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
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 - What is the purpose of the task?
- What is the mathematics knowledge that may be useful?
- 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 - What tools can you use from your Mathematical Toolkit to help student learning?
- 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
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
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 - What is the purpose of the task?
- What is the mathematics knowledge that may be useful?
- 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 - What tools can you use from your Mathematical Toolkit to help student learning?
- 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- 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?
| 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)
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
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.