7801 eps adapted unit

8/8/2019 7801 EPS Adapted Unit

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7801EPS Assignment Tutor: Barbara Garrick

7801 EPS Middle Years Schooling Assignment 1bTutor: Barbara GarrickStudents:

Nicola Martin s2758226 Susanne Kimura s2620717

Araba Baiden 2625722

Nicola Martin s2758226 Susanne Kimura s2620717 Araba Baiden 2625722


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Theme/Strand: FDPRP, algebra, handling data

Unit title: MP3 players

Target group of pupils: Year 9

Timing of unit: Autumn term

Curricular targets: Construct simple scatter graphs on paper and using ICT. (HD: part of step 7)

Use the equivalence of fractions, decimals and percentages to compare proportions; calculatepercentages and find the outcome of a given percentage increase or decrease. (FDPRP: step 7)

Express simple functions in symbols; represent mappings expressed algebraically. (SFG: step 6)

Construct functions arising from real-life problems and plot their corresponding graphs; interpretgraphs arising from real situations. (SFG: step 8)

Other curricular targets

Know that if the probability of an event occurring is p , then the probability of it not occurring is (1 p ). (Probability: step 7)

Unit description

In this unit pupils investigate buying and using an MP3 player. They compare different MP3 players,using proportional reasoning.

The pupils will need access to ICT and, if possible, the internet to research prices and data about MP3players. If the internet is not available, a range of shopping catalogues will provide the sameinformation.



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Unit overview

Phase Lesson overview Homework

1 Introduction to the unit (one lesson)

Introduce the curricular targets and allow some self-assessment against the targets.

During this lesson pupils will collect the data that they willuse through the unit and in the summary phase andrepresent these data with a scatter diagram.

23 Main development phase (four lessons)

Pupils will work on:

proportionality and ratio

working out percentages without a calculator

constructing equations and solving equations, usinggraphs

simple probability.

4 Summary links and judgements (one lesson)

The aim of this lesson is to make links with the other workthat pupils will be doing in mathematics lessons on ratio andproportion and handling data.

Pupils should have the opportunity for self-assessmentagainst the curricular targets through discussions with theadults in the lesson.

Unit assessment questions (to be given to pupils in advance)

Resource 1.1 to be used to answer the question: How do you construct a scatter graph and whatis it telling you?

How do you work out the value added tax (VAT) on an MP3 player costing 149.00 (before tax)bought abroad?

If the total cost of an MP3 player decreases by 24%, how would you work out the new price?

Which MP3 player is the best value for money?

Resources: internet, shopping catalogues, lesson resource sheets including exemplar GCSEquestions

Other useful strategy resources:

Framework for teaching mathematics: Years 7, 8 and 9

GCSE booster files

Progression maps



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Lesson plans

Lesson 1

Objectives Discuss how data relate to a problem.

Gather data from specified secondary sources including printed tablesand lists from ICT sources.

Construct scatter diagrams on paper and interpret in context.

Starter Explore how much pupils know about MP3 players by asking a rangeof questions such as these.

What is an MP3 player?

How much music can you store on one?

How might we compare MP3 players?

Suggest the following hypothesis:

The more expensive the MP3 player, the larger the memory.

Discuss how pupils might go about testing this hypothesis, includingthe type and amount of data they should collect. Agree a way torecord the data. A sample chart is given on Resource sheet 1.1 .

Mainactivity

Whole-class discussion, collaborative paired work, individual work

In this lesson, following some whole-class and individual work, pupilswork in pairs to draft joint statements in response to an agreedhypothesis. They record their statements individually. The teachingassistant will need to support pupils in managing the drafting process.

Give pupils, in pairs, about 10 minutes to collect the data, using theinternet or catalogues. The teaching assistant may need to interveneto help some groups get started. Take a sample of the data frompupils and record on the board, using the agreed table. Ask whether the table helps to test the hypothesis.

List the following graphs on the board: bar chart, line graph, pie chart,scatter graph. Ask which of these would help in testing the hypothesis.Ask pupils to discuss this briefly, in pairs, and agree an answer. Takefeedback and pursue pupils suggestions for inappropriate graphs,asking how to label axes and construct the graphs. Encourage pupilsto recognise why all but the scatter graph are inappropriate.

Focus pupils on the labelling and scale on the two axes.

Q. What scales should we use to help us to position these pointsaccurately?

Start to model drawing the scatter graph, and then ask pupils to starttheir own scatter graphs for their data, again thinking carefully aboutscale. As pupils complete their scatter graphs, ask them to work inpairs to use the graph to test the hypothesis. Ask them to work in pairsto write statements to support or reject the hypothesis. They shoulddraft their statements on whiteboards and refine them verbally beforewriting them up individually. Some pairs will need intensive support in

managing the process. The teaching assistant may choose to helpsome pairs with the drafting.



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Plenary Ask each pair to join another pair to compare graphs and statements.Give pupils a few minutes to improve their own statements and ask afew to explain their conclusions to the class.

Give pupils a GCSE question about scatter diagrams for homework.(Resource sheet 1.2 )



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Lesson 2

Objectives Use the equivalence of fractions, decimals and percentages to compareproportions.

Starter Ask the following question.

A 5 gigabyte (GB) player costs 70. Would a 4 GB player costing 59be better or worse value for money? How do you know?

Ask pupils, in pairs, to find two MP3 players from their own lists that aregood value for money and two that are poor value for money. Ask a coupleof pairs to explain their reasoning.

Main Whole-class discussion, collaborative paired work, pairs to fours

In this lesson pupils work collaboratively, in pairs, to find efficient ways of calculating. They will need to work in the same pairs as in lesson 1.

Set pupils the challenge of finding the MP3 player in their own list that isthe best value for money in terms of memory size. Explain that they willneed to give clear evidence of their method of comparison, and that theyshould use a calculator if appropriate. It is important that pupils begin touse terms such as pounds per gigabyte or gigabytes per pound. You andthe teaching assistant will need to direct pairs of pupils to make appropriatecalculations and interpret the answers. Some pupils may find Resourcesheet 2.1 helpful.

Ask each pair of pupils to compare their methods with another pair. Whichseems to be the most efficient method? If both pairs have used the samemethod, can they find a different method?

Collect and record on the board two or three different methods used bypupils. Ask the class to choose an efficient method for this context.

Plenary Use the exemplar GCSE examination questions on Resource sheet 2.2(proportionality).

Split the class into two groups, with one group working in pairs on question1 and the other on question 2. After 5 minutes choose two pairs to explaintheir methods for question 1, and a further two pairs for question 2.

Ask pupils to reflect on efficient methods for examination questions.



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Lesson 3

Objective Calculate simple percentages and find the outcome of a given percentageincrease or decrease.

Starter Ask these questions.

What is 10% of 160? How did you work this out?


What is 2.5% of 160? How did you work this out?

What other percentages of 160 can you work out?

Ask pupils to record questions and answers on mini-whiteboards or in their exercise books. Take feedback and reinforce mental methods.

Record their examples on the board, using a web diagram to show the linksfrom one percentage calculation to the next.

Main activity Whole-class discussion, collaborative work in pairs, pairs to fours

In this lesson pupils work collaboratively, in pairs, to solve problems andshare their solutions with other pairs. The teaching assistant may need to bebriefed that a 15% reduction is the same as 0.85. You and the teachingassistant will need to provide very clear guidance for pairs who are strugglinginitially. Allow calculators even for simple calculations.

Introduce the following activity.

Jakes mum has an electrical shop selling MP3 players. Business isntgood so she decides to have a sale and reduces the price of everything by15%. Jakes mum finds an easy way to reduce each price by just

multiplying the original price by a number. What number does she multiplyby?

Pupils should discuss this in pairs and work on whiteboards. For pairs whoare struggling, you could scaffold the problem by giving them a calculation todo mentally, or with jottings. They need to appreciate that the new price is85% of the old. The teaching assistant will need to work through this withsome of the pairs. Before summarising, ask each pair to join another pair toshare their results and challenge thinking. Ask for one spokesperson fromeach group of four.

What would Jakes mum multiply by if she reduced the price of everythingby 18% instead of 15%?

To tackle this problem, pupils need to have generalised from the 15%reduction above.

What would she multiply by if she was increasing the price of everythingby 5%?

Two further questions are given on Resource sheet 3.1 .

Plenary Identify some other questions that you would like to explore.

Why does Jakes mums method work?

Ask pupils to devise some percentage increase and decrease questions togive to a partner to work out. Can they use Jakes mums method?



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Lesson 4

Objective Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from realsituations.

Starter Revise percentage increases and decreases, using mental methods, byasking questions such as these.

Decrease a price of 60 by 10%, 15%, 25%, 40%.

Increase a price of 25 by 10%, 5%, 1%.

Ask pupils to explain their methods for some of them.

What multiplier would you use for a decrease of 25%?

What multiplier would you use for an increase of 50%?

Main activity Whole-class discussion, collaborative paired work, individual work

In this lesson pupils work collaboratively, in pairs, to solve problems. Theyrecord solutions individually. The teaching assistant will need to support lessable pairs of pupils to get them started on the problems and to draftsummaries of their findings.

Pupils are now going to explore two options for downloading music on theMP3 player, and consider the advice they would give about how to select themost economical. Details of the two deals are given on Resource sheet 4.1 .Pupils should price each option, assuming that the subscription is for onemonth only.

Give pupils, in pairs, about 5 minutes to complete the table for the first option,Tangent tracks . They should draft their answers together on a whiteboardbefore recording individually. The teaching assistant should support slowstarters to begin recording.How did pupils calculate the cost of 100 tracks? Take brief feedback.

Give a further 5 minutes for pupils individually to complete the table for Cosine cuts .

Explain that pupils are now going to represent the data for both options onthe same set of axes and use this graph to consider the advice they wouldgive on the most economical.

What range of numbers do you need on the N -axis? ( N = number of downloads)

What scale might you use? (Encourage pupils to choose their own

scales.) What range and scale for the C -axis? ( C = cost)

Pupils should work on these questions in pairs and prepare joint responses.

Ensure that pupils understand that they must use a linear scale on each axis.

Give pupils about 10 minutes to construct and label the graphs of the twofunctions, working as individuals.

Ask pupils, in pairs, to draft, on their whiteboards, some statements aboutwhat the graphs tell them about the two options and to record the advice theywould give to a possible customer. They should write these up individually,once the draft is agreed. The teaching assistant should support less able

pairs through the drafting process.Plenary Present the following questions and discuss one of them.



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Q. What is happening where the two lines cross? How does this inform theadvice that you would give?

Q. What difference would it make if the subscription was for two months?three months?

Ask pupils to explore the other question for homework.



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Lesson 5

Objectives To work out the probability of an event occurring and to know that if theprobability of an event occurring is p , then the probability of it not occurring is

(1 p ).

Starter Discuss this question.

What is the probability of picking your favourite song from a player if it ison random?

Main activity Whole-class discussion, collaborative paired work

In this lesson pupils work collaboratively, in pairs, to discuss and recordprobabilities. The teaching assistant will need to support less able pairs ingetting started and managing their discussions.

Set the scene, where pupils have put their favourite albums onto their MP3

player. The pupils pick their ten favourite songs at first. Get them to list themand number the list from 1 to 10.

Say that there is a random button on an MP3 player that lets the MP3 player play 10 tracks randomly.

What is the probability of picking track 1?


What is the probability of not picking track 1 at random?

Pupils should work collaboratively, in pairs, to answer these questions, usingwhiteboards to record answers.

Ask the pupils, in pairs, to make a new list of their ten titles, then cut them out

and put them in a bag. They draw them out, one at a time, and make a list of the titles as they appear. To maintain the randomness, they will need toreplace the slips after each draw, otherwise the probabilities will not allremain at 1/10 as the activity progresses. The teaching assistant may need tosupport some pairs to start promptly and work quickly.

Discuss the idea of randomness with the class and how all outcomes wereequally likely.

As a challenge, use a six-sided dice and discuss whether a 6 is easier toscore than a 3.

Use a ten-sided spinner or dice and let the pupils make a list of their favouritetracks in the order that the spinner/dice generates the numbers. Ask pupils todiscuss in pairs what will happen if the same number comes up before all tenhave been heard and whether the titles put in a bag avoids this.

Discuss what the probability will be in random mode of any given track if track1 is no longer available? Track 3? Track 10?

Plenary Extend the problem to an MP3 player with 1000 then 2500 tracks recorded.

Summarise the results, that if the probability of an event occurring is 1/10 thenthe probability of it not occurring is 9/10 and generalise to p and (1 p ).

Ask the pupils, in pairs, to think of some events with given probabilities andthen give the probability that each event will not occur (using mini-whiteboards).

Challenge the class to work out the probability that the MP3 player, set onrandom, would play track 1 and then follow it with track 2.



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Lesson 6

Objectives To reflect on the unit of work and write two targets for further development for each pupil.

Starter Give pupils a copy of Resource sheet 6.1 and explain that during the lesson they willneed to assess their understanding of each of the objectives. Explain that pupils shoulddevise their own examples to illustrate what they are able to do (or provide someproblems for pupils to work on).

Main Individual working and self-assessment within pairs

Focus for learning conversations

During this part of the lesson, pupils should have learning conversations with theteacher or teaching assistant, focused on Resource sheet 6.1 and the questionson the GCSE resource sheets . The following prompts (taken from theprogression maps) may be useful questions to assess pupils progress towards

the stated objectives informally. Encourage the teaching assistant to select theappropriate prompts carefully, to suit the pupils current levels of understanding.

Construct simple scatter graphs, on paper and using ICT. (HD part of step 7)

How do you construct a scatter graph and what is it telling you?

Whats important when choosing the scale for the graph?

Is this graphical representation helpful in addressing the hypothesis? If not, why and what would you change?

Use the equivalence of fractions, decimals and percentages to compareproportions; calculate percentages and find the outcome of a givenpercentage increase or decrease. (FDPRP step 7)

Which sets of equivalent fractions, decimals and percentages do you know?

From one set that you know (e.g. 1 / 10 0.1 10%), which others can you deduce?

Talk me through how you would increase/decrease a price of 12 by, for example, 15%. Can you do it in a different way? How would you find themultiplier for different percentage increases/decreases?

The answer to a percentage increase question is 10. Make up an easy question.Make up a difficult question.

Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations. (SFGstep 8)

What do the axes represent?

In the context of this problem, does every point on the line have ameaning? Why?

What does this point on the graph represent?

What does this part of the graph represent?

What sort of questions could you use your graph to answer?

Plenary Use the plenary to give pupils opportunities to talk about what they have learned

during the unit of work and what they have found difficult, using the learningobjectives detailed on lesson 6 resource sheet as a focus. Encourage them to talkabout how they can transfer the skills learnt back into other mathematics lessons.



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Based on pupils responses and their traffic lighting on lesson 6 resource sheet , askpupils to write two targets for future development. The teaching assistant will need tosupport many of the pupils in setting targets for future work alongside you.



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Resource sheet 1.1 MP3 players

MP3 player name Number of gigabytes(GB)

Cost ()

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Questions

Was your graph what you were expecting?

If you were to buy a player for $200 how many gigabytes would you expect?

If a player had 4 gigabytes, how much would you expect to pay?



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7801EPS assignment 1b Tutor: Barbara Garrick

Resource sheet 1.2

Lesson 1 Homework

Katie recorded the heights and the lengths of the strides of ten boys in her form. These arethe results.

Height (cm) 170 172 175 173 172 177 176 175 182 181

Length of stride(cm) 87 89 86 91 92 91 94 90 94 96

(a) Complete the scatter diagram below to show these results.The first four points have been plotted.

(b) Comment on the relationship between the height and the length of stride for theten boys.



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MP3 player name Number of gigabytes(GB)

Cost ($) Cost per gigabyte

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Questions


What other method could you use to find the best value for money MP3 player?

Would you buy this MP3 player?



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Resource sheet 2.2

Lesson 2 MP3 players

Question 1

The table show the exchange rates between pounds and euros and dollars.

1 =

USD ($) 1.97

Euro () 1.48

(a) A tourist is travelling to New York. She changes 650 into US dollars ($). How much does sheget?

(b) A German company is buying goods in the UK. They change 2000 euros () into GB pounds(). How much will they get (to the nearest pound)?

Question 2

A breakfast cereal is available in two sizes.

95p 1.68

(a) Work out the cost of 100 g of Wheat Pops when bought in the 400 g box (to the nearestpenny).

(b) Work out the cost of 100 g of Wheat Pops when bought in the 750 g box (to the nearestpenny).

(c) Which is better value?


400 g 750 g

WheatPops

Wheat Pops


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Question 1

(a) A new breakfast cereal is sold in boxes as shown below. What is the volume of the box?

(b) To promote the cereal, the company is offering 10% extra free. What is the new volume?

(c) A new designer suggests adding 10% to all dimensions to make the box. Would this work?Explain your answer.

Question 2

An MP3 player is priced at 65. In a sale, the price is reduced by 15%. What is the new price?

Study Plus unit MP3 players 1

25 cm

15 cm8 cm


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7801 EPS Schooling in the Middle Years Tutor: Barbara Garrick


Tangent tracks

$20.00 per month and 50cents per download

Number of songsdownloadedduring onemonth ( N )

1 2 3 4 5 6 10 100

Cost ( C ) $20.50

Equation: C =

Cosine cuts

$17 per month and 70cents per downloadNumber of songsdownloadedduring onemonth ( N )

1 2 3 4 5 6 10 100

Cost ( C ) $17.70

Equation: C =

___________________________________________________________________

Construct graphs for both options, using the same set of axes. Where do the graphs meet?

What does this point of intersection mean?

Which download service would you use? Why?



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Resource sheet 6 MP3 players

Objective Example from the MP3 player project Example from a different context

I can constructand interpret ascatter graph

I can calculatesimple

percentages

mentally

I can calculate the

outcome of apercentageincrease or decrease

I can useproportion to solve

a problem

I can interpret agraph from a real-

life problem



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Adaptations

IntroductionThe adaptations to each lesson have been given in the tables below. In addition the final unit will beAustralia centric i.e. all UK centric references will be changed or removed.All resources sheets would be adapted to Australian dollar, GST and any UK centric concepts wouldbe removed. The finalised resource sheets are in the Adapted Unit

Formative assessment will be conducted throughout the adapted lessons. In diverse classroomsstudents may be at different levels of the syllabus and hence students should be graded on wherethey are at. A matrix will be used to tick off achievements as the teacher catches the studentsreaching themLesson Original Adaptation

Lesson 1 Adaptation Double or tripl

Objectives Discuss how data relate to a problem.

Gather data from specified secondary sources includingprinted tables and lists from ICT sources.

Construct scatter diagrams on paper and interpret incontext.

Lesson Objectives : Essentcreate tables of values for ligraphing. Data ; Students wand displayed. Data interpreuse of descriptive statisticsgraphs. Literacy Glossaryand displayed.

Starter Explore how much pupils know about MP3 players byasking a range of questions such as these.



How might we compare MP3 players?Suggest the following hypothesis:

The more expensive the MP3 player, the larger thememory.

Discuss how pupils might go about testing this hypothesis,including the type and amount of data they should collect.Agree a way to record the data. A sample chart is given onResource sheet 1.1 .

Introduction to the unit (onewill engage students straighAsk students to Think aboutThink Pair Share . Effectistudents.

During discussions a glossacreated to help all children ube particularly beneficial for second language.

During the discussion aboutcould be used to comparewill be allowed to use a varito help them engage and sonegotiated.

A hypothesis will be agreed comparison method. E.g. c

higher the cost or the mor Students will also be askedassistance may be necessaEach group will discuss howagreed hypothesis, what dashould be represented andare benefited as they can dithought process. Show studrecorded in tables and howchart - Resource sheet 1.1.

Groups will begin to collect

about how they wish to repr paper and pencil table. Eve prefer to work with pen and



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Lesson Original Adaptation

Main Whole-class discussion, individual work

In this lesson, following some whole-class pupils to draft astatement in response to the hypothesis. They record their statements. The teaching assistant will need to supportpupils in managing the drafting process.

Give pupils, in pairs, about 10 minutes to collect the data,using the internet or catalogues. The teaching assistantmay need to intervene to help some groups get started. Askwhether the table helps to test the hypothesis.

List the following graphs on the board: bar chart, line graph,pie chart, scatter graph. Ask which of these would help intesting the hypothesis. Ask pupils to discuss this briefly, inpairs, and agree on an answer. Take feedback and pursuepupils suggestions for inappropriate graphs, asking how tolabel axes and construct the graphs. Encourage pupils to

recognise why all but the scatter graph are inappropriate.Focus pupils on the labelling and scale on the two axes.

Q. What scales should we use to help us to position thesepoints accurately?

Start to model drawing the scatter graph, then ask pupils tostart their own scatter graphs for their data, again thinkingcarefully about scale. As pupils complete their scatter graphs, ask them to work in pairs to use the graph to testthe hypothesis. Ask them to work in pairs to writestatements to support or reject the hypothesis. They shoulddraft their statements on whiteboards and refine themverbally before writing them up individually. Some pairs willneed intensive support in managing the process. Theteaching assistant may choose to help some pairs with thedrafting.

Class to work in small group

By working in cooperative gdrafting process will be assiencourage higher order thinany gifted and talented stud

Students groups will be givewill allow deeper understanassistance will be utilised toGroups will present their fin

Class discussion on type of collected. List all the graphexamples using similar infor by the Essential Learnings.

Use open ended questioninmore appropriate than the oscatter plot with student collgraph is labelled. By doing thave the opportunity to shoteacher can find any misconallows the student to grasp twell as auditory/verbally. Siorder thinking.

Refocus activity as a classmake sure they are large enin the class.

Refer students to an onlinehttp://www.amathsdictionaryOnline dictionary is more stistudents. It also gives studecomputers the chance to faTeacher to create posters inexamples of different graphemphasis on scatter plots aexamples. Showing real lifeacknowledge and value the

Ask students to then graph tuse it to test the hypothesis.Constructing their own graphypothesis causes studentsfrom the concrete to the abstheory). The presentation of students to clear up any co

Ask each pair to join another pair to compare graphs andstatements. Give pupils a few minutes to improve their ownstatements and ask a few to explain their conclusions to theclass.

Give pupils a GCSE question about scatter diagrams for homework. ( Resource sheet 1.2 )

Students can choose to useengagement and is a valua

Extension Students may ufirst activity to test if their ch

one. Extension activities arestudents in the class to challorder thinking.

http://www.amathsdictionaryforkids.com/http://www.amathsdictionaryforkids.com/


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Lesson 2 Adaptation Double period

Objectives Use the equivalence of fractions, decimals and percentagesto compare proportions.

Lesson Objectives : Essentdecisions can be made bas

benefit analysis. Literacy created and displayed.

Starter Ask the following question.

A 5 gigabyte (GB) player costs 70. Would a 4 GBplayer costing 59 be better or worse value for money?How do you know?

Ask pupils, in pairs, to find two MP3 players from their ownlists that are good value for money and two that are poor value for money. Ask a couple of pairs to explain their reasoning.

Adapted to AUS $

Value for money activity willfew groups to present their f students fosters learning thproximal development). It allike dynamic/setting in the ccomfortable discussing their from other students. Studen

Main Whole-class discussion, collaborative paired work, pairs tofours

In this lesson pupils work collaboratively, in pairs, to findefficient ways of calculating. They will need to work in thesame pairs as in lesson 1.

Set pupils the challenge of finding the MP3 player in their own list that is the best value for money in terms of memorysize. Explain that they will need to give clear evidence of their method of comparison, and that they should use acalculator if appropriate. It is important that pupils begin touse terms such as pounds per gigabyte or gigabytes per pound. You and the teaching assistant will need to directpairs of pupils to make appropriate calculations andinterpret the answers. Some pupils may find Resourcesheet 2.1 helpful.

Ask each pair of pupils to compare their methods withanother pair. Which seems to be the most efficient method?If both pairs have used the same method, can they find adifferent method?

Collect and record on the board two or three different

methods used by pupils. Ask the class to choose anefficient method for this context.

Class discussion

Students groups are askedthe best value for money inthe criteria allows the studeasked to give clear evidencstudents may use diagramsgraphs, reviews online (ICT)be easy to read for any studimpairment.

Show a video on cost compsized packages. This is real

just presume that the larger packets. But this is not alw

Create posters for display acomparing items with cost aposters give the students ahave completed which woulvisual learning style. Give recan be compared before ma

Students will present their c

teaching students.

Use the exemplar GCSE examination questions onResource sheet 2.2 (proportionality).

Split the class into two groups, with one group working inpairs on question 1 and the other on question 2. After 5minutes choose two pairs to explain their methods for question 1, and a further two pairs for question 2.

Ask pupils to reflect on efficient methods for examinationquestions.

Assessment Resource shsuitable for visually impaireeasy to difficult. Ask studentneeded to accommodate for

Class reflective discussion

Lesson 3 Adaptation Double period



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Objective Calculate simple percentages and find the outcome of agiven percentage increase or decrease.

Lesson Objectives : Essentsense: Students will calculaworld examples to calculateGlossary of terms and defini

Starter Ask these questions. What is 10% of 160? How did you work this out?


What is 2.5% of 160? How did you work this out?

What other percentages of 160 can you work out?

Ask students to record questions and answers on mini-whiteboards or in their exercise books. Take feedback andreinforce mental methods.

Record their examples on the board, using a web diagramto show the links from one percentage calculation to thenext.

Convert this Activity into a wthat the worksheet can be eimpairment in the class. Asanswer the questions on theopen ended questions in or misconceptions.

Record their examples on ththe links from one percenta

Mainactivity

Whole-class discussion, collaborative work in pairs, pairs tofours

In this lesson pupils work collaboratively, in pairs, to solveproblems and share their solutions with other pairs. Theteaching assistant may need to be briefed that a 15%reduction is the same as 0.85. You and the teaching assistant will need to provide very clear guidance for pairswho are struggling initially. Allow calculators even for

simple calculations.Introduce the following activity.

Jakes mum has an electrical shop selling MP3 players.Business isnt good so she decides to have a sale andreduces the price of everything by 15%. Jakes mumfinds an easy way to reduce each price by justmultiplying the original price by a number. What number does she multiply by?

Pupils should discuss this in pairs and work onwhiteboards. For pairs who are struggling, you couldscaffold the problem by giving them a calculation to domentally, or with jottings. They need to appreciate that thenew price is 85% of the old. The teaching assistant willneed to work through this with some of the pairs. Beforesummarising, ask each pair to join another pair to sharetheir results and challenge thinking. Ask for onespokesperson from each group of four.

What would Jakes mum multiply by if she reduced theprice of everything by 18% instead of 15%?

To tackle this problem, pupils need to have generalisedfrom the 15% reduction above.

What would she multiply by if she was increasing theprice of everything by 5%?

Class discussion, collaborat

Students will work in their gr class.

Group work gets the studenengaged in task



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Identify some other questions that you would like toexplore.

Why does Jakes mums method work?

Ask students to devise some percentage increase anddecrease questions to give to a partner to work out. Canthey use Jakes mums method?

Students will work in their gr

Lesson 4

Objective Construct linear functions arising from real-life problemsand plot their corresponding graphs; discuss and interpretgraphs arising from real situations.

Lesson Objectives : EssentStudents will understand hointerpretation is simplified thstatistics e.g. scatter plots. IGlossary of terms and defini

Starter Revise percentage increases and decreases, using mentalmethods, by asking questions such as these.

Decrease a price of 60 by 10%, 15%, 25%, 40%.

Increase a price of 25 by 10%, 5%, 1%.

Ask pupils to explain their methods for some of them.



Class discussion on what ththe last 3 lessons. A videoUsing the video as a introduhold of the students attentiopercentages. This works eslearners.

Teacher will ask questions (discussions with students thGuidance might be to organi

whole class through conceInteractive learning program(interactive and engaging re

http://www.amathsdi

Percentage calculathttp://www.math.coent.htm

Mainactivity

Whole-class discussion, collaborative paired work,individual work

In this lesson pupils work collaboratively, in pairs, to solveproblems. They record solutions individually. The teachingassistant will need to support less able pairs of pupils to getthem started on the problems and to draft summaries of their findings.

Pupils are now going to explore two options for downloading music on the MP3 player, and consider theadvice they would give about how to select the mosteconomical. Details of the two deals are given onResource sheet 4.1 . Pupils should price each option,assuming that the subscription is for one month only.

Give pupils, in pairs, about 5 minutes to complete the tablefor the first option, Tangent tracks . They should draft their

Class discussion on downlo

Think individually, Pair dclass.

After class discussions studoptions for downloading mu

Give students 10 minutes (lgrasp a deeper meaning). Tresource sheet. The teachedifficulties via observation aactivity aids the teacher in ais kept informal.

Ask students, how did they

Give a further 10 minutes tooption, Cosine Cuts.

http://www.amathsdictionaryforkids.com/http://www.math.com/everyone/calculators/calc_source/percent.htmhttp://www.math.com/everyone/calculators/calc_source/percent.htmhttp://www.amathsdictionaryforkids.com/http://www.math.com/everyone/calculators/calc_source/percent.htmhttp://www.math.com/everyone/calculators/calc_source/percent.htm


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answers together on a whiteboard before recordingindividually. The teaching assistant should support slowstarters to begin recording.

How did pupils calculate the cost of 100 tracks? Take brief feedback.

Give a further 5 minutes for pupils individually to completethe table for Cosine cuts .

Explain that pupils are now going to represent the data for both options on the same set of axes and use this graph toconsider the advice they would give on the mosteconomical.


What scale might you use? (Encourage pupils to

choose their own scales.) What range and scale for the C -axis? ( C = cost)

Pupils should work on these questions in pairs and prepare joint responses.

Ensure that pupils understand that they must use a linear scale on each axis.

Give pupils about 10 minutes to construct and label thegraphs of the two functions, working as individuals.

Ask pupils, in pairs, to draft, on their whiteboards, somestatements about what the graphs tell them about the twooptions and to record the advice they would give to apossible customer. They should write these up individually,once the draft is agreed. The teaching assistant shouldsupport less able pairs through the drafting process.

Students will work in their gr questions. Allow students tICT may be more stimulatin

Give students about 10 minthe two options.

Students will make statemeStudents will agree what thethinking about buying some

Present the following questions and discuss one of them.

Q. What is happening where the two lines cross? Howdoes this inform the advice that you would give?

Q. What difference would it make if the subscription wasfor two months? three months?

Ask pupils to explore the other question for homework.

Lesson 5

Objective To work out the probability of an event occurring and toknow that if the probability of an event occurring is p , thenthe probability of it not occurring is (1 p ).

Lesson Objectives : Essential Leaunderstand theoretical or experimvarious ways and analysed to mak

Students identify all possible outcthese sample spaces, order the lik using experimental data.

Starter Discuss this question. What is the probability of picking your favourite song from a

Show video on what probability isengaging way of starting the lesso



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Lesson Original Adaptation player if it is on random?

Mainactivity

Whole-class discussion, collaborative paired work

In this lesson pupils work collaboratively, in pairs, todiscuss and record probabilities. The teaching assistant will

need to support less able pairs in getting started andmanaging their discussions.

Set the scene, where pupils have put their favourite albumsonto their MP3 player. The pupils pick their ten favouritesongs at first. Get them to list them and number the listfrom 1 to 10.

Say that there is a random button on an MP3 player thatlets the MP3 player play 10 tracks randomly.



What is the probability of not picking track 1 atrandom?

Pupils should work collaboratively, in pairs, to answer thesequestions, using whiteboards to record answers.

Ask the pupils, in pairs, to make a new list of their ten titles,then cut them out and put them in a bag. They draw themout, one at a time, and make a list of the titles as theyappear. To maintain the randomness, they will need toreplace the slips after each draw, otherwise theprobabilities will not all remain at 1/10 as the activity

progresses. The teaching assistant may need to supportsome pairs to start promptly and work quickly.

Discuss the idea of randomness with the class and howall outcomes were equally likely.

As a challenge, use a six-sided dice and discuss whether a6 is easier to score than a 3.

Use a ten-sided spinner or dice and let the pupils make alist of their favourite tracks in the order that the spinner/dicegenerates the numbers. Ask pupils to discuss in pairs whatwill happen if the same number comes up before all tenhave been heard and whether the titles put in a bag avoidsthis.

Discuss what the probability will be in random mode of anygiven track if track 1 is no longer available? Track 3? Track10?

Use MP3 player to do the pr groups if there are enoughclass activity. Audio elemenMP3 player grounds the acti

If students struggle with concan be used which demonst

Extension Extend the problem to an MP3 player with 1000 then 2500tracks recorded.

Summarise the results, that if the probability of an eventoccurring is 1/10 then the probability of it not occurring is 9/10and generalise to p and (1 p ).

Ask the pupils, in pairs, to think of some events with givenprobabilities and then give the probability that each event

Use online activities, gamescards to further explore pro

Use of games will nicely finiassessment in lesson 6.



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will not occur (using mini-whiteboards).

Challenge the class to work out the probability that the MP3player, set on random, would play track 1 and then follow itwith track 2.



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ReferencesUnit of work adapted from: http://nationalstrategies.standards.dcsf.gov.uk/node/86822

Essential Learnings QSA Website

Garrick, Barbara (2010) Lecture and tutorial notes.

http://nationalstrategies.standards.dcsf.gov.uk/node/86822http://nationalstrategies.standards.dcsf.gov.uk/node/86822http://nationalstrategies.standards.dcsf.gov.uk/node/86822http://nationalstrategies.standards.dcsf.gov.uk/node/86822


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ADAPTED UNIT



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Table of ContentsAdaptations ......................... ........................... ........................... ........................... ................. ...... ...... ... 20

Introduction ......................... ........................... ........................... ........................... ...... ....... ...... ... 20References .......................... ........................... ........................... ........................... ......................... ...... . 28

Unit description ........................... ........................... ........................... .................... ...... ....... ...... .. 31Strands of Mathematics covered and level ................................................................................ 31Curricular targets .......................... ........................... ........................... ........................... ............. 31

Unit overview ....................... ........................... ........................... .......................... ........................... ...... 32Lesson plans 1-6 ........................ ........................... ........................... .......................... ................... ...... . 33

Lesson 1 ................................................................................................................................... 34Objectives ........................ ........................... ........................... ......................... ...... ...... ..... 34Starter ........................... ........................... ........................... .......................... ........ ...... ..... 34Main activity ......................... ........................... .......................... ...................... ...... ...... ..... 35Conclusion ....................... ........................... ........................... ........................ ...... ...... ...... 35

Lesson 2 ........................ ........................... .......................... ........................... ....... ...... ....... ...... .. 36Objectives ........................ ........................... ........................... ......................... ...... ...... ..... 36Starter ........................... ........................... ........................... .......................... ........ ...... ..... 36Main .......................... ........................... ........................... ........................... ........... ...... ..... 36Conclusion ....................... ........................... ........................... ........................ ...... ...... ...... 36

Lesson 3 ........................ ........................... .......................... ........................... ....... ...... ....... ...... .. 37Objective ........................ ........................... ........................... .......................... ........... ...... . 37Starter ........................... ........................... ........................... .......................... ........ ...... ..... 37Main .......................... ........................... ........................... ........................... ........... ...... ..... 38Conclusion ....................... ........................... ........................... ........................ ...... ...... ...... 38

Lesson 4 ........................ ........................... .......................... ........................... ....... ...... ....... ...... .. 39Objective ........................ ........................... ........................... .......................... ........... ...... . 39Starter ........................... ........................... ........................... .......................... ........ ...... ..... 39Main .......................... ........................... ........................... ........................... ........... ...... ..... 40Conclusion ....................... ........................... ........................... ........................ ...... ...... ...... 40



Resource sheet 1.1 Lesson 1 : Price per gigabyte ........................... .......................... ................... ...... . 44Resource sheet 1.2 Lesson 1 : Scatter Graphs ......................... .......................... ........................... ...... 45Resource sheet 2.1 Lesson 2 : Price per gigabyte ........................... .......................... ................... ...... . 46Resource sheet 2.2 Lesson 2 : Exchange Rates ........................ .......................... .......... ....... ...... ...... .. 47Resource sheet 3.1 Percentage Increases & decreases ........................... ................. ...... ...... ...... ...... . 48Resource sheet 4.1 MP3 Download Worksheet ................................................................................... 49Resource sheet 6.1 student self-evaluation grid .......................... .......................... .......... ...... ...... ...... .. 50



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Unit: MP3 players

Unit descriptionIn this unit students investigate buying and using an MP3 player. They compare different MP3 players,using proportional reasoning.

The students will need access to ICT and, if possible, the internet to research prices and data aboutMP3 players. If the internet is not available, a range of shopping catalogues will provide the sameinformation.

Strands of Mathematics covered and level Fractions, Decimals, Percentages, Ratios, Proportion, algebra, handling data

Target level: Year 9

Curricular targets

Construct simple scatter graphs on paper and using ICT. Essential Learning Data; Collecting and handling data, exploring and presenting data, identifying andinterpreting variation Levels 3,4,5 Queensland Maths Syllabus)

Use the equivalence of fractions, decimals and percentages to compare proportions; calculatepercentages and find the outcome of a given percentage increase or decrease. EssentialLearning Number; Numeration, Number sense, computation, connection, Levels 3,4,5Queensland Maths Syllabus)

Express simple functions in symbols; represent mappings expressed algebraically. EssentialLearning Algebra; Patterns, functions, equivalence, representations Levels 3,4,5Queensland Maths Syllabus)

Construct functions arising from real-life problems and plot their corresponding graphs; interpretgraphs arising from real situations. Essential Learning Data; Collecting and handling data,Exploring and presenting data, Identifying and interpreting variation Levels 3,4,5Queensland Maths Syllabus)

Know that if the probability of an event occurring is p , then the probability of it not occurring is (1 p ). (Essential Learning Chance; Likelihood, judgements Levels 3,4,5 Queensland MathsSyllabus)


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Unit overviewPhase Lesson overview

1 Introduction to the unit (2 lesson) show a video http://www.youtube.com/watch?v=8ZjGpQ10xWE

Introduce the curricular targets and allow some self-assessment against the targets.

Students will also be asked to form small groups (teacher assistance may be necessary)

Ask students to think about how they will begin their investigations. Pair students todiscuss their ideas, Share with the class their ideas. During discussions a glossary of terms and meanings will be created to help all children understand.

During this lesson students in small groups or pairs students will collect the data that theywill use throughout the unit. Initially the data will be represented in table format. Thestudents will be given the option to use pencil and paper or a spreadsheet application torecord the data. In the summary phase the data will be represented using a scatter diagram.

Groups will begin to collect data, students will be given a choice about how they wish torepresent the data to begin with an excel table or paper and pencil table.

23 Main development phase (7+ lessons)

students will work on:

proportionality and ratio

working out percentages without a calculator

constructing equations and solving equations, using graphs

simple probability.

4 Summary links and judgements (1 lesson)

The aim of this lesson is to make links with the other work that students will be doing inmathematics lessons on ratio and proportion and handling data.

Students should have the opportunity for self-assessment against the curricular targetsthrough discussions with the adults in the lesson.

Unit assessment questions (to be given to students in advance)

Resource 1.1 to be used to answer the question: How do you construct a scatter graph andwhat is it telling you?

How do you work out the value added tax (GST) on an MP3 player costing $149.00 (before

tax) bought overseas? If the total cost of an MP3 player decreases by 24%, how would you work out the new price?


Formative assessment will be conducted throughout the lessons. In diverse classrooms students maybe at different levels of the syllabus and hence students should be graded on where they are at. Amatrix will be used to tick off achievements as the teacher catches the students reaching them.

Resources: Internet, shopping catalogues, lesson resource sheets including questions on resourcesheets. Access to computers required. Students asked to bring MP3 players to lesson 5 if they haveone or can borrow one. Other students can use computers loaded with a media player with a randomfeature.

Other useful strategy resources:

Essential Learnings: Year 9
http://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=8ZjGpQ10xWE


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Lesson plans 1-6


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Lesson 1

ObjectivesDiscuss how data relates to the problem.

Gather data from specified secondary sources including printed tables and lists fromICT sources.

Construct scatter diagrams on paper and interpret in context.Essential Learnings Algebra; Students will create tables of values for linear andsimple non linear functions graphing. Data ; Students will understand how data iscollected, and displayed. Data interpretation is simplified through tables, the use of descriptive statistics e.g. scatter plots. Introduction to other graphs. Literacy Glossary of terms and definitions will be created and displayed.

Starter Explore how much students know about MP3 players by asking a range of questions such as these.

Introduction to the unit (one lesson) show videos http://www.youtube.com/watch?v=8ZjGpQ10xWE

http://www.youtube.com/watch?v=2Z8JdV_shak&feature=related

Ask students to think about the following questions



How might we compare MP3 players?

Then students should discuss their ideas in pairs.

Show a video which answers some of the questions:http://www.youtube.com/watch?v=kQXj5yB12QE&feature=related

Go through the questions with students as part of a class discussion:

During discussions a glossary of terms and meanings will be created and written outby each student. This helps all children understand the new terminology but isparticularly helpful for students who have English as a second language as they canalso add the term in their own language.

During the discussion about MP3 players a list of features that could be used tocompare MP3 players will be created. Students will be allowed to use a variety of methods to compare MP3 players to help them engage and so that the learning isstudent centred and negotiated.

Get groups to come up with a hypothesis that matches their chosen method of comparing MP3 players. E.g. the following for memory:

The more expensive the MP3 player, the larger the memory.

Further class discussion on hypothesis Think Pair ShareDiscuss how students might go about testing this hypothesis, including the type andamount of data they should collect. Agree a way to record the data. A sample chartwhich uses gigabytes as a comparison method is given on Resource sheet 1.1.However students will have the option to use a spreadsheet.

Students will also be asked to form small groups (teacher may assign separatetasks if necessary to some group members in order that all students are includedand have the opportunity to be challenged appropriately).

Each group will discuss how they might go about testing this hypothesis, what datawill be collected and how it should be represented and recorded. Show studentsICT examples of how data can be recorded in tables and how that data can berepresented in graphs.
http://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=2Z8JdV_shak&feature=relatedhttp://www.youtube.com/watch?v=kQXj5yB12QE&feature=relatedhttp://www.youtube.com/watch?v=kQXj5yB12QE&feature=relatedhttp://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=8ZjGpQ10xWEhttp://www.youtube.com/watch?v=2Z8JdV_shak&feature=relatedhttp://www.youtube.com/watch?v=kQXj5yB12QE&feature=related


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Main activityClass to work in small groups of 4 students

Students in pairs will be given 20 minutes to collect data, using internet or catalogues (supplied by teacher).

The teaching assistant may need to intervene to help some groups get started. Takea sample of the data from students and record using an interactive board. Discusswith class whether table of data helped to test the hypothesis.

Class discussion on type of graphs that could be used for the data collected. List allthe graphs that the students come up with. Show examples using recognisabledata, of all the graphs types covered by the Essential Learnings

bar chart

line graph

pie chart

scatter graph

Ask which of these would help in testing the hypothesis. Ask students to discuss thisbriefly, in pairs, and agree an answer.

Take feedback and pursue students suggestions for inappropriate graphs, askinghow to label axes and construct the graphs. Encourage students to recognise whyall but the scatter graph are inappropriate.

Work through the creation of a scatter plot with class collaboration put emphasis onwhat goes on the axes and how it is labelled. Draw sample on board or use aninteractive whiteboard.

Refer students to website http://www.amathsdictionaryforkids.com/ look up scatter graph. Teacher to create posters in advance which give students examples of different graphs and how they are used and particular emphasis on scatter graphsand how they are used in real world examples.

Ask students create the scatter graph using the data they collected then use it to

test the hypothesis. Focus students on the labelling and scale on the two axes.Each group will present their findings.

Question to focus on appropriate scale

What scales should we use to help us to position these points accurately?

ConclusionGroups will present their graphs and findings to the class. If some students usedpencil and graph paper and others spreadsheets and electronically created graphsthen also discuss pros and cons of technology versus pencil and paper. Both havetheir place.

Assessment Students will have created a scatter plot to compare size and pricesof MP3 players and presented their findings.

Extension Students may use additional features not used in the first activity to testif their chosen comparison method was the best one.
http://www.amathsdictionaryforkids.com/http://www.amathsdictionaryforkids.com/


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Lesson 2 Adaptation Double period plus one period

ObjectivesUse the equivalence of fractions, decimals and percentages to compareproportions.

Essential Learnings Number ; Financial decisions can be made based on theanalysis of benefits cost-benefit analysis. Literacy Glossary of terms anddefinitions will be created and displayed.

Starter Show a video on cost comparison.

Ask the following question.

A 5 gigabyte (GB) player costs $190. Would a 4 GB player costing $160 be better or worse value for money? How do you know?

Ask student groups, to find two MP3 players from their own lists that are good valuefor money and two that are poor value for money. Ask a few groups to explain their reasoning.

MainWorking in groups (same groups as in Lesson 1). Students will have the help of ateaching assistant.

In this lesson students work collaboratively, in their groups, to find efficient ways of calculating.

Create posters for display around the classroom with examples on comparing itemswith cost and size, cost and number of items.

Students groups are asked to find which MP3 Player in their list is the best value for money in terms of their own criteria. . Explain that they will need to give clear evidence of their method of comparison, and that they should use a calculator asappropriate. Students may use diagrams depicting differences, computer tables,graphs, online reviews (ICT) etc. It is important that students begin to useappropriate terms such as dollars per gigabyte or gigabytes per dollar.

The teacher and the teaching assistant will need to direct groups of students tomake appropriate calculations and interpret the answers when needed. Somestudents may find Resource sheet 2.1 helpful.

Ask each group to compare their methods with another group. Which seems to bethe most efficient method? If both pairs have used the same method, can they find adifferent method?

Collect and record on the board two or three different methods used by students.Ask the class to choose an efficient method for this context.

Create a worksheet in size 16 font giving examples on how to work out dollars per gigabyte. Create Posters for display around the classroom with examples oncomparing items with cost and size, cost and number of items. Give real worldexamples of other items that can be compared before making a purchase.

ConclusionUse the Resource sheet 2.2 (proportion).

Split the class into two groups, with one group working in pairs on question 1 andthe other on question 2. After 5 minutes choose two pairs to explain their methodsfor question 1, and a further two pairs for question 2.

Students will present their comparisons to the class.


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Lesson 3

Objective Essential Learning Numeration, number sense: Students will calculatepercentages and work with real world examples to calculate discounts and priceincreases. Literacy Glossary of terms and definitions will be created and displayed.

Starter Discuss some terms used in respect to percent e.g. discount, Sales Tax, inflation etc.Watch a video about percentage discounts: http://www.teachers.tv/videos/43402Create a work sheet with an appropriate font and size for visually impaired students.Ask students to work in groups to answer the questions on the sheet. The Teacher will ask students open ended questions in order to facilitate and clear up anymisconceptions.

What is 10% of $160? How did you work this out?

What is 5% of $160? How did you work this out?

What is 2.5% of $160? How did you work this out?

What other percentages of $160 can you work out?

Record their examples on the board, using a web diagram to show the links from onepercentage calculation to the next.
http://www.teachers.tv/videos/43402http://www.teachers.tv/videos/43402


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MainClass discussion, collaborative work in groups of fours

Students will work in their groups to complete the worksheet. Solutions will be sharedwith the class. The teacher will work closely with groups to make sure all of thestudents are learning. Calculators are allowed to be used for this activity.

Introduce the following activity (Note The teaching assistant may need to be briefedthat a 15% reduction is the same as 0.85) You and the teaching assistant willneed to provide very clear guidance for any students that are struggling initially. Allowcalculators even for simple calculations.

Jakes mum has an electrical shop selling MP3 players. Business isnt good so shedecides to have a sale and reduces the price of everything by 15%. Jakes mum findsan easy way to reduce each price by just multiplying the original price by a number.What number does she multiply by?

Students will discuss within their groups and do the working out in their workbooks.Encourage peer mentoring for students who are struggling. Assistance may be givenin how to calculate using their calculators. Groups will share their results with theclass.

Extension work:

What would Jakes mum multiply by if she reduced the price of everything by 18%instead of 15%?

To tackle this problem, students need to have generalised from the 15% reductionabove.

What would she multiply by if she was increasing the price of everything by 5%?

Extension Activity given in Resource sheet 3.1

Students should discuss their groups. For groups who are struggling, you couldscaffold the problem by giving them a calculation to do mentally, or with jottings. Theyneed to appreciate that the new price is 85% of the old. The teaching assistant willneed to work through this with some of the pairs. Before summarising, ask each

group to join another group to share their results and challenge thinking. Ask for onespokesperson from each group of four.

What would Jakes mum multiply by if she reduced the price of everything by 18%instead of 15%?

To tackle this problem, students need to have generalised from the 15% reductionabove.

What would she multiply by if she was increasing the price of everything by 5%?


Conclusion Identify some other questions that you would like to explore. Why does Jakes mums method work?

Ask students groups or a member of each group ( jigsaw special needs studentcould do this) to devise some percentage increase and decrease questions to give toanother group to work out. Can they use Jakes mums method?


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Lesson 4

Objective Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations.Essential Learning - Students will understand how data is collected, and displayed.

Data interpretation is simplified through tables, the use of descriptive statistics e.g.scatter plots. Introduction to other graphs. Literacy Glossary of terms anddefinitions will be created and displayed.

Starter Class discussion on what they have already covered in class over the last 3 lessons.Show students a video to review percentages: http://www.youtube.com/watch?v=S-SVpCyJWCs

What are percentages: http://www.youtube.com/watch?v=Wzoc1SafT94&feature=related

The teacher will ask questions (diagnostic assessment) to determine that allstudents are progressing and to determine if any areas need revising. Studentsasked to look at the following website to gain greater understandinghttp://www.amathsdictionaryforkids.com/ and try using a percentage calculator tocheck their results.http://www.math.com/everyone/calculators/calc_source/percent.htm

Revise percentage increases and decreases, using mental methods, by askingquestions as follows -

Decrease a price of $60 by 10%, 15%, 25%, 40%.

Increase a price of $25 by 10%, 5%, 1%.

Ask students to explain their methods for some of them. Ask the following:


http://www.youtube.com/watch?v=S-SVpCyJWCshttp://www.youtube.com/watch?v=S-SVpCyJWCshttp://www.youtube.com/watch?v=S-SVpCyJWCshttp://www.youtube.com/watch?v=Wzoc1SafT94&feature=relatedhttp://www.youtube.com/watch?v=Wzoc1SafT94&feature=relatedhttp://www.amathsdictionaryforkids.com/http://www.math.com/everyone/calculators/calc_source/percent.htmhttp://www.youtube.com/watch?v=S-SVpCyJWCshttp://www.youtube.com/watch?v=S-SVpCyJWCshttp://www.youtube.com/watch?v=Wzoc1SafT94&feature=relatedhttp://www.youtube.com/watch?v=Wzoc1SafT94&feature=relatedhttp://www.amathsdictionaryforkids.com/http://www.math.com/everyone/calculators/calc_source/percent.htm


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Main Class discussion on downloading music and how this can be done.Think individually, Pair discuss with a partner, Share with the class.

After class discussions students will explore the two fictional options for downloading music for the MP3 player.

In this lesson students work collaboratively, in pairs, to solve problems. They willrecord solutions individually. The teaching assistant will need to support less ablepairs of students to get them started on the problems and to draft summaries of their findings.

Students are now going to explore two options for downloading music on the MP3player, and consider the advice they would give about how to select the mosteconomical. Details of the two deals are given on Resource sheet 4.1 . Studentsshould price each option, assuming that the subscription is for one month only.

Give students 10 minutes to complete the table for the first option, Tangent tracks.They should write their answers on the resource sheet. They should write their answers on the resource sheet. The teacher will help out students who are havingdifficulties via observation and open-ended questioning. This activity aids theteacher in assessing the students but assessment is kept informal.

Ask students how they calculated the cost of 100 tracks?

Give a further 10 minutes to complete the table for the second option, Cosine Cuts.

Explain that students will represent the data for both options on the same set of axes and use this graph to consider what would be the most economical deal.

Show video: http://www.teachers.tv/videos/43432 about best phone deals and howto calculate


What scale might you use? (Encourage students to choose their own scales.)

What range and scale for the C -axis? ( C = cost)Students will work in their groups and prepare group responses for questions.Allow students to do this on the computer, the use of ICT may be more stimulating.

Ensure that students understand that they must use a linear scale on each axis.

Give students about 10 minutes to construct and label the graphs of the two options.

Students will make statements about what the graphs tell them and to record whatthey would tell a customer who was thinking about buying some downloaded music.

Conclusion Present the following questions and discuss one of them.Q. What is happening where the two lines cross? How does this inform the advice

that you would give?Q. What difference would it make if the subscription was for two months? three

months?

Ask students to explore the other question for homework.


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Lesson 5

Objectives To work out the probability of an event occurring and to know that if the probabilityof an event occurring is p , then the probability of it not occurring is (1 p ).

Starter Watch quick probability video: http://www.teachers.tv/videos/43442Discuss this question.

What is the probability of picking your favourite song from a player if it is onrandom?

Main Whole-class discussion, collaborative paired work In this lesson students work collaboratively, in pairs, to discuss and recordprobabilities. The teaching assistant will need to support less able pairs in gettingstarted and managing their discussions.

Set the scene, where students have put their favourite albums onto their MP3player. The students pick their ten favourite songs at first. Get them to list them and

number the list from 1 to 10.Say that there is a random button on an MP3 player that lets the MP3 player play10 tracks randomly.



What is the probability of not picking track 1 at random?

Students should work collaboratively, in pairs, to answer these questions, usingwhiteboards to record answers.

Ask the students, in pairs, to make a new list of their ten titles, then cut them outand put them in a bag. They draw them out, one at a time, and make a list of thetitles as they appear. To maintain the randomness, they will need to replace theslips after each draw, otherwise the probabilities will not all remain at 1/10 as theactivity progresses. The teaching assistant may need to support some pairs to startpromptly and work quickly.

MP3 players can also be used to do this activity. Start play on a play list of tensongs mark in a table which song is played. Restart play list and repeat 10 times.

Discuss the idea of randomness with the class and how all outcomes wereequally likely.

As a challenge, use a six-sided dice and discuss whether a 6 is easier to scorethan a 3.

Use a ten-sided spinner or dice and let the students make a list of their favouritetracks in the order that the spinner/dice generates the numbers. Ask students todiscuss in pairs what will happen if the same number comes up before all ten havebeen heard and whether the titles put in a bag avoids this.

Discuss what the probability will be in random mode of any given track if track 1 isno longer available? Track 3? Track 10?


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Conclusion Extend the problem to an MP3 player with 1000 then 2500 tracks recorded.Summarise the results, that if the probability of an event occurring is 1/10 then theprobability of it not occurring is 9/10 and generalise to p and (1 p ).

Ask the students, in pairs, to think of some events with given probabilities and thengive the probability that each event will not occur.

Challenge the class to work out the probability that the MP3 player, set on random,would play track 1 and then follow it with track 2.

Use online activities, games such as ludo, snakes and ladders and cards to further explore probability and chance.


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Lesson 6

ObjectivesTo reflect on the unit of work and write two targets for further development for eachstudent.

Starter

Give students a copy of Resource sheet 6.1 and explain that during the lesson they

will need to assess their understanding of each of the objectives. Explain thatstudents should devise their own examples to illustrate what they are able to do (or provide some problems for students to work on).

MainIndividual working and self-assessment within pairs

Focus for learning conversations

During this part of the lesson, students should have learning conversations with theteacher or teaching assistant, focused on Resource sheet 6.1 and the questions onthe resource sheets. The following (taken from the Essential Learnings) may beuseful questions to assess students progress towards the stated objectivesinformally. Encourage the teaching assistant to select the appropriate promptscarefully, to suit the students current levels of understanding.

Construct simple scatter graphs, on paper and using ICT.How do you construct a scatter graph and what is it telling you?

Whats important when choosing the scale for the graph?

Is this graphical representation helpful in addressing the hypothesis? If not, whyand what would you change?

Use the equivalence of fractions, decimals and percentages to compareproportions; calculate percentages and find the outcome of a givenpercentage increase or decrease.

Which sets of equivalent fractions, decimals and percentages do you know?

From one set that you know (e.g. 1/10 0.1 10%), which others can you deduce?

Talk me through how you would increase/decrease a price of 12 by, for example,15%. Can you do it in a different way? How would you find the multiplier for differentpercentage increases/decreases?

The answer to a percentage increase question is 10. Make up an easy question.Make up a difficult question.

Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations.

What do the axes represent?

In the context of this problem, does every point on the line have ameaning? Why?

What does this point on the graph represent?

What does this part of the graph represent?

What sort of questions could you use your graph to answer?

ConclusionUse the Conclusion to give students opportunities to talk about what they havelearned during the unit of work and what they have found difficult, using the learningobjectives detailed on lesson 6 resource sheet as a focus. Encourage them to talkabout how they can transfer the skills learnt back into other mathematics lessons.

Based on students responses and their traffic lighting on lesson 6 resource sheet,ask students to write two targets for future development. The teaching assistant willneed to support many of the students in setting targets for future work alongside theteacher.


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Resource sheet 1.1 Lesson 1 : Price per gigabyte

MP3 player name Number of gigabytes (GB) Cost ()

12

3

4

5

6

7

8

9

10

11

12

13

14

15

Questions

Was your graph what you were expecting? If you were to buy a player for $200 how many gigabytes would

you expect? If a player had 4 gigabytes, how much would you expect to pay?


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Resource sheet 1.2 Lesson 1 : Scatter GraphsKatie recorded the heights and the lengths of the strides of ten boys inher form. These are the results.

Height (cm) 170 172 175 173 172 177 176 175 182 181Length of stride (cm) 87 89 86 91 92 91 94 90 94 96

1. Complete the scatter diagram below to show these results.The first four points have been plotted.

2. Comment on the relationship between the height and the length of stride for the ten boys.



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Resource sheet 2.1 Lesson 2 : Price per gigabyteMP3 player name Number of

gigabytes (GB)Cost ($) Cost per gigabyte

12

3

4

5

6

7

8

9

10

11

12

13

14

15

Questions

Which MP3 player is the best value for money? What other method could you use to find the best value for money

MP3 player? Would you buy this MP3 player?



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Resource sheet 2.2 Lesson 2 : Exchange Rates

The table show the exchange rates between Australian dollars and USdollars and Euros.

A$1 =USD ($) .93Euro () .68

1. A tourist is travelling to New York. She changes A$650 into USdollars (US$). How much does she get? (2 marks)

2. A German company is buying goods in Australia. They change2000 euros () into Australian Dollars ($). How much will they get

(to the nearest dollar)?

Question 2

A breakfast cereal is available in two sizes.

95c

$1.68

1. Work out the cost of 100 g of Wheat Pops when bought in the400g box (to the nearest cent).

2. Work out the cost of 100g of Wheat Pops when bought in the 750gbox (to the nearest cent).

3. Which is better value?


400 g750 g

WheatPops Wheat

Pops


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Resource sheet 3.1 Percentage Increases & decreasesQuestion 1(a) A new breakfast cereal is sold in boxes as shown below. What isthe volume of the box?

1. To promote the cereal, the company is offering 10% extra free.What is the new volume?

2. A new designer suggests adding 10% to all dimensions to makethe box. Would this work? Explain your answer.

Question 2An MP3 player is priced at 65. In a sale, the price is reduced by 15%.What is the new price?


25 cm

15 cm

8 cm


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Resource sheet 4.1 MP3 Download Worksheet

Tangent tracks

$20.00 per month and 50cents per downloadNumber of songsdownloadedduring onemonth ( N )

1 2 3 4 5 6 10 100

Cost ( C ) $20.50

Equation: C =

Cosine cuts$17 per month and 70cents per download

Number of songsdownloadedduring onemonth ( N )

1 2 3 4 5 6 10 100

Cost ( C ) $17.70

Equation: C =

Construct graphs for both options, using the same set of axes. Where do the graphs meet? What does this point of intersection mean? Which download service would you use? Why?



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Resource sheet 6.1 student self-evaluation grid

7801 eps adapted unit

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