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Securing Progress in Mathematics
Scheme of Work for Year 5
Scheme of Work: Mathematics Year 5
Contents and the intended use of each section within the Scheme of 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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Scheme of Work: Mathematics Year 5
Essential Learning in Mathematics
Summary of Essential Learning in Year 5
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Count forwards and backwards from any number in powers of ten including through zero; interpret negative numbers
and Roman numerals in context; determine prime, square and cube numbers
Identify the value of digits in whole and decimal numbers; round numbers to the nearest power of ten and decimals to
nearest whole number and to one decimal place; write decimals and percentages as fractions
Add and subtract mentally pairs of numbers with up to four digits; use formal written methods to add and subtract
whole numbers and decimal numbers in context; add and subtract fractions with related denominators
Recall and use multiplication facts to 12 x 12 to multiply and divide mentally and identify factors and multiples; use
formal methods to multiply numbers with up to four digits by 1- or 2-digit numbers, and to divide numbers with up to
four digits by 1- or 2-digit numbers; multiply whole numbers by proper fractions to get whole number answers
Convert between units of measure and time; calculate the perimeter and area of rectangles and composite shapes
and volumes of cuboids; read, interpret and use data presented in tables, line and time graphs
Recognise and name 3-D shapes from 2-D drawings; draw straight lines accurately and draw and measure angles in
degrees; apply the properties of triangles and rectangles and identify regular polygons; reflect and translate shapes
on grids including the coordinates in the first quadrant
Problem Solving, Reasoning, Communicating
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Pupils solve problems that involve two or more steps and a range of measures and decimal numbers. They use and convert between standard metric
units and begin to use approximate equivalents for the most common imperial units of measure where the context makes it appropriate. Pupils apply
the four operations and combinations of these operations to logic problems that involve finding missing values or optimum solutions that meet given
conditions. They apply scaling to given measurements to calculate the increases or decreases between a scale drawing and its realisation. Pupils read
and interpret information presented in tables, including timetables, and graphs, including line graphs that show a relationship between two continuous
variables such as temperature and time. They solve problems that require the calculation of simple fractional and percentage parts of quantities in
order to compare the size of the proportional parts.
Pupils use their knowledge of factors and multiples to sort and test relationships between numbers. They determine whether a number is prime, square
or a cube and offer reasons for their decisions. Pupils generate linear sequences and describe in words the term-to-term rule. They use properties of
angles at a point or on a straight line to calculate missing angles, explaining how they arrived at their answers. Pupils explore the properties of familiar
shapes and begin to make and test deduction about lengths of sides and the angles.
Pupils read positive and negative numbers accurately, convert between decimal numbers and fractions and translate percentages into fractions. They
explain how to order, add and subtract fractions that are multiples of the same number and read and interpret improper fractions and mixed numbers.
Pupils describe the effect of multiplying and dividing whole numbers by 10, 100, or 1000. Pupils read angles in degrees and name angles by their size.
They describe reflections and relate a reflection to lines of symmetry, find the position of points following a reflection or translation.
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Scheme of Work: Mathematics Year 5
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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associating objects, shapes and events with their names (e.g. M is 1000, CM is 900; 4³ = 4 × 4 × 4; cm² represents square cm; this makes it a reflex angle)
stating, repeating and recalling facts aloud, and explaining how they can be used and applied (e.g. one tenth is 10% so three tenths is 30%; 15 030 is 15
thousand and 30 so take away 9 020 will leave 6 thousand and 10; the diagonals of a rectangle cross to make four triangle which are all isosceles)
describing the relationship between two or more items, shapes, events or sets (e.g. only this fraction is bigger than one as the denominator is bigger than
the numerator; 37 must be prime as I cannot find any factors but 27 is not prime as 3 × 9 = 27; the 16:48 train is after the 4.25pm train)
identifying properties and describing them (e.g. a right angle is 90º and this reflex angle is 3 right angles so is 3 × 90º; when I reflect the shape it does not
change shape only position and now it points in a down; the numbers in this sequence are getting bigger as I add a quarter each time)
framing an explanation, reasoning and making deductions (e.g. I know the polygon I made has equal sides but this angle is bigger than this one so it is not
regular; 48 is not a square number as 7² = 7 × 7 = 49; 63 divided by 5 has remainder 3, I think numbers with 3 units will have remainder 3 if I divide by 5)
Learning the Language of 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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Scheme of Work: Mathematics Year 5
Key Mathematical Vocabulary: Year 5
Number
Count in multiples of, count forward, count backwards through zero, consecutive; positive number, below zero, negative number, integer; negative
one, negative two ..., minus one, minus two ..., number line; one thousand, ten thousand, ten thousand and one ..., one hundred thousand, one
hundred thousand and one ..., one hundred thousand one hundred and one ... one hundred and one thousand one hundred and one ... million; place
value, digit, units, ones, tens, ... ten thousands, hundred thousands, millions; single-digit number ... seven-digit number; Roman numerals, I ... IV, V,
VI ... IX, X, XI ... XXXIX, XL, XLI ... XLIX, L, LI, LII ... LX, LXI ...C ... CDXCIX, D... CMXCIX, M ... MMXIV; partition, exchange, exchange for one
thousand, exchange for ten hundreds; numerals, place holder; greater than (>), less than (<); fewer, fewest, least; estimate, round up/down,
approximate, check, round to nearest ten, nearest hundred ... nearest hundred thousand; prime, prime number, square, cube
Calculation
(mental and
written)
Addition, increase, sum, total; subtract, subtraction, take away, decrease, fewer, less, difference between; add sign (+), subtraction sign (-), equals
sign (=), equivalence; calculate, calculation, mental calculation, formal written method, columnar method; double, scale up; halve; share out equally,
equal groups of, left, left over, remainder; divide, divide by, divide into, divisible by, quotient, remainder after division; factor, factor pair, prime factor,
composite number, division fact, short division, scale down; count in twos ..., count in tens, count in hundreds, repeated addition, array, rows,
columns; number of equal groups; multiply, multiple, product, multiplication, short multiplication, multiplication fact, multiplication table; multiplication
sign (×), division sign (÷); commutative rule, commutative operation, associative, associative law, distributive law; inverse, inverse operation
Fractions
Whole, proper fraction, improper fraction, mixed number, denominator, numerator, unit fraction, non-unit fraction, equivalent fractions, simplify,
cancel; fraction of, proportion, equal parts, share equally; halves; quarters, four quarters make a whole; two quarters make a half; thirds, one third,
one third of ... three thirds make a whole ... fifths, sixths, sevenths, eights, ninths, tenths, hundredths, thousandths; one eight, two eights ... eight
eighths, one whole, one and one eight, one and two eights ...; decimal numbers, decimal point, decimal place, one decimal place ... three decimal
places; whole number boundary, bridging zero; ones, tenths, hundredths; round to nearest whole number, percentage (%), parts per hundred
Measurement
Units of measure, metric unit, imperial unit, yard, pound, pint; measurement, scale, scale drawing; equivalent units, convert, conversion, mixed units,
intervals, value of interval; length, perimeter; standard units of length, kilometre, metre, centimetre, millimetre; weight, mass, scales; standard units
of weight, kilogram, gram; standard units of capacity, volume, litre, millilitre; temperature, degree Centigrade (ºC), thermometer; cold colder, freezing,
freezing point, boiling; calendar, leap year, seven days, week, fortnight, twelve months, (one year), 24 hours, (one day), 60 minutes (one hour), 60
seconds (one minute); duration, sequence of events; analogue clock, digital clock, 12-hour clock, 24-hour clock; a.m., p.m., noon, midnight; thirteen
fifty, fifty minutes past one p.m., ten to two in the afternoon; area of 2-D shape, square cm (cm²), square m (m²); volume cubic cm (cm³)
Geometry
Point; plane, 2-D shape, perimeter, area; straight, triangular, rectangular, rectilinear, composite, circle, circular; corner, side; 3-D shape, surface, flat
surface, face, edge, vertex, vertices; cube, cuboid, sphere, cylinder, cone, pyramid, prism; triangle, isosceles, equilateral; quadrilateral, square,
rectangle, parallelogram, rhombus, trapezium, kite; polygon, pentagon ... decagon, regular, irregular; symmetric, line of symmetry, vertical,
horizontal; orientation; rotate, clockwise, anti-clockwise, degrees, protractor, right-angle turn (90º); acute (< 90º) acute (> 90º, < 180º), reflex (> 180º)
reflex angle; half turn (180º), angles about a point (360º); perpendicular, parallel lines; coordinates, plot, axes, quadrant; translation, reflect, reflection
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, line graph; title, label; number fewer,
least number, total number, maximum number; scale, unit size, number of units represented, units per interval, units per picture
Problem
solving,
Reasoning,
Communicating
Explore, investigate, use, apply, analyse, interpret; solution, method, strategy; rearrange, organise, maximum, minimum; combine, separate, join,
link; build, draw, represent, sketch, measure, record, show your working; sign, symbol, notation, resource; show how, show why, represent, identify;
recite, repeat, recall; explain why, what, how, when; give a reason, justify, if, so, as, because, and, not, cannot; same, same as, different, example,
counter-example; visualise, imagine, see in your head, pattern, relationship; sequence, term, position, generate, predict, rule, rule, test
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5
Scheme of Work: Mathematics Year 5
End-of-Year Learning Objectives for Year 5
Record of coverage
A. Number – rounding and place value
A1. Can read, write and order whole numbers with 6 or more digits and identify the values of the digits
A2. Can read, write and order decimal numbers with up to 3 places and identify the values of the digits
A3. Can count forwards and backwards in powers of 10, round to nearest power of 10, round decimals to whole numbers and tenths
A4. Can read, write and interpret negative numbers and count through zero
A5. Can read numbers written using Roman numerals: I, V, X, L, C, D, M
B. Number – calculation (mental and written)
B1. Can add and subtract mentally 1- and 2-digit numbers and multiples of 10, 100, 1000 to and from given whole numbers
B2. Can use formal written methods to add and subtract whole 4-digit numbers and decimal numbers with up to 3 places
B3. Can recall the multiplication tables to 12 x 12 and use to identify factor pairs and common factors of two numbers
B4. Can use known facts to multiply and divide mentally including multiplying and dividing by 10, 100 and 1000
B5. Can use efficient formal written methods to multiply numbers with up to 4-digits by a 1- or 2-digit number
B6. Can use efficient formal written methods to divide numbers with up to 4-digits by a 1- or 2-digit number
B7. Can use rounding to give approximate solutions to calculations and check answers
B8. Can record the remainder after division in different ways and interpret remainders in the context of the problem
B9. Can identify, recognise and use common prime numbers, square numbers and cube numbers
C. Number – fractions, including decimal and percentages
C1. Can order, name, write and convert between mixed numbers and improper fractions and generate equivalent fractions
C2. Can compare, add and subtract fractions whose denominator are multiples of the same number
C3. Can express fractions whose denominators are multiples of 100, 10, 5 and 2 as percentages and decimal equivalents
D. Measurement
D1. Can measure accurately using metric units for length, weight, capacity and convert between common metric units
D2. Can calculate the perimeter of composite rectilinear shapes and the area of simple rectangular shapes in cm²
D3. Can estimate volume and capacity using practical resources
D4. Can convert between units of time, read and use 12-hour and 24-hour notation, and calculate time intervals
E. Geometry – properties of shapes, position and direction
E1. Can draw angles in degrees, estimate, compare and name angles
E2. Can identify and use the sums of angles at a point, on a straight line and other 90º multiples to calculate missing angles
E3. Can describe and use the properties of rectangles and regular polygons to determine related facts
E4. Can translate and reflect shapes, use coordinates in the first quadrant to describe position and movement of shapes
F. Statistics – read, interpret tables and line, time graphs
F1. Can read, interpret and represent data in tables, including timetables, and use information presented in a line graph
G. Problem solving, reasoning, communicating
G1. Can solve problems involving time, money, measures, use links to fractions, decimals and percentages in calculations
G2. Can determine term-to-term rules for sequences, use known facts to make deductions about numbers, shapes, angles
G3. Can represent problems and solutions using symbols and diagrams and share explanations and reasons for choices
©Nigel Bufton MATHSEDUCATIONAL LTD
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Scheme of Work: Mathematics Year 5
Assessment Recording Sheet
Mathematics in Year 5
Autumn term
Name:
Spring term
Summer term
5.1 – Working towards expectations
5.2 – Meeting expectations
5.3 – Exceeding expectations
Key:
Class:
A. Number – rounding and place value
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
B. Number – calculation (mental and written)
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
C. Number – fractions, including decimal and percentages
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
D. Measurement
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
E. Geometry – properties of shapes, position and direction
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
F. Statistics – read, interpret tables and line, time graphs
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
G. Problem solving, reasoning, communicating
5.1
5.2
5.3
5.1
5.2
5.3
5.1
5.2
5.3
End-of-year assessment of progress and attainment in mathematics
Summary report:
Overall end-of-year assessment in mathematics:
Working towards Year 5 expectations
Meeting Year 5 expectations
Teacher:
©Nigel Bufton MATHSEDUCATIONAL LTD
Exceeding Year 5 expectations
Date of final assessment:
7
Scheme of Work: Mathematics Year 5
Week-by week Planner Year 5
Autumn Term (First half term)
Week 1
Number
Main Teaching:
Notes/examples
Read these numbers and
 Recognise and read
give the value of the 6
the powers of 10;
digits: 63 678; 623 451; 616
10,100...1 000 000;
006; 6 600 060...
use to partition and
down
up
combine numbers
300
400
 Read and write whole What number is in the
numbers with 6 or
middle? Is 329 closer to 300
more digits; identify
or 400? What is 329 to the
the place values of
nearest 100? We round
the digits
down to 300 the 300s
 Read scales with
numbers up to and including
whole and decimal
the middle number 350. The
number intervals and
rest we round up to 400.
identify mid points
Round 6740 to the nearest
 Round whole
1000.
numbers to the
down
Up
6000
6500
7000
nearest power of 10
This
line
helps
us
see
if
 Read and write
6740 is closer to 6000 or
numbers with up to 3
7000. We round to 7000.
decimal places
Round 3.54 to the nearest
 Identify the value of
whole number.
decimal digits as

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10ths,100ths,1000ths
Round numbers with
2 decimal places to
the nearest whole
number and to 1
decimal place
Apply rounding when
solving problems
down
3
up
3.5
4
We round to 4. Round 3.54
to 1 decimal place.
down
3.50
up
3.55
3.60
It’s below 3.55 so we round
to 3.5. What value is the 7
in: 2.17, 1.72, 0.117
Mental Work:
 Recall multiplication facts to 12x12
 Read large whole numbers and decimal numbers
 Round numbers to required accuracy
Extension Work:
 Explore prefixes mega, giga, tera in number & ICT
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 2
Number/Measurement
Main Teaching:
 Count forward and
back in steps of
powers of 10 from any
given number
 Recognise the impact
on digits and their
place value when
adding or subtracting
pairs of multiples of
powers of 10
 Count up from 0 in
steps of single-digit
numbers; apply to
counts in multiples of
10, 100, 1000...
 Use formal column
methods for addition
and subtraction of 3-,
4-digit whole numbers
 Apply counts in 60s to
conversion of time
between seconds,
minutes and hours
 Solve problems
involving the
conversion between
units of time
 Solve missing number
problems involving
one unknown number
Notes/examples
Count up in steps of 100
from 407. Stop. We have
reached 907; how many
100s have we added to
407? As we cross from the
900s to 1000s what
changes? Which digits
remain unchanged; why?
Count back in 1000s from
11 026. What boundaries
did we cross this time? At
what number did we stop;
why? How many 1000s
have we subtracted from
11 026? Read my number:
7 301 582. What must I
add/subtract to change the
digit 3 to 4; the 5 to 2; 7 to
1; 0 to 8...? Count forward
from 0 in 6s; now in 60s.
Recite the 60 times table.
How many minutes in 4
hours...? How many
seconds in 8 minutes...?
Count in 3s; in 30s. Count
in 9s; in 90s. If we can
count in 1-digit steps we
can count in 10s, 100s,
1000s... Count in 4s, 400s,
4000s....
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 Apply x, ÷ facts to calculations with powers of 10
 Use x, ÷ by 60 to convert between sec, min and hrs
Extension Work:
 Solve missing number problems in context of time
Week 3
Geometry/Measurement
Main Teaching:
Notes/examples
 Know that angles are
measured in degrees,
I can use my 2 plates to
a right angle is 90º, a
make angles about the
whole turn is 360º
 Use º symbol, estimate centre point. If I turn it a
quarter of the way around,
and compare the size
what red angle do I make?
of an angle and its
A right angle... Angles are
complement to 360º
measured in degrees. 1
 Draw and measure
right angle is 90 degrees,
angles using a
which we write as 90º.
protractor, including
Count in 9s and now in
acute, obtuse and
90s. If I turn and make an
reflex angles
angle of 2 right angles,
 Measure angles in
how many degrees is this
triangles; draw
triangles, measure and angle; and 3 right angles;
and a complete turn. So
sum its angles,
there are 360º in one
conjecture and test
complete turn. If I make ½,
 Confirm that angles
¾, 2, 1½ turns how many
about a point sum to
degrees is that...? Is this
360º and angles on a
angle acute? Is it obtuse?
straight line to 180º
What is your estimate? If
 Convert multiple right
my red angle is 120º, what
angles to degrees
size is the blue angle? My
 Calculate the
red angle is 60º what’s its
complement of angles
complement to 90º, 180º,
 Solve missing angle
360º? Show me a reflex
problems involving 1
angle. Is the complement
unknown angle on a
to 360º of an acute angle
straight line or about a
always a reflex angle?
point
Mental Work:
 Add and subtract numbers to make 90, 180, 360
 Compare, estimate angles in 2-D and 3-D shapes
 Use x, ÷ by 90 to convert right angles to degrees
Extension Work:
 Draw, measure and sum angles in quadrilaterals
8
Scheme of Work: Mathematics Year 5
Autumn Term (First half term)
Week 4
Measurement/Number
Main Teaching:
Notes/examples
I walk 7km how many m
 Measure, compare
and sort lengths using do I walk; how many cm,
the metric units m, cm, mm? Each week I drive
85km. How many m is
mm
that? The distance to the
 Measure, compare
and sort weights using moon is 384 400 km. How
many m is that? 384 400
the metric units kg, g
000m. How do we convert
 Measure, compare
between km and m? How
and sort capacities
many km in 1 million m?
using the metric units
Step ½m. How many steps
l, ml
would you take to walk a
 Estimate lengths,
1km? Everyone walk
weights, capacities
around the playground in
 Know equivalences
½m steps for 3 minutes.
between metric
How far did you walk?
measures and use to
How can we get a good
convert between the
estimate of how far the
units km to m; l to ml;
class walked in 3 minutes?
kg to g
What units do we use to
 Multiply and divide
whole numbers by 10, measure capacity? What
is a kilolitre. I drink 2l of
100, 1000 with a
whole number answer liquid per school day. How
many school weeks will it
 Convert units of time
take to drink 1 kl? How
involving hours, days,
many 250ml bottles can be
weeks, years
filled from 1kl? Estimate
 Solve practical
the capacity of these
problems that involve
bottles in ml. Use water to
estimating and taking
find their capacities. How
measurements,
can we find the capacity of
calculating and
this room?
rounding
Week 5
Geometry/Measurement
Main Teaching:
 Identify familiar 3-D
shapes from 2-D
representations and
state their properties
 Interpret simple
isometric drawings of
3-D shapes and build
the shapes using
interlocking cubes
 Draw on an isometric
grid representations of
3-D shapes made
from cubes
 With a ruler, measure
and draw accurately
lines of given length
 With a protractor,
measure and draw
accurately angles of
given size
 Draw a triangle
accurately given
information on its
angles and its sides;
find additional
information by
measuring
 Solve missing angle
problems involving
unknown angles on a
straight line or about a
point
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 Add and subtract sequences of 1-digit numbers
 Add and subtract sequences of multiples of 10, 100
Extension Work:
 Explore relationship between 1l and 1kg of water
Mental Work:
 Identify 2-D and 3-D shapes from given properties
 Work out complements of angles to 90º, 180º, 360º
 Estimate length in cm, weight in g, capacity in ml
Extension Work:
 Draw cuboids to scale given their dimensions
©Nigel Bufton MATHSEDUCATIONAL LTD
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.
.
.
.
These shapes are drawn
on an isometric grid. What
3 shapes can you see?
How many cubes can you
see in shape C? Use the
grid to draw A, which is 1
cube. Now draw 2
connected cubes like B but
in all possible orientations.
Do the same for 3
connected cubes.
Here are pictures of
connected cubes. Work
out how many cubes you
need to build the shape
then build it. All shapes will
stand up as shown.
To shape C I want you to
remove 1 base cube and
add 2 cubes above the
base. Draw your shape.
To shape B I want you to
add 5 cubes. Draw your
shape. Ask someone to
use it to make your shape.
Week 6
Number
Main Teaching:
Notes/examples
Imagine a hot air balloon.
 Practise formal
You pull a red cord for hot
column methods for
addition/subtraction of air; it goes up 1m per pull.
4-digit whole numbers Pull a blue cord and it goes
down 1m per pull. The
 Recognise numbers
balloon is in the air. The
either side of 0 are
pilot sets his levelling
positive or negative;
gauge to zero. He gives 9
count back through 0
tugs on the red cord. Later
and forward from a
he gives 3 tugs on the blue
negative number in
cord. We calculate 9-3=6,
steps of any size
to work out that the gauge
 Read scales with
shows 6. He gives the blue
positive and negative
8 tugs; later he tugs the red
numbers
cord twice. Write down the
 Interpret negative
calculation (6-8+2) and
numbers in context;
work out the number on the
carry out addition and
gauge. Back at 0m.
subtraction
calculations where the The pilot pulls the blue 5
times and then the blue 4
answer may be
more times before he tugs
positive or negative
the red 6 times. What’s on
 Generate and extend
the gauge now?
number sequences
Work out the gauge
including those with
numbers for these
negative numbers
 Describe in words and calculations. Each time
start at 0. 4-7; 7-4; 4+6-8;
symbols the term-to4-8+6; 5-7-3; 5-3-7; 10-6-4
tem rule for a linear
List calculations with 3
sequence
numbers that give answers:
 Solve word problems
4, 0, -5, -2, 2...
involving negative
What numbers are hidden:
numbers in context
-5+█=1;4-█+2=-3;█-8+4=1
such as temperature
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 + and - pairs of 1-digit numbers with + or - answers
 Complete number sentences with + or - answers
Extension Work:
 Describe sequence rules algebraically: tn=tn-1 - 4...
9
Scheme of Work: Mathematics Year 5
Autumn Term (Second half term)
Week 1
Number
Main Teaching:
Notes/examples
My sheet of addition and
 Add and subtract
subtraction calculations
mentally numbers in
has errors. Correct the
the 1000s
errors. What errors did I
 Practise formal
make; what target would
column methods for
you set me?
addition and
Recite the 3 times table to
subtraction of 4-digit
3x12. Now recite the 3
whole numbers
 Use and apply mental times table with multipliers
10, 20, 30... Now use
and written methods
multipliers 100, 200... and
of division and
multiplication to solve then 1000s.What is 360÷3;
1800÷3...? Use another
problems involving
money and measures times table...
When we multiply a 2-digit
 Multiply and divide
number by 1-digit number
whole numbers by
we multiply the 1s then the
10, 100, 1000 with a
10s and add. For a 3-digit
whole number
number we multiply the 1s,
answer
10s then 100s and add. For
 Multiply 2-, 3- and 4digit numbers by a 1- 4-digit numbers we have
1000s too. Describe the
digit number using a
formal written method patterns in these
 Read, write and order calculations? Explain the
method; use it to multiply
large numbers and
decimal numbers with by a 1-digit number.

up to 3 decimal
places
Solve missing digit
problems involving
multiplication
68
x 4
32
240
272
268
x 4
32
240
800
1072
1
3268
x
4
32
240
800
12000
13072
Find the four
1
missing digits: █ 4x█=█ █4
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 Solve simple missing number or digit problems
1 1 1
1
 Count from a whole numbers in steps of , , or
2 3 4
10
Extension Work:
 Solve multiplication problems with missing digits
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 2
Number
Main Teaching:
 Estimate answers to
multiplication and
division calculations
using rounding
 Apply knowledge of
table facts to
compare the size of
answers to
calculations
 Recall and use the
inverse
relationships to
check answers
 Use the symbols <,
>, = to record
comparisons
between numbers
and calculations
 Divide 2-digit
numbers by a 1digit number using a
formal written
method
 Use and apply
written methods of
multiplication and
division to solve
problems involving
whole numbers
 Solve missing digit
problems involving
multiplication
Mental Work:
 Use rounding to estimate x and ÷ calculations
 Multiply multiples of 1 and 10 by 25, 50, 75 & 100
 Use known facts to estimate x and ÷ calculations
Week 3
Number/Geometry/Measurement
Main Teaching:
Notes/examples
Recite the 9 and 90 times
 Know that a right
tables. Turn through 3...8
angle has 90º; use º
right angles, how many
symbol and convert
degrees is that? A square
multiples of right
has how many right angles;
angles to º and vice
in degrees? What are the
versa
 Identify the sum of the interior angles at the
corners of my green
interior angles in 2-D
shapes where corners shape? 8 angles are right
are 1 or 3 right angles angles. 4 angles have 3
right angles. How many
 Draw 2-D shapes,
right angles is that? What
whose corners are
is the sum of the angles in
either 1 or 3 right
angles, given the sum º? In º find the sum of the
angles in these shapes?
of its interior angles
 Make and test a
generalisation about
the sum of interior
Make a shape with rightangles of 2-D shapes
angled corners that sum to
whose corners are 1
720º. Can you make a
or 3 right angles;
shape with right-angled
explain thinking and
corners that sum to 900º?
reasoning
Ethan says “99x4 is easy:
 Extend the 9 times
100x4=400; 400-4=396.” Is
table to 90, 99 and
he right? Work out the 99
999 times tables;
times table. Describe any
identify patterns in the patterns you find. He says:
numbers and use to x
“501÷99 is easy too, it’s 5
and ÷ large numbers
with remainder 6.” Work
 Generate and extend
out the 999 times table.
number sequences
How can you use these 2
that involve decimals
tables to calculate: 408÷99
and 8998÷999...?
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 Read & add numbers to 100 in Roman numerals
 Count from any whole numbers in decimal steps
Extension Work:
 Solve division problems with missing digits
Extension Work:
 Describe sequence rules algebraically: t n=tn-1 +1.5...
Notes/examples
Estimate 48x6. What did you
multiply? Estimate 88÷6
What did you divide? Work
out 25x3. What is 75÷3;
75÷25? Remember x and ÷
are inverse operations. Will
87÷3 be bigger or smaller
than 25? Bigger as 87 gives
us more to share between 3.
To work out 87÷3 we start
with the 80. Count out the
10s of 3:10x3=30; 20x3=60;
30x3=90. Stop too big. We
can only get 20 3s out of 80.
We write the 2 in the tens
column, as 20 is 2 tens, and
write the 60 below the 87
and subtract. This leaves 27
3
T
2
8
6
2
2
U
9
7
0
7
7
0
4
T
2
9
8
1
1
U
4
6
0
6
6
0
Now we find the 3s in 27
which is 9. This means
87÷3=29. Work out 29x3 to
check. Explain how to use
this method for 96÷4.
Practise this method for 2digits divided by 1-digit
numbers. Find the missing
digits: █4÷█=█1
10
Scheme of Work: Mathematics Year 5
Autumn Term (Second half term)
Week 4
Number/Statistics
Main Teaching:
Notes/examples
 Multiply and divide Dividing by powers of 10 moves digits
whole and decimal right. Look at this pattern:
1÷10=0.1;2÷100=0.02;3÷1000=0.003
numbers by 10,
Multiplying by powers of 10 moves
100 and 1000
digits left. Look at the pattern:
where answers
0.001x10=0.01; 0.002x100=0.2;
have up to 3
0.003x1000=3
decimal places
Explain the rule for the moving digits.
 Explain the effect
Present this in a table we can refer to.
of x and ÷ of
÷ move right
x move left
whole and decimal
1
÷10
0.1
0.01
x1000
10
numbers by 10,
1
÷100
0.01
0.01
x100
1
1
÷1000
0.001
0.01
x10
0.1
100 and 1000
When dividing or multiplying by 10,
 Construct, read
100, 100, decide if the answer will get
and interpret
smaller or bigger, which way the
information in a
digits must move and how far they
table
are to move. Remember, division can
 Convert fractions
with denominators be represented as a fraction:
1
1
2
10, 100 or 1000 to 1÷10 is and =0.1; 2÷100 is
10
10
100
2
3
decimal equivalent
and
=0.02; 3÷1000 is
=0.003.
100
1000
and vice versa
0.1
0.12
0.123
 Write 10ths as
1
12
123
100ths and
10
100
1000
1000ths etc
The number of decimal digits is the
 Add and subtract
same as the number of zeros in the
10ths, 100ths,
10ths, 100ths or 1000ths. What is
1000ths and
0.307 as a fraction? There are 3
convert the
decimal digits so we use 1000ths and
307
9
answers to
write:
. What is
as a decimal?
1000
100
decimals
100 has 2 zeros so 2 decimal digits.
 Read scales with
We write 0.09. We must put the 0 in
fraction or decimal
9
90 900
front of the 9. Remember = =
number intervals
10
100 1000
Mental Work:
 Identify the value of decimal digits in 10ths,100ths,1000ths
 Add and subtract decimals < 10 with 1 decimal place
 Give complements to 1 of decimals with 2 decimal places
Extension Work:
 Generate, explore and apply the 49 and 499 times tables
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 5
Geometry/Measurement
Main Teaching:
Notes/examples
 Use mathematical
language to name
and describe 3-D
shapes, prisms,
pyramids, cylinders,
cones, spheres etc
My rectangular card is
 Identify properties of 16cm by 12cm. What size
3-D shapes and sort is each small square?
by their properties;
2cm by 2cm. If I cut the
using tree, Venn or
card along the red lines I
Carroll diagrams
can fold my card into an
 Plot points on a
open box or tray like this.
coordinate grid in
How long, how high, how
the first quadrant
wide, is my tray? If I
 Draw 2-D shapes on unfold my tray can you
coordinate grids;
see how to work these
identify the lines of
measurements out before
symmetry and
I fold it? I pack the tray
coordinates of
with 1cm by 1cm cubes.
missing corners or
How many layers of cubes
points on sides
will I have? How many
 Build cubes and
cubes in each layer? How
cuboids from
many cubes will I need to
interlocking cubes
fill the tray? The answer is
and recognise that
the volume of my tray in
the number of cubes 1cm by 1cm cubes, which
used describes the
we write as cm³.
volume
Make a tray 16cm by
 Make trays from
10cm by 5cm. What size
card and find the
card do you need to start
volume using cm
with? Find out how many
cubes; calculate
centimetre cubes will fit
volume in cm³
into your tray so it is full.
Mental Work:
 Imagine, name 3-D shapes given properties
 Identify the squares to 12² and cubes to 10³
 x 3 1-digit numbers, solve missing digit problems
Extension Work:
 Measure volume and capacity of trays in cm³, ml
Week 6
Number
Main Teaching:
Notes/examples
 Read and write a
decimal as a
fraction 10ths
100ths or 1000ths If the blue rectangle is one
 Understand how
whole rectangle, how many
and use mixed
whole rectangles are there? 2
numbers to
1 blue + 1 green. What part
describe whole
of the whole rectangle is the
and part shapes
red shape? It has 8 squares
 Express quantities or 2 columns of 4. A whole
as mixed numbers shape has 12 squares or 3
8
2
and improper
columns of 4. It is or so
12
3
fractions
we have 2⅔ whole
 Convert improper
rectangles. How many ⅓
fractions to mixed
rectangles in total? Yes 8. It
numbers and vice
means we have 8 thirds. We
versa
2
8
write: 2 = . How many
 Recognise that
3
3
improper fractions small squares in a whole
represent whole
rectangle; in the part shape;
numbers when the and altogether? 12, 8 and 32.
8
32
numerator is a
We write: 2 = .
12
12
multiple of its
If the large square is now the
denominator
whole shape, what fraction of
 Understand that
large squares can you see?
per cent % means
per 100 and know
100% represent a
whole; write
Convert these improper
%ages as
fractions to mixed numbers:
6 7 8 9 10 11
fractions with
, , , , , ,... What is the
5 5 5 5 5 5
denominator 100
50 60 100
pattern? Convert: , ... ?
and as decimals
5 6
10
Mental Work:
 Give complements of fractions to a whole number
 Multiply simple mixed numbers by whole numbers
 Divide simple improper fractions by whole numbers
Extension Work:
 Explore the value of the 4th decimal number
11
Scheme of Work: Mathematics Year 5
Spring Term (First half term)
Week 1
Number/Measurement/Statistics
Main Teaching:
Notes/examples
 Convert between units What is 4hr 36min + 2hr
of time including years, 48min? We add the hrs
then min: 6hr (36+48)min.
months, weeks, days,
As there are 60 min in 1hr
hr, min, sec
we write: 36+48=70+14
 Work out fraction of hr
=60+24=1hr 24min. The
or min, answer in
answer is 7hr 24min. We
whole units
 Calculate fractions of a can record in a table:
hr
min
+
hr
min
period of time such as
4
36
+
2
48
a sixth of a minute
6
70
+
0
14
 Read, write and
7
10
+
0
14
interpret times, and
7
24
+
0
0
passages of time using When subtracting we can
analogue and digital
subtract the hrs. Subtract
12- and 24-hour clocks min we must decide if we
exchange 1hr into 60 min
 Read and interpret
hr
min
- hr min
timetables and use to
4
36
2
48
plan events such as
2
36
0
48
visits or journeys
1
60+36
0
48
 Add and subtract times
1
12+36
0
0
in hr and min that
1
48
0
0
cross the 60 boundary I travel for 48min each
day. Over 5 days how
 Multiply and divide
times by whole
long am I travelling?
numbers and give
5x48=10x24=240min
answers in hr, min or
240÷60=24÷6=4 so 4 hrs.
as a fraction of a unit
I swim 40 lengths in 1hr
10min. How long does it
 Solve problems
involving time, convert take me to swim 1 length?
1hr 10min = 70min
answer to most
70 7
3
appropriate units
70÷40= = =1 min
40 4
4
Mental Work:
 Use x, ÷ by 60 to convert hr to min; min to sec
 Convert 24hr times to 12hr times using am, pm
 Round times to nearest hr or min
Extension Work:
 Add and subtract times in min and sec and 24hr
times in hr and min and in hr, min and sec
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 2
Number
Main Teaching:
Notes/examples
When we divide by a 1-digit
 Use multiplication
number we work out
and division facts to
multiples of 100s, 10s, 1s,
find factors of 2- and
write them down and
3-digit numbers and
subtract. This is a method of
multiples of 10 and
long division method.
100; find factor pairs
T U
H T U
and common factors
1
4
1
4
2
 Know and use the
7 9
8 7 9
9
4
priority of operations;
7
0
7
0
0
construct equivalent
2
8
2
9
4
number sentences to
2
8
2
8
0
support mental
0
1
4
calculations e.g.
1
4
0
1824÷6=912÷3=304;
788÷7=700÷7+70÷7+ We can use the short
18÷7=100+10+2 r 4
method of division. Instead
=112 r 4
of writing down each step
we do an extra calculation in
 Understand that a
our heads.
prime number has
T
U
H
T
U
only 2 factors;
1
4
1
4
2
determine 1- and 27 9 28 7 9 29 14
digit prime numbers;
We work out how many 7s
recall first 10 primes
will go into the 9; a short cut
and use to generate
to working out how many
composite numbers
10s of 7 go into 90. The
 Divide 2- and 3-digit
answer is 1. The 2 left over
numbers by a 1-digit
we carry over to the 8 to
number using formal
make 28. 7s into 28? 4, we
written methods of
put the 4 in the 1s column.
long and short
Explain and use the method
division; apply to
to ÷ by1-digit numbers.
solve problems
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 Determine factors of given number; identify primes
 Convert %age to fraction in 100th and to decimals
Extension Work:
 Explore tests of divisibility for 2, 3, 4, 5, 6 and 9; look
for any patterns in the multiples of 11
Week 3
Number
Main Teaching:
Notes/examples
When we multiply by a 1-digit
 Use multiplication
number we multiply the 1s,
and division facts
10s, 100s, 1000s, write them
to find multiples of
down and add. This is a
2-digit numbers
method of long multiplication.
and of multiples of
TU
H TU
ThH TU
10 and 100; find
87
387
4387
common multiples
x 6
x 6
x
6
and lowest
42
42
42
480
480
480
common multiples
5
2
2
1
8
0
0
1
8
00
 Know and use the
1
2322
24000
priority of
1 1
26322
operations to write
11
equivalent number We can use the short
method of multiplication.
sentences and to
Instead of writing down each
support mental
step we do an extra
calculations e.g.
calculation in our heads.
8x45=4x2x45=
TU
H TU
ThH TU
4x90=360;
87
387
4387
7x89=7x90-7x1=
x 6
x 6
x
6
630-7=623
522 2322
26322
4
5 4
25 4
 Calculate square
and cube numbers We know 7x6=42 so we write
the 2 in the 1s column, and
and use ², ³ signs
carry the 4 into the 10s. We
 Multiply 2-, 3- and
4-digit numbers by now deal with 10s. We know
8x6=48 and add 4 to get 52
a 1-digit number
to get the 10s. We write the 2
using formal
in the 10s column and 5 in
written methods of
the answer, or we carry the 5
long and short
into the 100s column.
multiplication;
Explain and use the method
apply to solve
to x by1-digit numbers.
problems
Mental Work:
 Recall x facts to 12x12 use to derive ÷ facts
 Determine multiples of 2 given numbers
 Work out squares and cubes of numbers to 10
Extension Work:
 A square number is the sum of consecutive odd
numbers. True or false?
12
Scheme of Work: Mathematics Year 5
Spring Term (First half term)
Week 4
Measurement/Geometry
Main Teaching:
Notes/examples
Star has 9 identical sticks
 Use mathematical
language to describe of 6 linked 1cm cubes.
properties and name She says: “The volume of
prisms and pyramids a stick is 6 cubic
centimetres.” She pushes
by referring to the
shape of the base as the 9 sticks together to
form a shape with square
appropriate; identify
ends. She says: “This is a
and sort 3-D shapes
square-based prism.” Is
by their properties
including the shapes she right? What is the
volume of her shape?
of faces
 Recognise volume is Draw Star’s shape on an
isometric grid. Draw the
measured in cubic
faces of Star’s shape.
units cm³, m³; relate
this to cube numbers With 12 sticks of cubes
what prisms could Star
 Measure and
make? What is the volume
calculate in cm³ or
of each prism? Varsha
m³ the volumes of
builds a layer of blue and
square- and
red blocks.
rectangular-based
He adds
prisms or cuboids
on three
 Express in words the
more identical layers. How
rule for calculating
many blocks has he used?
the volume of cubes
What is the volume of his
and cuboids
shape if each block is a
 Work out the
4cm cube?
dimensions of a
Si’s rectangle is
rectangle given its
6cm by 4cm.
perimeter and the
What’s
its
perimeter? Jo’s
ratio of the sides or
the perimeter or area rectangle is twice as long
as it high. The perimeter is
and one of its sides
36cm, what’s its length?
Mental Work:
 Calculate the square and cube of a number
 Calculate volume of cuboids area of base & height
 Estimate volume of cuboid against known volume
Extension Work:
 Find volume & capacity of plastic cuboid container
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 5
Number/Measurement
Main Teaching:
 Read and identify the
values of points on
scales that have
whole number,
decimal and fraction
intervals
 Calculate the size of
intervals on partially
numbered scales
 Construct, extend
and describe
sequences involving
fractions or decimals
 Calculate lengths
and use a ruler to
draw accurately lines
and intervals in cm
and mm
 Represent families of
fractions visually and
use to identify pairs
of equivalent
fractions and to
compare fractions
 Work out unit and
proper fractions of
measures and other
quantities by
identifying the value
of one part in the
appropriate strip and
then scaling up
Notes/examples
Draw a 4 rectangles each
12cm by 1cm. Divide the
strips into 12, 6, 4 and 3.
What fractions can we write in
each section of these strips?
How many 12ths is equivalent
1 4
to one third? We write = .
3 12
Identify as many pairs of
equivalent fractions as you
can. How can we divide our
unit strip into 5ths, 8ths and
10ths? What is 12cm in mm?
Work out 120÷5... Draw the 3
strips divided into 5ths, 8ths
and 10ths. Identify new pairs
of equivalent fractions. What
fractions are missing? 7ths
and 9ths and 11ths. Draw the
3 fractions strips accurately.
Use your fraction strips to
5
3 4
5 3
5
decide if > ; < ; = ;...?
8
4 9
6 7
11
Which strip would we use to
work out ninths? If a strip
represents 56ml, in m what is
1
4
the value of of 56ml and
9
9
of 56ml? Use strips to work
out fractions of measures
Mental Work:
1 2 3 4
 Count in steps of , , , ;
1
,
3
,
7
,
9
5 5 5 5 10 10 10 10
& 100ths
 Generate equivalent fractions to a given fraction
 Calculate unit fractions of quantities (exact answers)
Extension Work:
1
 Describe sequence rules algebraically: t n=tn-1 - ...
4
Week 6
Number/Measurement
Main Teaching:
 Find perimeters and
areas of rectilinear
shapes drawn on
square grids
 Estimate the areas of
irregular rectilinear
shapes
 Recognise perimeter
is measured in linear
units and area in
square units cm², m²
 Describe in words
and symbols the
rules for finding
perimeter and area
of squares and
rectangles and apply
to simple composite
rectilinear shapes
 Using square grids
draw sequences of
rectilinear shapes;
identify and describe
growth patterns in
areas and perimeters
of these shapes
 Test generalisations
about relationships
between perimeters
of rectilinear shapes;
make generalisations
test, explain, reason
Notes/examples
Jan and Dan have made
this pattern of shapes on a
cm grid. “We add the next
size of square to make our
new shape and fill in the
yellow squares to make a
big rectangle. We have
used 1, 2, 3 and 4 cm
squares. We then find the
perimeters of the rectangle
and the yellow shape.” Jan
says: “I think the perimeter
of the shape made up of
just blue and green squares
is always the same as the
big rectangle.” Dan says: “I
think the yellow shape has
the same perimeter as the
perimeter of the previous
rectangle.” Are they right?
Test their claim to see if you
agree or not. Explain your
thinking and reasoning.
Mental Work:
1 2 3 4
 Count in steps of , , , ;
1
,
3
,
7
,
9
5 5 5 5 10 10 10 10
& 100ths
 Given dimensions, find area/perimeter of rectangle
 Visualise shape made from cut or folded rectangle
Extension Work:
 Draw rectilinear shape with given perimeter or area
13
Scheme of Work: Mathematics Year 5
Spring Term (Second half term)
Week 1
Number
Main Teaching:
Notes/examples
We have used short
 Multiply and divide
multiplication to multiply by a
whole and decimal
1-digit number. We use long
numbers by 10, 100
multiplication to multiply by a
and 1000 where
2-digit number. We still do
answers have up to 3
calculations in our heads. To
decimal places
multiply by 34 we multiply by
 Carry out mental
the 4 just as we’ve been
calculations
doing then multiply by the 30
with/without jottings
in a similar way.
that involve the four
ThH T U
ThH T U
operations
87
387
 Know and use
x34
x 34
2
3 2
brackets, the rules and
348
1548
priority of operations to
2
2 2
write equivalent
2610
11610
2958
13158
number sentences and
1
to support mental
We know 7x4= 28 so we put
calculations e.g.
the 8 in the 1s column, and
13x8+13x12=
carry the 2 into the 10s
13x(8+12)=13x20=260 column. This time we write 2
1.2x6-0.7x6=
close to 8. 8x4=32 and add
(1.2-0.7)x6 =0.5x6=3
the 2 so we have 34 10s. We
 Multiply 2-, 3- and 4write 4 in the 10s and 3 in
digit numbers by a 1the 100s. Now we multiply by
or 2-digit number
30. As this is a 10s number
using formal written
we can write a 0 in the 1s
methods of long and
column and multiply by 3.
short multiplication
7x3=28 so 8 in the 10s and
 Solve problems that
carry 2 into the 100s ready to
involve scaling
add. 8x3=24, add the 2 we
measurements up or
carried and write 26. Add up
down from and to
the products for the answer.
make scale drawings
Mental Work:

Recall x facts to 12x12 use to derive ÷ facts

Add and subtract sequences of 1-digit numbers
 + and - sequences of multiples of 10, 100
Extension Work:
1 1 1 1
 Count back from whole numbers in steps of , , ,
2 3 4 10
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 2
Geometry/Measurement
Main Teaching:
Notes/examples
 Estimate the size of
Estimate the size of each
an angle about a
angle made by the 2 lines
point and in a shape
What must the 4 angles
 Name angles as
sum to? What must the 2
acute, obtuse, reflex
angles on the straight line
and right angled;
sum to? Which angles are
recognise convex
equal? If one of the angles
and concave angles
is 130º what size are the
in shapes
other 3 angles? Draw and
 Measure and draw
cut out 3 identical triangles.
angles in degrees
Mark the angles a, b and c.
using a protractor
Can you put them together
 Measure sides and
to make a straight line?
angles in triangles
Which of the angles meet
and quadrilaterals
 Recognise the angles on a straight line? What do
of a triangle sum to 2 you think the 3 angles of a
triangle sum to? (180º or 2
right angles or 180º
right angles). Draw a
 Use angle properties
quadrilateral.
of triangles to find
Mark a point inside.
sums of angles in
Join it to each of the
quadrilaterals and
quadrilateral’s corners.
other polygons
How many triangles are
expressed as right
inside the quadrilateral?
angles and degrees
How many right angles, º
 Explore the
do the quadrilateral’s
properties of
angles sum to? Now try a
rectangles and
pentagon, hexagon... Can
squares by folding
you see a pattern? Explain.
and measuring; use
Cut out a rectangle. Fold it,
the properties to
measure angles, sides and
deduce related facts
describe what you notice.
about the shapes
Mental Work:
 Calculate complements to 90, 180, 360
 Calculate missing angles about points & in triangles
 Use mathematical language to describe 2-D shapes
Extension Work:
 Explore regular & irregular polygons with ICT tools
Week 3
Statistics
Main Teaching:
Notes/examples
 Read scales, with
and without,
numbered intervals;
use given
information to
calculate the size of
intervals and to label The line graph shows the
the scales on a line
temperature of an oven. It
graph
was switched on at 4:30pm.
 Read and interpret
The horizontal axis is in
data presented in
minutes and the vertical
tables and convert
axis is temperature in ºC. At
this to a time or line
4:50pm it reached 160ºC to
graph
heat food. Later at 200 ºC a
chicken was put in the oven.
 Annotate a graph
Label the axes and use the
with vertical and
graph to tell a story.
horizontal straight
The table below shows the
lines to read values
 Tell the story of data temperature in an office. On
from a bar chart, and the day the heating broke
down. Use the data to draw
time or line graphs
a line graph with time along
 Solve problems
the horizontal axis. When
involving sums,
temperature is below 18 ºC
differences, time
the office is closed. For how
intervals etc using
long was it closed? When
information
presented in a line or were temperatures between
21 ºC and 23 ºC?
time graph
Time
Temp
Time
Temp
 Solve problems by
08:00 19ºC
15:30 16 ºC
gathering information
09:30 22 ºC 17:00 24 ºC
from tables and
11:00 25 ºC 18:30 22ºC
charts, including
12:30 19 ºC 20:00 19 ºC
14:00 16 ºC
timetables
Mental Work:
 Identify points on partially numbered scales
 + and - pairs of 1-digit numbers with + or - answers
 + and - 2-digit decimals with 1 or 2 decimal places
Extension Work:
 Use ICT to evaluate different graphs for a data set
14
Scheme of Work: Mathematics Year 5
Spring Term (Second half term)
Week 4
Number
Main Teaching:
Notes/examples
We have used the short
 Carry out mental
division to divide by a 1-digit
calculations
number. We use long
with/without jottings
division to divide by a 2-digit
that involve the four
number. Will 875÷16 have a
operations
remainder? Explain why 16
 Know and use
is not a divisor of 875.
brackets, the rules
H T U
and priority of
5
4
r 11
operations to write
1 6
8
7
5
equivalent number
8
0
sentences and to
7
5
support mental
6
4
calculations e.g.
1
1
55÷13+10÷13=
Since we are dividing by 16
(55+10)÷13=65÷13=5 it is useful to derive the 16
86÷7-51÷7=
times table
1x16
16
(86-51)÷7=35÷7=5
we can refer
2x16
32
 Use mental
to as we do
3x16
48
calculations to
the division.
4x16
64
generate times tables
We cannot
5x16
80
6x16
96
for 2-digit number
divide the 8
:
:
by 16 so we
 Divide 2- and 3-digit
work out how many 16s will
numbers by a 1-or 2go into 87. There are 5 as
digit number using
5x16=80 so we write 5 in the
formal written
10s and subtract to get 7.
methods of long and
Now we involve the 5 and
short division
use 75. There are 4 16s in
 Solve problems that
75 as 4x16=64 and 5x16=80
involve scaling
is too big. We write 4 in the
quantities and
1s column and subtract; the
measurements up by
remainder is 11, we write:
multiplying and down
11
by dividing
874÷16 = 54 r 11, or 54 .
16
Mental Work:
 Recall x facts to 12x12; derive related x, ÷ facts
 Say if and why a given fraction is <, > or = 1/2
 Round mixed, decimal numbers to required accuracy
Extension Work:
 ÷ powers of 10 by 3, 6.. look at pattern in remainders
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 5
Number
Main Teaching:
 Multiply and divide
whole numbers, and
those involving
decimals with up to 3
decimal places, by
10, 100 and 1000
 Find factor pairs of
numbers; use the
vocabulary of
product, composite
number, prime
number and prime
factor
 Express numbers to
100 as a product of
its prime factors
 Solve multi-step
word problems
involving + and representing the
problem in a picture
to annotate and
interpret and to
identify the
calculations
 Solve puzzles
involving missing
numbers given
information about its
factors
 Test conjectures
about numbers and
explain reasoning
Notes/examples
Tom and Pam buy pens.
They spend £5.50. Tom
pays 94p more than Pam.
How much do each pay?
Start with a picture to
represent the problem.
550p
Which bar is Tom/Pam?
Who paid more for the pen?
How much more? Annotate
our picture. They paid 550p
but if Pam had paid the
same as Tom the total
would increase by 94p to
644p.
Tom?
Pam?
94p
644p
Tom spent half of this £3.22
and Pam £2.28p.
Ali and Ram share £2.12 in
2p coins. Ali ends up with
40p less than Ram. How
many 2p coins do each end
up with? Draw and annotate
a picture.
What 2-digit number whose
digits sum to 9 has factors 5
and 6?
What 3-digit number has
factors 6 and 8 if its digits
sum to 15?
Do square numbers have an
odd number of factors?
Mental Work:
 Convert %age to fraction in 100th and to decimals
 Calculate unit fractions of quantities, exact answers
 Calculate 10, 25 & 50% of quantities, exact answers
Extension Work:
 Use ICT to explore the factors of p²-1 (p is prime>2)
Week 6
Geometry
Main Teaching:
Notes/examples
 Plot and identify points
on coordinate grid in the
first quadrant
 Draw shapes by plotting
the corners given their
coordinates and label
the corners
 Translate shapes;
describe a translation,
What are the coordinates
giving the direction and
of the corners of the green
distance of the change
shape? I reflected this
in position
shape twice and translated
 Recognise that for a
it once. Describe the
translation the size and
reflections and translation.
orientation of the shape
Identify the coordinates of
is unaltered and only
the corners of the shapes
position is affected
in their new positions.
 Reflect shapes; describe On another grid of the
a reflection by
same size, a triangle has
describing the mirror line corners at A(5,7), B(8,6)
(line of reflection) as
and C(6,5). I reflect it in the
horizontal or vertical and horizontal line and the
a point through which it
vertical line that both pass
passes
through the point (4,4). I
also translate the triangle
 Recognise that for a
reflection the size of the
down 4 and left 4 units.
shape is unaltered but
Draw the shapes, label its
position and orientation
corners and record the
is affected
coordinates of the corners
 Generate patterns using of the new triangles. Has
any triangle changed its
repeated reflections or
shape or size or
translations of a simple
orientation?
shape
Mental Work:
 Identify points and movement on a coordinate grid
 Visualise a translation & identify changes to a shape
 Visualise a reflection & identify changes to a shape
Extension Work:
 Explore how Rangoli designs are constructed
15
Scheme of Work: Mathematics Year 5
Summer Term (First half term)
Week 1
Number
Main Teaching:
Notes/examples
Work out: 8.9+5.725 and
 Use formal written
8.9-5.725. We include
column methods to
zeros to set out decimals
add and subtract up
so the points are lined up.
to 4-digit whole
numbers and
8 9 10
8.900
8. 9 0 0
decimals with up to 3
+ 5.725
- 5. 7 2 5
decimal places
14.625
3. 1 7 5
 Practise formal written
1
methods to multiply 3For a Year 5 party I need
and 4-digit whole
numbers by 1-, 2-digit 7 loaves (£1.35 each); 3
numbers and divide 3- packets of ham (£2.19
each) and 2 blocks of
and 4-digit whole
cheese (£3.48 each). How
numbers by 1-digit
much will it all cost?
numbers
Work out the covered up
 Solve problems
numbers to make these
multiplication and
statements correct:
division problems;
88█÷7=1█7; █57x6=15█2
record remainders as
324÷█=█6; 16█÷6=2█
whole numbers or
My 2 numbers sum to 16.
fractions in the
context of the problem One number is prime the
other is a square number.
 Solve missing digit
What are my 2 numbers?
problems involving
My number a is double my
multiplication and
number b; a+b is 21.
division
What are my 2 numbers?
 Know and use the
My number is cubed to
prime, square and
give an odd number with 3
cube numbers
digits. What 3-digit
 Identify and describe
numbers are possible?
patterns; conjecture
Are 4³-1³; 5³-2³; 6³-3³; 7³and test; explain
4³...all multiples of 9?
reasoning
Mental Work:
 Read, order large numbers in words & numerals
 Recall x facts to 12x12; derive related x, ÷ facts
 Calculate squares, cubes; recall primes to 19
Extension Work:
 Explore the factors of square & cube numbers
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 2
Number/Measurement
Main Teaching:
Notes/examples
Read these numbers: 4.5;
 Read and write
8.65; 3.905... Identify the
decimals with up to
value of 5 in each number.
3 decimal places;
What is 8.105 as a fraction?
identify the value of
There are 3 decimal digits so
the digits after the
105 8105
decimal point
we have 1000ths: 8
=
1000 1000
 Represent decimals The table shows how units of
with up to 3 decimal metric measure relate
places as fractions
Metric units
with denominators
1km
1000m
1m
1000mm
1000, 100 or 10
1m
100cm
 Recognise the
1cm
10mm
relationship
1kl
1000l
between the units of
1l
1000ml
metric measure and
1kg
1000g
1g
1000mg
convert between
Remember: kilo means 1000
them
units; centi means one 100th
 Measure capacity,
and milli one 1000th of a unit.
weigh, length; read
We multiply and divide by
and record
1000, 100 or 10 to convert
measurements
using mixed units or between these units. What is
1.25km in m? x1000: write
as a decimal of the
1250m. What is 50g in kg?
larger units
50
 Add and subtract
We ÷ by 1000. 50÷1000=
1000
measurements that
so 0.050kg or 0.05kg. What is
use decimal
5075ml in l? We ÷ by 1000 to
notation and apply
5075
get
we have 3 zeros so 3
1000
to problems
decimal digits: 5.075l. What is
including those
involving perimeters 3500ml in l? ÷1000 gives 3l
500ml or 3.5l. What is 5080g
of composite
in kg? ÷1000 5kg80g 5.080kg.
rectilinear shapes
Mental Work:
 State equivalences between fractions and decimals
 Convert measurements to kilo, centi or milli units
 Calculate complement to a given unit eg 350 ml to1 l
Extension Work:
1 1 1 1
 Count back from whole numbers in steps of , , ,
2 4 5 10
Week 3
Geometry
Main Teaching:
Notes/examples
The exterior angles a, b, c
 Compare, measure
of a triangle are marked
and draw acute,
below.
a
obtuse and reflex
angles in degrees
b
using a protractor
c
 Know that the angles
Draw triangles of your
at a point sum to
own. Measure their
360ºand adjacent
exterior angles and find
angles on a straight
the sum a+b+c. What do
line sum to 180º
you notice? Can you make
 Measure the interior
and exterior angles in a general statement about
the sum of the exterior
triangles; conjecture
angles of a triangle?
and test
generalisations about
the sums of these
Draw a large triangle you
angles
can walk around. Start at
 Draw triangles, using
a ruler and protractor, the corner with the star.
Walk in the direction of the
given information on
arrow. At each corner turn
the lengths of sides
through the exterior angle
and size of angles
so you face along the next
 Recognise 3-D
shapes from their 2-D side. Repeat until you are
back at and ready to move
representations
along the red arrow. How
 Name faces on 3-D
many degrees did you turn
shapes including
prisms and pyramids; as you went once around
the triangle? Draw a large
combine cut-outs of
quadrilateral. Measure the
the faces of 3-D
exterior angles and sum.
shapes to make
Walk around it once.
simple nets and
Explain what you notice.
check the fit
Mental Work:
 Recognise 3-D shapes from 2-D representations
 Name the angles in 2-D and 3-D shapes
 Visualise & name shapes from their descriptions
Extension Work:
 Explore the properties of quadrilaterals using ICT
16
Scheme of Work: Mathematics Year 5
Summer Term (First half term)
Week 4
Number/Measurement
Main Teaching:
Notes/examples
 Read accurately linear Remember % means parts
and circular scales that per hundred. 1% is 1
100
involve partially
What is 65% as a fraction?
labelled and unlabelled What does 100% tell us?
intervals
To work out 1% we divide
 Work out intervals on
by 100. Once we know 1%
scales with whole,
we can scale up to find
decimal and positive
other %ages.
and negative numbers, £1 has 100 pence. It
including intervals of
means 1% is 1p. What is
time on a clock
10% of £1; 20% of £1...
 Recognise per cent, % A supermarket sale offers
means per 100 and to
30% off all clothes. What
find 1% of a quantity
does this mean? Jeans
involves dividing by
cost £25, what will I pay?
100
£25 is 2500p and 1% of
1
 Scale up 1% to find
2500p is
so we get
100
larger percentages of
25p.10% is 25px10=£2.50
quantities
and 30% is 3x£2.50 =
 Convert percentages
£7.50. Put this is a table:
to decimal and


fractional equivalents
and vice versa
Solve problems
involving calculating a
fraction of a quantity
Solve problems
involving calculating a
percentage of a
quantity including a
reduction in cost
100%
1%
10%
30%
Cost
Whole
2500p
÷100
25p
x10
250p
x3 750p=£7.50
£25 - £7.50
£17.50
What would I pay for:
a jumper costing £36
socks costing £8
a coat costing £44
Which is more 50% of £20
or 20% of £50?
Mental Work:
 Convert %age to fraction in 100th and to decimals
 Calculate unit fractions of quantities, exact answers
 Calculate 10, 25 & 50% of quantities, exact answers
Extension Work:
 Interpret sequence rules expressed algebraically to
count on, back from whole numbers in fraction steps
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 5
Number/Measurement
Main Teaching:
Notes/examples
We can use the formal
 Practise and use the
method to multiply decimal
formal written method
numbers by 1- and 2-digit
to multiply 3- and 4numbers. We carry out the
digit whole numbers
division as usual. In the
and decimals with up
to 2 decimal places, by answer we must place the
1- and 2-digit numbers point so there are the
same decimal places as in
 Measure length,
the number we multiply.
weight and capacity,
H T U .t
H T U .t h
using metric units, m,
9 .5
3 8. 7 6
cm, mm; kg, g; l, cl, ml
x 27
x
34
3
3 3 2
 Convert between
6 6. 5
1 5 5. 0 4
different units of metric
1
2 2 1
measures; express
1 9 0. 0
1 1 6 2. 8 0
2 5 6. 5
1 3 1 7. 8 4
measures in mixed
1
1
units or as a decimal of Road signs give distances
the larger units
5
in miles. 1km is about of
 Recognise and use
8
a mile The distance by
approximate
road to a town is 24 miles,
equivalents to convert
how many km it that?
between metric and
common imperial units We used to buy petrol in
gallons. My converter says
 Solve problems
1gallon = 3.78541178litres.
involving converting
How many litres would a
between units of time:
5,500 gallon tanker hold?
weeks, days, hours...
The USA still weighs items
 Solve problems
in pounds (lbs). A pound is
involving decimal
about 0.45kg. A rare fish
notation with up to 3
called an opah weighed
decimal places, in the
180lbs. What was the
context of measures
weight of the fish in kg?
and money
Mental Work:
 Convert between units by x and ÷ by 10, 100, 1000
 Recall units of time and convert between units
 + and - decimals with 1 non-zero decimal place
Extension Work:
 Explore imperial and metric units of measure: litres
and pints; grams and ounces; yards and metres
Week 6
Number
Main Teaching:
Notes/examples
We can use the formal
 Practise and use the
method to divide decimal
formal written method
numbers by 1- and 2-digit
to divide 3- and 4-digit
numbers. We line up the
whole numbers and
decimal point in the answer
decimals with up to 2
to the decimal point in the
decimal places, by 1dividend. We do the division
and 2-digit numbers
as usual.
 Add and subtract
H T U
simple fractions with
4
5 . 3
the same denominator
1 5
6
7
9 . 5
and with related
6
0
denominators
7
9
 Convert improper
7
5
fractions to a mixed
4
5
4
5
fraction
0
 Multiply simple
The
answer
has
1
decimal
fractions by a whole
place: 679.5÷15=45.3.
number
Letters represent decimal
 Recognise the
number < 1. Totals for 4 of
equivalence of
the rows and columns are
common fractions to
shown. Find the missing
decimals and
numbers and totals?
percentages
A
B
C
B
1.5
 Solve problems and
A
C
D
B
1.4
puzzles involving
C
C
C
C
2.0
missing numbers and
D
A
C
C
1.5
1.3
1.7
1.7
1.8
quantities
Pentagons, squares and
 Solve problems
triangles in a box share a
involving totals made
total of 49 sides. How many
up of combinations of
of each shape are in the
up to 3 multiples of 1box?
digit numbers
Mental Work:
 Recall and use multiplication and division facts
 Calculate complements of fractions to whole numbers
 Compare fractions with equal & related denominators
Extension Work:
 315 divisible by 7 as 2x3+15=21 and 21 is divisible by
7. Does this work for other numbers?
17
Scheme of Work: Mathematics Year 5
Summer Term (Second half term)
Week 1
Number/Measurement
Main Teaching:
Notes/examples
Estimate the weight of an
 Estimate weight,
capacity and volumes orange, plum and grape?
Use your estimate to
of objects, scale up
work out approximately
and measure to
how many pieces of each
compare
fruit there be in 0.25kg?
approximations
Weigh each piece of fruit
against exact values
and scale up to 0.25kg. Is
 Know that 1 cubic
your estimating precise?
centimetre displaces
Estimate the volume of
1ml of water and use
each piece of fruit in cm³.
to measure volumes
Identify the numerator or
of irregular shapes
the denominator in these
 Work out a fraction
equivalent fractions:
that is equivalent to
2
█ 3
█ 3
6 2
8
another fraction given
= ; = ; = ; =
5
10 5
25 4
█ 3
█
its numerator or its
What is one third of 45g?
denominator
What is ¾ of 1l in ml?
 Convert improper to
What is 1⅛ of 4m in cm?
mixed fractions and
What is 23/5 of 500g?
vice versa
Hanna counts out her
 Add and subtract
stickers. If I had 3 more I
fractions with
would have ¼ of all 60
denominators that
stickers. How many
are multiples of one
stickers has she?
another
Tim eats ⅔ of his chews.
 Multiply proper
He gives ¼ of what he
fractions and mixed
has left to Clea who eats
numbers by whole
these 3 chews. How
numbers in the
many chews did Tim
context of measures
have at the start?
 Solve multi-step
What are the answers to:
2
7 5
1
3 7 2 1
problems involving
+ ; + ;1 - ; - ?
5
10
6
2
4 8 3 9
fractions
Mental Work:
 Recall and use multiplication and division facts
 Extend sequences of multiples of 2s to 12s
 Calculate fractions of quantities, exact answers
Extension Work:
 Measure volume and capacity and convert units
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 2
Number
Main Teaching:
Notes/examples
 Read, write and order The Roman numerals for the
numbers 1 to 10 are:
whole and decimal
I
ll
lll
lV
V
numbers including
1
2
3
4
5
those with
Vl
Vll
Vlll
lX
X
placeholder zeros
6
7
8
9
10
 Round decimal
Remember the l, V and X are
numbers to the
1, 5 and 10, and L and C are
nearest whole
50 and 100.
number and tenth
X
XX
XXX
XL
L
 Read negative
10
20
30
40
50
numbers in context,
LX LXX LXXX XC
C
from scales and
60
70
80
90 100
calculate intervals
The next 2 symbols are D and
between two integers M. They are 500 and 1000. We
 Read and use
can now write large numbers
Roman numerals l, V, using Roman numerals.
X, L, C, D and M;
C
CC
CCC
CD
D
record and identify
100
200
300
400
500
years written using
DC DCC DCCC CM
M
Roman numerals
600
700
800
900 1000
 Generate and extend
Can you see the underlying
number sequences
rules apply again this time with
that cross zero, and
the 100, 500 and 1000? The C
with decimal or
behaves like the X and l; the D
fractional steps
like the L and V. We write the
 Convert percentages
year 2010 as MMX. A grave
to decimal and
stone had the year of a death
fractional equivalents CMLXXXll on it? What year
and vice versa
was it? Write other years using
 Solve problems
Roman numerals. What does
involving simple
the 11 times table look like in
percentages of
Roman numerals?
quantities
Mental Work:
 Round number to required degree of accuracy
 Calculate multiples of 10% and 5% of given quantities
 Complete number sentences with + or - answers
Extension Work:

Explore how the Mayan’s number system used . and ̶
Week 3
Geometry
Main Teaching:
Notes/examples
 Compare, measure
and draw acute,
obtuse and reflex
angles in degrees
using a protractor
 Know that the angles
What are these 2 shapes
at a point sum to
called? What do the
360ºand adjacent
arrows and little squares
angles on a straight
tell us? What are the lines
line sum to 180º
inside the shapes called?
 Interpret and use the
List the properties of a
conventional
rectangle. And of the
markings for parallel
lines and right angles trapezium. Draw similar
trapeziums and rectangles
 Measure the angles
with their diagonals and
about parallel lines
and interior angles of cut them out. Measure the
angles and cut along the
quadrilaterals;
diagonals and look for any
conjecture and test
generalisations about properties. Conjecture and
test them out with other
the relationship
shapes.
between angles
Alice has drawn 4 identical
 Use the properties of
quadrilaterals. She says “I
angle sums to find
can always fit my 4
missing angles
quadrilaterals around a
 Know that regular
point with no spare space.
polygons have equal
Rectangles and squares
sides and equal
angle and a square is are easy, but other shapes
work too.” Test her
regular quadrilateral
conjecture. What does it
 Make simple
tell us about the angles in
deductions and
a quadrilateral?
explain reasoning
Mental Work:
 Estimate the size of acute, obtuse & reflex angles
 Calculate angles about point, on straight lines
 Visualise quadrilaterals from their descriptions
Extension Work:
 Explore practically angles around parallel lines
18
Scheme of Work: Mathematics Year 5
Summer Term (Second half term)
Week 4
Number
Main Teaching:
Notes/examples
In the 14 times table tell me
 Practise and use
any facts you know? Yes 1x14
formal written
and 10x14. We will add,
column methods
subtract, double and halve
to add and
facts we have to work out all
subtract up to 4the facts?
digit whole
1 x 14
14
numbers and
2 x14
28
decimals with up
3 x14
42
to 3 decimal
4 x14
56
places
5 x14
70
6 x 14
84
 Practise and use
7 x 14
98
formal written
8
x
14
112
methods to
9 x 14
126
multiply and divide
10 x14
140
3- and 4-digit
11x14
154
whole numbers
12x14
168
and decimals with How can we find 3x14? Add
up to 2 decimal
the 2x14 and 1x14. What do
places, by 1- and
we do to get 6x14? Double to
2-digit numbers
get 4x14; 8x14... add or
subtract to work out 7x14...
 Add, subtract and
Can you see any patterns?
double facts to
What unit digit is in 17x14?
construct the 14,
What multiples of 14 will have
16, 18
a 6 digit in the units? Is 1347
multiplication
divisible by 14? Why not?
tables
Could 734 by a multiple of 14?
 Identify and
Is it? Why not? Work out the
describe patterns
in the unit digits in 16, 18 times tables. Write out
the 12, 14, 16 and the 12 times table too. Look for
patterns and relationships.
18 times tables
Describe them. Explain how
and relationships
between the digits they inform mental calculation.
Mental Work:
 Recall and use multiplication and division facts
 Calculate simple fractions & %ages of quantities
Extension Work:
 Extend to construct 22, 24, 26, 28 times tables;
identify patterns in the digits and use to calculate
©Nigel Bufton MATHSEDUCATIONAL LTD
Week 5
Number
Main Teaching:
 Solve multi-step word
problems involving the
four operations;
represent the problem
in a picture to annotate
and interpret and to
identify the required
calculations
 Solve problems where
two unequal quantities
are to be scaled up or
down while keeping
the relative sizes fixed
 Solve simple ratio
problems in context by
scaling up or down
 Solve missing digit
problems involving the
four operations
 Generate number
sequences that involve
fractions and
decimals; identify and
describe sequences
using term-to-term
rules
 Identify, generate and
describe patterns in
tables of numbers;
generalise and test
and explain thinking
and reasoning
Notes/examples
For every 2 cups of flour
add half a spoon of salt.
How much salt in 8 cups?
At a large party, every plate
has 3 sandwiches; 2 cakes
and 1 piece of fruit. In one
room there are 14 plates,
how many cakes are there?
Another room has 36
sandwiches; how many
plates are there? The third
room the total number of
cakes, sandwiches and fruit
comes to 120. How many
plates are in that room?
Fill in this x table:
x
1
2
3
:
12
1
1
2
3
2
2
4
6
3
3
6
9
...
12
Find the sum of the
numbers in the 3 by 3
square. Now work out the
sums of other squares of
numbers which have 1 in
the left-hand corner. What
do you notice? Can you
explain why the answers
follow a pattern? What are
the sums of the rows and
columns? What does the 12
by 12 square add up to?
Mental Work:
 Recall and use multiplication and division facts
 Scale 2 quantities up or down retaining relative size
Extension Work:
 Count on, back from whole numbers in fraction steps
predict the number of steps to reach a target number
Week 6
Number/Measurement/Geometry
Main Teaching:
Notes/examples
 Measure and work
out the perimeter of
composite rectilinear
shapes
 Identify and apply the
symmetry and
structure of rectilinear
shapes to calculate
areas and perimeters
Describe the structure and
 Use a rectangle as a
symmetry of each shape.
template to generate
Explain how you use this to
sequences that
work out the area and
follows a pattern and
perimeter of the shapes so
rule; describe in
you don’t count each
words the rule used
individual squares? Marlie
to generate the
makes shape sequences
sequence
using blue and red 6cm by
 Calculate the area
4cm rectangles. Find the
and perimeter of a
areas and perimeters of her
sequence that is
3 shape sequences. She
constructed from
continues her pattern of
rectangles; predict
shapes. Describe how to
the area and
calculate the area and
perimeters for
sequences of a given perimeter of her shapes
number of rectangles sequences. What is the
area and perimeter of a 4,
and check by
5...10... shape sequence?
calculation
 Calculate missing
lengths of sides in
rectangles and
simple composite
rectilinear shapes
Mental Work:
 Visualise & describe composite rectangular shapes
 Calculate simple areas & volumes given dimensions
Extension Work:
 Femi uses 3cm by 2cm rectangles to build a shape
5cm by 6cm. How? What rectangles can he make?
19