Developing a Math Unit Plan: Stage 3 Numbers and Algebra, Year 5-6

This document outlines a comprehensive unit plan for teaching whole numbers and algebraic concepts to Year 5 and 6 students (Stage 3) aligned with the NSW Mathematics K-10 Syllabus. The unit, which spans eight lessons, focuses on developing students' understanding of place value, comparison of whole numbers, factors, multiples, Highest Common Factor (HCF), and Lowest Common Multiple (LCM). The plan incorporates a variety of learning experiences, including quantifying numbers, place value patterns, and the application of number theory to problem-solving. Each lesson includes specific syllabus content, learning activities, resources, and assessment strategies. A summative assessment task, involving an overhead spinner activity, is designed to evaluate students' comprehension of these concepts. Furthermore, the unit includes a detailed unit overview, problem-based lessons, and a marking rubric aligned with the NESA Common Grade Scale to assess student performance and skills development, demonstrating alignment with the Australian Professional Standards for Teachers.

MATHEMATICS K-6

Planning a unit
(Adapted from NSW Education Standards Authority https://syllabus.nesa.nsw.edu.au/support-
materials/sample-units/)
1. Stage 3: Numbers and Algebra – Whole Numbers 1
Working Mathematical outcomes of Stage 3 for Year 5 – 6
MA3 – 1 Working Module: By the end of session, students should have a strong sense of
numbers with respect to whole numbers. They could be able to draw on a variety of relationship
and strategies in a wide manner, of numbers for solving problems within new situations
MA3 – 2 Working Module: Students have a strong sense of numeracy related to base ten
systems to millions and thousands. They should have knowledge of how to use place value
patters for understanding new ideas and applying reasoning to computational problems including
mental mathematics in a real world and mathematical situations.
1

2. Mind map the content
2
Factors and multiples:
of whole numbers
HCF and LCM of
whole numbers
Place value:
generalised place
value patterns
Comparison: whole
numbers to 7 digits
Quantifying numbers:
interpret as a mixed
number expression
Whole
numbers

3. Develop a sequence of 8 learning events
 Quantifying numbers: interpret as a mixed number expression
 Place value: generalised place value patterns
 Comparison: whole numbers to 7 digits
 Factors and multiples: of whole numbers
 HCF: of whole numbers
 LCM: of whole numbers
 Application of number theory: solve problems with respect to whole numbers
 Summative Assessment
3

4: Unit Overview
Unit Overview
Unit Title:
Numbers and
Algebra
Stage: 3 Class: Year 5
Syllabus Outcomes: Whole Number 1
MA3 – 1 Working Module: By the end of session, students should have a strong sense of
numbers with respect to whole numbers. They could be able to draw on a variety of relationship
and strategies in a wide manner, of numbers for solving problems within new situations
MA3 – 2 Working Module: Students have a strong sense of numeracy related to base ten
systems to millions and thousands. They should have knowledge of how to use place value
patters for understanding new ideas and applying reasoning to computational problems including
mental mathematics in a real world and mathematical situations
Unit Focus:
In this unit, students will learn to describe and apply mathematical concepts to solve real life
based and mathematical problems. Through generalising and recognising the number patterns,
regarding with place value they become able to formulate and create specific solutions easily. By
the end of Stage 3, learners will ask questions and undertake the investigations and use
appropriate technological applications including problem-solving strategies for demonstrating
the fluency in concepts of mathematics. They can also use mathematical terminology to give
valid reasons while comparing and selecting from all possible solutions, as well as making
connections via existing knowledge and understanding.
Lessons Syllabus
Content
Learning experiences Resources Assessment
1. Quantifying
numbers:
interpret as a
mixed number
expression
(I) Definition of
whole numbers
to differentiate
how it is
different from
set of other real
― Acknowledge the students
with concept of whole
numbers by providing simple
definitions with number of
illustrations that differentiate
whole numbers from other
Website:
MathOpenRef
= Quantifying
numbers to
manipulate the
numbers and
Worksheets
and Sample
discussion
4

numbers
(II) Represent
the whole
numbers on
number line
(III) Find a part
of whole as a
percentage
(IV) Find
percentage as a
part of a whole
(V) Find the
whole from a
percentage and
a part
number systems.
― Ask students to
differentiate whole numbers
and identify its relationship
with other number systems
― Acknowledge the students
how to represent whole
numbers on number line, that
help in analysing them that
every succeeding number is
greater than its preceding
ones whereby, difference
between numbers can be
evaluated by counting
number of blocks on number
line
― Providing the smart
classes will help teachers to
demonstrates the mentioned
topic more effectively
― Ask some questions after
teaching the basic concept of
whole numbers to analyse
how much students are able
to understand further parts
― Now, ask some basic
questions to students about
the concept of percentage to
evaluate the teaching
methods that need to be
applied for acknowledging
differentiate
whole numbers
from other
numbers like
natural,
integers,
fractions and
more
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them how to find a part of
whole number as a
percentage.
― Use a number of
illustrations to demonstrate
how to find whole numbers
into percentage form as –
find a percentage of quantity
like half of a litre is 50%,
quarter of 1 kg rice is 25%
and so on.
― Further, reversing the
above process, now teach the
methods that are used for
represent the percentage form
of numbers into whole,
like 50% of 100 is half of
number i.e. 50, 75% of 180 is
3/4th of number i.e. 135 etc.
― Use strategy like
Multiples, benchmark
fractions and benchmark
fractions, etc. for calculating
a percentage of any amount
(75% of 180)
2. Place value:
generalised place
value patterns
(I)
Understanding
place value
system
(II) Numeral
― Review the concept of
whole numbers to warm up
the students before
introducing the next topic,
inform them which topic is
going to be discussed now,
e-learning
classes to
demonstrate the
place value and
number system
Project
assignments
6

recognition and
identification of
place value
(III) Producing
number names
of any size
(IV) Interpret
numbers in
different ways
(V) Partition
numbers by
their place value
(VI) Record
numbers and
represent them
in expanded
notarial form
(VII) Estimate
whole numbers
to the nearest
hundred,
thousand, ten
thousand etc.
that will arise curiosity and
encourage them to give their
co-operations to teachers to
understand the same
― Place value refers to a
process of building blocks of
numbers, so, the teachers
introduces place value and
number systems to show the
parts of a place value chart.
― Give some activities to
students to plot numbers as
per their value in number
system starting from range of
ones, tens, hundreds and to
millions. This would help in
analysing the number of
zeros of each digits in a
number.
― For recognising the
numbers and its names via
identification of place
― Give projects to students
to make charts representing
the number system with their
names as per place value
― Demonstrate how to
represent numbers in
expanded notation form
through various types of
illustrations starting from 3
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digit numbers to 7 digits.
― another main topic that
need is to bring attention of
students towards concept of
estimation and how it helps
in conceptualising new ideas
to calculate the exact values.
― Review the entire
concepts of place value
system and demonstrates the
topics on SMART Board by
using ICT resources
3. Comparison:
whole numbers to
7 digits
(I) Generalised
place value
pattern then
arrange numbers
of any size in
increasing and
decreasing order
(II) Compare
numbers using
the place value
system
― Warm up: Activity will be
performed in classroom
where students give practice
exercise to analyse their prior
knowledge of number
comparison of 1 and 2-digits
using number line technique
― A presentation will be
provide to gain attention of
students towards generalised
place value pattern of
different-different size
numbers, to demonstrate the
concept of ascending and
descending orders.
― Demonstration of numbers
through place value systems
and comparison them
accordingly. Teachers
Teacher
modelling or
Explicit
instruction
Sample
Papers
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through digital techniques of
teaching demonstrate how
identifying place value will
help in estimating which
value is greater. (967, 452, 23
< 967, 452, 95).
― Assessments will be
provided to students to
measure their knowledge and
provide them practicing
exercise to enhance their
knowledge
4. Factors and
multiples: of
whole numbers
(I) Generalised
the factors
(II) Generalised
the multiples
(III) Test of
divisibility of
prime numbers
like 2, 3, 5, 7
and 11
(IV)
Understanding
through
investigations
the greatest and
least factor
― Prior knowledge will be
provided to students about
the concept of generalisation
of multiples and factors
― warm up: Some practice
exercises will be provided to
students to recognise the
multiplicity rules. For this
purpose, divisibility test will
be provided.
― test of divisibility tests
rules include 2, 3, 5, 7 and 11
will be demonstrated via
various illustrations like 2 is
a factor of those numbers
whose digits ends up at 0, 2,
4, 6 and 8. Similarly, further
concepts will be elaborated.
― Meanwhile, some warm
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au –
openlearncreate
- mod –
resource – view
topic
Assessment
sheets
9

up exercise will be provided
by playing some activities in
the classroom where
everyone given the tasks to
identify common multiples
― Knowledge regarding with
greatest and lowest common
factors will be provided at the
end and teachers through
various examples
demonstrate students how
both concepts are different
from each other
5. HCF: of whole
numbers
(I) Recognise
the concept of
factors
(II)
Understanding
the concept of
common factors
(III) Methods to
find the Highest
common factor
of two whole
numbers using
listing methods
(IV) Methods to
find the Highest
common factor
of two or more
than two whole
― HCF of two or more
numbers are identified
through divisibility test of
prime numbers
― To identify the common
factors, two main methods
will be demonstrated in
classrooms that are listing out
the factors and prime
factorisation methods
― under listing methods,
encircle the common factors
of numbers then multiple
them, will help students to
understand the concept of
HCF.
― After listing methods,
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au –
openlearncreate
- mod –
resource – view
topic
Assessment
sheets
10

numbers of 2
and 3-digits by
prime
factorisation
methods
prime factorisation technique
will be described, whereby
numbers are represented in
prime factored form
― Now, flexibility to
factorise the numbers will be
created under learners by
helping them where to use
listing methods and where to
use prime factorisation
methods. For this purpose, e-
learning class or Cuemath
class will be provided to
students where they will
experience the concept of
finding HCF
― teachers will provide some
assessments to students to
recognise the concept of
higher common factors
6. LCM: of
whole numbers
(I) Recognise
the structure of
multiplications
to understand
the related
multiples
(II) Determine
all multiples of
given whole
numbers
― Concept of LCM and
identifying the factors of two
or more numbers again will
be demonstrated by using
divisibility test of prime
numbers
― Both listing out the
factors and prime
factorisation methods will
utilise to identify the LCM
of numbers also like it is
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u.au –
openlearncreat
e- mod –
resource –
view topic
Work book
11

(II) Find
lowest
common
multiples of 2
and 3-digits
numbers by
Listing of
multiples
(III) Methods
to find LCM:
Prime
factorisation
done in previous topic of
HCF.
― To find lowest common
factors, again common
factors are encircles in
listing methods.
― After listing methods,
prime factorisation
technique will be described
to identify the LCM of
numbers
― Further, for creating
flexibility under learners to
factorise the numbers will
again demonstrate by using
e-learning class or Cuemath
class.
― teachers will provide
practice exercise at the end
of assessments to students to
recognise the concept of
lowest common multiples
7. Application of
number theory:
solve problems
with respect to
whole numbers
(I) Relationship
between LCM
and HCF
(II) Solve word
problems using
concept of
factors and
multiples
― relationship will be
defined between LCM and
HCF of two numbers as –
Product of two numbers =
Product of LCM and HCF.
― Word problems based on
real life situations will be
framed and demonstrate how
above concepts of whole
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au –
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resource – view
topic
Sample sheets
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(II) Explore
real-life based
problems to use
concept of
whole numbers
to solve
(III) Identify
estimated value
of mathematical
problems using
whole number
patterns
numbers and different
concepts can be applied to
solve the same.
― ICT will be utilised under
classroom to help learners
how real-life based problems
can be solved
mathematically.
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5. Developing problem-based lessons
The problem based lessons will be prepared on the basis of following learning activities -
1.1 Comparing and ordering
◦ Place value lessons
◦ Writing number quiz
◦ Lesson quiz
◦ Rounding Quiz
◦ Estimation
◦ A quick quiz for accessing the students skills regarding with place value system
1.2 Mental Maths
◦ Properties worksheets
◦ Mental Maths worksheets
◦ Recognising the number value or place value patterns
◦ Tricky questions
◦ Create a poster to show the different place value system
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6. Lesson 8. Summative assessment
SUMMATIVE ASSESSMENT TASK
Stage 3 Whole Number
Activity Name: Overhead spinner
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Context
This activity demonstrates the place value chart, where using the overhead spinner six digit
numbers, comparison of whole numbers from left to right, line up the digits and more
Description of Activity
Spinner shows the numbers from 0 to 9 which is perfect learning activity to demonstrate the
concept of place value of whole numbers. This game activity is systematically help in engage
students in group-based learning which strengthen and develop the sense of whole numbers, by
stimulating engagement, participation as well as mathematical reasoning.
Under this game, students are asked to move the spinners and write numbers from left to write
in place value chart. This will help in recognising the multi-digit numbers, where a digit in one
place will represent 10 times of the other digit which is placed to its right. For example – 500 is
50 times of 10.
Outcomes
 Understanding the place value of whole numbers from ones to billions
 Students will learn the relationship between place value of two numbers
 Similarities and differences between number value patterns
Criteria for assessing learning
 Estimation of result through recognising the multi-digit number patterns without actual
calculation
 Development of mathematical reasoning
 Developing flexibility in solving mathematical problems with less mathematical errors
 Development of mental computation of whole numbers with knowledge of using
manipulative
 Working with others
Recording evidence of learning
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Identification of
similarities and
difference of number
patterns
✓ Providing
directions/Instructions
✓ Cooperative learning ✓
Questions, cues with
advance learning
✓ Summarizing the
result
✓ Differentiated assignments ✓
Hands-on experiences ✓ Direct Instructions ✓ Mathematical Models ✓
Presentations ✓ Test Assessment ✓ Other learning activities ✓
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7. Development of Rubric
Summative Task Marking Rubric
Criteria A B C D E
Estimation of
result through
recognising
the multi-digit
number
patterns
without actual
calculation
Students have
extensive
knowledge
regarding with
comparing the
numbers
thoroughly
Better
knowledge of
estimating the
result
Explanations
shows the
substantial
understanding
of whole
number
concept
Students have
little
understanding
of whole
numbers
especially to
solve world-
problems
Limited
knowledge of
understanding
the underlying
concepts
Development
of
mathematical
reasoning
Students have
capability to
use refine and
complex
mathematical
reasoning
Effectively
usage the
mathematical
reasoning
Have
evidences for
development
of
mathematical
reasoning
Little evidence
of reasoning
No evidence
of reasoning
Developing
flexibility in
solving
mathematical
problems with
less
mathematical
errors
More than
90% steps and
mathematical
solutions have
no
mathematical
errors
Almost 80%
result and
solutions are
attempted with
no
mathematical
errors
70 to 80%
solutions are
free from
mathematical
errors
50% steps
have
mathematical
errors
Almost 75%
steps of
solutions
contains
mathematical
errors
Working with
others
Students have
engaged
cooperatively
with others
Students take
participation
in learning
activities but
Students have
less
collaborative
skills
Cooperation
have seen
under students
but more
No
cooperation
have been
seen
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throughout the
lessons and
learning
activities
has trouble to
listening on
suggestions of
others
however, have
prompted to
stay on group
task
throughout the
lesson
interventions
are needed to
stay them in
task
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REFERENCES
Trouche, L. (2019). The ‘resource’approach to mathematics education. Springer Nature.
Huang, R., Takahashi, A., & da Ponte, J. P. (2019). Theory and Practice of Lesson Study in
Mathematics. Springer International Publishing.
Tan, P., Lambert, R., Padilla, A., & Wieman, R. (2019). A disability studies in mathematics
education review of intellectual disabilities: Directions for future inquiry and
practice. The Journal of Mathematical Behavior. 54. 100672.
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