EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
EDMA310/360 Mathematics unit planner
Daniel Dopierala
Unit Overview
The unit consists of a variety of activities to immerse students in the world of decimal fractions.
The activities have been designed to have students fully realising the need to know about place
value and fractions in order to use and calculate decimal fractions effectively. The five sessions
included herein focus on the fundamental aspects of decimal fractions beginning with place
value and understanding of the decimal point which stretches out to using decimal fractions in
real life contexts even if this has been kept to a seemingly minimum level within the session
plans. The overriding idea has been for students to understand the operational side of decimal
fractions and to gain a foothold on their use in mathematics.
Unit title: Decimal Fractions
Content maths area: Fractions and Decimals
Grade/year level: Grade 5 AusVELS Level 5
Learning Focus (ideas extrapolated from AusVELS):
Number and Algebra Number and Place Value  Fractions and Decimals

Compare and order common unit fractions and locate and represent them on a number line
(ACMNA102)

Investigate strategies to solve problems involving addition and subtraction of fractions with the
same denominator (ACMNA103)

Recognise that the place value system can be extended beyond hundredths (ACMNA104)

Compare, order and represent decimals (ACMNA105)
Rationale:
Learning about decimal fractions is important for students as decimal fractions are consistently
used in real life applications. Caswell (2006) relates to the fact that decimals appear in many
areas of society such as money and measurement and students should learn how decimal
fractions work and thus be able to attain a conceptual understanding. Students may at any time
encounter certain misconceptions and similarly, teachers need to utilise students’
misconceptions in order to identify what needs to be taught and how to not only address these
misconceptions but to capitalise on them by enacting sound teaching techniques that can
ultimately strengthen students’ understanding of decimal fractions. Getting students to think in
an open-ended way has been a foundational goal in the development of this unit planner.
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
Assumed prior knowledge of students:
Prior knowledge of students will be assumed to have consisted in some immersion of
fraction activities from previous units, as well as place value which will greatly improve
their chances for success in learning how to calculate and use decimal fractions.
Grouping strategies to support learning:
The teacher will group students according to their ability level and perhaps have a high
group and low group so then the teacher can offer additional scaffolding and assistance
to the low group with every session.
Overview of assessment:
Across the ball, formative assessment will be used for the whole of the five sessions as
well as cognitive assessment in order to find how students’ thinking is operating in their
calculating of decimal fraction tasks. Some assessment will consist of anecdotal
assessment but a greater part will be recording students’ progression which differs from
session to session depending on the task.
References:
Caswell, R. (2006). Developing Decimal Sense. Australian primary mathematics classroom. 11
(4), 25-28
Roche, A. (2005). Longer is larger—or is it? Australian primary mathematics classroom. 10 (3),
11-15.
Roche, A. (2010). Decimats: Helping Students to Make Sense of Decimal Place Value. 15 (1),
4-10.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and Middle School
Mathematics: Teaching Developmentally. Pearson: Sydney, NSW.
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
MATHEMATICS UNIT PLANNER
Topic: Decimal Fractions
Key mathematical understandings
(2-4 understandings only; written as statements believed to be
true about the mathematical idea/topic):

Use previous knowledge of fractions to gain
an understanding of decimal fractions

Developing decimal number sense

Gaining an understanding of place value
(tenths, hundredths, thousandths)
Learning and using decimal numbers
beyond hundredths (i.e. thousandths)

Using concrete and visual representations
to calculate and check decimal fractions
Year Level: 5
Term:
2
Week: 2
Date: 1/04/2015
Key AusVELS Focus / Standard Mathematics
Content strand(s):
Number and Algebra
Sub-strand(s):
Fractions and Decimals
Level descriptions:
 Recognise that the place value system can be extended beyond hundredths (ACMNA104)
 Investigate strategies to solve problems involving addition and subtraction of fractions with
the same denominator (ACMNA103)
 Recognise that the place value system can be extended beyond hundredths (ACMNA104)
 Compare, order and represent decimals (ACMNA105)
Proficiency strand(s):
 Understanding includes making connections between representations of numbers, using fractions to represent
probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing
transformations and identifying line and rotational symmetry
 Fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using
estimation to check the reasonableness of answers to calculations and using instruments to measure angles
 Problem Solving includes formulating and solving authentic problems using whole numbers and measurements
and creating financial plans
 Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving
fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data
investigations and interpreting data sets
Key skills to develop and practise
Key equipment / resources:

Learn about part-to-whole relationships

Base 10 grid paper

Linking abstract concepts to real-life examples.

Deciwire

Gain an understanding of place value (hundreds,
tens, ones, tenths, hundredths, thousandths)

‘Decimal Cards’


Decimat
Using representations, concrete materials
(Deciwire, fractional strips) to inform decimal
fraction thinking so as to allay misconceptions.

Using thinking models as with a number line so as
to show order, and compare decimal fractions.
Key vocabulary (be specific and include definitions of key words
appropriate to use with students)







Part-to-whole thinking
Hundreds, Tens, Ones, Tenths, Hundredths,
Thousandths
Decimal Fractions, Decimals, Decimal Point
Number line
Base ten grids/models
Deciwire
Representation, Visualising
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
Key probing questions
Possible misconceptions

Understanding place value

Understand place value with respect to 0

Misunderstanding the use of the decimal point

Not fully understanding tenths, hundredths and
Mostly mathematical contexts that entail:
thousandths as well as tens and ones in terms of
identifying a decimal fraction’s components.

Links to other contexts
Not recognising decimal fractions as being a
“What happens if I place the decimal point here
(.148 1.48), what is the decimal now?” “Which one
is larger, how do you know?”
“Why is one decimal fraction larger, why is one
decimal fraction smaller?” “What makes you say that?”
“Which one is larger?”
Show answer with greater than ˃ or less than ˂
symbols.
“What do you notice about the second decimal
fraction in comparison to the first?
Sporting contexts such as scoring and statistics
Money-currency, counting money, petrol prices
Measurement and size
fraction or number (i.e. a number that can be
Learning strategies/
skills
counted)
Analysing
Checking
Classifying
Co-operating
Considering options
Designing
Elaborating
Estimating
Explaining
Generalising
Hypothesising
Inferring
Interpreting
Justifying
Listening
Locating information
Making choices
Note taking
Observing
Ordering events
Organising
Performing
Persuading
Planning
Predicting
Presenting
Providing feedback
Questioning
Reading
Recognising bias
Reflecting
Reporting
Responding
Restating
Revising
Seeing patterns
Selecting information
Self-assessing
Sharing ideas
Summarising
Synthesising
Testing
Viewing
Visually representing
Working independently
Working to a timetable
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
MATHEMATICAL
FOCUS
Session 1
Students will learn
about decimal
fractions and will
learn to label
decimal fractions
(i.e. tenths,
hundredths).


Decimal Point
Focus
Naming-tenths,
hundredths,
thousandths
‘TUNING IN’
(WHOLE CLASS FOCUS)
The teacher shows a chart
with a decimal fraction with
0.5 and the headings
shown underneath in a
tabular format Probe
students’ thinking by
asking what they can see.
Stress the dot point, and
emphasise the ones,
tenths and also highlight
the ‘ths’ and spend 2-3
minutes showing place
value
Teach students 0.5, as
being half of whole. “Why
do you think this may be?”
‘INVESTIGATIONS
SESSION’
‘REFLECTION & MAKING
CONNECTIONS
SESSION’
ADAPTATIONS
ASSESSMENT
STRATEGIES
The teacher has the
students sitting on the floor
in a circle. Firstly, the
teacher has a batch of
play-dough. The teacher
divides the play-dough into
equal parts. Probe
students thinking: “What
have we done?” “How
many parts do we have
now?” Secondly, hand out
a batch of play-dough for
EACH student. Ask
students to divide into 2
pieces. Then get the
students to divide it into 4
pieces.
“How many parts are there
now?”
Students are given decimal
cards with a decimal point
in which they split
play-dough into parts such
as with 2 pieces of playdough and keeping 1 and
dividing the other half into
2 pieces again while
putting one piece aside
and retaining the other.
The result would be 1.5 or
Enabling prompt: To
strengthen the key
mathematical idea, show a
grid consisting of 10
squares. 5 are shaded, 5 a
blank. How many times
does 5 go into 10: 2 times
(twice)?
Anecdotal assessment as
well as recording how
students are managing
with the content and
whether the next planned
session can be explored
and if not, some more
time needs to be
focussed on relating
decimal fractions to
fractional part-to-whole
thinking.
“If I had one big piece of
play-dough which is the
whole, and now I have 2
parts, how many parts of
the whole are there?”
If there are 2 parts, what
does one piece of playdough represent What is
that as fraction?
𝟏
𝟐
this is a
half. Decimal fraction
equivalent.0.5 is one half
1
2
Students are to continue
and manipulate the playdough into different
segments.
Therefore there are two
partsNow circle one of
the two parts. Now circle
the other part. How many
circles are there? 2. [This
is to reinforce the idea that
5 goes into 10 twice as
from before.]
“How many of these circled
squares are there?” 2.
“How many of the two
circles have shaded
squares.” “One circle. Out
of how many?” 2. One out
of two or
Use a checklist to record
whether students
understand the decimal
fraction concepts and
especially the purpose of
the decimal point.
1
2
Extending prompt:
Encourage students to
work out how they might
attempt to create
hundredths or even using
the play-dough.
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala

Session 2
Students will
manipulate
concrete
materials to
create a
decimal
fraction.
TUNING IN
Show the class Base ten
grid
Show the class, two
squares on the smartboard.
Underneath it, clearly label
that one of the squares
represents ones, the other
tenths, and third square is
not a whole square but a
square divided into 100
smaller squares.
There are 2 ones, 3 tenths
and 5 hundredths.
INVESTIGATIONS
SESSION
Deciwire which uses 10
sets of 10 to make 100, is
a great way to perform
more visual
representations of
fractions. Get students to
think deeply about how
fractions can be seen as
20
decimal fractions.
REFLECTION & MAKING
CONNECTIONS SESSION
Rational number wheel
Students will use the
concrete material known as
rational number wheel to
show a particular fraction.
They will then write down
the equivalent decimal
35
fraction i.e. 2
= 2.35
100
100
If 100 is the whole 1.0,
then the decimal point that
could be placed on top
would be .20 ∴ it is .2
.20
1.00
Base ten strips and square
Deciwire
Have the students show
4
is .4 as it is 4 tenths,
10
explicitly teach that
because it is after the
decimal point, tenths is the
40
first unit.
is the same
100
as .4 as the denominator is
now 100 but the numerator
is also larger. There is an
additional zero on both the
numerator and
denominator in reference
4
to
ADAPTATIONS
Enabling prompt: Refer
back to the base ten grids,
and guide students through
recognising part-whole
thinking and get them
thinking about the whole as
100 and what might each
row contain; fundamental
base 10 thinking.
Extending prompt: Have
students showing larger
fractions that they can
interpret into their
respective equal decimal
70
fractions. 4
100
4 and 7 tenths 4.7
ASSESSMENT
STRATEGIES
Throughout investigations
session and reflection
and making connections
session, recognise if
students are correctly
using rational number
wheel and have an
understanding of the
fundament behind the
activity. Beforehand
though, the teacher
should evaluate student’s
progress with their
understandings
concerning Deciwire and
10 groups of 10 being
100 and how students
can understand this prior
to specific decimal
fraction thinking even
though the two go hand in
hand.
10
25
20
40
70
100
100
100
100
Get students to think of
other ways to say the
fractions 6 tenths and 5
hundredths OR 65
hundredths.
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
Session 3
 Students will
manipulate
concrete
materials to
create a
decimal
fraction.
Session 4
 Students will
be learning
how to
differentiate
sizes of
fractions for the
purpose of
ordering and
comparing
fractions.
Tuning in: Showing
Deciwire to the students
and going through some
quick examples which
refreshes their mind from
session 2 and this is
designed to get students
thinking about base 10
fractions again.
TUNING IN
Show these numbers on
the smart board:
0.9
0.10
‘Eyes to eyes, knees to
knees’, students quickly
turn to the person next to
them and discuss which
one is larger or smaller.
Teacher asks “Why is one
decimal fraction larger, why
is one decimal fraction
smaller?” “What makes you
say that?”
REFLECTION & MAKING
CONNECTIONS SESSION
INVESTIGATIONS
SESSION
Decimat activity
Students, working
individually roll two dice,
and if 3 and 1/10 appear,
and if the students
understand it correctly,
they record 3/10 and the
equivalent decimal 0.3 on a
scoresheet.
Show class ordering game,
where students working in
pairs order decimals with
their fraction equivalent.
Extending prompt:
“What happens if I place
the decimal point here
(.148 1.48), what is the
decimal now?” “Which one
is larger, how do you
know?”
INVESTIGATIONS
SESSION
REFLECTION & MAKING
CONNECTIONS SESSION
Students order a range of
decimal fractions
Comparing fractions: Get
students to compare
fractions 0.875 and 0.084
“Which one is larger?”
Show answer with greater
than ˃ or less than ˂
symbols. Repeat for 0.345
And 0.445. 4.53 and 1.453
0.893 and 0.89
0.3
0.8
0
0.5
0.3
0.01
0.7
0.1
0.87
0.5
1
1
1
2
1
How did you work out the
order? What helped you to
work out and decide on the
position that you placed a
particular decimal fraction?
ADAPTATIONS
Enabling prompt:
Reteach the concept of the
Deciwire and how it
represents tenths and
hundredths
Now using these
fractions, get students to
label all the place values
(tens, ones, tenths,
hundredths, thousandths
ADAPTATIONS
Enabling prompt: Think
about 1 as whole and what
9 parts of that whole “.9”
Extending prompt:
There is a choice for
chocolate cake slices that
have the following portion
sizes: 0.4, 0.34, 0.6, 0.09
Which chocolate cake slice
would you prefer from the 5
sizes listed above? Draw a
representation of how
these sizes may look.
ASSESSMENT
STRATEGIES
Assess students’ ability to
understand and visualise
the connection between
fractions and decimal
fraction through the use
of Decimats.
Assess students’ ability to
order fractions.
Assessing these can be
through a rubric based on
3 points: Understands the
concept being ‘High’, Has
a fair understanding being
‘Medium’ and Requires
more work in order to
understand being ‘Low’.
ASSESSMENT
STRATEGIES
Rove around and notice
what students are doing.
Use appropriate
questioning to probe their
thinking. “Tell me why
0.875 is larger than
0.084.”
Get students to justify
their thinking throughout
the lesson.
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
Session 4
 Students will
use their place
value
knowledge to
calculate
addition and
subtraction
problems
TUNING IN
Open Task: Teach
students that saving money
is important.
If you earn $100 for
working one day and you
save $60, how much
money have you saved—
WORK OUT and SHOW
YOUR ANSWER AS A
DECIMAL FRACTION
6
100
Session 5
 Students will
be learning
how to
differentiate
sizes of
fractions for the
purpose of
ordering and
comparing
fractions.
.06
TUNING IN
Show these numbers on
the smart board:
0.9
0.10
‘Eyes to eyes, knees to
knees’, students quickly
turn to the person next
to them and discuss
which one is larger or
smaller. Teacher asks
“Why is one larger, why
is one smaller?” “What
makes you say that?”
INVESTIGATIONS
SESSION
REFLECTION & MAKING
CONNECTIONS SESSION
Students work
independently to write a
decimal fraction that has
the value of
--6 tens
--6 tenths
--7 thousandths
Get students to work out a
number of addition and
subtraction problems using
decimal fractions.
Now do –4 tens
--8 tenths
--5 hundredths
--0 thousandths
“What do you notice about
the second decimal fraction
in comparison to the first?
For example:
6.80
+ 4.77
REFLECTION & MAKING
CONNECTIONS SESSION
Students order a range of
decimal fractions
Using the context of height
of 5 students, list 5 decimal
fractions that will challenge
students to put in order.
They are to list these
decimal fractions from least
to greatest.
0
0.5
0.3
0.01
0.7
0.1
0.87
0.5
1
1
1
2
1
Extending prompt: More
complex decimal fractions
to add and subtract
7.8
- 5.6
INVESTIGATIONS
SESSION
0.3
0.8
ADAPTATIONS
Enabling prompt: On the
smart board write a 4 digit
decimal 4.0918. “Is it
closer to 4 or 5?
ADAPTATIONS
Enabling prompt: Think
about 1 as whole and what
9 parts of that whole “.9”
Extending prompt:
There is a choice for
chocolate cake slices that
have the following portion
sizes: 0.4, 0.34, 0.6, 0.09
Which chocolate cake slice
would you prefer from the 5
sizes listed above? Draw a
representation of how
these sizes may look.
ASSESSMENT
STRATEGIES
Use a checklist to see
record if students once
again understand the
important place value
concepts and also
understand adding and
subtracting decimal
fractions. Get students to
also assess a peer.
ASSESSMENT
STRATEGIES
Record students’
reasoning with their
decimal fraction ordering.
Are they experiencing
misconceptions about
certain decimal fractions.
How did you work out the
order? What helped you to
work out and decide on the
position that you placed a
particular decimal fraction?
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
Appendix A– [Session 1
Tuning in Activity.
Decimal Cards example
4
0 5
Ones
Tenths
5
6
Hundredths Thousandths
2 0
Hundreds
Tens
Ones
Tenths
Hundredths Thousandths
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EDMA310 Assignment 2—Mathematics Unit Planner Daniel Dopierala
Appendix B—[Session 3]
Decimat
10