Common Misconceptions with Fractions and Decimals
Misconception
Half means just one whole cut into two
pieces
For example – many children will wrongly
say that this circle has
been cut into thirds.
Fractions of the whole are whole
numbers in themselves.
For example to think that when a cake is
cut into half you get two cakes (which
implies you get more, when in fact it’s
just 2 halves of the whole, which is less)
Misconception
Fraction symbols incorrectly
identified.
For example to read 1/3 as three
quarters or to write three quarters as
3’ 1/4’s or simply not being able to read
fraction symbols.
Misconception
The bigger the number on the bottom,
the bigger the fraction.
This results to wrongly ordering unit
fractions. For example to think that 1/6
is bigger than 1/2
Misconception
The size of a fraction depends solely
on the number at the bottom
(denominator) and you can ignore the
number on the top (numerator).
For example: to think that 1/4 is bigger
than 7/8.
What needs to be taught
Use regions (continuous models) and sets (discrete
models), to emphasis fractions as being equal
pieces or fair shares.

Book 7 p.11 “Fair Shares” - CA to AC


Bev Dunbar book ”Fractions”
Stations involving cubes, playdough containers, shapes,
blocks, beads, pegboards, geoboards,
What needs to be taught
Showing the language behind the fractions. – what
the “ths” code is.

Book 4 p.6 “Fraction Pieces” CA, AC, EA, AA

Book 4 p.6 “Creating Fractions” AC,EA,AA,AM,AP

Book 4 p.7 “Non-Unit Fractions” EA, AA, AM, AP

Book 4 p.8 “Packets of Lollies” EA, AA, AM, AP
What needs to be taught
Understanding that the number on the bottom
tells us how many parts the whole has been divided
into. The more parts there are the smaller each
portion will be.

Book 4 p.18 “Who Has More Cake” AA, AM, AP

Exploring fraction circle kits and fraction wall kits

Rotating Regions
What needs to be taught
Fractions greater than 1 - to show the need to
coordinate the top and bottom numbers to
determine the size of the fraction. The number on
the bottom means how many parts the whole has
been divided into, and the number on the top
means how many of those parts are chosen.

Book 7 p. 20 “Fraction Circles” AC to EA

Fraction Circles Game – dice (1/4, 3/4, 1/2, 1/8, 3/8, 5/8)

Book 7 p. 22 Independent Work “Fractions in a Row”
Misconception
3
/4 is always more than 1/2,
Not making reference to the whole.
Misconception
Wrongly convert fractions to ratios
and vice versa
For example to think that 1/2 = 1:2 as a
ratio, when in fact 1/2 is 1:1 as a ratio
What needs to be taught
Understanding that fractions are operators as well
as numbers and must always be related to the
whole. i.e. When is 1/4 bigger than a 1/2? Make a
fuss of the whole.

Book 4 p.18 “Little Halves and Big Quarters” - AM, AP

Going from Part to whole – using parts of a shape and
parts of a set

Book 7 p.26 “Birthday Cakes” EA to AA

Book 7 p.28 Independent Work:Chocolate Chip
Cheesecake (MM7-1) & Mystery Stars (MM7-8)

Doug Clark’s chocolate bars. (Tables set up with 1,2,3 or
4 bars on them. shared between 9 people)

Bead number lines – double number lines
What needs to be taught
Understanding the relationship between ratios and
fractions through visual representation

Book 7 p.30 “Seed Packets”
- EA to AA
Misconception
What needs to be taught
Fractions and decimals are negative locating fractions on a number line to show that
numbers
fractions are numbers as well as operators & that
For example to think that 5/8 or 0.45 an infinite set of fractions exist between whole
are less than 0
numbers.
.
Misconception
Fractions are added together by
adding the top numbers together then
adding the bottom numbers together.
For example to think that 3/5 + 2/4 = 5/9

Counting in halves, thirds etc. and marking fractions along
a number line

Book 7 p.32 “Trains” EA to AA

Book 7 p.28 Fraction Circles Independent Work –
Fraction in a Row

Book 4 p.29 “Locating Decimal Fractions” AM, AP

Questions like mark 3 numbers between 4.3 and 4.4 on
the number line

Brian Storey’s decimal number line game
What needs to be taught
Understanding equivalence between fractions

with like denominators e.g.1/4 + 1/4 and with related
denominators e.g. 1/2 + 1/4 (use fraction walls, & kits)

Book 5 Additional Material “Comparing Apples with
Apples” AA to AM

with any fractional numbers e.g. 2/3 +
understanding of equivalence needed)
13
/20 (thorough
To teach equivalence between fractions;

Book 4 p.20 “Who Gets More” AM, AP

Book 4 p.30 The Same But Different” AM, AP
Misconception
What needs to be taught
Wrongly expressing fractions as Understanding that decimals (and percentages) are
decimals.
special cases of equivalent fractions in that they
1
For example to think that /2 is 0.2
always involve tenths, hundredths or thousandths
etc. Practise is needed in order to convert
fractions to equivalent decimals

Book 4 p.19 “Super Licorice” AA, AM

Book 7 p.41 “Decimats” AA to AM
Misconception
Decimals are two independent sets of
whole numbers separated by a decimal
point
This often leads to incorrectly ordering
decimals. For example to think that 0.67
is bigger than 0.8
What needs to be taught
Misconception
Incorrectly adding and subtracting
decimals.
For example to think that 3.4 + 1.8= 4.12
What needs to be taught
Visual understanding of what tenths and
hundredths actually represent

Book 7 p.38 “Decimal Pipes” AA to AM


Book 4 p.20 “Who Wins?” AA, AM, AP
Decimal Keyboards and Decimal Arrow Cards
understanding how the numbers on the left and right of
the decimal point contribute to the size of the number

Book 7 p.38 “Decimal Pipes” AA to AM

Book 7 p.30 “Candy Bars” AA to AM (No longer in Bk 7)
Misconception
What needs to be taught
When you multiply fractions and seeing that although whole numbers get bigger
decimals the total gets bigger and when they are multiplied the reverse is true for
when you divide they get smaller.
fractional numbers. When something is multiplied
For example to think that 4/6 x 5 will be by a fractional number the answer gets less
5 times bigger than 4/6 , when in fact When something is divided by a fractional number
the answer is only 31/3.
Misconception
the answer gets bigger.

Book 7 p.63 Folding Fractions and Decimals” AM to AP

Brian Storey’s Decimal Grid

The Maze Game
What needs to be taught
Incorrectly solve problems involving Finding relationships between units of different
fractions, proportions and ratios
quantities and converting between fractions,
decimals and percentages

Book 7 p.56 “Extending Hot Shots” AM to AP

Book 7 p.61 “Extending Mixing Colours” AM to AP

Book 4 p.21
percentages AP

Book 4 p.21 “Difficult Fractions to Percentages” AP
“Equivalent
Fractions,
Decimals
&