National Curriculum Aims:
Medium Term Planning Year 5 Theme 9
Theme Title: Problem-solving using mental and written strategies
KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims
Fluency
The main focus of this theme is to provide varied opportunities for pupils to rehearse and develop mental and
written strategies to solve problems. Pupils will use the standard written methods for all four operations to calculate
the answers to money and measures problems: If James drove 145.7km further than Anita, who drove 65.27km, how
much further did James drive than Anita? Pupils will apply a range of mental strategies (see Wandsworth calculation
policy) including the use of the distributive law. A prize of £188 is shared between 8 winners. How much do they
each receive? (160÷8)+(28÷8)=23.5 Pupils will use their knowledge of decimal and fraction equivalence to show the
remainder as a decimal. Pupils will explore types of numbers such as factors, primes, square, cube and composite
numbers and use these to develop calculation strategies, for example using factors to break down and reorder
multiplication of two-digit by one-digit calculations. Continuing from previous themes, pupils will investigate the
relationship between square and cube numbers and the addition and subtraction of fractions: What is 3/4 of a bar of
chocolate added to 6/8 of a bar? They will also solve problems in the context of measures where fractions are
multiplied to give a mixed number answer. Pupils will then interpret the mixed number as a measure: the capacity of
a thimble is one eighth of a 320ml beaker. How much does the thimble hold? Pupils could use bar models to help
illustrate the problem. Pupils will solve scaling problems by linking division and fractions of measures: What is the
size of a model dog if it is 1/4 of the size of the real thing that measures 120cm?
SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson
 identify 3-D shapes, including cubes and other cuboids, from 2-D representations
 know angles are measured in degrees: estimate and compare acute, obtuse and
reflex angles
 draw given angles, and measure them in degrees (°)
 identify:
 angles at a point and one whole turn (total 360o)
 angles at a point on a straight line and ½ a turn (total 180°)
 other multiples of 90°
 use the properties of rectangles to deduce related facts and find missing lengths
and angles
 distinguish between regular and irregular polygons based on reasoning about equal
sides and angle
 identify, describe & represent the position of a shape following a reflection or
translation, using appropriate language, & know that the shape has not changed.
N.C.
Number—Addition and Subtraction Number—Multiplication and Division
 Add and subtract whole numbers with  Identify multiples and factors, including finding all factor pairs of a number, and
STATUTORY
Reasoning
Problem-Solving
more than 4 digits, including using
formal written methods (columnar
addition and subtraction)
 Add and subtract numbers mentally
with increasingly large numbers
 Use rounding to check answers to
calculations and determine, in the
context of a problem, levels of
accuracy
 Solve addition and subtraction multistep problems in contexts, deciding
which operations and methods to use
and why.






Approx. 4 weeks
common factors of two numbers
establish whether a number up to 100 is prime and recall prime numbers up to
19
Multiply and divide numbers mentally drawing upon known facts
multiply numbers up to 4 digits by a one- or two-digit number using a formal
written method, including long multiplication for two-digit numbers
Divide numbers up to 4 digits by a one-digit number using the formal written
method of short division and interpret remainders appropriately for the context
by rounding and as fractions and decimals
Recognise and use square numbers and cube numbers, and the notation for
squared (2) and cubed (3)
Solve problems involving multiplication and division including using their
knowledge of factors and multiples, squares and cubes
solve problems involving addition, subtraction, multiplication and division and a
combination of these, including understanding the meaning of the equals sign
Solve problems involving multiplication and division, including scaling by simple
fractions and problems involving simple rates.
Fractions (including decimals & percent Add and subtract fractions with the same
Measurement
 solve problems involving
converting between
units of time
denominator and denominators that are
multiples of the same number
 use all four operations
 Multiply proper fractions and mixed numbers by to solve problems
involving measure [e.g.,
whole numbers, supported by materials and
length, mass, volume,
diagrams
money] using decimal
 Solve problems involving numbers up to three
notation, including
decimal places
scaling.
 Solve problems which require knowing
percentage and decimal equivalents of 1/2, 1/4,
1
/5, 2/5, 4/5 and those fractions with a
NON-STATUTORY
Pupils connect multiplication by a fraction to using
fractions as operators (fractions of), and to division,

building on work from previous years. This relates to
Pupils practise using the formal written
scaling by simple fractions, including fractions > 1.
methods of columnar addition and

Pupils practise adding and subtracting fractions to
subtraction with increasingly large
become fluent through a variety of increasingly comnumbers to aid fluency
plex problems. They extend their understanding of
They practise mental calculations with
They use and understand the terms factor, multiple and prime, square and cube
adding and subtracting fractions to calculations that
increasingly large numbers to aid fluency numbers.
exceed 1 as a mixed number.
(for example, 12 462 – 2300 = 10 162).
They understand the terms factor, multiple and prime, square and cube numbers
They practise adding and subtracting decimals, inand use them to construct equivalence statements (e.g. 4 x 35 = 2 x 2 x 35; 3 x 270 =
cluding a mix of whole numbers and decimals, deci3 x 3 x 9 x 10 = 92 x 10).
mals with different numbers of decimal places, and
Pupils use and explain the equals sign to indicate equivalence, including in missing
complements of 1 (for example, 0.83 + 0.17 = 1).
number problems (for example, 13 + 24 = 12 + 25; 33 = 5 x )
© Wandsworth & Merton Local Authorities, 2014 Distributivity can be expressed as a(b+c) = ab+ac in preparation for algebra
Pupils use their
knowledge of place
value, multiplication
and division to convert
between standard units.
Pupils use all for
operations in problems
involving time and
money, including
conversions (e.g. days to
weeks, expressing the
answer as weeks and
days).
National Curriculum Aims:
Medium Term Planning Year 5 Theme 9: Problem-solving using mental and written strategies
EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims
Fluency
KEY QUESTION ROOTS to be used and adapted in different contexts
Use the fact (3x 75 = 225) to work out 450 ÷ 6 and 225 ÷ 0.6
Is it always, sometimes or never true that a square number has an even number of factors?
What’s the same, what’s different about 4(10+6) and (4x10)+(4x6)? Draw it. Show it using arrays.
Convince me….. that 14 x 8 = 4 x 2 x 2 x 7
Give an example of two square numbers that when added together give another square number...and another and
another. Can you explain why this works?
Making an estimate Which of these number sentences have the answer that is between 0.5 and 0.6….11.74 - 11.18
or 33.3 – 32.71
True or false? 1 2/3 - 4/3 < 1. Prove it.
Making links Apples weigh about 170 g each. How many apples would you expect to get in a 2 kg bag?
The answer is 43, what is the question?
True or false? Are these number sentences true or false? 6.17 + 0.4 = 6.57…….. 12 – 0.9 = 8.3 Give your reasons.
Reasoning
Tom gets £4 pocket money
each week. The following
week, his dad decides to
increase it by a 1/4. How
much does he get the
following week? How much
the following week?
497 chocolate eggs are
packed into boxes of 4.
How many boxes are filled?
Problem-Solving
1 2 4 r1
1
4
4 9 7
24 r1 = 24 1/4 = 24.25
So there is 1 egg left over
out of space for 4. So 24
boxes are filled.
1
/6 x 8 = 1 2/6 (1 1/3)
‘One sixth, eight
times’
OR
‘One sixth of 8’
8 ÷ 6 = 1.33˙ or 1 2/6
Use the Sieve of Eratosthenes to explore
patterns created in a grid using multiples.
What do we call the numbers left
untouched? (See nrich.maths.org/7520)
The Lego model of the tower of
Big Ben is a tenth of the size of
the real thing. In reality, it
measures approximately 96.3m
tall. How tall is the model?
1
Sally builds her own model. It is /3 of the
size of the Lego tower. How tall is Sally's
model?
The total area of the
green sections is 7 x 8
which is the same as
(7 x 6) + (7 x 2) = 56m2
I can also say…..
7 x (6 + 2) = 56m2
6m
1m 2m
A different number of digits
A mix of whole numbers and
decimals
See Wandsworth LA Calculation Policy for more detail on
developing mental and written procedures!
Can some of the key thematic ideas be delivered as part of a mathematicallyrich, creative topic? Suggested ideas:
DT link—Model-building
Study life-size proportions and measurements of toys, vehicles or buildings
linked to a text studied in English.
Use scaling by whole numbers and fractions to build scaled-up and scaleddown models.
 The proportions of this toy car are _cm by _cm by_cm. Draw a model of the
car that would by 3 times as big. What would the proportions be?
 The proportions of this dolls house are……..build a dolls house that is 1/4 of
the size.
I think two prime
Non-Routine Problem: Pupils investigate
numbers added
prime and cube numbers to find out if this statement is together make a
sometimes, always, never true. Is there a systematic way cube number.
of working through the problem? Is there a pattern in the
results? What generalizations can be made about primes and
numbers?
John ran 3.46km of
a 10km race. How
far would he have
to run in order to
finish the race?
Decimals with a different
number of decimal places
7m
What are the factors of 36? Which factors are prime
factors? How do you know?
Which factors are composite numbers? Why aren’t
they prime?
How many pairs of factors does this number have?
Why does it have an uneven number of factors?
Decimals in the context of
Use FACTOR PAIRS to multiply and divide
money and measures
Six people pay £84 for a 84 x 6
concert ticket. How
(60x6)+(24x6)
much do they pay in
360+144 = 504
total?
James is making
a cake. The
recipe 1/6 kg of
flour. How much
flour is needed
for 8 cakes?
Pupils will become increasingly
fluent in adding and subtracting:
1
Can you use the
distributive law
to multiply larger
numbers?
/6 x 12 =
What is a sixth of 12 metres?
A seedling is 1/6 of the size of a larger
plant, which is 12m tall. How tall is
the seedling?
8
/10 of one kg of potatoes was added to a
shopping bag containing 0.4 of a kg of
carrots. What does the shopping weigh?
weigh?
8
/10 + 2/5
8
/10 + 4/10 = 12/10
800g
= 1 2/10 of a kg
= 1kg and 200g
= 1.2kg
Approx. 4 weeks
400g
Seven lorries are used
to transport 72 crates
of bananas each.
How many crates are
on the lorries?
630 bunches of
bananas are packed
into boxes of 14. How
many boxes are
needed?
© Wandsworth & Merton Local Authorities, 2014
72 x 7 =
8x9x7=
8x7x9=
56 x 10 = 560
560 - 56 = 504
3
“A factor pair of 72
is 8 and 9. I can
rearrange the
factors to make the
calculation easier…..
I can do 56 x 10 and
adjust.”
“A factor pair of 14
is 7 and 2 so I can
divide 630 by 7 then
halve.”
630 ÷ 14
= 630 ÷ 7 ÷ 2
= 90 ÷ 2
= 45