Unit Outline

Mathematics is a key learning area for all students and essential to an individual's ability to fully participate in society. The teaching of mathematics at all levels is changing in response to research into its teaching and learning and to ongoing changes in society. Research has shown that significant numbers of students become less positive about mathematics and their own ability to do mathematics during the later years of their primary education and in their early secondary education. Teachers of senior primary school mathematics must be able to teach in ways that facilitate students' learning and also be able to extend these students when needed. This unit will enable students to study topics in mathematics of particular relevance in the later primary years and the early secondary years, including integers, proportional reasoning, measurement, geometry, statistics and probability and introductory algebra.

Intended Learning Outcomes

As per the Assessment and Results Policy 1.3, your results will reflect your achievement against specified learning outcomes.

On completion of this unit, you will be able to:


1.	Demonstrate knowledge of mathematical topics relevant to Year 5 to Year 8, including real numbers, indices, proportional reasoning, algebraic thinking, geometry, statistics and measurement
2.	Apply theoretical and practical knowledge of mathematics content and pedagogy to plan and design coherent teaching sequences which reference Year 5 to Year 8 content
3.	Make informed decisions in selecting examples, resources, and questions when teaching topics in mathematics
4.	Communicate in written form in a scholarly manner, with correct usage of English and mathematical conventions

Requisites


REQUISITE TYPE	REQUISITES
Pre-requisite	EPR220 or ESH220

Alterations as a result of student feedback

How will I be Assessed?

For more detailed assessment information please see MyLO.

Assessment schedule


ASSESSMENT TASK #	ASSESSMENT TASK NAME	DATE DUE	WEIGHT	LINKS TO INTENDED LEARNING OUTCOMES
Assessment Task 1:	Secret Numbers	Week 3	10 %	LO1, LO4
Assessment Task 2:	Working with Prime Numbers	Week 5	40 %	LO1, LO2, LO3, LO4
Assessment Task 3:	Lesson Sequence	Week 13	50 %	LO1, LO2, LO3, LO4

Assessment details

Assessment Task 1: Secret Numbers

Task Description:

Here are two problems for you to solve:

Problem 1 – the secret number:
Pretend that you ask a friend to go through the following steps:
Think of a number between 1 and 9 and keep it secret.
Double it.
Add five.
Multiply by five.
Add another number between 1 and 9.
Subtract 25
Tell you the answer.
You can then tell your friend their secret numbers.

Problem 2 – The magic 4:
Pretend that you ask a friend to go through the following steps:
Think of a number and keep it secret.
Double it.
Add 2.
Divide by 2.
Add 3.
Subtract the original number.
You then tell your friend that the answer is 4.

For both these problems choose a number and go through the steps.
How is it that you know the answer? Will these problems work for all numbers? Answer these questions, giving an explanation.

To be submitted via MyLO dropbox as a Word document.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 2.5

Task Length:

600 words equivalent

Due Date:

Week 3 (11/Mar/2024)

Weight:

10 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Demonstrate the ability to extract the mathematical knowledge needed to solve a problem	LO1
2	Demonstrate the ability to communicate a mathematical solution, using appropriate mathematical terminology and English conventions	LO4

Assessment Task 2: Working with Prime Numbers

Task Description:

This task is based on the Australian Curriculum Descriptor for Year 7: represent natural numbers as products of powers of prime numbers using exponent notation (AC9M7N02). This task is also suitable for Year 6: identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations (AC9M6N02) and for Year 5: express natural numbers as products of their factors, recognize multiples and determine if one number is divisible by another (AC9M5N02).

Activity
If you have a relative who is in Years 5,6 or 7 at school, or you know a child who is in one of these years, do this activity with him or her. Make sure a parent or guardian is present during the activity. If you do not know a child of the relevant age, do this activity with a friend, but choose a friend who is not very confident in mathematics.
This activity needs small tiles or the blocks that are used for children’s play. If you do not have access to these, you will need to make 20 squares of either cardboard or stiff paper, making sure they are all of the same size.
The activity:
Ask your student to see how many different rectangles they can make with 6 tiles. Record the rectangles they find and include them in your report (see below). You may sketch their rectangles or take photographs.
For example, the number 4 can be represented by two rectangles (placed side by side in a line or two by two).

Now ask your student to repeat this activity with 7 tiles. Record what the rectangle they find. What do they notice? Why can they make more than one rectangle with 6 tiles, but only one rectangle with 7 tiles? Make notes of their response and include them in your report.
Now ask them to repeat this activity with 5, 8, 11,13, 15 tiles (in that order). At each step, record their choice of rectangles and include them in your report.
What do they notice? Which of these numbers has only one possible rectangle? When they have indicated that some of the numbers can only have one rectangle, you may tell them that these numbers are known as prime numbers.
Ask the student to guess what they think the next prime number might be and ask them to test this with the tiles. Record their response and include it in your report.
Now ask them to find the factors for each of the numbers they have used before. You might need to explain what you mean by this. Record their response and include it in your report.
Now ask them to factorise the number 20. If they do not go down to the level of prime factors, prompt them to do so. Include their response and yours, in your report.
Report
Write a report that includes the following:
A description of this teaching experience including a summary of the student’s responses as previously requested. Do you think the student now understands the definition of a prime number? How do you know?
Ways in which you believe the activity to have been successful or unsuccessful.
What you would change if you were to do this activity again.
How you would use the factorisation of 20 as an introduction to indices.
What mathematics you needed to know before you could carry out this activity.
Describe another activity for introducing students to prime numbers. Compare it with the rectangle activity you have just completed. What are the advantages and disadvantages of each method?

To be submitted via MyLO dropbox as a Word document.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 2.1, 2.3, 2.4, 3.4 & 5.1

Task Length:

1400 words equivalent

Due Date:

Week 5 (05/Apr/2024)

Weight:

40 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Provide a clear explanation of the students’ responses and the mathematical learning that was achieved (25%)	LO1, LO2
2	Demonstration of the mathematics knowledge, PCK, and Horizon knowledge for the tile activity. Demonstration of the mathematics knowledge and PCK for the extension activity in Step 7 (30%)	LO1, LO2, LO3
3	Choice of alternative activity for introducing students to prime numbers with a clear explanation of the advantages and disadvantages for this choice compared with the tile activity (30%)	LO1, LO2, LO3
4	Communicate through the use of appropriate writing and mathematical conventions including APA referencing, punctuation, grammar, spelling, sentence structure and word choice (15%)	LO4

Assessment Task 3: Lesson Sequence

Task Description:

Choose a topic from the Australian Curriculum (current version), Mathematics, for either Year 6, Year 7 or Year 8 that will either introduce new knowledge to the students, or add new concepts to a previously known topic. Plan a guided discovery activity for this topic that will take approximately one hour to complete. In this plan you will include:

The Australian Curriculum Level, content descriptor and the elaboration you will target.
The specific objective for this lesson.
The prior knowledge that these students will need to have.
Your introduction to the task to gain the students’ interest.
The activity content – what the students will do.
The resources you will use, including use of ICT if relevant.
How you will assess if learning has taken place.
An example of a difficulty that you expect students may show and how you will address this.
Then write a paragraph justifying your choice of activity and assessment, using contemporary educational literature.
Explain how the knowledge the students learn in this lesson is important for their future mathematical study.

NB1: you may source your activity from the internet or a mathematics teaching journal if you wish. If you do this, the source must be fully referenced, and adapted for your own use.
NB2: This is not a lesson plan. Do not include information such as timing of each section of the lesson and classroom management procedures.

To be submitted via MyLO dropbox as a Word document

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 1.2, 2.1, 2.2, 2.3, 2.5, 3.1, 3.2, 3.4 & 5.1

Task Length:

2000 words equivalent

Due Date:

Week 13 (27/May/2024)

Weight:

50 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Demonstrate understanding of the key mathematical ideas (25%)	LO1
2	Demonstrate Pedagogical Content Knowledge with the choice of activity, knowledge of possible misconceptions and choice of assessment (50%)	LO2, LO3
3	Communicate through the use of appropriate writing and mathematical conventions including APA referencing, punctuation, grammar, spelling, sentence structure and word choice (10%)	LO4

How your final result is determined

To pass this unit, you need to demonstrate your attainment of each of the Intended Learning Outcomes, achieve a final unit grade of 50% or greater, and pass any hurdle tasks.

Submission of assignments

Where practicable, assignments should be submitted to an assignment submission folder in MYLO. You must submit assignments by the due date or receive a penalty (unless an extension of time has been approved by the Unit Coordinator). Students submitting any assignment in hard copy, or because of a practicum finalisation, must attach a student cover sheet and signed declaration for the submission to be accepted for marking.

Requests for extensions

If you are unable to submit an assessment task by the due date, you should apply for an extension.

A request for an extension should first be discussed with your Unit Coordinator or teaching support team where possible. A request for an extension must be submitted by the assessment due date, except where you can provide evidence it was not possible to do so. Typically, an application for an extension will be supported by documentary evidence: however, where it is not possible for you to provide evidence please contact your Unit Coordinator.

The Unit Coordinator must notify you of the outcome of an extension request within 3 working days of receiving the request.

Late penalties

Assignments submitted after the deadline will receive a late penalty of 5% of the original available mark for each calendar day (or part day) that the assignment is late. Late submissions will not be accepted more than 10 calendar days after the due date, or after assignments have been returned to other students on a scheduled date, whichever occurs first. Further information on Late Penalties can be found on the Assessments and Results Procedure.

Review of results and appeals

You are entitled to ask for a review of the marking and grading of your assessment task if there is an irregularity in the marking standards or an error in the process for determining the outcome of an assessment. Details on how to request a review of a mark for an assignment are outlined in the Review and Appeal of Academic Decisions Procedure.