Year 5 Theme 1: Using place value to solve problems
KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims
Approx. 4 weeks
SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson
Fluency
The main focus of this theme is the understanding of number to at least 1,000,000 to support mental
calculation. Children will be developing their fluency of working within this range of numbers, including
comparing, counting (e.g. 2653, 2753, 2853….), rounding and solving problems, building on the concrete
and pictorial representations used previously. What is the missing number: 17.85— = 17.22? Drawing on
their knowledge of place value, children will develop fluency with a range of mental calculation strategies
(see blue box over page). E.g. What is the value of 7 in 3 274 162? Write 4 + 6⁄10 + 2⁄100 as a decimal.
1— = 0.83). Counting decimals using a number line (5.2, 5.1, 5, 4.9 …) is forwards and backwards, and
children will identify the term-to term rule (e.g. add 0.5). Different units of measure and decimal numbers
(including thousandths), building on Year 4 division by 10/100, will be incorporated throughout the various
contexts presented to the children. Mrs Jones bought 12.5 m of fabric on Monday, and then another 70 cm
on Tuesday. How much did she buy altogether? Children will justify their approaches to one another,
explaining methods used and demonstrating an understanding of the underpinning place value. Children
will check their own levels of accuracy in both calculations and solving problems by rounding and
estimating, including making sense of the answer.
A bank of ideas taken from Year 4 to be selected as appropriate to meet the needs of
your class:
 Count forwards/backwards in multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 100 & 1000
 Identify, represent & estimate numbers (up to 5 digits) using different representations
 Add & subtract two two-digit numbers mentally
 Recall and use multiplication & division facts for multiplication tables up to 12 x 12
 Multiply & divide numbers mentally, including multiplying three numbers and multiplying/dividing numbers by 10 and 100
 Recognise, compare and round decimal numbers up to two decimal places
 Recognise and write decimal equivalents to ¼, ½ and ¾
 Read, write and convert time between analogue and digital clocks (12/24 hour)
 Compare and classify geometric shapes based on their properties and sizes
 Interpret data presented as bar charts and time graphs
NC.
National Curriculum Aims:
Medium Term Planning
STATUTORY
Reasoning
Fractions
Number—Calculation (+,-,x,÷)
read, write, order and compare numbers to at
least 1 000 000 and determine the value of each
digit
Recognise & use thousandths & relate them to tenths,
hundredths& decimal equivalents
 Add and subtract numbers mentally with  convert between different units of
metric measure (for example,
increasingly large numbers
kilometre and metre; centimetre and
 Use rounding to check answers to calculametre; centimetre and millimetre;
tions and determine, in the context of a
gram and kilogram; litre and
problem, levels of accuracy
millilitre)
 Solve addition and subtraction multi-step
problems in contexts, deciding which op use all four operations to solve
erations and methods to use and why.
problems involving measure [for
 Multiply & divide whole numbers and
example, length, mass, volume,
those involving decimals by 10, 100 &
money] using decimal notation,
1000
including scaling.
Read, write, order & compare numbers up to 3 dp
Read and write decimal numbers as fractions
count forwards or backwards in steps of powers of
Round decimals with two dp to the nearest whole num10 for any given number up to 1 000 000
ber and to one dp
Round any number up to 1 000 000 to the nearest Solve problems involving number up to 3 dp
10, 1000, 10 000 and 1000 000
Solve number problems and practical problems
involving all of the above.
NON-STATUTORY
Problem-Solving
Number—Place value
Pupils identify the place value in large whole
numbers.
They continue to use number in context, including
measurement. Pupils extend and apply their
understanding of the number system to the
decimal numbers and fractions that they have met
so far
They should recognise and describe linear number
sequences, including those involving decimals,
and find the term-to-term rule
© Wandsworth & Merton Local Authorities, 2014
Pupils extend counting from year 4, using decimals,
bridging zero e.g. on a number line
They add decimals, including a mix of whole numbers and
decimals, decimals with different numbers of places, and
complements of 1 (e.g. 0.83 + 0.17 = 1), and mentally add
tenths, and one-digit numbers and tenths. They say, read
& write decimal fractions and related tenths, hundredths
& thousandths accurately and are confident in checking
the reasonableness of their answers to problems. They
should go beyond measurement/money models of
decimals e.g. solving puzzles involving decimals
Measurement
They practise mental calculations with
increasingly large numbers to aid fluency for
example, 12 462 – 2300 = 10 162).
Pupils use their knowledge of place
value and multiplication and division to
convert between standard units.
Pupils use and explain the equals sign to
indicate equivalence, including in missing
number problems (e.g. 13 + 24 = 12 + 25; 33
= 5x )
Pupils use addition and subtraction 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 1: Using place value to solve problems
EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims
Approx. 4 weeks
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 mathematically-rich, creative topic?
KEY QUESTION ROOTS to be used and adapted in different contexts
Fluency
 If I know……. Then how could I work out…….? (using knowledge of x/÷ 10/100/1000)
 Show me how you know that you are right Does 999 gives the same answer when rounded to the nearest 10, 100 or Suggested ideas:
1000?
The Perfect Bedroom. Given a budget, children are tasked with
 What is the same? What is different? (.)
designing the bedroom of their dreams, including furniture and
 What do you notice? Round 343997 to the nearest 1000. Round it to the nearest 10000. What do you notice?
 True or false? Are these number sentences true or false? 6.17 + 0.4 = 6.57, 8.12 – 0.9 = 8.3 Give your reasons.
decorations. They draw plans to scale (converting m to cm/mm)
 Do, then explain Show the value of the digit 5 in these numbers? 350114 567432 985376 Explain how you know.
and cost each item. Materials can be bought in different sizes/
 Show me……. the number 98 with place value counters, 1.250l on the jug/scale, …
lengths to involve addition/subtraction.
 Top tips Explain how to round decimal numbers to one decimal place?
 What comes next?
Non-routine problem: missing numbers logic puzzle.
646000-10000= 636000
Which numbers could make the following equation correct?
636000 –10000 = 626000
+
x
÷
= 50
626000- 10000 = 616000 ….
Reasoning
Play ‘Zap the digit’: In pairs choose a decimal to enter into
a calculator e.g. 47.25. Take turns to ‘zap’ (remove) a
particular digit using subtraction. For example to ‘zap’ the
2 in 47.25 subtract 0.2 to leave 47.05.
A number rounded to the
nearest thousand is 76000
What is the largest possible
number it could be?
Partition decimals using both decimal and fraction notation for example recording 6.38 as
6 + 3⁄10 + 8⁄100 and as 6 + 0.3 + 0.08. Children write a decimal given its parts: e.g. they record
the number that is made from 4 wholes 2 tenths and 7 hundredths as 4.27
Using what the children know to calculate with decimals.
Mental addition and subtraction strategies:
Problem-Solving
 Children should be able to respond rapidly to oral or written
questions, explaining the strategy used, e.g. 750 take away
255, take 400 from 1360, 4500 minus 1050, subtract 3250
from 7600, 1800 less than 3300, 4000 less than 11 580
 Derive quickly related facts, e.g. 80 + 50 = 130, 130 – 50 = 80,
800 + 500 = 1300, 1300 – 800 = 500
 Derive quickly number pairs that total 100 or pairs of multiples of 50 that total 1000, e.g. 32 + 68 = 100 or 150 + 850 =
1000
 Identify and use near doubles, e.g. work out 28 + 26 = 54 by
doubling 30 and subtracting first 2, then 4, or by doubling 26
and adding 2
 Add or subtract the nearest multiple of 10, 100 or 1000 and
adjust, e.g. adding or subtracting 9, 19, 29 ... to/from any two
-digit number
 Work out mentally by counting up from a smaller to a larger
number e.g. 8000 – 2785 is 5 + 10 + 200 + 5000 = 5215
 Understand and use language associated with addition and
subtraction, e.g. difference, sum, total
© Wandsworth & Merton Local Authorities, 2014
What is two hundred and seventy six centimetres to
the nearest metre?
Emily, Ben and Nisha collect money for charity. Emily
collects £2.75 more than Nisha. Ben collects £15.
Nisha collects £7 less than Ben. Altogether how much
money do the three children collect?
Use of manipulatives to represent the place value may include
place value counters, dienes and number lines.
E.g. the hundred dienes block can represent one whole, and therefore the rod
is a tenth, and the unit a hundredth.
Using scales as number lines:
I know that 65.90 is
equivalent to
6590⁄100