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Teaching and learning

A range of suggested learning activities have been provided for each module in Units 1–2. It should be noted that the activities included cover a range of the Learning goals and Applications for each Module, but not all of them. Some activities could be completed within one class and others could be completed over an extended period. They include learning activities that involve group work, class discussion, and practical application of skills. Many of the learning activities could be adapted for use in other Modules or Units, or developed into assessment tasks. All are intended to be examples that teachers will use and/or adapt to suit the needs of their own students. It should be noted that teachers are encouraged to develop teaching and learning activities specifically suited to the needs to their students and context.

Included external links are for teacher reference purposes. They do not constitute VCAA endorsement of the views or materials contained on these sites and teachers need to ensure that any information or activities are appropriately adapted to meet the requirements of the VPC Numeracy Curriculum Design (1 January 2023 – 31 December 2027).

Unit 1 and 2

Unit 1

Exemplar 1 – Module 1: Personal Numeracy - Movies

Focus Areas: Location and Systematics

Focus Area: Location

Learning Goal

  • find location and direction in relation to everyday familiar places within the vicinity
  • find location and direction with everyday, simple and familiar maps and technologies
  • use everyday oral directions using informal language such as left/right, up/down, front/back, under/beside/over

Application

  • orally describe location of familiar, local places
  • use interactive and paper maps to locate highly familiar places or objects
  • give and follow simple oral directions to highly familiar locations

Focus Area: Systematics

Learning Goal

  • find common and familiar information and data inputs
  • read data outputs
  • summarise information

Application

  • input simple data into familiar apps
  • read simple output data
  • interpret simple output data

The Problem Solving Cycle

The problem solving cycle

Planning

Personal Numeracy: The focus of the context for this unit is using technology for planning and scheduling.

This plan demonstrates the problem-solving cycle as a five week learning program.

Timeline Activity Module

Week 1

Introduce the context

Introduce the context of personal numeracy – the mathematical requirements for personal organisation involving transport and travel and planning a day out.

Identify the issue(s)

Teacher to introduce the problem of planning a day out at the movies.

Students will use the problem-solving cycle to undertake a series of activities related to planning their day out, including selecting a movie at an appropriate time, choosing their preferred seats and describing the location of their seats and using public transport to travel to the movie cinema.

At all stages, students will undertake activities alongside their problem-solving cycle which are designed to address the Learning Goals and Applications that are required for the mathematics at each stage.

Consider which technologies will help to examine this issue and support the learning of the mathematics that is outlined in the area of study.

Using the Problem Solving Cycle - Step 1 - Identify the mathematics

Teacher leads a discussion on how students go about planning or organising to go out with friends. This should include factors such as date or day, time, location to meet, travel arrangements etc.

Give students the scenario of planning a trip to see a movie with friends and using public transport to get to the cinemas.

The next step is to identify the mathematics. Begin by discussing

  1. What is the purpose of the task?
  2. What is the mathematics knowledge that may be useful?
  3. What processes or calculations will be needed?

This provides a clear path for the teacher to then teach the mathematics.

Using the Problem Solving Cycle - Step 2 - Act on and use the mathematics

The teacher provides a series of activities that support student learning with the mathematical knowledge and skills. This sits alongside the investigation and supports the context that is being studied.

At all times the teacher considers

  1. What tools can you use from your Mathematical Toolkit to help student learning?
  2. Plan time to complete the relevant mathematical processes and calculations.

Using Technology for Planning and Scheduling
Learning Goal:
Find common and familiar information and data inputs
Read data outputs
Summarise information
Application:
Input simple data into familiar apps
Read simple output data
Interpret simple output data

Activity 1– What technology can we use?

Activity 2 – Use the technology

1: Personal Numeracy

Week 2

Activity 3 - Directional Language part 1
Activity 4 – Directional Language part 2
Activity 5 – Interactive VS Paper Maps
Activity 6 – Determining Input and Output Information

1: Personal Numeracy

Week 3

Using the Problem Solving Cycle - Step 3 - Evaluate and reflect

The activities in this section relate to the section of the problem solving cycle - evaluate and reflect. A core part of evaluation and reflection is going back reviewing the mathematics. At times this may involve starting the cycle again at the ‘act on’ a phase.

Questions to consider include:

  • Does the mathematics make sense in relation to the topic?
  • Is the mathematical process you have chosen the most appropriate for the question or task?
  • Can you justify the mathematics you have undertaken?
  • Check and reflect your work – are your answers what you expected?
  • Review and reflect on the reasonableness – do you need to make adjustments?
  • Do you need someone to check your work with you?

Activity 7 - Should we blindly follow?

Using the Problem Solving Cycle - Step 4 - Communicate and Report

The activities in this section relate to the section of the problem solving cycle – communicate and report, requiring students to be able to represent and communicate their mathematical results.

Questions that may guide this process include:

  • How will you communicate each of your results?
  • What methods have you learnt that you will include?
  • What methods will you use that are hand-drawn or hand-calculated?
  • What methods will you use that are completed with technology?
  • What software will you use to make your final presentation?

Activity 8 – Sharing our plans

1: Personal Numeracy

Week 4 & Week 5

Activity 9 – Assessment Task – Plan a trip to the movies

1: Personal Numeracy

Teaching

Unit plan descriptor

This unit has students exploring Personal Numeracy with the Focus areas: Location and Systematics. There are many hands-on activities where students gather their own understanding of planning a day out.

This unit explores all three Learning Requirements concurrently as mandated by the curriculum and supports the learning of all activities.

The four stages of the Problem Solving Cycle are supported by the inclusion of the multiple learning activities.

All the activities are contextualised with the issue of using technology for planning and scheduling.

Students are taken through the stages of the problem-solving cycle over a five week period.

When students are completing the technology components, they are working towards successfully building their Mathematical Toolkit – Learning Requirement Three. Opportunities presented in these tasks include: using online applications for planning and paper and interactive maps to locate places of interest. This is not an extensive list and teachers are encouraged to use as many technologies as are available within the confines of the classroom.

Integrated unit suggestion

VPC Literacy Unit 1: This unit could form part of an integrated unit with VPC Literacy Unit 1 Module 1 – Literacy for personal use and Module 2 – Understanding and creating digital texts.

Suggested resources/required equipment

General classroom stationery supplies which support student learning and teaching in mathematics. These may include, but not be limited to:

  • Student workbooks or paper
  • Pens and pencils
  • Paper maps

Access to the internet and computers or tablets is essential.

Technologies may include:

  • Google Maps
  • PTV website
  • Cinema booking sites
  • Online interactive maps
  • Phones for apps and calculations where permissible by the Principal

This list is not exhaustive, and teachers are encouraged to use extra materials and resources that support the learning for their students in their classrooms.

Unit 1: Module 1: Personal Numeracy with Focus Areas: Location and Systematics

This section details the activities.

Please note: These activities must not be taught in isolation from the Problem Solving Cycle, or the Mathematical Toolkit.

These activities are detailed in this table to help with implementation, but must be read in conjunction with the planning table.

Focus Area: Location
Focus Area: Systematics

Activity 1

What technology can we use?

Students explore the different websites and applications that are used for planning and scheduling, identifying what information is required to be entered into them (input data) and what information we then receive (output data).

  • The teacher leads a brainstorm to generate a list of the technology we use for the purpose of planning and scheduling. For the purpose of this unit the list should include websites and apps such as; Maps, PTV, Village/Hoyts cinema etc.
  • The teacher demonstrates the use of Google Maps, the PTV app and a cinema booking app. Whilst doing this ask student to look out for and make note of the information you are entering into the websites/applications and what information is given back to us.
  • The class define the terms; inputs – information goes into the technology and outputs – information comes out of the technology.
  • Students share their ideas and create a combined class list of inputs and outputs.
Focus Area: Location
Focus Area: Systematics

Activity 2

Use the Technology

Students practice inputting data into the websites and applications and interpreting the output data using given scenarios.

  • The teacher provides students with a list of scenarios to input into the planning apps explored in the previous task such as:
    • Determine the fastest route to drive from school to Melbourne Aquarium. Take a screen shot of the directions given. Now determine if the suggested route changes if you want to arrive at the aquarium at 9am tomorrow. Take a screenshot of the fastest route.
    • Determine the suggested route to walk from your house to school. Take a screenshot of the suggested route. Is it the same as the route you take to school?
    • Determine how you could catch public transport from school to Melbourne Aquarium. Compare the travel time to the driving directions previously determined.
    • Find out what movies are showing at your local cinema on Friday night.
Focus Area: Location

Activity 3

Directional Language – Part 1

Students explore the words used to give direction or indicate a location. Students then practice using directional language by describe the location of objects around the room.

  • The teacher leads a brainstorm with students making a list of all the words we use everyday that give directions or indicate a location,
    • Left, Right
    • Up, Down
    • Front, Back
    • Behind
    • Under, Over
    • Besides, Next to
    • Above, Below
    • Inside, Outside
  • The teacher places objects around the room. In pairs, students describe the location of an object to their partner who has to guess which object they are describing.
  • The teacher leads a discussion to reflect on the art of orally giving directions and what makes directions good or bad.
Focus Area: Location

Activity 4

Directional Language – Part 2

Students continue to practice their use of directional language. First students describe a chosen location within the school. Then they give oral directions to a different location within the school that a partner has to follow.

  • In pairs, students think of a specific place within the school and orally describes to their partner the location of the chosen place in relation to other familiar places within the school. Their partner has to try and correctly guess the chosen place.
  • In pairs, students individually think of a common location in the school and writes directions on how to get there from the classroom. They give their directions to their partner, keeping the final location a secret. Then, using only the written directions, students move around the school to reach their partners secret location.
  • The teacher leads a discussion to reflect on the task – did the directions lead to the correct location? What worked well or didn’t work well?
Focus Area: Location

Activity 5

Interactive vs Paper Maps

Students explore a variety of paper maps for familiar locations and their interactive online equivalents. Students use the maps to find specific locations and to give directions to another student.

  • The teacher shows students a variety of paper maps for locations such as the local shopping centre, Melbourne zoo, Melbourne aquarium etc. as well as the interactive online equivalents.
  • The teacher leads a discussion with students comparing the features that are shown on both types of maps. Discuss the positives and negatives of each type of map (paper and interactive).
  • Students find specific locations on each of the maps such as the toilets, information desk, food outlet, bus stop, entrances and exits, first aid etc.
  • The teacher leads a discussion on which type of map was easier to use, guiding students to think about what made the maps easier or harder to use.
  • Students select a location of interest on one of the maps and use the map and other locations on the map to give directions to another student, who needs to follow the directions to find the location.
Focus Area: Location
Focus Area: Systematics

Activity 6

Determining Input and Output Information

Using the scenario of planning a trip to the movies, travelling by public transport. With support student determine appropriate input information required to plan the trip and the expected output information they could receive.

  • The teacher gives students the scenario of planning a trip to the movies, where they have to catch public transport to the cinemas.
  • The teacher leads a discussion with students, guiding them to determine the input information they will require before planning the trip and what output information they will receive. This should include things such as:
    • Where they are going (input)
    • Day, date, time (input)
    • What movie they want to see (input)
    • Movie time (output)
    • Location of seats in cinema (output)
    • Time to meet at the cinema (input)
    • Public transport route (output)
    • Travel time (output)
    • Time to leave (output)
  • The teacher supports the students to make decisions about the input information they need to plan their trip to the movies, ensuring the decisions they have made are reasonable.
Focus Area: Location

Activity 7

Should We Blindly Follow?

Class discussion on things that can go wrong if directions or information from planning apps is not first evaluated for appropriateness. Students are supported to evaluate review the solutions for the scenarios from Activity 2.

  • The teacher leads a discussion with students on the perils of blindly following directions or outputs from planning applications. Students share a time or story when they were led astray by navigation app or something similar.
  • The teacher introduces Step 3 of the Problem-Solving Cycle and discuss the importance of review and reflecting on results to make sure they are reasonable and appropriate.
  • Students reflect back on their solutions to the scenarios from Activity 2 and consider the following:
    • Do the solutions make sense? How do you know?
    • Do you need to make any adjustments to the information you have input?
    • What errors could others have made?
Focus Area: Location

Activity 8

Sharing Our Plans


Students explore how we communicate plans and practice using a variety forms of communications, such as written notes, text messages, phone calls etc.

  • The class discuss how we share or communicate plans we have made. Include such things as:
    • Who needs to know what we are doing?
    • What information do they need to know?
    • How can we explain our plans?
  • Students communicate their solutions to the scenarios from Activity 2 using a variety forms of communication such as; a written note, a text message, phone call etc.
Focus Area: Location
Focus Area: Systematics

Assessment task

Plan a trip to the movies

This assessment task combines the Learning Requirements 1, 2, and 3 cohesively as mandated in the curriculum guidelines.

The assessment adheres to the curriculum requirement to include all three Learning Requirements. Learning requirement 2 allows students to use the Problem Solving Cycle within the context and skills outlined in Learning Requirement 1, and Learning Requirement 3 involves students using their Mathematical Toolkit to support Learning Requirement 1 and 2. 

Assessment Task: Students must plan a trip to the local cinemas to see a movie with a friend and they must travel by public transport.

To complete the tasks students are required to complete the following:

  • Select a movie session to go to, based on the input information decided on in Activity 6 and follow the process of booking tickets, including selecting where to sit.
  • Write a SMS message to your friend informing them of the movie details and describing where you’ll be sitting.
  • Determine how to get to the cinemas via public transport, making note of the route, departure location and time, arrival location and time, and travel time.
  • Role play a phone conversation with your friend, who is lost (e.g. somewhere in the centre or at the bus stop) and can’t find their way to the cinemas. You can use a map of the cinema complex/shopping centre to help you give the directions. Your friend should follow your directions, by drawing them on paper map of the cinema complex/shopping centre to make sure they can find you at the cinemas.

Problem Solving Cycle:

Support students through the Problem Solving cycle as they complete the requirements of the task.

Step1 – Identify the mathematics

Students write the purpose of the task in their own words, including the specific parameters (input information) they determined in Activity.

Students list the specific mathematical skills or knowledge they will need to complete the task including any associated costs, times, public transport routes, and directions. Prompt students to think about the skills or knowledge they have developed by completing the unit activities.

Step 2 – Act on and use mathematics

Students use the appropriate technology and applications to complete each of the task requirements needed to plan their trip to the movies. Ask students to keep evidence of their planning – such as notes or screen shots. 

Step 3 – Evaluate and reflect

Students review their plans to make sure they are reasonable and appropriate and make any changes to their plans if it is required. Students could share these with a peer to check for reasonableness.

Step 4 – Communicate and report

Students present their plan to their teacher, explaining the details of their trip to the movies and be ready to justify all choices made.

For assessment, students should submit:

  • The movie details including location, session time and a screenshot of the chosen seat location.
  • A copy of the text message to their friend.
  • The details of the public transport route they will take including the form of public transport, departure location and time, arrival location and time, total travel time and a screenshot of the PTV app
  • A copy of the map that shows the oral directions given during the role play

Exemplar 2 – Module 1: Personal Numeracy - Sharing our plans

Focus Area: Location & Systematics

Focus Area: Location

Learning Goal

On completion of this module the student should be able to:

  • find location and direction in relation to everyday, familiar places within the vicinity
  • find location and direction with everyday, simple and familiar maps and technologies
  • use everyday oral directions using informal language such as left/right, up/down, front/back, under/beside/over.

Application

Demonstration of the learning goals requires students to apply a variety of skills. The following applications assist students to demonstrate they have met the learning goal.

  • apply a variety of skills. The following applications assist students to demonstrate they have met the learning goal.
  • orally describe location of familiar, local places
  • use interactive and paper maps to locate highly familiar places or objects
  • give and follow simple oral directions to highly familiar locations.

Focus Area: Systematics

Learning Goal

On completion of this module the student should to be able to:

  • find common and familiar information and data inputs
  • read data outputs
  • summarise information.

Application

Demonstration of the learning goals requires students to apply a variety of skills. The following applications assist students to demonstrate they have met the learning goal.

  • input simple data into familiar apps
  • read simple output data
  • interpret simple output data.

The Problem Solving Cycle

The problem solving cycle

This unit has been designed for students 16-18 years old diagnosed with Autism Spectrum Disorder and Intellectual Disability in an independent specialist school. They are attending school full time and will undertake a Certificate I VET Certificate one day per week.

Planning

Personal Numeracy:
Personal numeracyrelates to the mathematical requirements for personal organisational matters involving money, time and travel for participation in community-based activities and events.

Timeline Activity Module

Introduction

Introduce the context

This exemplar explores Unit One Personal Numeracy with the Focus Areas of Location and Systematics, as outlined in accordance with the VCAA’s publication Victorian Pathways Certificate: Numeracy – Curriculum Design. All Learning Goals and Applications have been addressed.

The context of Personal Numeracy includes time and travel, planning to travel, and money required with travelling. Over a course of several activities, students are supported and encouraged to build their skills and application of the Learning Goals for Location and Systematics, in accordance to Learning Requirement 1; resulting in the class working together to plan an excursion, invite another class to participate, and execute the excursion. These

Prior to this, students are exploring maps, directional language, creating their own maps, working with maps and current technologies build their Mathematical Toolkit, in accordance to Learning Requirement 3 The Mathematical Toolkit. These activities have been designed with structure to support the needs of the students to provide a regular routine and regular exposure to the Problem Solving Cycle, in accordance to Learning Requirement 2.

Identify the issue(s)

Students will be supported activities within the classroom and out in the local community to gain knowledge of location, direction, maps and public transport to be able to plan an excursion where the class invites another class to join them on an excursion to a local destination, such as a cafe. These activities are hands-on and appropriate to the needs of the students and allow the students to have created their own purpose-built resources as a class resource and for their own personal use later on.

The teachers are very supportive throughout all lessons and provide many opportunities for continuous skill growth and development, often revisiting mini-lessons to reinforce main concepts.

Using the Problem Solving Cycle - Step 1 - Identify the mathematics

Teachers lead the discussion for the excursion and the class choose the destination.

The next step is to identify the mathematics. Begin by discussing

  1. What is the purpose of the task?
  2. What is the mathematics knowledge that may be useful?
  3. What calculations will be needed?

This provides a clear path for the teacher to then teach the mathematics.

Using the Problem Solving Cycle - Step 2 - Act on and use the mathematics

The teacher then provides a series of activities that support student learning with the mathematical knowledge and skills. This sits alongside the investigation and supports the context that is being studied.

At all times the teacher considers

  1. What tools can you use from your Mathematical Toolkit to help student learning?
  2. Plan time to complete the relevant mathematical calculations and processes.

Using the Problem Solving Cycle - Step 3 - Evaluate and reflect

The activities in the assessment section relate to the section of the problem solving cycle - evaluate and reflect. A core part of evaluation and reflection is going back reviewing the mathematics. At times this may involve starting the cycle again at the ‘act on’ a phase. 

Questions to consider include:

  • Does the mathematics make sense in relation to the topic?
  • Is the mathematical process you have chosen the most appropriate for the question or task?
  • Can you justify the mathematics you have undertaken?
  • Check and reflect your work – are your answers what you expected?
  • Review and reflect on the reasonableness – do you need to make adjustments?
  • Do you need someone to check your work with you?

Using the Problem Solving Cycle - Step 4 - Communicate and Report

  1. How will you communicate each of your results?
  2. What methods have you learnt that you will include?
  3. What methods will you use that are hand-drawn or hand-calculated?
  4. What methods will you use that are completed with technology?
  5. What software will you use to make your final presentation?

 

Module 1: Personal Numeracy

Assessment

Task – students will plan and invite another class to join them on an excursion to their chosen destination, and execute the excursion with support from the teaching staff

Module 1: Personal Numeracy

Week 1-2

Activity 1 – Design a map of the school

Module 1: Personal Numeracy

Week 3-4

Activity 2 - Design a map of the neighbourhood

Module 1: Personal Numeracy

Week 5-6

Activity 3 - Using your map of the neighbourhood

Module 1: Personal Numeracy

Week 7-8

Activity 4 - QR Code Scavenger Hunt

Module 1: Personal Numeracy

Week 9-10

Activity 5 - Planning a route

Module 1: Personal Numeracy

Week 11-12

Activity 6 – Planning short excursions

Module 1: Personal Numeracy

Week 13-14

Activity 7 – Planning longer excursions

Module 1: Personal Numeracy

Week 15-18

Activity 8 - Plan and share a final excursion

Module 1: Personal Numeracy

Teaching

Unit plan descriptor

Where am I going?

In this unit, students will learn about the location of familiar landmarks and how to get to them. In the first half of the unit, students will learn how to create maps with real images and objects, describe the appropriateness of maps vs technology, follow and give verbal and visual instructions whilst walking around their local community.

Once students have mastered these skills in the local community they will investigate technology such as Google Maps and the PTV app to find their way to locations that are further afield e.g. local cafes, shopping centres and their work experience.

Over the course of the unit, students will move from participating in excursions lead by staff to having more independence to choose locations, establishing supports that help them regulate and lead others through activities.

Integrated unit suggestion

Numeracy Unit 1 – Module 2; This unit may be integrated with elements of Module 2: Financial Numeracy to support students to learnt about how to pay for their travel (in the case of this cohort, paying for a service such as travel is quite an abstract concept and so will not be taught in this way).

Numeracy Unit 2 – Module 3; the unit may be integrated with Module 3: Health and recreational numeracy, with the Focus area Quantity and measures as students explore time and length concepts.

Suggested resources/required equipment

Required

  • iPad or iPhone with 4G data enabled
  • Myki cards for each student
  • PTV app loaded onto digital device

Suggested

  • Companion cards for all students with additional needs
  • Paper timetables of local public transport
  • Local area maps

This section details the activities.

Please note: These activities must not be taught in isolation from the Problem Solving Cycle, or the Mathematical Toolkit.

These activities are detailed in this table to help with implementation but must be read in conjunction with the planning table.

Focus Area: Systematics

Activity 1

Design a map of the school

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch an online video about prepositions (search YouTube)
  • Students are introduced to the problem solving cycle - phrased as a series of questions

Body

Introduce the context and identify the mathematics

What mathematics language do we use when accessing the world around us?

  • Students refresh each of the main prepositions they are familiar with by watching a series of video models
  • Students come to the board and use the board pens to demonstrate their understanding of positions by moving visuals around the screen
  • Students demonstrate their understanding of prepositions by using real objects to arrange items in different positions e.g. put the water bottle on the table, put your pencil in the cup
  • Students watch a motivating video from YouTube about mapping skills

Act on and use the mathematics

  • Students watch a visual forewarning of the activity and understand the technology (iPad) that they will need and how to use it
  • Students walk around the school and take photos of key points in the school e.g. classroom doors, playground equipment, toilets
  • Students return to class, print the photos they have taken and use them to fill in the gaps on a large map of the school

Conclusion

  • Students are asked a short series of summary questions about their learning and are asked to engage with the map to answer questions using prepositions
Focus Area: Systematics

Activity 2

Design a map of the neighbourhood

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch an online video about prepositions

Body

  • Students refresh each of the main prepositions they are familiar with by watching a series of video models
  • Students demonstrate their understanding of prepositions by using real objects to arrange items in different positions e.g. put the water bottle on the table, put your pencil in the cup
  • Students watch a motivating video from YouTube about mapping skills
  • Students watch a visual forewarning of the activity and understand the technology (iPad) that they will need and how to use it

Act on and Use mathematics

  • The teacher leads a discussion about size and appropriateness of map size and features
  • Students walk around the neighbourhood and take photos of key points in the school e.g. houses, gardens, stop signs, roundabouts, shops, post-boxes etc.
  • Students return to class, print the photos they have taken and use them to fill in the gaps on a large map of the neighbourhood

Evaluate and reflect

  • Students are asked to discuss the practicality of the A0 size map and suggest alternatives that would be easier to carry

Conclusion

  • Students are asked a short series of summary questions about their learning and are asked to engage with the map to answer questions using prepositions
Focus Area: Systematics

Activity 3

Using your map of the neighbourhood

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch an online video about prepositions

Body

  • Students demonstrate their understanding of prepositions by using real objects to arrange items in different positions e.g. put the water-bottle on the table, put your pencil in the cup
  • Students watch a motivating video from YouTube about using GoogleMaps
  • Students watch a visual forewarning of the activity and understand the technology (iPad) that they will need and how to use it
  • Students use the neighbourhood map they made in the last activity to plan a route to particular destinations (changes each lesson) in the local environment e.g. shops, post-box
  • Students explore Google Maps app and other technologies which can be used to orient to particular places. Use a compass and map to create a list of instructions on how to get to particular destinations and check answer in Google Maps, practising directional language learnt including up, down, left, right, etc.

Communicate and report

  • Students then use Google Maps live view and their written answers to navigate to the place on the map
  • Students are asked to discuss the practicality of their map vs Google Maps on an iPad

Conclusion

  • Students are asked a short series of summary questions about their learning and are asked to engage with the map to answer questions using prepositions
Focus Area: Systematics

Activity 4

QR Code Scavenger Hunt

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch a video about prepositions

Body

  • Students demonstrate their understanding of prepositions by using real objects to arrange items in different positions e.g. put the water bottle on the table, put your pencil in the cup
  • Students watch a motivating video from YouTube about using QR codes
  • Students watch a visual forewarning of the activity and understand the technology (iPad) that they will need and how to use it

Act on and use mathematics

  • Students follow a QR code scavenger hunt (with imbedded motivating videos) which has been designed by the teacher in the local environment
  • Once students have grasped the concept – they will create their own QR code scavenger hunt (motivating videos selected by the teacher but clues about the next destination from students)
  • Students invite their peers in other classes to complete the scavenger hunt

Conclusion

Communicate and reflect

  • Students are asked a short series of summary questions about their learning and are asked to reflect on the success of the event and what could improve it next time
Focus Area: Location
Focus Area: Systematics

Activity 5

Planning a route

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch an online video about directions
  • Students are introduced to the problem-solving cycle - phrased as a series of questions

Body

  • Students demonstrate their understanding of prepositions by using real objects to follow different directions to move about the classroom
  • Students watch an online motivating video from YouTube about using QR codes
  • Students work together to select a preferred destination such as a café to visit within walking distance of the school.
  • Students plan directions to get there and test them out in person using GoogleMaps and by walking themselves
  • Students write an invitation to another class to join them at the café
  • (Final lesson) students walk to café together following directions at each point along the way

Conclusion

Communicate and reflect

  • Students are asked a short series of summary questions about their learning and are asked to engage with the map to answer questions using prepositions
Focus Area: Location
Focus Area: Systematics

Activity 6

Planning short excursions

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)

Identify the mathematics

  • Students watch an online video about directions

Body

  • Students demonstrate their understanding of prepositions by using real objects to follow different directions to move about the classroom
  • Students watch a motivating video from YouTube about using the PTV app
  • Students read through a forewarning about checking the PTV app to see when trams are arriving

Act on and use mathematics

  • Initially the scheduling component of the activity (how long is it going to take to walk to the tram stop) is mitigated from the activity by the teacher
  • Students plan and participate in a series of short excursions to destinations selected by the teacher that are 1-2 tram/bus stops away from school
  • Two lessons are spent planning the activity and one is spent engaging in the activity

Conclusion

  • Evaluate and reflect
  • Students plan next stages of their outing
  • Students are asked a short series of summary questions about their learning and are asked to engage with the PTV app to get the tram appropriately

Communicate and report

  • Students reflect on what they learnt during the process about timetables, catching public transport and time
Focus Area: Location
Focus Area: Systematics

Activity 7

Planning long excursions

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch a video about directions
  • Students discuss the problem-solving cycle - phrased as a series of questions

Body

  • Students demonstrate their understanding of prepositions by using real objects to follow different directions to move about the classroom
  • Students watch a motivating video from YouTube about using the PTV app
  • Students read through a forewarning about checking the PTV app to see when trams are arriving
  • Students take more responsibility to plan a longer excursion to larger destinations with specific purposes e.g. Bunning, Kmart
  • Students will access the PTV app at the tram stop to set a visual timer for themselves so they are able to better comprehend how long they have to wait
  • Students take pictures at the different steps along the way and then return to class to match the photo they have taken with each step of the social story.

Conclusion

Communicate and report

  • Students are asked a short series of summary questions about their learning and are asked to engage with the PTV app to get the tram appropriately and the factors that need to be considered when planning a longer excursion e.g. checking the weather, knowing how long the walk may take, public transport running late / cancelled etc.

Core Conclusion

  • Students pack away materials relevant to the lesson and move to get their schedules
Focus Area: Location
Focus Area: Systematics

Assessment task

Plan and share a final excursion

  • Students will plan and invite another class to join them on an excursion to their chosen destination, and execute the excursion with support from the teaching staff
  • Using the skills gained from this unit, students will agree and plan an excursion to an agreed destination, such as a café.
  • Students will go into the other class, invite them with a small speech and written invitation with information, and execute the excursion on the day.

Staff should support the students with the four steps of the Problem-Solving Cycle.

Step 1 – Identify the mathematics

With support from the teachers, students will

  • Find the location and find it on the map
  • Agree on a meeting time at the café
  • Use their maps and/or PTV app to plan the travel route to the café – and include the needs of everyone on the trip (does someone in this class or the other class have mobility issues that need to be considered?, is there a second bus scheduled in case we miss the first one? etc)
  • Check how much it will cost to travel via public transport
  • Look up the menu to share with the other class to allow students to have enough money on the day and to check for any dietary purposes
  • Find the phone number of the café to make the booking
  • Create the invitations for the other class – complete with all details of the school day beforehand, travelling as a group together using public transport/walking, approximate times out of school, and returning to school time, and the appropriate permission form will accompany this (created by the teacher).

Step 2 – Act on the mathematics

  • Set tasks in small groups, and guide students with their goals. Check in regularly to provide positive support and role-modelling for problem solving purposes.
  • Have regular check-ins as whole class meetings to see where people are up to – how they are travelling – to give it an inclusive vibe but also to allow students to help problem solve with each other.

Step 3 – Evaluate and Reflect

  • Bring the class together – and have their work on display for everyone to review together. Allow only positive feedback and supported feedback – bring in the concept of positive team work and constructive criticism that leads to improvements.
  • Ask students to justify the choices they have made – not to put them on the spot – but to allow them to talk through what they have done – so they can see their work in its entirety (this is a useful tool when you are highlighting something that needs tinkering or something that has been forgotten).

Make a list of excursion checks – such as but not limited to:

  • Has proof-reading of the invitation been done?
  • Has the date been checked on the calendar?
  • Is the time the same as the booking with the café?
  • Have the travel plans been checked? Reminders sent out about any travel costs?
  • Have the permission forms been made to be attached to the invite?
  • Has a first aid kit been booked to take out?
  • Has someone checked the weather to make sure we know what to wear and/or pack?
  • Excursion day information – where are we meeting before starting our excursion? What time are we leaving?
  • Is the café and menu link available and on the invite?
  • Is the invite created?

Step 4 – Communicate and Report

  • Time to bring it all together – create an invitation that is appealing but with all the important information!
  • Plan a group of students to go into the other class and invite them publicly – and pass out the invitations with permission forms attached. This group of students can explain the excursion, the travel plans, explain the café and what style of food is on offer, etc

Prior to the excursion, the class can appoint teams of students different jobs – to help working as a team to get there and back. There could be two shifts – one getting the group to the café, and one returning the group back to school – if there are enough students wanting to do it – or students can work in bigger groups and have two roles for the day?

Possible ideas for jobs – which are all supported by the teaching staff:

  • Event Planner / Logistics Specialist – (overall leader who is a good problem solver, calming, has a good understanding of all the tasks)
  • Personal Assistant (checking the roll with the teacher)
  • Travel guides (executing the travel plans and getting everyone to the destination)
  • Concierges (students who approach the café upon arrival and let them know they are there)

Exemplar 3 – Module 2: Financial Numeracy - Winner, winner, chicken dinner

Focus Areas: Number and Change

Focus Area: Number

Learning Goal

  • Place value and numbers up to 1000
  • Whole numbers and monetary amounts up to $1000
  • Addition and subtraction (with no borrowing or decomposition) of whole numbers and familiar monetary amounts into the 100s
  • Common, simple unit fractions such as 1/2, 1/4 and 1/10
  • Common decimals and percentages such as 0.5, 0.25, 50%, 25%

Application

  • Identify place value and read whole numbers up to 1000
  • Perform calculations of addition and subtraction with simple whole number amounts and familiar monetary amounts (into the 100s)
  • Recognise and understand very common simple unit fractions, decimals and percentages.

Focus Area: Change

Learning Goal

  • Pattern prediction with shapes
  • Repeating patterns with one element such as with shapes or $2, $4, $6, $8, …
  • Changes and number matching with simple numbers for examples, prices increasing or decreasing, matching corresponding numbers.

Application

  • Recognise changes in numerical values such as prices increasing or decreasing with a common fixed price discount
  • Number matching and comparison of simple numbers in context such as matching prices from receipts to on-the-shelf items
  • Predict pattern continuation with shapes. For example, triangle, square repeating pattern
  • Demonstrate patterns with one element. For example, $2, $4, $6, $8, …

The Problem Solving Cycle

The problem solving cycle

Planning

Financial Numeracy: The focus of the context for this unit is money management.

This plan demonstrates the problem-solving cycle as a five week learning program.

Timeline Activity Module

Week 1 - 2

Introduce the context

The context is the student’s own ability to manage money and becoming financially responsible. The teacher may introduce the topic with class discussions about money and what can happen if we don’t know how to manage our money.

Identify the issue(s)

Teacher to introduce the issue of money management and becoming financially responsible.
Students will use the Problem-Solving Cycle to undertake a series of activities related to understanding financial documents, earning money, and making responsible choices about using their money.

Students will undertake activities to achieve the learning goals and applications.

Each activity contains one complete problem solving cycle.

Activity 1 – Numbers Numbers Everywhere?

Activity 2 – Earning Money

Module 2: Financial Numeracy

Week 3 & Week 4

Activity 3 – Spending our money

Module 2: Financial Numeracy

Week 5

Assessment Task – Winner Winner Chicken Dinner

Module 2: Financial Numeracy

Teaching

Unit plan descriptor

This unit has students exploring Financial Numeracy with the Focus areas: Number and Change. There are many hands-on activities where students gather their own understanding of managing money.

This unit explores all three Learning Requirements concurrently as mandated by the curriculum and supports the learning of all activities.

The four stages of the Problem-Solving Cycle are supported by the inclusion of the multiple learning activities.

All the activities are contextualised with the issue of managing money.

Students are taken through the stages of the Problem-Solving Cycle over a five week period.

When students are completing the technology components, they are working towards successfully building their Mathematical Toolkit – Learning Requirement Three. Opportunities presented in these tasks include: using the FairWork pay calculator, online shopping sites and restaurant menus. This is not an extensive list and teachers are encouraged to use as many technologies as are available within the confines of the classroom.

Integrated unit suggestion

VPC Literacy Unit 1: This unit could form part of an integrated unit with VPC Literacy Unit 1 Module 1 – Literacy for personal use and Module 2 – Understanding and creating digital texts.

VPC WRS Unit 1: This unit could also form part of an integrated unit with VPC Work Related Skills Unit 1 relating to workplace conditions (pay) and applying for an employment opportunity.

Suggested resources/required equipment

General classroom stationery supplies which support student learning and teaching in mathematics. These may include, but not be limited to:

  • Student workbooks or paper
  • Pens and pencils
  • Calculators
  • Post-It notes
  • Copies of a range of financial documents, including payslips
  • Images of supermarket shelf labels

Access to the internet and computers or tablets is essential.

Technologies may include:

  • FairWork Pay calculator
  • Online shopping sites
  • Online restaurant menus
  • Calculators
  • Phones for apps and calculations where permissible explicitly granted by the Principal

This list is not exhaustive, and teachers are encouraged to use extra materials and resources that support the learning for their students in their classrooms.

This section details the activities.

Please note: These activities must not be taught in isolation from the Problem Solving Cycle, or the Mathematical Toolkit.

These activities are detailed in this table to help with implementation, but must be read in conjunction with the planning table.

Focus Area: Number

Activity 1

Numbers Numbers Everywhere?

In this activity students explore a variety of financial documents such as household bills, supermarket receipts, bank account statements etc. in order to recognise and understand the financial information displayed on them.

Step 1 - Identify the mathematics

In this stage students identify the task and purpose, and to then identify the mathematics involved

The teacher displays a variety of financial documents around the classroom and lead a discussion with the following questions:

  • What information would you expect to see on financial documents?
  • What skills or knowledge would we need to be able to understand them?
  • What sorts of numbers might be found on the documents?

Step 2 - Act on and use the mathematics

In this stage students choosing the mathematics and the mathematical tools to use, and performing the required calculations and processes.

  • The teacher instructs students to move around the room to examine each of the financial documents and identify the numerical information that is displayed. Students write down numbers they find, separating them into two categories; amounts or other numerical information (e.g. account numbers, dates, phone numbers etc.).
  • The teacher leads a discussion asking students to share the numerical information they found on the documents. Discuss how to read each of the numbers correctly and what each of the numbers mean.
  • Students select a financial document of choice and annotate the numerical information that is shown on it, explaining what each of the numbers mean, for example:
    • the total amount due is two hundred and forty dollars. This is how much you have to pay ninety-one days, this is how long the billing period is 3% this is how much the total is reduced by if paid on time

Step 3 - Evaluate and reflect

In this stage students consider the appropriateness and reasonableness of their results and adjust if necessary, including redoing any calculations

  • Support students to check over their annotations prompting with the following questions:
    • Have you correctly read all the numerical information?
    • Have you made any errors with place value?
    • Check your annotations with someone else who has the same document – are they similar?

Step 4 - Communicate and Report

In this stage students consider the best method/s to produce their findings, and to ensure they have communicated it sufficiently so that the audience is clear on the numbers and message being presented.

  • Students partner up with someone with a different financial document. They use their annotations to share and explain how to read and understand the financial document to their partner.
Focus Area: Number
Focus Area: Change

Activity 2

Earning Money

In this activity has students explore wages, pay rates and penalty rates.

  • Students examine payslips to identify the key information such as hours worked, pay rate, gross pay, tax withheld, any other deductions or allowances, and net pay.
  • Students also perform calculations and use the FairWork website to ensure they have been paid correctly.

Step 1 - Identify the mathematics

In this stage students identify the task and purpose, and to then identify the mathematics involved

  • The teacher asks students if anyone has a part-time or casual job. Lead a discussion about what it is like to earn money and if there are other ways that we can earn money other than having a job.
  • The teacher asks students with a job if they have ever checked if they are getting paid correctly and leads a discussion with the following information.
    • What information would you expect to see on a payslip?
    • What words or terminology do we need to know or understand?
    • What mathematical calculations would be needed to check our payslips?
    • What tools can we use to make sure we are getting the correct pay rates?

Step 2 - Act on and use the mathematics

In this stage students choose the mathematics and the mathematical tools to use, and performing the required calculations and processes.

  • The teacher provides students with a sample payslip for a relevant job such as fast food restaurant, supermarket or retail shop – and if students have a job they can use one of their own payslips. Ask students to identify the key information that is on their payslip including: hours worked, pay rate, gross pay, tax withheld (if any), any other deductions or allowances, net pay, and YTD pay.
  • The teacher asks students to perform the relevant calculations to check that the payslip is correct and no errors have been made.
  • The teacher leads a discussion with students about penalty rates and what double pay, time and half etc might mean. Demonstrate how to use the FairWork pay calculator to find the minimum pay rate and penalty rates. Note: if you click on ‘why’, then ‘details’ it shows the % loading added to the base rate. Lead a discussion on what the %loading figures mean in terms of fractions and decimals.
  • Students use the FairWork pay calculator to check their own pay rates to ensure they are being paid correctly.

Step 3 - Evaluate and reflect

In this stage students consider the appropriateness and reasonableness of their results and adjust if necessary, including redoing any calculations

  • The teacher supports students to review their work and decide if it is reasonable and to check over the calculations performed.

Step 4 - Communicate and Report

In this stage students consider the best method/s to produce their findings, and to ensure they have communicated it sufficiently so that the audience is clear on the numbers and message being presented.

  • The teacher asks students to share if their pay slips are correct. They will need to be able to explain and justify their calculations and information they have found.
Focus Area: Number
Focus Area: Change

Activity 3

Spending Our Money

In this activity students explore what things they spend money on and how to make decision about what to spend.

  • The teacher leads a brainstorm with students asking them to list all the things they spend money on or want to spend money one. The class categorise these as committed expenses - must pay, not negotiable e.g. phone bill, rent or board or discretionary expenses – can be changed or adjusted e.g. take-out food, going out with friends.
  • Students explore the things they spend money on and how to make decision about what to spend. This task requires students to:
    • Select items to purchase: Students compare supermarket shelf items to determine which items are better value for money. Students also compare the cost of selected items from different shops.
    • Calculate staff discount: Students calculate the cost of selected items if they were to use a staff discount of 10%, 25% and 50%.
    • Calculate change: Students practice a variety of strategies for calculating change to determine what is the easiest method for themselves to use

Step 1 - Identify the mathematics

In this stage students identify the task and purpose, and to then identify the mathematics involved

  • The teacher asks students to think about what skills or knowledge they need to have to be able to make decisions about spending money. This should include:
    • Knowing much they have to spend
    • Knowing how much things cost and working out best value for money.
    • Different strategies for calculating staff discounts, such as 10%, 25%, 50%
    • Different strategies for calculating change

Step 2 - Act on and use the mathematics

In this stage students choose the mathematics and the mathematical tools to use, and performing the required calculations and processes.

Task 1: Comparing items to purchase

  • The teacher shows students a selection of shelf labels of supermarket items.
  • Students identify the information that is shown including the item price, the size or weight of the item and the unit price.
  • Students select a series of similar items e.g. same item but different brands, or same brand but different package size and determines which is ‘better value for money’. They should do this for at least 3 different series of items.
    Note: this could be done through an excursion to a local supermarket, asking students to take photos of shelf labels and bring them to class, or the teacher providing a selection of appropriate shelf label photos.
  • Students choose three different items they would like to purchase such as clothing, shoes, concert ticket, mobile phone, gaming console etc.
  • Students research how much it would cost to purchase each item from at least two different shops or suppliers, making note of cost of the items, any additional costs such as shipping charges, and any discounts.

Task 2: Calculating staff discount

  • The teacher asks students who have jobs and what their staff discount is.
  • The teacher explicitly teaches different strategies for calculating 10%, 25% and 50% discounts, including identifying the fraction and decimal equivalents.
  • Students select items from their place of work, or a suitable place of work and calculate how much it would cost if they had a 10%, 25% and 50% staff discount.
  • If students have a different staff discount amount (e.g. 5% or 20%), the teacher supports them to calculate this discount as well.

Task 3: Calculating change

  • The teacher explains to students that knowing and understanding number patterns helps us to calculating change.
  • The teacher provides students with a series of repeating shape patterns and asks them to continue the pattern.
  • The teacher provides students with a series of repeating number patterns, counting by 5s, 10s, 20s, 50s, and 100s. Ask students to identify the number pattern, continue the pattern and find missing numbers.
  • The teacher leads a discussion about the idea that doing ‘vertical subtraction’ isn’t always practical when trying to work out change. Explicitly teach different strategies for calculating change, such as counting on, mental subtraction left to right etc.
  • The teacher provides students with a range of scenarios for which they have to calculate change.

Step 3 - Evaluate and reflect

In this stage students consider the appropriateness and reasonableness of their results and adjust if necessary, including redoing any calculations

  • The teacher supports students to review their work and decide if it is reasonable and to check over the calculations performed. Prompt with the following questions:
    • Do your answers seem reasonable?
    • Have you performed the calculations correctly?
    • Do you want someone to check over your work, or are you happy with it?

Step 4 - Communicate and Report

In this stage students consider the best method/s to produce their findings, and to ensure they have communicated it sufficiently so that the audience is clear on the numbers and message being presented.

  • Students choose the best methods to present and communicate the following:
    • Task 1 – the items they selected as being the best value for money in both parts A and B, explaining and justifying their choices.
    • Task 2 – how much they save using their staff discount
    • Task 3 – their preferred method for calculating change and how they use it.
Focus Area: Number
Focus Area: Change

Assessment task

Winner Winner Chicken Dinner

The assessment adheres to the curriculum requirement to include all three Learning Requirements. Learning Requirement 2 allows students to use the Problem-Solving Cycle within the context and skills outlined in Learning Requirement 1, and Learning Requirement 3 involves students using their Mathematical Toolkit to support Learning Requirements 1 and 2.

Assessment Task: This task requires students to plan a dinner out with friends at a chosen restaurant and they have been ‘given’ a $100 voucher. In part 2 of the task students need to calculate how much a public holiday surcharge of 10% of the bill would be. Then decided if they would need to change their menu items in order to not overspend.

  • The teacher informs students that they have been ‘gifted’ a $100 voucher to their favourite restaurant and they are going to take 3 friends out to dinner. They need to decide what they are going to order, making sure there is enough food for everyone. Remind them not to forget drinks!
  • The goal is to spend as close to $100 as possible.
  • Inform students that on public holidays the restaurant has a 10% surcharge on the total bill. Instruct students to calculate how much the surcharge would be if they went on a public holiday and to adjust their choices, if required, to ensure they do not overspend.

Step 1 - Identify the mathematics

In this stage students identify the task and purpose, and to then identify the mathematics involved

Ensure students understand the requirements of the task and ask them:

  • What information do you need to complete the task?
  • What mathematical calculation will you perform?
  • What happens if you spend under or over the voucher amount?

Step 2 - Act on and use the mathematics

In this stage students choose the mathematics and the mathematical tools to use, and performing the required calculations and processes.

  • Students select a restaurant to spend their voucher at, and look up the menu. They use the menu to choose what they will order, showing all calculations as they go.
  • Students then calculate the public holiday surcharge amount, and make the necessary changes to their order.

Step 3 - Evaluate and reflect

In this stage students consider the appropriateness and reasonableness of their results and adjust if necessary, including redoing any calculations.

  • Support students to review their work and decide if it is reasonable and to check over the calculations performed. Prompt with the following questions:
    • Do your menu choices seem reasonable?
    • Have you performed the calculations correctly?
    • Did you under or over spend? Do you need to make any adjustments?
    • Do you want someone to check over your work, or are you happy with it?

Step 4 - Communicate and Report

In this stage students consider the best method/s to produce their findings, and to ensure they have communicated it sufficiently so that the audience is clear on the numbers and message being presented.

  • The teacher instructs students to write a menu plan to give to their friends explain the menu choices they have made, including the change to the menu if they go on a public holiday.

Rubrics

Exemplar 1 – Module 1: Personal Numeracy - Movies

Exemplar 2 – Module 1: Personal Numeracy - Sharing our plans

Exemplar 3 – Module 2: Financial Numeracy - Winner, winner, chicken dinner

 

Unit 2

Exemplar 1 – Module 3: Health and Recreational Numeracy - Making change

Focus Area: Shape & Quantity and Measures

Focus Area - Shape

Learning Goal

On completion of this module the student should to be able to understand:

  • common and familiar one- and two-dimensional shapes such as lines, triangles, circles and squares
  • common properties of different one- and two-dimensional shapes such as size, colour, number and type of sides (straight/curved).

Application

Demonstration of the learning goals requires students to apply a variety of skills. The following applications assist students to demonstrate they have met the learning goal.

  • recognise common and familiar one- and two-dimensional shapes
  • name common and familiar one- and two-dimensional shapes
  • construct common and familiar two-dimensional shapes
  • categorise similar shapes according to common classifications.

Focus Area – Quantity & Measures

Learning Goal

On completion of this module the student should to be able to:

  • use common and familiar basic metric measurements and quantities such as length, mass, capacity/volume, time and temperature in everyday ways such as personal height and weight, door height, liquid measurement, temperatures
  • recognise common and familiar units such as m, cm, Kg, L, degrees C
  • recognise 12-hour digital time, including minutes and hours on digital clocks, and hours, quarter-, and half-hours on analogue clocks
  • recognise day and month dates.

Application

Demonstration of the learning goals requires students to apply a variety of skills. The following applications assist students to demonstrate they have met the learning goal.

  • estimate lengths of highly familiar objects or items
  • order and compare simple everyday measures and quantities
  • recognise familiar and commonly used units of metric measurement
  • read common and familiar dates and times using digital and analogue clocks.

The Problem Solving Cycle

The problem solving cycle

This unit has been designed for students 16-18 years old diagnosed with autism spectrum disorder and intellectual disability in an independent specialist school. They are attending school full time and will undertake a Cert 1 VET Certificate one day per week.

Planning

Health & Recreational Numeracy

Health and recreational numeracy relates to accessing, understanding and using foundational mathematical information to be aware of issues related to health and well-being, or when engaging in different recreational activities.

Timeline Activity Module

Introduction

Introduce the context

This exemplar explores Unit Two Health and Recreational Numeracy with the Focus Areas of Shape and Quantity and Measure, as outlined in accordance with the VCAA’s publication Victorian Pathways Certificate: Numeracy – Curriculum Design. All Learning Goals and Applications have been addressed.

The context of health has been explored in terms of Health and Recreation.

Identify the issue(s)

The contexts explored include personal health and wellbeing, and craft and social enterprise.

Students explore by exploring the big idea that not everyone has access to water and soap, and have a guest speaker from Orange Sky come to inform the class about their commitment to helping the community. They connect these concepts to their social enterprise – Glow for Giant Steps – a soap making integrated project with WRS – and look at the production of the soap, the sales figures, and adjusting their orders whilst looking at the importance of personal hygiene.

Using the Problem-Solving Cycle - Step 1 - Identify the mathematics

Teacher led discussion on possible topics that students will use as the basis for their investigation. Once the class has agreed on a topic, the class will proceed together.

The next step is to identify the mathematics. Begin by discussing

  1. What is the purpose of the task?
  2. What is the mathematics knowledge that may be useful?
  3. What calculations will be needed?

This provides a clear path for the teacher to then teach the mathematics.

Using the Problem-Solving Cycle - Step 2 - Act on and use the mathematics

The teacher then provides a series of activities that support student learning with the mathematical knowledge and skills. This sits alongside the investigation and supports the context that is being studied.

At all times the teacher considers

  1. What tools can you use from your Mathematical Toolkit to help student learning?
  2. Plan time to complete the relevant mathematical calculations and processes.

Using the Problem-Solving Cycle - Step 3 - Evaluate and reflect

The activities in the assessment section relate to the section of the problem solving cycle - evaluate and reflect. A core part of evaluation and reflection is going back reviewing the mathematics. At times this may involve starting the cycle again at the ‘act on’ a phase.

Questions to consider include:

  • Does the mathematics make sense in relation to the topic?
  • Is the mathematical process you have chosen the most appropriate for the question or task?
  • Can you justify the mathematics you have undertaken?
  • Check and reflect your work – are your answers what you expected?
  • Review and reflect on the reasonableness – do you need to make adjustments?
  • Do you need someone to check your work with you?

Using the Problem-Solving Cycle - Step 4 - Communicate and Report

  1. How will you communicate each of your results?
  2. What methods have you learnt that you will include?
  3. What methods will you use that are hand-drawn or hand-calculated?
  4. What methods will you use that are completed with technology?
  5. What software will you use to make your final presentation?

Module 3: Health and Recreational numeracy

Assessment

Making Change: ‘Providing Access to Soap and Water’

Students will work together as a class to create a newsletter that combines:

  • The important of soap and water for hygiene
  • The important information from the Guest Speaker – Orange Sky
  • Research statistics showing how Orange Sky is making a big difference for it’s communities
  • Ways that people can help in the community
  • Highlighting their social enterprise – Glow for Giant Steps – soap making integrated WRS project – summary of soap making process, photos, sales figures, timeline it takes, etc

Module 3: Health and recreational numeracy

Every Week during the unit

Activity 1 – Daily Numeracy – Morning Meeting

Activity 2 – Daily Numeracy – Afternoon Meeting

Module 3: Health and recreational numeracy

Weeks 1-2

Activity 3 – Melt and Pour Part 3A

Module 3: Health and recreational numeracy

3-4

Activity 3 – Melt and Pour Part 3B

Module 3: Health and recreational numeracy

5-6

Activity 3 – Melt and Pour Part 3C

Module 3: Health and recreational numeracy

7-10

Activity 3 – Melt and Pour Part 3D

Module 3: Health and recreational numeracy

Integrated with Module 1

Activity 4 – Navigating Public Transport

Module 3: Health and recreational numeracy

Week 11-12

Activity 5 – Water Use

Module 3: Health and recreational numeracy

Week 13-14

Assessment
Making Change: ‘Providing Access to Soap and Water’

Module 3: Health and recreational numeracy

Teaching

Unit plan descriptor

In Unit 2, students explore Module 3 Health and Recreational Numeracy with the Focus Areas of Shape and Quantity and Measures. There are many hands-on activities where students gather their own data to explore measurement in different contexts

In order to support the student cohort of learners with autism and intellectual disability this module has been broken down further into 3 separate integrated units to support student learning by teaching skills in functional contexts. These units are:

1. Morning Meeting: Students start each day by addressing core areas of their program including day, date, season and time. Concepts are supported through different colours for each day and month to support students with low reading comprehension skills. Students are presented with a schedule of activities for the day in their preferred receptive style – this may be a list or series of pictures which represent each activity. These activities are paired with digital or analogue times which are varied over the course of the year as student’s master the concepts. Students will use the internet to research the daily temperature and pair this knowledge visually with what it means e.g. hot = wear shorts, cold = wear a jumper. Teacher questioning will test all of these concepts which may be answered verbally, visually or with support of Augmentative and Alternative Communication.

2. Melt and Pour: This unit is integrated with a range of modules as listed below. Students will create a social enterprise called Glow for Giant Steps. As part of this unit, students will make soap/candles/bath products which require them to use their measurement skills to weigh, assess liquid quantities, temperatures and other measurements. Students will first refresh their knowledge of 2D and 3D shapes before exploring what weight of solid soap they need to fill various 3D shapes. Initially, the students will use 3D shape models to produce shapes for their business, which over time can be changed to more decorative styles.

3. Where am I going?: This unit is integrated with Unit 1 – Module 1 Personal Numeracy. Once students are familiar with exploring their local environments they will start to explore how they can travel further afield by using public transport. Students will use the PTV and Google Maps apps to work out how to get to a destination testing their time telling skills to catch transport on time to arrive a work experience or other activities.

This unit explores all three Learning Requirements in accordance with the the VCAA’s publication Victorian Pathways Certificate: Numeracy – Curriculum Design.

The four stages of the problem solving cycle (Learning Requirement 2) are supported with the inclusion of the multiple learning activities.
All the activities are contextualised with the issue of a social Enterprise – Glow for Giant Steps.

When students are completing the technology components, they are working towards successfully building their Mathematical Toolkit – Learning Requirement 3. Opportunities presented in these tasks include: using a calculator to perform calculations, online applications to create and conduct surveys and using spread-sheet software to perform these calculations and using spread-sheet software to present graphs and tables. This is not an extensive list and teachers are encouraged to use as many technologies as are available within the confines of the classroom.

Integrated unit suggestion

Through the Melt and Pour activity students will create a social enterprise called Glow for Giant Steps making candles and moulded soaps. The measurement skills taught in this unit may be integrated across:

PDS Unit 2; to find opportunities to connect with the community and practice socially appropriate interactions via operating a Pop-Up stall in the school carpark to sell soaps.

WRS Unit 1 & 2;

  • Unit 1 to explore soap and candle making as an interest/capability
  • Unit 2 to host a launch party for their business

Literacy Unit 1 & 2;

  • Unit 1 – Module 2: to create and make a presentation at the launch party to explain to others the purpose of their business
  • Unit 2 – Module 1: to share these made products with other organisations such as Orange Sky

Suggested resources/required equipment

Beneficial resources:
Smart phone – using smart assistants to support understanding of time
Computer – for researching weather, transport times

Required equipment:
Supplies for melt and pour soap making

This section details the activities.

Please note: These activities must not be taught in isolation from the Problem Solving Cycle, or the Mathematical Toolkit.

These activities are detailed in this table to help with implementation but must be read in conjunction with the planning table.

Focus Area: Quantity and measures

Activity 1

Daily Numeracy – Morning Meeting

Introduction

  • Students are sitting at their desks in the classroom looking at the Interactive Whiteboard (IWB)
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch an online hello song (search greeting songs on YouTube)

Body

Introduce the Context and Issues

We need to know the date so that we can work effectively and plan our lives and work activities

Act on and Use the Mathematics

  • Look at the calendar to establish the day/date/month/ year. This calendar should be presented visually on the wall with visual images to indicate key activities for each day of the week e.g. work experience on Friday.
  • Students respond to teacher to label day, date, month, year.
  • Students use a smart assistant or the internet to research the weather and temperature that day and complete a short sequence of activities to explain what that means in terms of dressing e.g. wear a jumper when it is 10 degrees.
  • Students are lead through their schedules for the day looking at each of the activities they are completing. Each of these activities should be paired with a time to enable questioning e.g what is happening at 11:00? When is Lunch? When is home time?

Conclusion

  • Students place their schedules in their folders
Focus Area: Quantity and measures

Activity 2

Daily Numeracy – Afternoon Meeting

Core introduction

  • Students are sitting at their desks in the classroom looking at the Interactive Whiteboard (IWB)
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)

Introduction

  • Students watch an online goodbye song (search greeting songs on YouTube)

Body

Re-introduce the Context and Issues

  • It is important to reflect on what we have done each day so that we can prepare and modify our strategies for a more efficient tomorrow

Act on and Use the Mathematics

  • Look at the calendar to establish the day/date/month/ year. This calendar should be presented visually on the wall with visual images to indicate key activities for each day of the week e.g. work experience on Friday.
  • Students respond to teacher to label day, date, month, year

Evaluate and reflect

  • Did the calendar match our experiences today?
  • Students refer to the visual calendar to identify the key activity of their day and point to it on their individual schedules

Communicate and report

  • Students create a sentence reflective of their learnings that day e.g. “Today on Tuesday I went to work experience and learnt how to make coffees”
  • The teacher pulls up a series of pictures that were taken during the session and students are supported to copy these images into a PowerPoint presentation and make a comment about the images

Conclusion

  • Students place their schedules in their folders
Focus Area: Shape
Focus Area: Quantity and measures

Activity 3A

Melt and Pour - Part A

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch a familiar video about 2-D shapes

Identify the Mathematics

  • Students discuss how they can apply their knowledge of shapes in practical ways as they build their social enterprise Glow for Giant Steps

Body

  • Students are reintroduced to and revise their knowledge of shape and measurement
  • Students revise their knowledge of certain shapes with a bingo activity
  • Students revise their knowledge of shape in the real world to ‘find’ shapes in the environment and describe them through pictures and playing online games https://pbskids.org/peg/games/highlight-zone
  • Students look at objects that are motivating to them and describe them in terms of their shape using language e.g. ‘a tram is rectangular’, ‘the ball is a sphere’.

Conclusion

  • Students reflect on the different shapes that they can see and what language is used to describe them
Focus Area: Shape
Focus Area: Quantity and measures

Activity 3B

Melt and Pour - Part B

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch a familiar video about 2D shapes

Body

  • Students revise their knowledge of shape in the real world to ‘find’ shapes in the environment and describe them through pictures and playing online games https://pbskids.org/peg/games/highlight-zone
  • Students play various games  https://pbskids.org/games/shapes which explore shape and measurement and size
  • Students look at laminated shapes and organise them by their different attributes e.g. all shapes with 4 sides, all shapes with curved edges
  • Students look at objects that are motivating to them and describe them in terms of their shape e.g. the tram is rectangular

Conclusion

  • Students reflect on the different shapes that they can see and what language is used to describe them
Focus Area: Shape
Focus Area: Quantity and measures

Activity 3C

Melt and Pour – Part C

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch videos about making melt and pour soap

Act on and use the Mathematics

  • Students use their knowledge of shapes to label and discuss 3D shape products that have been prepared by the teacher

Body

  • Students explore different soaps that have been prepared in advance that are different shapes e.g. cube, rectangular prism, pyramid
  • Students describe these shapes in terms of their nets and 2D qualities
  • Students follow visual forewarnings to make soap including use of the microwave to measure digital time, digital and analogue thermometers to measure the temperature of the soap, measuring cylinders and syringes. Students measure liquid quantities and weights of soaps before and after melting to calculate volume of different sized objects.

Conclusion

  • Students reflect on the unit of measurement that was the focus of that session and explore other ways it could be applied to their world

* integrated with WRS Unit 2 – students will make and sell these soaps to the local community. A log of sales will be kept to establish which is the most popular soap shape

Focus Area: Shape
Focus Area: Quantity and measures

Activity 3D

Melt and Pour - Part D

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch videos about making melt and pour soap

Body

Evaluate and reflect

  • Students continue making soap and exploring the relationship between length, volume and weight
  • The teacher will address temperature in the melting process
  • Students will consult the data collection to soap sales to graph which has been the most popular shaped soap over the sales period
  • The class will discuss the making of different soap shapes and discuss which shapes should be focussed on for sale

Conclusion

Communicate and report
Students will respond to questions describing each of the soap shapes available and suggest reasons why some soaps had more successful sales than others and modify the selection of soaps that are made the following weeks to reflect the popularity of each shape.

Focus Area: Shape
Focus Area: Quantity and measures

Activity 4

Integrated with Unit 1
**This is integrated with Unit 1 – Module 1 – Personal Numeracy

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch a video about directions
  • Students discuss the problem solving cycle – how can we use mathematics to help us access public transport?

Body

Identify the mathematics

  • Students demonstrate their understanding of prepositions by using real objects to follow different directions to move about the classroom
  • Students watch a motivating video from YouTube about using the PTV app
  • https://www.youtube.com/watch?v=dAZYsT-n-2s

Act on and use the mathematics

  • Students use PTV app/google maps to navigate to public transport – calculating times it will take them to get to various places as well as using schedules to work out what time tram/bus/train they are going to get.
  • Students read through a forewarning about checking the PTV app to see when trams are arriving
  • Students plan a longer excursion to larger destinations with specific purposes e.g Bunnings, Kmart
  • Students will access the PTV app at the tram stop to set a visual timer for themselves so they are able to better comprehend how long they have to wait

Conclusion

Evaluate and Reflect

  • Students are asked a short series of summary questions about their learning and are asked to engage with the PTV app to get the tram appropriately and the factors that need to be considered when planning a longer excursion e.g. checking the weather, knowing how long the walk may take

Communicate and Report

  • Students report how they will modify their excursion next time based on discussion of the above factors
Focus Area: Shape
Focus Area: Quantity and measures

Activity 5

Water Use

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)

Identify the mathematics

  • Students discuss liquid quantities of water based on their volume knowledge from Activity 3
  • Students watch a video about saving water

Body

  • Students explore the different ways that they use water each day during their lives e.g. showers, drinking water, watering plants at the community garden.

Act on and use the mathematics

  • Students estimate how much water they use within a day and track this over a week by filling in a spread sheet
  • Students use the internet to calculate how much water a shower uses (e.g 9L/minute) to calculate the quantity of water they use each day.

Conclusion

Evaluate and reflect

  • Students reflect on their number and think about ways in which they can reduce their water use
Focus Area: Shape
Focus Area: Quantity and measures

Assessment task

Making Change: ‘Providing Access to Soap and Water’

Task - Students will explore the idea that ‘not everyone has access to soap and water’, and write a newsletter article that combines:

  • The important of soap and water for hygiene
  • The important information from the Guest Speaker – Orange Sky
  • Research statistics showing how Orange Sky is making a big difference for its communities
  • Ways that people can help in the community
  • Highlighting their social enterprise – Glow for Giant Steps – soap making integrated WRS project – summary of soap making process, photos, sales figures, timeline it takes, etc

Introduction

  • Students are sitting at their desks in the classroom looking at the IWB
  • Students check their visual or written schedule and mark off the previous activity
  • Students identify the session
  • Students read through visual lesson components for the session displayed beside the board (some students may have individual lesson components they can cross off along the way)
  • Students watch a video about saving water

Step 1 – Identify the Mathematics

Body

  • Students explore their access to water and describe how easy it is to access for them
  • Students recall their knowledge of hygiene practices and reflect on how they use soap and water across the day (especially during the COVID pandemic)
  • Students are told that not everyone has access to soap and water e.g. homeless people and how that can cause adverse health effects
  • Students are told of different ways in which they can help others
  • Guest speaker from Orange Sky – students are prompted with different questions to ask the employee from Orange Sky about what issues they see people face and how they help others

Step 2 – Act on the Mathematics

When the Guest Speaker arrives, make sure students have their prepared questions ready – and ensure they have a pen with them to write down their answers.

Research statistics to support the information – such as rates of people using Orange Sky services, how long they have been providing the services, health and hygiene affected back lack of water and soap, how we can provide help to Orange Sky and other organisations to help be a part of this solution.

Step 3 – Evaluate and Report

Students decide what they want to report on – Melt and Pour Soap Making project (sales figures, soap making process, photos, up-coming sales etc), research found about Orange Sky and questions answered by Guest Speaker, ways that we can support Orange Sky and other organisations.

Step 4 – Communicate and Report

Teacher to provide template and work with groups to support the writing process, drafting and final edits. 

Conclusion

Communicate and report

  • Students reflect on how they can use their business to support organisations such as Orange Sky.

Exemplar 2 – Module 3: Health and Recreational Numeracy - Paper planes

Focus Areas: Shape and Quantity & Measures

Focus Area - Shape

Learning Goal

  • Common and familiar one- and two-dimensional shapes such as lines, triangles, circles, squares, etc.
  • Common properties of different one- and two-dimensional shapes such as size, colour, number and type of sides (straight/curved).

Application

  • Recognise common and familiar one- and tw0-dimensional shapes
  • Name common and familiar on- and two-dimensional shapes
  • Construct common and familiar two-dimensional shapes
  • Categorise shapes according to common classifications

Focus Area – Quantity & Measures

Learning Goal

  • Use common and familiar basic metric measurements and quantities such as length, mass, capacity/volume, time and temperature such as personal height and weight, door height, liquid measurements, temperatures.
  • Recognise common and familiar units such as m, cm, Kg, L, degrees C
  • Recognise 12-hour time, including minutes and hours on digital clocks and hours, quarter- and half-hours on analogue clocks
  • Recognise day and month dates

Application

  • Estimate lengths of highly familiar objects or items
  • Order and compare simple everyday measures and quantities
  • Recognise familiar and commonly used units of metric measurements
  • Read common and familiar dates and times using digital and analogue clocks.

The Problem Solving Cycle

The problem solving cycle

Planning

Health and Recreational Numeracy: The focus of the context for this unit is a paper plane competition

This plan demonstrates the problem-solving cycle as a five week learning program.

Timeline Activity Module

eg: Week 1

Introduce the context

Introduce the context of Health and Recreational numeracy with the focus of selecting and folding paper planes for an in-class competition.

Teachers may like to show the movie Paper Planes as an introduction to this unit.

Identify the issue(s)

Teacher to introduce the problem of taking part in a class paper plane competition

Students will use the Learning Requirement 2 – the Problem-Solving Cycle - to undertake a series of activities related to selecting a design and making their paper plans, then measuring and making judgements about the furthers distance travelled, the longest flight time and the best tricks.

At all stages, students will undertake activities alongside their Problem-Solving Cycle which are designed to address the Learning Goals and Applications as outlined for the mathematics at each stage.

Consider which technologies will help to examine this issue and support the learning of the mathematics that is outlined in the Learning Requirement 3 – Mathematical Toolkit.

Using the Problem Solving Cycle - Step 1 - Identify the mathematics

Teacher leads a brainstorm with students to identify all the things we would need to know, clarify or do in order to take part in a paper airplane competition.

Inform students of the three categories of the paper plane competition, which are furthest distance travelled, longest flight time and best tricks.

The next step is to identify the mathematics. Begin by discussing

  1. What is the purpose of the task?
  2. What is the mathematics knowledge that may be useful?
  3. What processes or calculations will be needed?

This provides a clear path for the teacher to then teach the mathematics.

Using the Problem Solving Cycle - Step 2 - Act on and use the mathematics

The teacher provides a series of activities that support student learning with the mathematical knowledge and skills. This sits alongside the investigation and supports the context that is being studied.

At all times the teacher considers:

  1. What tools can you use from your Mathematical Toolkit to help student learning?
  2. Plan time to complete the relevant mathematical processes and calculations.

Activity 1 - Too cool to rule

Activity 2: It’s all a matter of time

Module 3: Health & Recreational Numeracy

Week 2

Activity 3 - Shape Scavenger Hunt

Activity 4 - Paper planes – what do they look like?

Activity 5 - What are the rules?

Module 3: Health & Recreational Numeracy

Week 3 & Week 4

Using the Problem Solving Cycle - Step 3 - Evaluate and reflect

The activities in this section relate to the section of the Problem-Solving Cycle - evaluate and reflect. A core part of evaluation and reflection is going back reviewing the mathematics. At times this may involve starting the cycle again at the ‘act on’ a phase.

Support students to consider the following:

  • Does your work make sense?
  • Have you correctly identified the shapes in your designs?
  • Compare your estimates with the actual measurements – what do you notice?
  • Do you need to make any changes to your work?

Using the Problem Solving Cycle - Step 4 - Communicate and Report

The activities in this section relate to the section of the problem solving cycle – communicate and report, requiring students to be able to represent and communicate their mathematical results.

Ask students to write a report for the school newsletter, including the following points:

  • A description of the paper plane competition and the relevant information about when and where it occurred
  • How students made their planes and the rules or restrictions they had to follow.
  • The winners of each category, and the how they were determined

Activity 6 - Design Time

Activity 7 - Competition Time

Module 3: Health & Recreational Numeracy

Week 5

Assessment Task – Design a prize

Module 3: Health & Recreational Numeracy

Teaching

Unit plan descriptor

This unit has students exploring Health and Recreational Numeracy with the Focus areas: Shape and Quantity and Measures. There are many hands-on activities where students gather their own understanding of designing paper planes for a competition.

This unit explores all three Learning Requirements concurrently as mandated by the curriculum and supports the learning of all activities.

The four stages of the Problem-Solving Cycle are supported by the inclusion of the multiple learning activities.

All the activities are contextualised with the issue of using technology for planning and scheduling.

Students are taken through the stages of the problem-solving cycle over a five week period.

When students are completing the technology components, they are working towards successfully building their Mathematical Toolkit – Learning Requirement Three. Opportunities presented in these tasks include: using online applications for planning and paper and interactive maps to locate places of interest. This is not an extensive list and teachers are encouraged to use as many technologies as are available within the confines of the classroom.

Integrated unit suggestion

This unit could form part of an integrated unit with VPC Literacy through the reading and writing of instructions or through a film analysis of the movie Paper Planes.

This unit could form part of an integrated unit with VPC Personal Development Skills focusing on team-work, communication, time management and problem solving skills.

Suggested resources/required equipment

General classroom stationery supplies which support student learning and teaching in mathematics. These may include, but not be limited to:

  • Paper
  • Coloured paper
  • Origami paper
  • Rulers
  • Measuring tools (e.g. tape measures, kitchen scales, body weight scales, measuring jug, stop watch, thermometer, digital thermometer)
  • Digital and analogue clocks
  • Post-it notes
  • Scissors
  • Glue or tape

Access to the internet and computers or tablets is essential.

Technologies may include:

  • Digital calendars or diaries
  • Digital measuring tools
  • Phones for apps and to take photos where permissible by the Principal

This list is not exhaustive, and teachers are encouraged to use extra materials and resources that support the learning for their students in their classrooms.

This section details the activities.

Please note: These activities must not be taught in isolation from the Problem Solving Cycle, or the Mathematical Toolkit.

These activities are detailed in this table to help with implementation but must be read in conjunction with the planning table.

Focus Area: Quantity and measures

Activity 1

Too cool to rule

Students use a variety of analogue and digital measuring tools to estimate then measure a selection of items from the classroom. The items selected must include length, mass, capacity/volume, time, and temperature.

  • The teacher shows students a range of measuring equipment including rulers, tape measures, kitchen scales, body weight scales, measuring jug, stop watch, thermometer, digital thermometer etc.
  • The teacher leads a brainstorm with students asking them to identify different objects or things that could be measured using the different measuring tools and what units of measurement would commonly be used.
  • Students classify the measuring tools as either analogue or digital, and discuss the benefits or disadvantages of using each type.
  • The teacher demonstrates, or ask students to come up and demonstrate, how to use each of the measuring tools and read them accurately.
  • The teacher instructs students to select an item in the room to measure using each of the different measuring tools. They must first estimate, then use the measuring tool accurately.
  • The items measuring must also include at least one instance of each of the following;
  • length (e.g. of the table, or personal height)
  • mass (e.g. weight of their pencil case or personal weight)
  • capacity/volume (e.g. amount of water in their drink bottle)
  • time (e.g. to walk across the room or to complete the activity as a whole)
  • temperature (e.g. personal temperature or temperature of a hot drink).
Focus Area: Quantity and measures

Activity 2

It’s all a matter of time

Students explore time as a unit of measurement including the different units of time, how they relate to each other and the different tools used to measure, record or display time. Students then compete a series of scenarios that require them to recognise time on both digital and analogue clocks and recognise day and month dates.

  • The teacher asks students to identify what the time is right now. Ask them to explain how they know this, and what does that ‘time’ actually mean.
  • The teacher leads a discussion with students about time as a unit of measure, including the different units of time such as seconds, minutes, hours, days, weeks, months, years etc.
  • The class discuss the relationship between the different units of time and the different tools or equipment we use to measure, record or display time.
  • The teacher explicitly teaches students how to read hours, quarter- and half-hours on an analogue clock, and provides real-life scenarios where work-places use these clocks, such as hospitals and hospitality, to give relevance and importance.
  • The teacher provides a series of scenarios that requires them to recognise time on clocks, and recognise day and month dates, such as:
  • Looking up the public holiday dates for the year and writing them in on a calendar or diary
  • Looking at a bus or movie timetable and matching the digital time to the time shown on analogue clocks
  • Creating a calendar of all the birthdays in the class, and seeing how many people have birthdays on Mondays, Tuesdays etc. throughout the year
  • Looking at the time shown on the classroom clock, and the world clock app and writing the different times down in words
Focus Area: Shape
Focus Area: Quantity and measures

Activity 3

Shape Scavenger Hunt

Students go on a scavenger hunt around the school to find examples of common shapes. Students take photos of the shapes, then identify the properties of each of the shapes. As a class, students group similar shapes together.

Students go on a scavenger hunt around the school to find examples of common one-and two-dimensional shapes, including lines, triangles, circles, squares etc. They take a photo of each shape they have found and return to the classroom.

Students draw each of the shapes found. Support students to name each shape and write down its properties including, size, colours, number and type of sides (straight/curved) how many corners etc.

As a class, group each similar shape together according to common and agreed upon classifications.

Focus Area: Shape
Focus Area: Quantity and measures

Activity 4

Paper planes – What do they look like?

Students investigate the shape and design of different types of paper planes, writing down the shapes they can see in the design and the approximate dimensions of the plane.

  • The teacher leads a discussion with students on the wide variety of shapes that paper planes come in.
  • Students find 4 different paper plane designs or provide a variety of premade paper plans to look at.
  • Students either draw or cut and past pictures of the designs.
  • Next to each picture students write:
  • The shapes they can see in the design
  • The approximate dimensions of the plane (length, width and height)
Focus Area: Shape
Focus Area: Quantity and measures

Activity 5

What are the rules?

Students determine the agreed upon rules, such as what can be used to make the plane, how each category will be conducted, what will be used to measure the distance or flight time etc.

  • Students create a flyer or poster that clearly shows the time, day and date of the competition.
  • Let students know that before they begin designing and testing their planes they need to come up with the rules of the competition. There are going to be three categories in which they will be competing. They are:
  • Furthest distance travelled
  • Longest flight time
  • Best plane tricks (if time permits)
  • The teacher leads a brainstorm with the class to determine the agreed upon rules, such as what can be used to make the plane, how each category will be conducted, what will be used to measure the distance or flight time etc.
  • For each category students must copy down the:
  • Rules of the competition
  • How they will test/judge the competition
  • List of items that are needed
  • Discuss with students when the paper plane competition will take place and ask students to create a flyer or poster that clearly shows the time, day and date of the competition.
Focus Area: Shape
Focus Area: Quantity and measures

Activity 6

Design Time

Students research different paper plane designs and select a design for each category (3 planes in total). While making their paper planes, students draw a top down and side view of each, write the shapes that can be seen during the making of each, estimate the length and width of each plan then measure the actual length and width.

  • Students are required to design and make a paper plane for each category, making sure they adhere to the agreed upon rules and restrictions of the competition. They can find and use designs from any resources.
  • Step 1: Students research different designs of paper plans and selects one for each category (3 planes in total). They should practice making the planes before deciding on a final design.
  • Step 2: After deciding upon the paper plane designs students are required to:
  • Write down or print a copy of the step-by-step instructions on how to make the chosen designs.
  • Draw a top down and side view of each paper plane.
  • Write the shapes that can be seen during the making of each paper plane.
  • Estimate the length and width of the paper plan.
  • Make your final version of each paper plane and write the actual measurements of length and width.
Focus Area: Shape
Focus Area: Quantity and measures

Activity 7

Competition Time

  • Before taking part in the competition students estimate how far their plane will travel (longest distance category) and how long their plan will fly before it touches a surface (longest flight time category)
  • Students take turns flying their planes and are given three chances for each of the competition categories.
  • Students need to make sure to record the results from each of their ‘runs’ e.g.

 

  • Ask students to look at each of their run times and select the best one. Students add their results to the class result sheet.  Lead a discussion with students looking at the class results and make a decision on who was the winner for each category.
  • Before starting the competition remind students of the rules and restrictions of each category.
Focus Area: Shape
Focus Area: Quantity and measures

Assessment task

Design a prize

This assessment task combines the Learning Requirements 1, 2, and 3 cohesively as per the curriculum guidelines.

The assessment adheres to the curriculum requirement to include all three Learning Requirements. Learning Requirement 2 allows students to use the Problem-Solving Cycle within the context and skills outlined in Learning Requirement 1, and Learning Requirement 3 involves students using their Mathematical Toolkit to support Learning Requirements 1 and 2.

Assessment Task:

  • Student research and create an origami award or prize that can be given to the paper plane competition winners.
  • The requirements of the task include:
    • Research different origami designs such as medals, stars or trophies and select the design you will make.
    • Estimate the measurements of your origami award. Write the actual measurements once you make the final product.
    • Draw a top down and side view of your origami award.
    • As you make the origami award, write down the shapes that can be seen during the making of it and in the final product.

Discuss with the students:

  • Ask students to create an origami award or prize to can be given to the paper plane competition winners.
  • Give students the requirements of the task:
    • Research different origami designs such as medals, stars or trophies and select the design you will make.
    • Estimate the measurements of your origami award. Write the actual measurements once you make the final product.
    • Draw a top down and side view of your origami award.
    • As you make the origami award, write down the shapes that can be seen during the making of it and in the final product.

Support students through the Problem-Solving Cycle as they complete the requirements of the task.

Step1 – Identify the mathematics

Students write the purpose of the task in their own words.

Students list the specific mathematical skills or knowledge they will need to complete the task. Prompt students to think about the skills or knowledge they have developed by completing the unit activities

Step 2 – Act on and use mathematics

Students use make their origami awards, completing each of the task requirements.

Step 3 – Evaluate and reflect

Students review their final product and make any adjustments or remake it if necessary.

Step 4 – Communicate and report

Students share their origami award with the class, explaining why it should be chosen as the prize for the competition winners. The class votes on best award, and the top three awards are selected to be given to the winners in each of the categories.

  • For assessment, students should submit:
    • A copy of the origami instructions
    • Their measurement estimations and final measurements
    • Top down and side view drawings
    • List of the shapes found in the final product.

Exemplar 3 – Module 4: Civic Numeracy - Saving water

Focus Areas: Data & Likelihood

Focus Area: Data

Learning Goal

  • Understand simple data collection by hand or with tables
  • Understand simple cases of data, graphs and infographics

Application

  • Collect and display simple data
  • Read simple graphs such as bar or pie graphs
  • Read simple tables
  • Identify and locate key facts from simple data

Focus Area: Likelihood

Learning Goal

  • Use everyday language to talk about the likelihood of an event occurring such as possible, impossible, unlikely, likely, certain, ‘Buckley’s chance’, “pigs might fly”, “dead-set”
  • Understand language and relative magnitude of simple and high familiar chance events.

Application

  • Recognise and use the everyday language of chance and likelihood
  • Use everyday language to compare and order different and simple magnitude of chance

The Problem Solving Cycle

The problem solving cycle

Planning

Civic Numeracy: The focus of the context for this unit is conservation of water.

This plan demonstrates the problem-solving cycle as a six week learning program.

Timeline Activity Module

Week 1 - 2

Introduce the context

Introduce the context of Civic numeracy with the focus of the ‘Target 155’ and ‘make every drop count’ campaigns (makeeverydropcount.com.au).

Teachers may like to lead a discussion on what students know about the ‘Millennium Drought’ and the severe water restrictions that were brought into Melbourne.

Identify the issue(s)

Teacher to introduce the problem of permanent water saving rules.

Students will use the Problem-Solving Cycle to undertake a series of activities related to exploring information related to how we use water and determining strategies to reduce water consumption – aiming to limit their household’s water consumption to 155 litres per person per day. This includes: collecting and reading data to determine the current household water usage, looking at weather information to determine the likelihood of rain, and determining water saving strategies.

Students will be required to submit a flyer, poster, or other document that shows the water saving strategies and how they will save water.

At all stages, students will undertake activities alongside their Problem-Solving Cycle which are designed to teach the Learning Goals and Applications that are required for the mathematics at each stage.

Consider which technologies will help to examine this issue and support the learning of the mathematics that is outlined in the area of study.

Using the Problem Solving Cycle - Step 1 - Identify the mathematics

Teacher leads a discussion with students asking what they know about water the permanent water saving rules.

Remind students that the goal is to be able to reduce the water consumption in their households.

The next step is to identify the mathematics. Begin by discussing

  1. What is the purpose of the task?
  2. What information or knowledge do you need to complete the task?
  3. What mathematics knowledge may be useful?
  4. What processes or calculations will be needed?

This provides a clear path for the teacher to then teach the mathematics.

Using the Problem Solving Cycle - Step 2 - Act on and use the mathematics

The teacher provides a series of activities that support student learning with the mathematical knowledge and skills. This sits alongside the investigation and supports the context that is being studied.

At all times the teacher considers

  1. What tools can you use from your Mathematical Toolkit to help student learning?
  2. Plan time to complete the relevant mathematical processes and calculations.

Activity 1 – Data Overload

Activity 2 – Can you trust what you see

Module 4: Civic Numeracy

Week 3

Activity 3 – What’s the weather doing

Activity 4 – Do we even need to be saving water?

Module 4: Civic Numeracy

Week 4 & Week 5

Using the Problem Solving Cycle - Step 3 - Evaluate and reflect

The activities in this section relate to the section of the Problem Solving Cycle - Evaluate and Reflect. A core part of evaluation and reflection is going back reviewing the mathematics. At times this may involve starting the cycle again at the ‘act on’ a phase.

Support students to consider the following:

  • Does your work make sense?
  • Have you correctly interpreted the information about water usage in your household?
  • Do your descriptions of the likelihood of certain weather events make sense?
  • Do you need to make any changes to your work?

Activity 5 – Determining our water consumption

Activity 6 – Water Saving tips

Module 4: Civic Numeracy

Week 6

Using the Problem Solving Cycle - Step 4 - Communicate and Report

The activities in this section relate to the section of the problem solving cycle – communicate and report, requiring students to be able to represent and communicate their mathematical results.

Support students to consider the following:

  • How will you communicate your recommendations to your household?
  • What tables, graphs or other information will you need to include?

Assessment Task – Make your recommendations

Module 4: Civic Numeracy

Teaching

Unit plan descriptor

This unit has students exploring Civic Numeracy with the Focus areas: Data and Likelihood (Learning Requirement One). There are many hands-on activities where students gather their own understanding of reading information from tables, graphs and infographics and using everyday language to describe the likelihood of weather events.

This unit explores all three learning requirements concurrently as mandated by the curriculum and supports the learning of all activities.

The four stages of the Problem-Solving Cycle are supported by the inclusion of the multiple learning activities.

All the activities are contextualised with the issue of water consumption and saving water.

Students are taken through the stages of the Problem-Solving Cycle over a six week period, as outlined in Learning Requirement Two.

When students are completing the technology components, they are working towards successfully building their Mathematical Toolkit – Learning Requirement Three. Opportunities presented in these tasks include: using online applications for reading data, tables and graphs and collecting and displaying simple data. This is not an extensive list and teachers are encouraged to use as many technologies as are available within the confines of the classroom.

Integrated unit suggestion

VPC Literacy: This unit could form part of an integrated unit with VPC Literacy through the reading and writing of articles and persuasive pieces related to climate change.

VPC PDS: This unit could form part of an integrated unit with VPC Personal Development Skills focusing on climate change, sustainability and other issues related to drought.

Suggested resources/required equipment

General classroom stationery supplies which support student learning and teaching in mathematics. These may include, but not be limited to:

  • Paper
  • Coloured paper
  • Rulers
  • Post-it notes
  • Scissors
  • Glue or tape
  • Pens, pencils and markers

Access to the internet and computers or tablets is essential.

Technologies may include:

This list is not exhaustive, and teachers are encouraged to use extra materials and resources that support the learning for their students in their classrooms.

This section details the activities.

Please note: These activities must not be taught in isolation from the Problem Solving Cycle, or the Mathematical Toolkit.

These activities are detailed in this table to help with implementation but must be read in conjunction with the planning table.

Focus Area: Data

Activity 1

Data Overload

Students explore a variety of graphs, charts, tables and infographics related to weather, climate change, water and drought exploring the different ways data can be presented and identifying the key features of graphs and tables.

  • The teacher presents a variety of graphs, tables and infographics related to weather, climate change, water and drought.
  • Students complete a ‘think-pair-share’, first looking quietly at the graphs, tables and infographic and making some notes about what they can see or notice, then sharing with a table partner, and finally participating in a whole class discussion.
  • During the class discussion, highlight the different ways data can be presented and the key features of graphs and tables including; titles, scale, key etc.
Focus Area: Data

Activity 2

Interpreting Data – Can you trust what you see?

Students work in small groups to read and interpret information from weather graphs and tables. Students then explore how graphs can be misleading and review their interpretations to see if they need to make any adjustments on the basis of some of the graphs being misleading.

  • The teacher presents a selection of graphs, tables and infographics related to weather, climate change, water and drought
    These could be the from Activity 1, but also include some graphs with deliberately misleading information such as not starting at zero, expanding or compressing scale to make changes seem more or less significant, not including a full data range e.g. only a few months of the year not the whole year, incorrect graph for data type etc.
  • The teacher supports students to group similar data sets together e.g. temperature, rainfall etc and in small groups write down what information they can gather or interpret from the graphs.
  • The teacher leads a discussion, drawing students’ attention to the deliberately misleading graphs. Point out why the graphs are misleading and discuss why misleading graphs might be used.
  • Students look back at their interpretations and see if they need to make any adjustments due to some of the graphs being misleading.
Focus Area: Data
Focus Area: Likelihood

Activity 3

What’s the weather doing?

Students explore the weather forecast and describe the likelihood of upcoming weather events. Students then further examine how the likelihood of rain is forecasted and interpret the likelihood of rain in the coming week.

  • Use the BOM website or other weather forecast resources to look at the weather forecast for the upcoming week.
  • The teacher leads a discussion with students to identify the information that is provided on the forecast.
  • Students use everyday language to describe the likelihood of upcoming weather events e.g. it is unlikely to be windy, you will certainly need an umbrella, the chance of snow is impossible etc.
  • Draw students’ attention to the how the chance of rain is shown on the forecast. Explain that the words; isolated, scattered, patchy and widespread used to be used. Discuss what they think each of the old forecast terms mean in relation to the likelihood of rain occurring.
  • Explain to students the percentage shows the likelihood of rainfall in that location.
    • E.g. if the chance of rain is 30% then there is a 1 in 3 chance of getting wet or a slight chance, but there is also a 70% chance or high chance of staying dry. Also explain that the possible rainfall shows how much rain is forecasted and is represented as a range between two values. The first value means the location has a 50% chance of receiving at least that amount of rain and the second represents a 25% chance of receiving at least that amount. E.g. for a forecast of ‘4 to 15mm’ the area has a 50% chance of receiving 4mm or more and a 25% chance of receiving 15mm or more.
  • Students review the rain forecast for the upcoming week and interpret the information to describe of the likelihood of rain each day.
Focus Area: Data
Focus Area: Likelihood

Activity 4

Do we even need to be saving water?

Students explore the information that is provided about Melbourne’s water storage levels and temperature and rainfall annual data and trends to determine how Melbourne’s water levels have changed over time and form connections between changing weather events and water supply levels.

  • The teacher leads a discussion with students on what the weather has to do with water storage levels and the conservation of water.
  • The teacher supports students to explore the information that is given about Melbourne’s water storage levels and how they have changed over time. (https://www.melbournewater.com.au/water-data-and-education/water-storage-levels#/) and temperature and rainfall annual data and trends (http://www.bom.gov.au/climate/)
  • Students discuss the following prompts:
    • What do you notice about Melbourne’s’ water storage levels?
    • Do we have enough water?
    • Do you notice any connection between weather/climate and water storage levels?
    • Does our water supply meet demand? Is this likely to change over time?
    • Can one person make a difference?
Focus Area: Data
Focus Area: Likelihood

Activity 5

Determining our water consumption

Students bring in a copy of a water bill from home and examine the information that is shown on it to determine the water consumption of the household. Students then complete the ‘Home water calculator’ (https://smartwatermark.org/watercalculator/) to further explore the water consumption of their household in more detail. Students share their results and information with the class to create a class data set on how much water is used in households. Students display this data using appropriate graphs and tables.

  • Ask students to bring in a copy of a water bill from home and support students to look at the data that is shown on it about the water consumption of the household. This usually includes:
    • The water use, a representation of the daily average water use over time, comparing with usage from the last 4 bills.
    • Average use per person, indicates the average daily water use per person and includes a comparison to the same time period from the previous year and the average consumption of other properties in the same postcode.
  • Students write down what they notice about the water usage in their home, including reference to the Target 155 goal.
  • Ask students to complete the ‘Home water calculator’ (https://smartwatermark.org/watercalculator/). They will need to have the following information for their household.
    • Bathroom: how many showers per day and average length of showers, number of shower heads and if they are water efficient or not, how many baths taken per week, number of toilets.
    • Laundry: type of washing machine and how many loads per week, how many times washing is done by hand per week
    • Kitchen: Do you have a dishwasher and how many loads per week, how many times wash dishes using the sink per week, any dripping taps or leaking toilets.
    • Garden: how many minutes hand water with a hose in summer per week, any sprinklers, drip irrigation or spray irrigation, the number/length used and hours used per week, how many hours hose is used for outside washing per week, number of water tanks.
  • Support students to interpret their results including:
    • What areas use the most water?
    • How does your household compare with the average household? Goal water usage?
    • Where could your household make changes to reduce your water consumption?
    • What is the likelihood your household would adopt changes?
Focus Area: Data
Focus Area: Likelihood

Activity 6

Water saving tips

Students brainstorm and explore water saving tips and strategies that can be applied to their households to reduce the amount of water they use. Students develop specific advice and recommendations, relating these water saving strategies to the likelihood of certain weather events.

  • The teacher leads a brainstorm with students about ways people can save water. Ask student to think about the impact has on saving water e.g. water fights/play in summer, re-washing clothes if they get rained on, hot showers/baths if cold, watering the garden etc.
  • Students can explore water saving tips on the ‘make every drop count’ count website and their local water supply company’s website.
  • Students are required to come up with specific advice and recommendations for their household to reduce their water consumption. They should also relate these water saving strategies to the likelihood of certain weather events e.g. check the weather before watering the garden, if there is a medium or high chance of rain then don’t water the garden.
Focus Area: Data
Focus Area: Likelihood

Assessment task

Make your recommendations

This assessment task combines the Learning Requirements 1, 2, and 3 cohesively as per the curriculum guidelines.

Assessment Task:

  • Students are required to present their water saving recommendations in a suitable format, such as a poster, flyer, report etc.
  • Students must include:
  • The current water consumption of the household.
  • The target water consumption and why the household should try and reduce their water consumption.
  • Specific water saving strategies (at least 5), why they have chosen them and how they will help reduce water consumption.
  • A link between the water saving strategies and the likelihood of certain weather events.

Support students through the Problem-Solving Cycle as they complete the requirements of the task. 

Step1 – Identify the mathematics

Students write the purpose of the task in their own words.

Students list the specific mathematical skills or knowledge they will need to complete the task. Prompt students to think about the skills or knowledge they have developed by completing the unit activities prior this task.

Step 2 – Act on and use mathematics

Students use class-time to compile their information and address each component in tasks.

Step 3 – Evaluate and reflect

Students review their final product and make any adjustments or remake it if necessary.

Step 4 – Communicate and report

Students are required to present their water saving recommendations in a suitable format, such as a poster, flyer, report etc.

For assessment, students should submit their final submission (poster, flyer, report etc.) with:

  • A display of the current water consumption of the household.
  • The target water consumption and why the household should try and reduce their water consumption.
  • Specific water saving strategies (at least 5), why they have chosen them and how they will help reduce water consumption.
  • A link between the water saving strategies and the likelihood of certain weather events.

Rubrics

Exemplar 1 – Module 3: Health and Recreational Numeracy - Making change

Exemplar 2 – Module 3: Health and Recreational Numeracy - Paper planes

Exemplar 3 – Module 4: Civic Numeracy - Saving water