816

Yellow14 =

28 =

416

Red18 =

216

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

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

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: 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

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

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: Explore patterns in units digit in other times tables

Extension Work: Make 0 to1 rulers to record equivalent fractions

Extension Work: Cut vertex off prisms/pyramids & explore new shape

Summer Term (First half term)Week 4 Week 5 Week 6Numbers/Measurement Number Statistics/MeasurementMain Teaching: Read and write in

words and numerals whole numbers beyond 1000 and decimal numbers with up to 2 places

Round whole numbers to the nearest 10, 100 or 1000, and decimals with up to 2 decimal

Notes/examples2612 147 5 9 4 7 3

The 3-row Sum Triangle is made of sums of the pairs of numbers in the row below: 7+5=12 and 5+9=14; 12+14=26. Fill in the blue Sum Triangle. What is the top number? Try some base numbers of your own. Can you make the top 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 1-

Notes/examplesOver time, Anna buys 4 times the number of apples to pears. She makes a table to show the numbers:

Pears Apples1 42 8: :

If she buys 12 pears, how many apples did she buy? Put numbers in our box picture. Why do we x by 4?

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

Notes/examples



places to the nearest whole number

Practise using mental methods and formal written column methods to add and subtract pairs of numbers with up to 4 digits

Read and write the Roman numerals using: l, V, X, L and C; use to construct Sum Triangles

Solve problems that involve identifying describing and applying patterns; conjecture and test; and follow a line of enquiry

35? Does only 1 set of 3 numbers give you 35? Can you use 3 odd base numbers to make 35? Or 3 even base numbers? Explore the top number when the base numbers are equal. Can you see patterns in the 3-row Sum Triangle numbers? Can you predict the top number given 3 base numbers? Now use a 4-row Sum Triangle and explore patterns in the triangle’s numbers. Use only odd or even base numbers. Can you predict top numbers with 4, 3 or 2 equal base numbers, 2 pairs equal, or 4 different base numbers? Make and test conjectures and follow a line of enquiry.

digit 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

ApplesPears

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 ...

PearsWe divide apples by pears. These problems all involve scaling up or down, x or ÷. We can put this in a table:

Given To find WeSmaller Bigger MultiplyBigger Smaller Divide

Smaller and

Bigger

How many times more

Divide bigger

by smaller

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

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: 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

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

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: Explore number patterns in Multiplication Triangles

Extension Work: Explore examples of multiplicative relationships

Extension Work: Use ICT packages to interpret similar time graphs

Summer Term (Second half term)Week 1 Week 2 Week 3Number Number GeometryMain Teaching: Recognise and write

decimal equivalents to: ¼; ½ ; ¾

Recognise and use diagrams to generate sets of equivalent

Notes/examples

In this fraction wall there are 5 whole strips. Into what fraction has each strip been divided? Use the equivalent lengths of

Main Teaching: Practise using

mental methods and formal written column methods to add and subtract pairs of numbers

Notes/examplesRoutine problem-How many 30cm lengths of ribbon can be cut from a ribbon of 4m? How much ribbon remains? -A blue Jug holds 350ml, 85ml more than the red jug. How much does the red jug hold?Non-routine problem

Main Teaching: Label a 2-D grid with

a vertical and horizontal axis with unit intervals

Use coordinates in the first quadrant to

Notes/examples



fractions Add and subtract

fractions with the same denominator

Generate fraction sentences for fractions with equal denominators, and identify complements to 1


Convert and write as decimals any number of tenths or hundredths and vice versa

Order decimals with up to 2 decimal places

Solve fraction and decimal measure and money problems

sections of the strips to identify equivalent fractions. ½ = ...; ⅓=...¼=...Jayla says: ‘If I multiply any fraction’s numerator and denominator by 2 the two fractions will be equivalent.’ Is she right? Test this with diagrams using the unit fractions: ⅓; ⅕; ⅙.. And the non-unit fractions: ⅔; ...⅘⅟10 ... ⅟10

0.1 ... 0.150

100...

50100

The strips are in 10 equal parts. The yellow strip is marked in tenths as fractions; blue as decimals, green as hundredths. What is 0.4 as tenths, as hundredths? What is ½ in tenths, hundredths, as a

decimal? If ½ is 50

100 what is ¼

in hundredths? How do we write ¼ as a decimal? And ¾?

with up to 4 digits Practise using

mental methods and formal written methods to multiply and divide whole numbers by a 1-digit number

Solve different types of word problems; decide when and how to draw and annotate box pictures to interpret and solve the problem

Solve logic problems that involve using the given information to discard and refine possible solutions; use place value and recall of number facts to test and isolate cases

- Mr Sims buys a cup of tea and a cake and spent £1.60. The cake was 3 times the cost of the tea. How much was the cake?-Al has 17 stickers; Bo has 10 and Ci has 6. How many stickers does Al give Bo and Ci so they have equal numbers of stickers?Correspondence problem- A menu offers me choices for my meal: fish or chicken; rice, chips or mashed potatoes; peas, beans, carrots or spinach. How many different meals can I have? -Twelve money boxes contain only10p, 20p and 50p coins. They each contain: 7 10p, 6 20p and 5 50p coins. In total, how much money is in all twelve boxes? Logic problem-My 3-digit number is less than 300. It’s odd and its digits sum to 13. What numbers could it be? It’s also a multiple of 7 what is it?-Place the digits 2, 2, 3, 3, 4, 4 in the TU sum to make a total of 90? Use the digits 1, 1, 1, 3, 3, 3, 4, 4, 4 in the HTU sum to make 600?

+

T U H T U

+

identify the position of points on a 2-D grid

Plot points for given coordinates and complete and identify shapes with these points as corners

Describe movement about a grid by giving the change in position in units left or right, up or down

Describe translations given the movements between points

Identify lines of symmetry of shapes presented in different orientations

Make symmetrical shapes on a coordinate grid by translating squares across and around a line of symmetry

There are 10 coloured squares on my grid. I move from the light red square to the dark red square. Describe my move: 6 right, 8 down. I move between 2 squares by going 2 left, 4 down. Which 2 squares did I move between? Blue to grey. Make a journey from square to square and write down the moves you make. Give it to a partner who has to give you, in order, the colours of the squares you visited. What are the coordinates of the points at the bottom left-hand corners of the squares? What are my translations from (3,2) to (9,5) to (2,8)? Which squares did I visit?

Mental Work: Recall and use 12x12 multiplication & division facts Count in thirds, quarters, fifths, tenths & hundredths Add and subtract tenths or hundredths to decimals

Mental Work: Recall & use 12x12 multiplication & division facts Identify remainders for 2-digit numbers ÷ by 6,7,8 Identify missing numbers from given information

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: Write 5ths, 20ths & 25ths as hundredths and decimals

Extension Work: Explore if other number sets make TU, HTU totals

Extension Work: Explore ICT coordinate plotting tools & translations

Summer Term (Second half term)Week 4 Week 5 Week 6Number Statistics/Measurement Number/MeasurementMain Teaching: Recognise and write

decimal equivalents to: ¼; ½ ; ¾

Compare fractions and decimals to ¼; ½ ; ¾;

Notes/examplesSuki says: ‘If I put a zero at the end of any number it always gets bigger.’ Is she right? Test this with whole and decimal numbers.

Main Teaching: Recognise that for

measurement data you use scales to compare and is continuous; count

Notes/examplesDepth cm Tallies Stream

>00; =<20 //// //// Low>20; =<40 //// />40; =<60 // Full>60; =<80 ////>80; =<100 //// High

Main Teaching: Read, write and

convert time between analogue and digital 12- and 24 hour clocks and convert hours to

Notes/examplesIt 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



use this method to sort fractions and position them on the 0 to 1 number line

Express decimals as tenths or hundredths and vice versa

Describe the effect of dividing 1- and 2-digit whole numbers by 10 and 100 and record the results as decimals

Order decimals with up to 2 places and apply to measure and money contexts

Make a conjecture: “I think that...”, test it and describe and explain observations and thinking with examples and pictures

Test whether a statement is true, sometimes true, or false; give reasons for decisions

What happens to 12 and 1.2 when you put a zero on the end of each number? Can you make a statement that is more accurate than Suki’s?Gary says: “0.25 is bigger than 0.8 as 25 is bigger than 8.” Why is he wrong? What picture could you use to explain to Garry that 0.8 is the bigger? What are the place values of the digits 2, 5 and the 8?

Ali says: “ 23 is bigger than

512 as

23 is over

12 and

512

isn’t” Draw a picture to help us see if Ali is right or not? List fractions you think are bigger than a half or smaller than a half. Explain how you decided. What fractions do you know that are bigger/smaller than a quarter? Which is smaller three quarters or 0.8?

data is in whole numbers and is discrete

Interpret discrete data presented in tables, pictograms and bar charts, and continuous data presented in tables and time graphs

Answer and pose questions from data presented in tables, charts and graphs

Interpret and label the scales on a time graph and use to identify and measure changes over time

Tell the time-based from data presented in a table or as a time graph

Estimate, compare and calculate using different measures, time and money

The table shows the depth in cm of water in a stream. The depth was measured every fortnight over a year. The water is described as low, full, or high. A high stream can flood the land. Write each row in a sentence e.g. The stream was full twice when the water was 40cm to 60cm deep. Write a story describing the year. Explain why you think rainfall caused the change in the stream’s depth. When did it flood?

This graph shows the cost of a heating an office over 12 hours. It was switched on at 06.30. The horizontal axis is time. The vertical axis is cost. Each interval is worth £3.50. Draw the graph. When was it switched off? When did the cost exceed £10..?

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-to-term 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

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 1319 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: 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

Mental Work: Read & interpret scales showing time & measures Interpret simple pictograms, bar charts & time graphs Add & subtract fractions, decimals with 1 or 2 places

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: Follow lines of enquiry by asking: “What if...”

Extension Work: Tell a time-based story; draw its time graph

Extension Work: Explore diagonal differences and other relationships


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