The purpose of this unit is to engage students in an integrated mathematics/technology context: technical knowledge (focused on fuel efficiency and vehicle running costs) through which they can apply their understanding of rates and proportions to solve problems involving distance and time. In turn, students develop their skills and knowledge on the Multiplicative Thinking and Patterns and Relationships mathematics learning progressions.
This cross-curricular, context-based unit aims to deliver mathematics learning, whilst encouraging differentiated, student-centred learning.
The learning opportunities in this unit can be further differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:
With student interest engaged, mathematical challenges often seem more approachable than when presented in isolation. The context presented in this unit around driving and its related costs (e.g. the cost of weekly commutes, efficiency of different car engines, performance of different fuels, performance of electric and petrol cars, annual cost of driving), could be enhanced through the making of connections to students' lives. For example, you might adapt the questions to allow students to investigate the fuel efficiency, weekly and annual cost, and performance of cars that are relevant to them (e.g. family or school vehicles, local buses).
The first session is an introductory activity that is aimed to spark the imagination of students, to introduce the need for a particular idea or technique in mathematics that would enable them to explore deeper into that context. It is expected that rich discussion may be had around the context and around the nature of the mathematics involved.
Following the introductory session, each subsequent session in the unit is composed of four sections: Introducing Ideas, Building Ideas, Reinforcing Ideas, and Extending Ideas.
Introducing Ideas: It is recommended that you allow approximately 10 minutes for students to work on these problems, either as a whole class, in groups, pairs, or as individuals. Following this, gather the students together to review the problem and to discuss ideas, issues and mathematical techniques that they noticed during the process. It may be helpful to summarise key outcomes of the discussion at this point.
Building Ideas, Reinforcing Ideas, and Extending Ideas: Exploration of these stages can be differentiated on the basis of individual learning needs, as demonstrated in the previous stage of each session. Some students may have managed the focus activity easily and be ready to attempt the reinforcing ideas or even the extending ideas activity straight away. These could be attempted individually or in groups or pairs, depending on students’ readiness for the activity concerned. The students remaining with the teacher could begin to work through the building ideas activity together, peeling off to complete this activity and/or to attempt the reinforcing ideas activity when they feel they have ‘got it’.
It is expected that once all the students have peeled off into independent or group work of the appropriate selection of building, reinforcing and extending activities, the teacher is freed up to check back with the ‘early peelers’ and to circulate as needed.
Importantly, students should have multiple opportunities to, throughout and at the conclusion of each session, compare, check, and discuss their ideas with peers and the teacher, and to reflect upon their ideas and developed understandings. These reflections can be demonstrated using a variety of means (e.g. written, digital note, survey, sticky notes, diagrams, marked work, videoed demonstration) and can be used to inform your planning for subsequent sessions.
The relevance of this learning can also be enhanced with the inclusion of key vocabulary from your students' home languages. For example, te reo Māori kupu such as pāpātanga (rate), hautau/hautanga (fraction, proportion, part of a whole), whakatairite (compare), raraunga (data), pāpātanga o te whiti (rate of change), and pānga rārangi (linear relationship) could be introduced in this unit and used throughout other mathematical learning.
The aim of this activity, which presents an opportunity to practise mathematical skills and knowledge in a science context, is to motivate students towards the given context and to inform teachers of students' understandings. Within this problem, students solve problems involving motion. Encourage the use of context-appropriate units.
This session focuses on describing and using a linear trend.
Introducing Ideas
Building Ideas
engine size (cc) | fuel efficiency (km/L) |
2500 | 10 |
2000 | 11.5 |
1800 | 12.1 |
2200 | 10.8 |
Reinforcing Ideas
Extending Ideas
This session focuses on using rates and proportions to compare data.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending Ideas
On the test day, 91 Octane cost $1.98 per L, 91 Octane cost $2.09 per L, 91 Octane cost $2.16 per L.
This session focuses on finding and describing a rate of change, for data given from a linear trend.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending Ideas
This session focuses on finding and describing a linear trend.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending ideas
This session focuses on finding and describing a linear trend.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending Ideas
Dear parents and whānau,
In class we have been applying understanding of rates and proportions to solve problems involving distance and time, within the context of fuel efficiency and vehicle running costs. Ask your child to share their learning with you.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/fuel-commute at 8:54pm on the 26th February 2024