The purpose of this unit is to engage students in applying their understanding of algebra to solve problems within the science - physical world context of electrical circuits. Subsequently, students develop their skills and knowledge on the following mathematics learning progression: Using Symbols and Expressions to Think Mathematically
This unit integrates mathematical skills and knowledge with the science learning area and provides opportunities for students to explore the relationships between currents in and voltages across different parts of a circuit.
To ensure engagement and participation in this unit, you should consider your students' prior knowledge of circuits, currents, voltage, electricity, as well as their understanding of graphical and algebraic techniques and linear relationships.
This unit includes practical activities that can be carried out using standard science lab equipment, or materials that can be purchased at electronics stores (wires, multi-meters, batteries and component resistors). You should ensure that any current reading is carried out in series, and that any voltage reading in parallel, regardless of whether multi-meters or ammeters and voltmeters are used. Ammeters (and multi-meters set to a current reading) are easily damaged if placed incorrectly. Check that ammeters and voltmeters are connected correctly with a very short momentary connection (the touch test) to see that the needle moves clockwise and not past the end of the scale.
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:
This unit is focussed on applying algebraic and graphic knowledge to the physical world context of electrical circuits. As such, it is not set in a real world context. You may wish to explore real world applications of this content in following, or additional sessions. For example, a community expert might be able to come to your class to discuss their use of circuits, and their knowledge of voltage, currents etc., in an occupation or leisure activity.
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 kauwhata (graph), tūtohi (table/chart of data), and pānga rārangi (linear relationship) might be introduced in this unit and then used throughout other mathematical learning.
Introduce the following context to students: The standard unit of power, the rate at which energy is transformed, is the watt. One watt is equivalent to one joule per second. Energy companies bill electrical usage in units of kilowatt hours (kWh). The average annual household electricity usage is 7600 kWh.
How many joules of electrical energy does the average daily household use?
Observe how your students use the given units of measurement to understand the mathematical relationship between quantities. Use these observations to locate your students on the following learning progression: Using Symbols and Expressions to Think Mathematically.
Discuss, drawing attention to the following points:
Household usage accounts for 13% of the total electricity usage in the New Zealand.
What is the total annual electricity usage in the New Zealand?
Why might energy companies measure energy in kWh rather than J?
Why might energy companies measure power in kW or GW rather than W or Js-1?
This session focuses on problem solving.
Introducing Ideas
Introduce the following problem to students: When the Smith family was at work and school for six and a half hours, they left enough lights and appliances running to draw a current of 30 A. An ampere, A, measures the amount of charge running through the meter every second. The power supplied to the house is at 230 V. A volt, V, is a measure of the amount of electrical energy transformed per unit charge.
How much electrical energy did the Smith family’s house use in their absence that day?
Discuss, drawing attention to the following points:
Building Ideas
Explain: Power, measured in W, is calculated from the rule P = VI:
Provide time for students to work through the following tasks, Remind and support students to use appropriate units in their calculations.
Reinforcing Ideas
Introduce the following context to students: Power, measured in W, is the rate at which energy is used. Power is the product of the voltage across and current through an electric supply electric circuit or any appliance using electricity.
Provide time for students to work through the following tasks. Remind and support students to use appropriate units in their calculations.
Extending Ideas
Provide time for students to work through the following task. Remind and support students to use appropriate units in their calculations.
Find the difference in energy usage of an oil heater that runs for 4 hours, drawing a current of 8.5 A on mains electricity over a 425 W panel heater that is left running for 12 hours.
This session focuses on using algebra to generalise the results of a practical investigation.
Introducing Ideas
Introduce the following context to students: Electrical current, in amperes (A) is defined as the rate of flow of charge. It is measured with an ammeter placed in series in a circuit. Look at the circuit below:
Provide time for students to work through the following tasks:
Discuss, drawing attention to the following points:
Building Ideas
Provide time for students to work through the following tasks:
Reinforcing Ideas
Introduce the following context to students: Current is the rate of flow of charge. The two resistors in the circuit above are the same size.
Provide time for students to work through the following tasks:
Provide time for students to build the above, using three 1.5 cells connected in series, to two resistors chosen from a selection of 50 Ω and 100 Ω resistors and connected in parallel so that A2 = 2A3. They should then be supported to do the following:
V (V)0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
I (A) |
Reinforcing Ideas
Provide time for students to work through the following tasks:
Extending Ideas
Introduce the following context to students: The relationship between current, voltage and resistance of an electrical component, or of a circuit, is known as Ohm’s Law. It is:
V = I R
Together, use this rule to find the current drawn by a 50 Ω kettle connected to mains electricity (230 V).
Discuss, drawing attention to the following points:
Building Ideas
Provide time for students to use Ohm’s Law, V = IR, to solve the following problems. Remind and support students to use appropriate units in their calculations.
Reinforcing Ideas
Extending Ideas
This session focuses on using algebraic techniques to solve problems involving power, voltage, current, and resistance.
Introducing Ideas
Building Ideas
Introduce the following context to students: A heater with resistance of 1500 Ω is connected to a 230 V supply.
Provide time for students to work through the following tasks. Remind and support students to use appropriate units in their calculations.
Reinforcing Ideas
Extending Ideas
Remind and support students to use appropriate units in their calculations.
Dear parents and whānau,
In class, we have been applying our understanding of algebra to solve problems within the science - physical world context of electrical circuits. Ask your child to share their learning with you.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/circuit-problems at 8:54pm on the 26th February 2024