National Curriculum Aims:
Medium Term Planning Year 5 Theme 6: Developing and using fractional equivalence to solve problems
KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims
Fluency
The main focus of this theme is to further develop children’s understanding of fractional equivalence
by adding, subtracting and multiplying them, and use this knowledge to solve problems. Fluency in
fractions (converting between equivalent, mixed numbers, improper fractions etc from Theme 3) is
crucial to support calculating with fractions (I know 2/8 = 1/4 so 2/8 + 1/4 = 2/4). There will be regular
opportunities to count in fractions to reinforce the concept of fractions as numbers. Ensure steps in
progression are clear (see over page). Children will learn that multiplying a fraction by a whole number
is to find a fraction of that number (Ben spent 5/6 of his pocket money: 5/6 of £3 = 5/6 x £3) , which in
turn is linked to division (“to find a sixth, you divide by 6”), and make connections with finding percentages of a number: 40% of 20m = 2/5 x 20. Giving the children a variety of problems to solve will require
them to demonstrate a range of strategies involving mental calculation and fractional equivalence, plus
some occasional written calculation. Estimations (making sense of the problem) and checking will ensure accurate answers, especially when a number of steps are involved: Azra scored 80%, Jazz got 3/4
of the marks and Issy achieved 20% more than Azra. If the test total was 60, how many marks did they
each score? Equivalence problems (36/5 = ÷ 10) will reinforce the use of the equals sign.
N.C.
Fractions (including decimals and percentages)
Approximately 3 weeks
SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson
 Count up and down in fractions
 Compare and order fractions whose denominators are all multiples of the same
number
 Read, write, order and compare numbers with up to three decimal places
 Recall multiplication and division tables
 Identify multiples and factors, including finding all factor pairs of a number, and
common factors of two numbers
 Distinguish between regular and irregular polygons based on reasoning about
equal sides and angles
 Complete, read and interpret information in tables
Multiplication and division
Addition and subtraction

STATUTORY
Reasoning
 recognise mixed numbers and improper fractions and convert from one form to the other and write math-



NON-STATUTORY
Problem-Solving


 multiply and divide numbers mentally drawing
 add and subtract numbers mentally
ematical statements > 1 as a mixed number [e.g. 2/5 + 4/5 = 6/5 = 1 1/5]
upon known facts
with increasingly large numbers
add and subtract fractions with the same denominator and denominators that are multiples of the same
 multiply and divide whole numbers and those
 use rounding to check answers to
number
involving decimals by 10, 100 and 1000
calculations and determine, in the
context of a problem, levels of
multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
 solve problems involving addition, subtraction,
accuracy
multiplication and division and a combination of
recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’,

solve addition and subtraction multithese,
including
understanding
the
meaning
of
the
and write percentages as a fraction with denominator 100, and as a decimal
equals
sign
step problems in contexts, deciding
solve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those
which operations and methods to use
 solve problems involving multiplication and divifractions with a denominator of a multiple of 10 or 25.
and why.
sion,
including
scaling
by
simple
fractions.
read and write decimal numbers as fractions [e.g., 0.71 = 71/100 ]
recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions. They extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils
connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.
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 scaling by simple fractions, including fractions > 1.
Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed
number. Pupils continue to practise counting forwards and backwards in simple fractions.
Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities. They mentally add and subtract tenths, and one-digit whole numbers and tenths.
Pupils should make connections between percentages, fractions and decimals (e.g., 100% represents a whole
quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and relate this to finding ‘fractions of’
© Wandsworth & Merton Local Authorities, 2014
They use and understand the terms factor, multiple
and prime, square and cube numbers.
Pupils interpret non-integer answers to division by
expressing results in different ways according to the
context, including with remainders, as fractions, as
decimals or by rounding (for example, 98 ÷ 4 = = 24 r
2 = 24 = 24.5 ≈ 25). 4 98 2 1 Pupils use and explain
the equals sign to indicate equivalence, including in
missing number problems (for example, 13 + 24 = 12
+ 25; 33 = 5 x _ ).
They practise mental calculations with
increasingly large numbers to aid fluency
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
(from Place Value)
National Curriculum Aims:
Medium Term Planning Year 5 Theme 6: Developing and using fractional equivalence to solve problems
EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims
Fluency
KEY QUESTION ROOTS to be used and adapted in different contexts
Spot the mistake: ⅖ + ⅕ = 3/10. How do you know?
Sometimes, always or never true: fractions are smaller than one; fractions can be written as decimals; when you
multiply one number by another the answer will be bigger
What do you notice? Find 30/100 of 200. Find 3/10 of 200. What do you notice? Can you write any other similar
statements?
Would you rather…. Have 20% of £200 or 25% of £180? Explain your reasoning.
Continue the pattern: ¼ + 7/4 = 2, 2/4 + 6/4 = 2, ¾ + 5/4 = 2 ….
¼ x 3 = , ¼ x 4 = , ¼ x 5 = . How many steps will it take to get to 3?
Show me… 4/6 + 1/3, 5/8 + 4/8, 3/6 + 1/3 + 2/6
The answer is …. 2 ¼. What is the question?
Fractions Jigsaw www.nrich.maths.org/5467
What do you notice
about ⅖ + ⅗ ?
Using equivalent
fractions:
Is the sum
more or less
than half?
Reasoning
So what does
1— ⅙ look like?
What is the sum of theses numbers?
How do you know?
⅜+⅜+⅛
Problem-Solving
I can explain both
methods to solve
5/8 x £320?
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?
Suggested ideas: Chocolate Heaven!
www.badseypublications.co.uk
 Estimate the fraction of the chocolate bar is shown?
 I eat 1/4 of a bar on Monday, 1/8 on Tuesday and 3/8 on Wednesday.
How much is left?
 If the chocolate is shared out equally between the seated children at
each table , which table would I be best to sit at?
(nrich.maths.org/34 )
 Mars bars come in a variety of sizes. Which would you say is the best
value for money, and why?
Fun size bags (250g) £1.85, 51g Mars Bar 60p, 7 pack Mars Bars £2.50,
Celebrations box (245g) £3. What is the average percentage of Mars
Bars in a box of celebrations? What is this as a fraction?
 Which chocolate bar has the highest percentage of cocoa solids? Can you
order the bars to show?
Infinite Chocolate trick
Watch, investigate, explain how it works….!
https://www.youtube.com/watch?
v=dmBsPgPu0Wc&safe=active
How many ways can you
make 0.68 using 2,3 or 4
decimal numbers? Which
ones can you convert to
fractions/percentages?
FDP Happy Families!
Match the flashcards containing equivalent fractions, decimals and percentages. Draw pictures/
diagrams to match. Hang
on a washing line. Find
your partner/family…
© Wandsworth & Merton Local Authorities, 2014
Approximately 3 weeks
Nine is half of a number. What is
one-third of the number?
http://
www.tes.co.uk/
teachingresource/KS3Maths-AddingfractionsCatchphraseGame-6121504