©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.
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©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
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

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.
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©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:
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

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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
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©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
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©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
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©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:
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©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
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©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
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