Math 2A Unit 4: Process Numbers for Stage 6 Year 11-12

Math 2A Unit 4: Process Numbers is a four-week course for Stage 6 Year 11-12 students. The course covers subtraction, missing and opposite numbers, completing equations, and collaborative learning. The curriculum focuses on Australian Professional Standards for Teachers, NSW educational standards, and the Australian Curriculum. The course includes creativity, ICT, and group activities to improve literacy, numeracy, and enhanced thinking.

Stage 6 syllabus 1
Math 2A

Math 2A 2
UNIT 4 PROCESS NUMBERS
Course Target: 15-18 year olds in stage 6 of Year 11-12
Number of Weeks: four
Number of Lessons: three
Number of hour/lesson: one
Unit Outline
Subtraction………………………………………………………………….
Missing and Opposite Numbers…………………………………………..
Completing Equations………………………………………………………..
Collaborative Learning………………………………………………………..
Collaborative Learning………………………………………………………….
Learning Objectives
 Preparation for tertiary Math
 Expound on number words
 Evaluation of patterns and repetition
 Advanced counting sequence
 Estimations and number operation
 Introduction to complex additions, subtractions, and reasoning.
Level 6 Key Concepts
 Complex numbers ( three digit numbers)
 Subtraction and Addition using digital calculators
 Extension of fractions, decimals, numeracy
 Decimals and fractions
 Process numbers ( addition, subtraction, multiplication, dividing )
Curriculum Focus
 Australian Professional Standards for Teachers (2018)
 Professional practice
 Mathematical concepts and a well-developed learning plan
 Interesting learning experience
 NSW educational standards for stage 6
 Australian educational policies and priorities
 The Australian Curriculum
Creativity, ICT and Group Activities
 Working with objects
 Concepts and interactive activities
 Physical and social activities that engage the child
 Innovative, coherent and student centered approaches
 Improved literacy, numeracy and enhanced thinking
 Reflective approach, through a wide range of tasks and examples

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Week 1: Subtracting
Lesson 1: Subtraction and shopping
Objectives: Use of teaching models to create differentiation, subtraction, and guided calculations.
Content
Subtract and make calculations from basic math in the financial world. Borrow money, pay and
count using shillings and cents. Purchase items and make a budget using online shopping
Teaching and Learning Strategies
 Evaluate students ability from beginner K-10
 Introduce student to practical lessons in financial math
 Develop the learners ability to make financial decisions from financial situations
 Illustrate the concept of deductions for shillings and cents
Resources
 Online shopping sites
 Subtraction exercises
 Time testing
 Repetition
Lesson 2: Three digit subtraction
Objectives: Improve student’s subtraction using tens, hundreds and thousands. Engage the
learner in complex subtraction using number sentences
Content
Make three-digit subtraction using real life situations. Create differentiation by grouping in place
value and regrouping.

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Teaching and learning strategies
 Use mathematical tasks with three digit numbers
 Use of a borrowing game for subtraction of whole numbers
 Experience subtraction and introduction to worksheet
 Independent learning with column numbers
 Mental subtraction of simple and complex numbers
Resources
 Number tasks
 Digital gaming
 Subtraction tables and worksheets
Lesson 3: Group Work
Objectives: To engage the student in interactive learning using cultural items in solving
subtraction problems using real life situations.
Content
Encourage student participation in groups of two with real life situations. Recap of subtraction
facts, and terminology.
Teaching and Learning Strategies
Use formal assessment and group discussions to assess student’s ability in writing and solving
subtractions. Encourage interpersonal skills and teamwork in problem solving. Support the
student in regrouping and use of mathematical vocabulary.
Resources
 Colorful cultural beads
 Subtracting worksheet

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 Group activities
Week 2: Mathematical Reasoning
Lesson 1: Missing and opposite Numbers
Objective: To solve mathematical problems through mathematical reasoning
Content
 Solving practical issues through critical thinking
 Using physical objects to count and apply mathematical concepts
 Solving through process
 Incorporating math skills in life
 Mathematical reasoning
Teaching Strategies Stage 6 Mathematical Life Skills for student development and participation (NSW, 2017) Application of mathematical operations in practical situations and conceptualization Maths practice for improved mindsets and motivation. Blended learning for integrated
maths
Resources
 Stage 6 Mathematics books
 Monitoring tools
 Formative assessment and evaluation
Lesson 2: Shapes and sizes
Objective: To incorporate actionable data in instructional learning for developing minds.
Evaluate shapes and patterns, geometry properties, circumference and area.

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Content
 Patterns, relationships and shape functions
 Similarities and differences in shapes ( 3 sided and 4 sided shapes)
 Interactive lessons on perimeter and area of basic shapes
 Axial symmetry and angles
Learning Strategies
 Use of classroom creativity and instructional design
 Use of observation and modification of lesson plan for effective response
 Physical objects-shapes and measurements ( circles, squares, and rectangles )
 Reasoning through logic and generalization
Resources
 Themed illustrations
 Art and craft shapes for illustrations
 Instructional course book
 Multiple choice questions
Lesson 3: Matching Numbers
Objectives: Allow the students to make sense with numbers through simulations. Use videos to
demonstrate number games with figures and complex numbers
Content
 Understanding of key Math concepts as stated in standard grade exams
 Calculating and use of numbers in measurement
 Tailor made questions for individual understanding and progress tracking

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Learning Strategies
 Continuation of K-10
 Introduction of Year 11 standard Math
 Use of procedure in memorizing and formula for mental connection
 Conceptualization and exploration of math strategies
Resources
 Standard grade exams
 Math extension 2 Stage 6
 Proficiency strands
 Content strands (Acara, 2009)
Week 3 Completing Equations
Lesson 1: Building statistics
Objectives: To learn how to borrow, and complete the equations through probability and
statistics.
Content
 Multiple digit numbers and distribution
 Subtracting in tens and thousands
 Multiple digit subtraction
 Justification of numbers through multiplication solution
Learning and Teaching Strategies
 Providing a pathway for secondary level mathematics
 Explaining mathematical applications
 Creating relationships between complex numbers

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 Reasoning with numbers and multiplication
 Informal assessment and giving inferences from deduction
 Group discussion on different applications
Resources
 Group discussion
 Classroom practice
 Assorted YouTube videos (Monk, 2017)
 Correlation and causation data
Lesson 2: Multiplication numbers
Objectives: Understand multiplication of 3-5 digit with a 2-4 digit number. Assist the student in
improving learning in preparation for higher education.
Content
 Multiplication and skip counting
 Connecting multiplication and additions
 Solving everyday problems
 Integers and decimals
Learning and Teaching Strategies
 Demonstrate knowledge and skill in multiplication of sets
 Interpret information from language and mathematical solutions
 Evaluate individual students achievement in previous stage
 Apply working math in real life context
 Identify opportunities in mathematical methods and models for application (Harman,
2014)

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Resources
 Multiplication tasks
 Sample assessments
 Multiplication worksheets (Homeschoolmath, 2003-2015)
 Syllabus outcome expectations
 Skip counting charts
Lesson 3: Advanced level Division
Objectives: To introduce the student to long division in preparation for higher learning
Content
 Long division
 Opposite operations
 Solving multiplication and divisions
Teaching and Learning Strategies
 Arranging and building division categories
 Reflection of division activities in number strategies
 Mental computations and patterns
 Repeating divisions with remainder strategies
Resources
 Common grade scale
 Changes to Stage 6 Assessment from 2018
 Sample Units
 Formal ( school based assessment

Math 2A 10
Week 4 Collaborative Learning
Lesson 1: Percentages
Objectives: Engage learners in practical tasks involving percentile math. Connect
previous level lessons on fractions with percentage calculations.
Content
 Diagrams and percentage techniques
 Digital diagrams representing percentages
 Transforming decimals and fractions into percentages
Teaching and Learning Strategies
 Integration of mixed numbers with fractions for comprehensive skills
 Generation of mathematical solutions through multiple strategies
 Interpretation of numbers through problem solving
 Plotting, reasoning and communicating fractions accurately
 Subtracting fractions and making complex operations as fractions
Resources
 Students work book
 Students learning groups
Lesson 2: Order of operation
Objectives: To elaborate the order of numerical operations in arithmetic. Compare and contrast
concepts in practical application. Follow up on previous lesson for an emphasis on concepts
Content
 Converting fractions as percentages of decimals and vice versa
 Multiplication verses divisions

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 Additions and subtraction of multiples
 Increase and decrease of percentages
Teaching and Learning Strategies
 Use of calculator methods for expressing percentages
 Engaging the learner in comparative measures of written and mental numbers
 Calculating increase in numbers and decreases
 Interpretation of numbers through trends and values
 Analyzing the ability to identify recurrence in numbers and sub strand relevance
Resources
 K-10 Mathematics
 Unit workbooks
 National Numeracy Learning Progression (NSW syllabus)
Lesson 3: Student learning needs
Objectives: To project the student assessment
Content
 Understanding money mattaers (National Numeracy Learning, 2018)
 Operating with numbers
 Intepreting numbers in real life
Teaching and Learning Strategies
 Students ability to grasp basic concepts in numbers
 Students ability to advance in learning math
 Strategic positioning for higher learning through a strong foundation

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 Comparative analysis of the learners progress in Math
 Successful application of elements and sub elements
Resources
 NSW syllabus
 Student assessment tasks
 Course learning objectives and outcome

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Reflection
Handling a math class with teenage students approaching high school is a challenge yet it
is also a great opportunity. From this experience, I noticed that learners at this age need
motivation to pursue professional training in higher learning. The use of self-regulated
approaches and group techniques is evident in this unit development (Schunk & Zimmerman,
2012). Classroom diversity is also inevitable because students come from different backgrounds.
Contemporary learning involves the use of multicultural techniques. Digital communication as
part of modern classroom techniques is also a necessity. This discussion identifies the
development of learner’s skills for a better outcome and the use of pedagogical strategies for
professional practices.
Motivational factors
Intrinsic and external motivation influences the learner’s fascination with subjects. I used
personal motivation and a positive group influence for this unit. In order to give math a sense of
relevance, I look a focus of these lesson tactics:
 Adding value to the topic of discussion
 Capturing the student interest
 Engaging their participation
 Enhancing their performance
 Simplification of concepts through multiple activities
Although intrinsic motivation matured through self-efforts, it became better with the
introduction of reward reinforcement. The use of assessment tests encouraged personal initiatives
through study and exercises. However, students at this level felt rewarded through an
encouragement a focus on the subject as a professional subject. In the unit, practical examples

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from real life situation such as financial management and shopping activities awaken the
student’s passion. On the other hand, external motivation comes from participation in class
(Watt, et al., 2012). Children from different socioeconomic backgrounds require access to equal
learning opportunities. The curriculum approach encourages equal opportunities for multiracial,
gender and social groups (Acara, 2009).
Skills outcome
The assessment of learning principles using professional practices in this case abides by
the curriculum needs. This shapes the Math lesson content with relevancy and contemporary
ideas. The figure below is an example of the digital classroom models. This model encourages
the use of internet videos in Math Lessons. Other models for tasks and performance evaluation
are in Appendix.
Figure 1: Model for classroom resources to encourage gender participation(Dayofstem, 2017)

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Literacy, numeracy and ICT
Understanding the students inspired the development of individual abilities. The choice
of learning material from ICT resources was based on the following:
 Student feedback for strong and weak points
 Student anticipation to discover more about the lessons
 Applicability of the work in the lessons and the next sections
 Existing lesson challenges such as complex analysis and concepts
Scaffolding
Research into math strategies include a solution plan that supports the development of
competencies through sucompetencies (Blum, Kolter, & Schukajlow, 2015). This shaped my
choice of the Australian strand and sub strand approaches to learning Math. By encouraging
learners to focus on higher learning through continuous education, the student develops a
desire to achieve more. Through student engagement, and digital technology I made the
topics simpler for a better grasp. Students in year 11-12 need a deeper understanding of
different approaches in Math. A curriculum focus on key topics places an emphasis on the
basics and provides exposure for the next level (NSW, 2017). The socio-cultural learning
theory and pedagogical theories used relate to the teaching area. Focusing on Math as part of
life while meeting the syllabus expectations hits the target (Jonassen & Land, 2012).
Task based Learning
Through continuation of learning and a wider scope of student activities, this syllabus
encouraged the teacher to know the student and their learning difficulties. Learners who
exhibit challenges in Multiplication may also experience challenges in lessons such as

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division. Progressive development starts with an understanding of the level of the learners in
order to bring out standard achievement and consolidate levels of literacy. Covering the
general capabilities such as thinking skills, IT skills and creativity is important for self-
management and group work activities. I used cultural objects like beads for learning in order
to support social competencies and content development. Engaging the student in
participatory learning and task based approaches optimizes skill development (National
Numeracy Learning, 2018).
Conclusion
The experience I obtained in the development of this unit highlights effective
teaching methods for professional practice with feedback from assessment. I used engaging
Stage 6 Syllabus that comprises of rigorous activities. Based on the complexities of advanced
Math for learners approaching high school, I used a unit with sub lessons. This simplified the
subject through learning principles that work. It also looked at the curriculum needs through
professional development. Engaging the student through multiple learning resources calls for
effective implementation strategies that prioritize on the educational policies while
incorporating the socio-cultural perspective. Shaping the student’s attitude towards learning
Mathematics determined the learner’s motivation, improved understanding and overall
outcome. Pedagogical strategies in lesson plans focus on units that optimize on the
development of the students skills.

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APPENDIX
LEARNING MODELS and WORKSHEETS
Marking RUBRIC
Evaluation Criteria Excellent
conceptualization
High
understanding
Moderate
understanding
Needs Practice
Understands
concepts
Shows exceptional
knowledge of
concepts
Has sound
knowledge
and
understanding
of concepts
Has good
knowledge of
basics
Has challenges
understanding
concepts
Recognizes
numeracy in
literacy language
Understands and
uses all concepts
and arithmetic
terminology
Understands
and uses a
good number
of concepts
and principles
Basic
comprehension
and
application of
some concepts
and principles
Limited use and
application of
math concepts
and principles
Ability to deal
with concepts
accurately and in
practical life
Correct and
accurate in
concept
application
Tries to apply
concepts
appropriately
Exhibits errors
in basic
computation
and
application
Faces major
challenges in
math
conceptualization
and applications

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Skip Counting (for memorization)
Figure 2: Skip counting chart, adopted from NSW (2015)
Multiplication Worksheet
a) 6387
× 567
b) 1984
× 431
c) 8231
×831
d) 9660

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× 691
e) 1578
× 975
Colorful beads for counting and illustration (Algebra bead game video)
Figure 3: Mabble Game (Attard, 2017)
Algebra Worksheet
Answer the following
i) 12x²+2=
ii) 4x²+2x-5=
iii) bx +5x-cx-cy
iv) x²+y²+3x+4x=

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v) If 3y-2=10 and 2y-1=7 what is the y value?
*Use the following website for more algebra: (gameshttps://www.youtube.com/watch?
v=V3dFHt9p5W8)
Arithmetic Statistics Worksheet
Answer the following
i) ( ¾+1/2) /1-1/15)=
ii) Calculate $ 800 shared among companies X, Y and Z where each gets 1/3 and the
remainder goes to an orphanage. How much is donated to the orphanage?
iii) There are 230 toys available for distribution in an online store. If there are 60 more
toys in a store than in a trunk, how many are in the trunk?
iv) Jack and Jean are brothers born in the 1990s. Jack is 7 years younger than Jean who is
30 years now. When was Jack born?
v) How many times is 2/1000 greater than 2/100000?

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References
Acara. (2009). Australian Curriculum Math. CommonWealth of Australia. Retrieved from
http://docs.acara.edu.au/resources/Australian_Curriculum_-_Maths.pdf
Australian Professional Standards for Teachers. (2018). Teacher Accreditation: Celebrating
quality teaching and inspirational teachers. Sydney: NSW Education Standards
Authority. Retrieved from
https://educationstandards.nsw.edu.au/wps/wcm/connect/8658b2fa-62d3-40ca-a8d9-
02309a2c67a1/australian-professional-standards-teachers.pdf?MOD=AJPERES&CVID
Blum, W., Kolter, J., & Schukajlow, S. (2015). Scaffolding mathematical modelling with a
solution. ZDM, 47(7), 1241-1254.
Dayofstem. (2017, December 1). 2018 professional learning Feb-June 2018. Retrieved from
Teacher professional learning: http://dayofstem.org/australia/2018-calendar/
Harman, S. (2014). Mathematics Specialist. Retrieved from Government of Western Australia:
https://senior-secondary.scsa.wa.edu.au/syllabus-and-support-materials/mathematics/
mathematics-specialist
Homeschoolmath. (2003-2015). Free Math Worksheets for Grade 6. Retrieved from Home
Schoool Math: https://www.homeschoolmath.net/worksheets/grade_6.php#multdiv
Jonassen, D., & Land, S. (2012). Theoretical foundations of learning envronments. Routledge.
Monk, M. (2017, Nov 5). Math B/ Methods Course Grade 11/12, high school Queensland,
Australia. Retrieved from Youtube: https://www.youtube.com/playlist?
list=PLzr5fRV1AGV9d_2Sp730_2QAAdx5alEF7
(2018). National Numeracy Learning. NSW Government. Retrieved from
https://education.nsw.gov.au/teaching-and-learning/student-assessment/smart-teaching-

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strategies/numeracy/number-and-algebra/multiplication-and-division/S2-multiplication-
and-division
NSW. (2015). Teaching Strategies: Stage 1 Mulyplication. Retrieved from Multiplication and
Division: https://education.nsw.gov.au/teaching-and-learning/student-assessment/smart-
teaching-strategies/numeracy/number-and-algebra/multiplication-and-division/S1-
multiplication-and-division
NSW. (2017). Mathematics life skills stage 6 syllabus. Retrieved from NSW:
https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/
stage-6-mathematics/mathematics-life-skills-2017
Schunk, D. H., & Zimmerman, B. J. (2012). Motivation an essential dimension of self-regulated
learning. In S. Dale, & B. Zimmerman, Motivation and self regulated learning (pp. 13-
42). Routledge.
Watt, H. M., Shapka, J. D., Morris, Z. A., Durik, A. M., Keating, D. P., & Eccles, J. S. (2012).
Gendered motivational processess affecting high school mathematics participation,
educational aspiractions and career plans: A comparison of samples from Australia,
Canada and the United States. Developmental Psychology, 48(6), 1594-1611.