Assignment 3 Unit Plan

 “Which Plumber to use”

Introduction:

Students will analysed which plumber they want to employ to do a job for them.  They will represent the cost in linear graph.  Compare two different plumbers cost.  Product a report of which one will be better to use in different size job.  Students will use Geogebra to compare the graph.

Duration:  5 lessons (50 minutes lessons)

Assessment:

Student will demonstrate elements of Level 6 standard in Mathematics and Information and Communications Technology.

Students will be assessed on:

            Understand difference between pronumeral and variable

            Understanding the meaning of gradient and constant in y = mx + c.

            Understand function notation.  Eg f(x) and g(x)

            Able to express the cost of the plumbers in Linear equation form.

Graphic representation of the cost

Understand scaling

Represent graph using Geogebra

Label the graph clearly.

Present information in a report format

VELS – Victorian Essential Learning Standards

Domain	Dimension	Element of standard
Mathematics	Structure	They recognise and explain the roles of the relevant constants in the relationships f(x) = ax + c, with reference to gradient and y axis intercept, f(x) = a(x + b)2 + c and f(x) = cax. They solve equations of the form f(x) = k, where k is a real constant (for example, x(x + 5) = 100) and simultaneous linear equations in two variables (for example, {2x – 3y = – 4 and 5x + 6y = 27} using algebraic, numerical (systematic guess, check and refine or bisection) and graphical methods.
	Working Mathematically	Students choose, use and develop mathematical models and procedures to investigate and solve problems set in a wide range of practical, theoretical and historical contexts (for example, exact and approximate measurement formulas for the volumes of various three dimensional objects such as truncated pyramids). They generalise from one situation to another, and investigate it further by changing the initial constraints or other boundary conditions. They judge the reasonableness of their results based on the context under consideration.  They select and use technology in various combinations to assist in mathematical inquiry, to manipulate and represent data, to analyse functions and carry out symbolic manipulation. They use geometry software or graphics calculators to create geometric objects and transform them, taking into account invariance under transformation
ICT	Focus	Students explore the distinction between legal and illegal uses of ICT and create information products that comply with ICT intellectual property law. This particularly relates to copyright.
	visualising thinking	Students use a range of ICT tools and data types to visualise their thinking strategies when solving problems and developing new understanding. They use visualising thinking tools and apply ICT techniques to support causal reasoning and to model and describe the dynamic relationship between variable and constant data values to test hypotheses. Students are efficient and effective in their use of appropriate ICT tools and editing techniques for assisting in visualising thinking. When solving problems, students discriminate between such tools and strategies based on their suitability for problem solving in new situations.
	Creating	Students apply a range of techniques, equipment and procedures that minimise the cost, effort and time of processing ICT solutions and maximise the accuracy, clarity and completeness of the information.

           

Teaching and assessment activities:

Lesson	Activities	Teacher explanation	Student outcome	VELS
1	Give a formula y = 3x + 2, draw up a table such as x Y 1 2 3 Plot each graph on Geogebra. Create a line of best fit. Can you read from graph what happen when x = 7?	Introduce Geogebra.  Explain to student they can access it via internet.  It is open source software. After activities, teacher explain the meaning of variables.	Understand difference between pronumeral and variable Able to express the cost of the plumbers in Linear equation form. Create graph to visiulised thinking.	Maths: Structure ICT: visualising thinking, Copyright issue.
2	Instead of plotting each point, student use notation f(x) = 3x + 2.  We see the graph the same as last lesson.	Explain the standard notation in Mathematics.	Understanding the meaning of gradient and constant in y = mx + c. Understand function notation.  Eg f(x) and g(x) Create graph to visiulised thinking. Student able to manage their files.	Maths: Structure ICT: visualising thinking. Creating
	Students enter g(x) = 2x + 3.  What can we see?	Teacher lead discussion on the function of m and c in the standard forms.
	Students need to save their work to be used again next lesson,
3	Students able to retrieve the file they saved from last lesson.		Students able to retrieve files from last lesson. Student understand the relation of zooming and scaling.	Maths: Working mathematically ICT: visualising thinking. Creating
	Students explore the graphic view options.  Students need to find answer to the following questions: 1.      What happen when the ratio in x-axis and y-axis changes? 2.      How can we zoon in to the intersection? 3.      What happen to the ratio when we change the minimum and maximum of x-axis without changing y-axis? 4.      What happen when we remove the number on the axes? 5.      What happen if we change the minimum and maximum of x-axis to 3 and 10?  Is there still intersection of the graph?  If so, will it be on the right hand side or the left?	Teacher lead class discussion to ensure students have sound understand scaling and zooming.
4,5	Student will be given the problem solving task. “You need a plumber to do a job.  When you rang John and Chris, you got two different quote.  John charge $150 for a call out fees and $80 for each hour.  Chris charge $100 for a call out fees and $100 for each hour.  When will John charge less then Chris?  And when will Chris charge less then John? At which point in time, they will cost the same?” Student present project in A3 size paper.  Include a print out of their graph.  Student could choose to present it in powerpoint format and submit electronically.		Able to express the cost of the plumbers in Linear equation form. Able to produce graphically presentation of the cost. Able to analysed and give answer. Present graph in the appropriate scale, ie, display the intersection of two graphs. Label graph clearly.	Maths: Structure, Working mathematically ICT: visualising thinking. Creating

Reference:

“Mitchelmore, M., & Cavanagh, M. (2000).  Students' difficulties in operating a graphic calculator.  Mathematics Educational Research Journal, 12(30), 254 – 268.”