Course Profile Mathematics, Locally Developed, Grade 10, Public

Unit 3: Home Entertainment

Time: 25 hours

Activity 1 | Activity 2 | Activity 3 | Activity 4 |

Activity 5 | Activity 6 | Activity 7 | Activity 8

Unit Description

Students investigate mathematical principles and applications in the context of real-life situations. They develop a greater understanding of fixed and variable rates in a financial context. Students use measurement and data collection skills to enhance their understanding of design, scale diagrams, and proportionality. The Pythagorean theorem is applied to solve real-life problems. By using appropriate technology and/or traditional methods, students construct, read, and interpret charts and tables as well as identify relationships, make inferences, and communicate observations. Opportunities for students to practise estimation skills and to judge the reasonableness of answers are provided throughout the unit.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: PRV.01, .02, MEV.01, .02, .04, GPV.02.

Specific Expectations: PR1.01, 1.02, 2.01, 2.02, 2.04, 2.05, 2.07, ME1.03, 2.05, 4.01, 4.02, 4.03, 4.04, GP2.01, 2.03, 2.04.

Activity Titles (Time + Sequence)

The following outline is a suggested sequence, with timing, for teaching Unit 3. These activities are designed to make sense of mathematics by working through concrete experiences to develop a degree of understanding of the various concepts. These activities are largely teacher-directed. Working with a partner is often done as parallel work where students provide support and encouragement for one another. The need for remediation and skill development can be addressed as it arises throughout the unit. The suggested timing should allow ample opportunity for task completion. An additional 300 minutes has been allowed for skill development throughout the unit. Design is an important component in the Grade 12 Workplace course and personal financial applications are a major component in the Grade 11 Workplace course. Much of the skill development in this unit is preparatory in nature for these future courses.

Activity 1	A Place for My Stuff (measurement; design; proportionality)	225 minutes
Activity 2	Where is the Remote? (numeracy; data analysis)	75 minutes
Activity 3	Did Pythagoras Watch TV? (Pythagorean theorem; proportionality; data analysis)	75 minutes
Activity 4	How Much Does This Really Cost? (numeracy; spreadsheet software; data analysis)	75 minutes
Activity 5	Let’s Get Organised (measurement; design; proportionality)	150 minutes
Activity 6	Dress It Up (measurement; numeracy; data analysis)	150 minutes
Activity 7	If I Had a Million Dollars! (data collection)	150 minutes
Activity 8	Summative Activity	300 minutes

*300 minutes: Time for instruction and skill consolidation or extension activities where required throughout the unit.

Prior Knowledge Required

Students arrive in the classroom from varied backgrounds with a wide range of skills. Measurement skills, data collection and analysis, numeracy skills and informed decision-making continue to be developed.

Unit Planning Notes

· This unit incorporates many concrete materials that must be organised prior to each activity.

· There are opportunities to use spreadsheet software and word processors.

· Some of the activities are completed over a number of days and involve keeping track of materials. Student folders would be very helpful.

· If completed work is organised in a portfolio, it will be very useful when completing the summative activity at the end of this unit. It can also be used while preparing for Unit 6.

Teaching/Learning Strategies

This unit requires flexibility of timing, while at the same time it requires structure so that students are engaged in meaningful tasks. Much of the work can be assessed formatively in preparation for the culminating performance task. Time has been built into the activities to address these needs and an additional 300 minutes is allotted for use as required at the teacher’s discretion.

Assessment and Evaluation

There are opportunities for assessment in all four Categories of the Achievement Chart in this unit. Many opportunities are available to collect data about Learning Skills. The summative assessment activity involves a performance task and a paper and pencil test.

Resources

Kelly, B. Measurement. Toronto: Queen’s Printer for Ontario. 1999.

Kelly, B. Geometry & Spatial Sense. Toronto: Queen’s Printer for Ontario. 1999.

Kelly, B. Data Management & Probability. Toronto: Queen’s Printer for Ontario. 1999.

Flewelling, G., and C. Lemenchick. Mathematics Assessment Grade 8. Vancouver: Gage. 1997.

Saunders, H. When Are We Ever Gonna Have to Use This? Palo Alto, CA: Dale Seymore Publications. 1988.

Activity 1: A Place for My Stuff

Time: 225 minutes

Description

In this activity, students measure dimensions of the classroom and all its relevant furnishings, then create a scale diagram. Templates of the objects are used to aid in the design of possible layouts.

Strand(s) and Expectations

Strand(s): Measurement, and Geometry and Proportionality

Overall Expectations: MEV.02, .04, GPV.02.

Specific Expectations: ME2.05, 4.02, 4.03, GP2.01, 2.03.

Planning Notes

· Students require tape measures, graph paper, coloured paper (for templates), rulers, scissors, glue, and envelopes.

· Copies of Rubric for Assessing and Evaluating Scale Diagrams (Appendix A) is to be provided for all students. A copy of this rubric should also be posted in the classroom.

· The teacher or the students prepare a sheet for recording the data gathered from classroom measurements.

· Wherever possible, provide opportunities for students to practise estimation skills and judge the reasonableness of their answers.

Teaching/Learning Strategies

Student activity

Students:

· work in pairs to complete this activity;

· measure and record the outer dimensions of the classroom;

· round off measurements to the appropriate unit;

· create an appropriate scale diagram of the classroom;

· estimate, then measure and record the relevant dimensions of all desks, filing cabinets, and other classroom furnishings;

· create colour-coded scale templates of appropriate furnishings (since this is a multi-day project, store templates in an envelope);

· manipulate the templates within the diagram to create different, workable classroom layouts;

· decide on their preferred layout and use it to create a final scale diagram;

· justify the rationale for their choices (one submission per pair of students).

Teacher facilitation

· A class discussion on the arrangement of furniture with respect to amount and type of furniture, room area, traffic flow, door and window placement, etc. could lead into this activity.

· The teacher should distribute and discuss Rubric for Assessing and Evaluating Scale Diagrams (Appendix A).

· Assist students to measure the dimensions of the classroom.

· With the students, construct an accurate scale drawing of the empty classroom noting the location of the door, window, boards, etc.

· Instruct students to estimate the relevant dimensions, then measure the furniture (desks, filing cabinets, etc.) in the classroom. Determine the required quantity of each item. This information is recorded in a chart (see sample worksheet).

· The teacher assists the students as needed in creating the templates and in producing the final diagram and layout. This process involves making templates of all furniture, exploring possible arrangements of the furniture and producing a final scale diagram to submit with oral and/or written justification of the chosen design.

Assessment/Evaluation Techniques

The Rubric for Assessing and Evaluating Scale Diagrams (Appendix A) can be used to assess the scale diagram produced by the students. The students could use the rubric to self-assess their work before submission. As the students work, observations of Teamwork and Initiative can be recorded by the teacher.

Sample Worksheet

Item	Estimated Relevant Dimensions	Measured Relevant Dimensions	Quantity
filing cabinet
student desks

Activity 2: Where is the Remote?

Time: 75 minutes

Description

In this activity, students investigate the costs of various television program packages. Monthly rates are used to make comparisons between cable costs and satellite system costs over a five-year period.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: PRV.01,.02, MEV.04, GPV.02.

Specific Expectations: PR1.01, 2.01, 2.04, ME4.04, GP2.01, 2.04.

Planning Notes

· Update the various costs used on the worksheets where appropriate.

· Prepare the worksheets.

Teaching/Learning Strategies

Student activity

Students:

· calculate and compare the 1-year costs and 5-year costs of various cable television and satellite packages;

· prepare a time-cost graph for a cable package and its corresponding satellite package and analyse the graph;

· speculate reasons why people invest in the different program packages (cable vs. satellite).

Teacher facilitation

· Initiate a class discussion of the advantages and disadvantages of cable TV programming costs versus purchasing a satellite dish.

· Assist students to calculate the 1-year and the 5-year costs of the Basic cable program option and the Basic satellite program option on worksheet 1.

· Discuss the differences in the 1-year and the 5-year costs between the cable and the satellite options.

· Worksheet 1 will be completed by the students, which leads them to make financial comparisons of other cable and satellite packages and interpret the results. (For 1-year, cable is less expensive; for 5-years, satellite is less expensive.)

· Assist the students (sample worksheet 2) to graph the comparison of rates for the Basic cable and satellite options. Graph time on the horizontal axis and total cost on the vertical axis. Discuss the appropriate scale and spacing for the axes.

· Discuss the meaning of the intersection point and during which time interval one package is more cost effective than the other.

· Students select a different cable package and its corresponding satellite package and prepare the graph and answer the questions as above.

· Circulate throughout the room to assist students as required.

· This activity could be completed using Quattro Pro spreadsheet software. This would provide a simple introduction to the software for those students who are unfamiliar with it.

Assessment/Evaluation Techniques

A quiz could be used to assess Knowledge/Understanding of the numeracy and graphing skills using an objective marking scheme. Communication could be assessed for the degree of clarity of the explanation, orally or in written form. Question 5 on worksheet 2 provides an opportunity for student self-assessment.

Sample Worksheet 1

Name of cable TV package	Initial Set-Up Cost ($)	Monthly Rate ($)	Total 1-year Cost ($)	Total 5-year Cost ($)
Basic	75	24.95
Deluxe	75	35.50
Deluxe + Movies	75	52.50
“The Works”	75	74.75

Name of satellite TV package	Initial Set-Up Cost ($)	Monthly Rate ($)	Total 1-year Cost ($)	Total 5-year Cost ($)
Basic	230	18.50
Deluxe	230	31.19
Deluxe + Movies	230	49.25
“The Works”	230	70.50

When is it less expensive to have cable TV services instead of satellite services?

Sample Worksheet 2

COMPARISON OF CABLE AND SATELLITE COSTS – BASIC PACKAGE

total cost ($)

This scale will go

from $0 to $1600

for this example.

It is suggested that

encrements of

$100 be used.

0 1 2 3 4 5 time (years)

1. Approximately where do the lines intersect?

2. What does this point of intersection represent?

3. For what time interval is cable TV less expensive?

4. Choose any other package from the chart and make your own graph and answer the above questions about your graph. Think about what scale will be appropriate for your graph.

5. What have you learned about cable TV package costs and satellite package costs that will help you decide which is best for you some day? What questions will you want to have answered when it is time to make the decision for your own TV?

Activity 3: Did Pythagoras Watch TV?

Time: 75 minutes

Description

In this activity, students apply the Pythagorean theorem to television design and marketing. Students make simple calculations and analyse these results to draw conclusions.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: PRV.01, .02, MEV.01, .04, GPV.02.

Specific Expectations: PR1.01, 2.01, 2.07, ME1.03, 4.01, 4.04, GP2.01, 2.04.

Planning Notes

· Provide flyers/advertisements from local television retailers.

· Prepare worksheet.

· Students require calculators.

Teaching/Learning Strategies

Student Activity

Students:

· investigate the dimensions of standard television screen sizes;

· apply the Pythagorean theorem to determine the height of a television screen given the measurement of the diagonal and the width;

· determine the ratio between the television screen’s width and height;

· round off where necessary;

· draw conclusions about the dimensions of standard television screens;

· hypothesize reasons for marketing televisions using the length of the diagonal.

Teacher Facilitation

· A discussion about television sizes could end by informing students that the advertised dimension of a television is the diagonal of the screen. Speculate on reasons for this marketing strategy.

· Assist the students in completing the first row of the chart (round off all calculations to one decimal place accuracy):

a) Use the Pythagorean theorem to calculate the height of the first television.

b) Reduce the width: height ratio of the dimensions to a “decimal value:1” ratio.

· Students finish the chart and use these results to complete a series of questions. If the calculations have been completed correctly, students discover that a television’s width: height ratio reduces to a 1.33:1 ratio. (The technical name for this is a “4:3 ratio”. Spend time discussing how to convert these ratios).

· Circulate throughout the room as students work to provide assistance as required.

· An extension activity could be to apply the newer 16:9 “Aspect Ratio” to television design.

Assessment/Evaluation Techniques

Application, Communication, and Problem Solving can be assessed in this activity. Assess Application of the Pythagorean theorem using an objective marking scheme. Assess Problem Solving and Communication by assessing the answer to question 3 on the worksheet. Work Habits could be observed throughout the activity.

Sample Worksheet

All given measurements are in inches.

Television “advertised as” (screen diagonal)	Television Screen Width	Television Screen Height (round off to one decimal place accuracy)	Width: Height Ratio (_____: 1, accurate to 2 decimal places)
13"	10.4"
19"	15.2"
27"	21.6"
32"	25.6"
36"	28.8"
43"	34.4"
55"	44.0"

1. Which dimension of the television screen is the largest? Explain how this influences the retailer’s marketing strategy.

2. a) A television has a screen height of 10.2. Use the width: height ratio to determine the width of the television.

b) What would be the length of the diagonal of this television?

3. Given a television with screen width of 23.2, determine how this TV would be advertised. Explain your reasoning.

Activity 4: How Much Does This Really Cost?

Time: 75 minutes

Description

In this activity, students compare the total costs of purchasing a television in one initial payment versus paying with monthly installments. Different installment plans are explored using spreadsheet software. Conclusions about advantages and disadvantages of the different payment plans are drawn.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: PRV.02, MEV.04, GPV.02.

Specific Expectations: PR2.01, 2.02, 2.04, 2.05, ME4.04, GP2.01, 2.04.

Planning Notes

· Prepare worksheets for students using a variety of monthly payment plans for a new television.

· Computers with Quattro Pro spreadsheet software are required.

Teaching/Learning Strategies

Student activity

Students:

· use spreadsheet software to calculate the total costs of different monthly payment plans;

· analyse results of different payment options to draw conclusions about total costs.

Teacher facilitation

· Initiate a class discussion of the advantages and disadvantages of paying in full for items at the time of purchase versus instalment purchasing.

· Have students estimate which payment option on the handout provides the best and the worst deal and have them justify their reasoning.

· Students enter data regarding different payment models into a spreadsheet program. There are two possible options:

· The cash prices could be given including tax (sample worksheet 1).

· The cash prices could be given and tax calculated within the spreadsheet (sample worksheet 2).

· Students record the total cost of the television including interest paid (in dollars) under each payment plan on their worksheet.

· Students draw conclusions about how different payment plans affect the total cost of items purchased.

· Students complete questions on their worksheet analysing spreadsheet results.

· An extension for this lesson includes a comparison of different interest rates on bank loans to purchase the television.

· Circulate throughout the room to assist students as required.

Assessment/Evaluation Techniques

Knowledge/Understanding of the calculation of instalment payments and the calculation of sales tax can be assessed using an objective marking scheme. Communication can be assessed using the explanation of the results. Work Habits and Organisational Skills could be observed and assessed while students complete the activity. Independence could be observed as students use the spreadsheet software.

Sample Worksheet 1

This is a sample of a page completed using spreadsheet software. The cash price includes tax and the calculations are done to determine the total cost and the interest paid using instalment payments. The spreadsheet could be set up as a template with the spacing, headings, and formulas in place so that students could enter the Item, Retailer, Monthly Instalment, Number of Months and Cash Price in the appropriate columns for each entry. They could then copy the answers onto a chart like the one in worksheet 3 and use the information to answer the questions about instalment buying.

	A	B	C	D	E	F	G
1	Item	Retailer	Monthly Instalment ($)	Number of Payments	Total Cost of Instalments ($)	Cash Price including tax ($)	Interest Paid ($)
2
3	27"TV	Eastside TV Sales	120	12		1100
4	27"TV	Eastside TV Sales	90	18		1100
5	27"TV	Eastside TV Sales	75	24		1100
6	24"TV	Westlane Furniture	90	12		750
7	24"TV	Westlane Furniture	75	15		750
8	24"TV	Westlane Furniture	65	18		750

1. Label the rows 1 to 8 and the columns A to G.

2. The formulas used are in columns E and G.

3. In column E, the values are obtained by multiplying the value in the same row in column C by the value in the same row in column D. The entry in cell E3 is “+C3*D3”. This cell is copied and then pasted into the other cells in column E.

4. The entry in cell G3 is “+E3-F3”. This cell is copied and then pasted into the other cells in column G.

5. Explain how lowering the monthly payment affects the total cost.

6. Why do retailers offer payment plans?

Sample Worksheet 2

This is a sample of a page completed using spreadsheet software. The cash price does not include tax and the calculations are done to determine the tax owing, the total cost and the interest paid using instalment payments. The spreadsheet could be set up as a template with the spacing, headings, and formulas in place so that students could enter the Item, Retailer, Monthly Instalment, Number of Months and Cash Price in the appropriate columns for each entry. They could then copy the answers onto a chart like the one in Worksheet 3 and use the information to answer the questions about instalment buying.

	A	B	C	D	E	F	G	H	I
1	Item	Retailer	Monthly Instal-ment ($)	Number of Pay-ments	Total Cost of Instal-ments ($)	Cash Price before tax ($)	Sales Tax (15%) ($)	Cash Price Including Tax ($)	Interest Paid ($)
2
3	27" TV	Eastside TV Sales	120	12		1000
4	27" TV	Eastside TV Sales	90	18		1000
5	27" TV	Eastside TV Sales	75	24		1000
6	24" TV	Westlane Furniture	90	12		715
7	24" TV	Westlane Furniture	75	15		715
8	24" TV	Westlane Furniture	65	18		715

1. Label the rows 1 to 8 and the columns A to I.

2. The formulas used are in columns E, G, H, and I.

3. In column E, the values are obtained by multiplying the value in the same row in column C by the value in the same row in column D. The entry in cell E3 is “+C3*D3”. This cell is copied and then pasted into the other cells in column E.

4. The entry in cell G3 is “+F3*.15”. This cell is copied and then pasted into the other cells in column G.

5. The entry in cell H3 is “+F3+G3”. This cell is copied and then pasted into the other cells in column H.

6. The entry in cell I3 is “+E3-H3”. This cell is copied and then pasted into the other cells in column I.

7. Explain how lowering the monthly payment affects the total cost.

8. Why do retailers offer payment plans?

Sample Worksheet 3

Teaching note: This can be used to do the calculations without the use of a spreadsheet. It could also be used for the students to copy their answers from the spreadsheet as they complete the calculations.

A television costs $1100, but may be purchased through instalment payments. Calculate the total cost of this television, and interest paid (in dollars) under each payment plan:

Television $1100 (cash price including taxes)

Monthly Instalment	Number of Payments	Total Cost of Television ($)	Interest Paid ($)
$120	12	120 x 12 = 1440	1440 – 1100 = 340
$90	18
$75	24

1. Explain how lowering the monthly payment affects the total cost.

2. Why do retailers offer payment plans?

Activity 5: Let’s Get Organized

Time: 150 minutes

Description

In this activity, students design and make a scale drawing of a home entertainment centre. Students create templates of the entertainment items. Students create a scale drawing of the entertainment centre that will hold the entertainment items.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: PRV.01, MEV.02, .04, GPV.02.

Specific Expectations: PR1.01, 2.04, ME2.05, 4.03, 4.04, GP2.01, 2.04.

Planning Notes

· Prepare overhead transparency of graph paper.

· Prepare worksheet.

· Students require graph paper, rulers, scissors, and Bristol board.

Teaching/Learning Strategies

Student activity

Students:

· complete worksheet;

· make scale drawings and templates of all items to be stored in the entertainment centre;

· make a scale drawing of the final entertainment centre.

Teacher facilitation

· Discuss with students home entertainment options.

· For this activity, one item to be stored in the entertainment centre is a television. Each student may select at least two additional items from the worksheet to be stored in their own entertainment centre.

· The dimensions of the entertainment centre are fixed. The width is 130 cm and the height is 95 cm.

· The dimensions of the television options given on the worksheet are the actual measurements of the screen and the cabinet. In order to fit into the entertainment centre a clearance of 5 cm on each side and 12 cm at the top are required. Fill in the missing dimensions on the worksheet for each television. (These same clearances are required for all of the items.)

· Determine an appropriate scale to use with all items. (If centimetre square graph paper is used, a suggested scale is 1 cm = 5 cm.) Use an overhead transparency of the graph paper to make a scale diagram of a television. Cut out the diagram of the television. Trace the dimensions of the television onto Bristol board. Cut out the template of the television from the Bristol board to use on the overhead projector.

· Students repeat this process to create templates of at least two other items for their entertainment centre.

· Students make an arrangement of the entertainment templates to be enclosed into their entertainment centre and glue the templates in this arrangement onto graph paper.

· It is assumed that interior shelves (horizontal) and walls (vertical) separate the templates. Students draw the interior shelves and walls of the entertainment unit on their diagram. (Thickness of the shelves and walls is allowed for when students add the 5 cm or 12 cm allowances around each item.) Teachers should assist students as needed with any calculations or design suggestions as they circulate throughout the room.

Assessment/Evaluation Techniques

Application of the skills for scale drawing can be assessed using the Rubric for Assessing Scale Diagrams, Appendix A. Students could use the rubric to self-assess or to peer-assess their drawing before submission. Problem Solving and Communication can be assessed by observing students as they complete the assignment and by assessing the entertainment centre arrangement for meeting the given criteria and appropriateness of selection of items to be included. A Level 4 solution would also include suggestions for use for any unused space.

Sample Worksheet

Entertainment Item	Width (cm)	Width including Clearance (Width + 5 cm + 5 cm)	Height (cm)	Height including Clearance (Height + 12 cm)
Television	63	63 + 5 + 5 =	55	55 + 12 =
VCR	43		9
DVD	43		10
stereo	34		17
bookshelf speakers	33		19
centre channel speaker	43		17
video game system	26		5

Activity 6: Dress It Up

Time: 150 minutes

Description

In this activity, students investigate the process of redecorating the classroom. Students take accurate measurements of key features of the classroom and then determine the amount and cost of materials required.

Strand(s) and Expectations

Strand(s): Measurement, Geometry and Proportionality

Overall Expectations: PRV.01, MEV.04, GPV.02.

Specific Expectations: PR1.02, ME4.02, 4.04, GP2.01, 2.04.

Planning Notes

· Provide metric tape measures for students to measure a series of lengths.

· Students work in pairs or in small groups.

· Catalogues and/or flyers of home renovating and decorating materials may be used.

Teaching/Learning Strategies

Student activity

Students:

· work in pairs or in small groups to measure the dimensions required to complete the activity;

· use formulas to determine the quantity of materials needed to paint walls, replace ceiling tiles, replace floor tiles, and replace baseboards;

· investigate the cost of materials, select appropriate materials and calculate the total cost of the project;

· record their work on provided charts.

Teacher facilitation

· Brainstorm ideas about what could be done to redecorate the classroom.

· Assist students to determine what measurements in the classroom need to be recorded (e.g., walls, ceiling, door) and to create the worksheet that will record the measurements (see sample
worksheet 1)

· Observe while students measure and record certain classroom dimensions (e.g., length, width, height of room, dimensions of doors, windows, cabinets or any other features unique to the room).

· Help students recall the method used to determine the perimeter and the area of a rectangle.

· Discuss with students what will be painted, carpeted, tiled, etc.

· Distribute flyers so students can investigate the cost of materials.

· Assist students in making reasonable choices to determine the cost of materials. While no budgeting is included in this activity, consistent choice of high-priced materials is not always feasible (see sample worksheet 2).

· Students should understand that they cannot purchase partial cans of paint, rolls of wallpaper, etc.

Assessment/Evaluation Techniques

An additional question or quiz could be used to assess Knowledge/Understanding and Application of measurements and calculations using an objective marking scheme. The teacher could observe Problem Solving as the students work selecting measuring tools, making choices and drawing conclusions.

Resources

Barry, Bill. The Real Game. New Brunswick: The Real Game Inc., 1998.

Schulz, Vicki. Life-Project. Toronto: Exclusive Educational Products, 1996.

Sample Worksheet 1

Section of the Room	Dimensions (to nearest m)	Area
Floor/Ceiling	e.g., 8 m x 5 m	8 x 5 = 40 m^2
Wall 1 (there are 2 of them)	e.g., (8 m x 3 m) x 2	8 x 3 x 2 = 48 m^2
Wall 2 (there are 2 of them)
Door
Window

Sample Worksheet 2

Material Costs

Material	Amount Required	Cost per unit ($)	Cost ($)
Paint		1 litre costs ______ and covers 15 m^2: number of cans required_______
Baseboard		________ per linear metre
		Total Cost ($)

Activity 7: If I Had a Million Dollars!

Time: 150 minutes

Description

In this activity, students design a survey relating to home entertainment options, collect and organise the data and use their results when making decisions in the summative activity.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: MEV.04, GPV.02.

Specific Expectations: ME4.03, GP2.04.

Planning Notes

· Gain access to computers if the students are going to word process the survey.

· Advertisement flyers or catalogues could be made available.

· This activity allows for the development and practise of skills required for the Grade 10 Test of Literacy and Numeracy (reading tables, etc.).

Teaching/Learning Strategies

Student activity

Students:

· make a list of items people might have in a home entertainment room;

· design a checklist-style survey sheet;

· collect data from people other than their classmates;

· add the data to a tally sheet with all of their classmates’ results;

· rank the results of the survey;

· use the results in the unit summative activity.

Teacher facilitation

· With the students, draw on previous discussions to produce a list of items people might have in a home entertainment room. Advertisement flyers and catalogues could be used to help provide ideas (e.g., stereo, television, pool table, sofa, chair, etc.).

· This list will be the basis for a checklist-style survey sheet (see sample worksheet).

· Students either create their survey sheet by hand or use a word processor.

· Before the next class, students ask 5 – 10 people to select their three favourite choices for inclusion in the entertainment room. Discuss bias of survey and sample population in order to have a fair survey.

· Assign a point value to each selection (e.g., a rating of 1 gets 5 points, a rating of 2 gets 4 points, etc.).

· Tabulate the class results on chart paper or on the blackboard.

· As a class, total the survey tallies and rank them from most popular to least popular.

· Each student should copy the results into their notebook for use in the unit summative activity.

Assessment/Evaluation Techniques

Assess Communication for clarity, and summary of findings. Assess Knowledge/Understanding from the accuracy and organisation of the tallies.

Resources

Kelly, B. Data Management & Probability. Toronto: Queen’s Printer for Ontario. 1999.

Sample Worksheet

Read the following list and rank, in order, your five favourite items for

inclusion in a home entertainment room.

television	loveseat
stereo	couch
CD player	bookshelf speakers
DVD player	stand-alone speakers
video games	amplifier
air hockey	fridge
pool table	telephone
VCR	coffee table
chair	end table

Activity 8: Summative Activity

Time: 300 minutes

Description

In this activity, students use scale drawing, the Pythagorean theorem, measurement, cost calculations and interpretation of a survey to complete the unit summative activity.

Strand(s) and Expectations

Strand(s): Patterns and Relationships, Measurement, Geometry and Proportionality

Overall Expectations: PRV.01, .02, MEV.01, .04, GPV.02.

Specific Expectations: PR1.01, 1.02, 2.01, 2.04, ME1.03, 4.01, 4.02, 4.04, GP2.01, 2.04.

Planning Notes

· It is suggested that the activity be separated into six worksheets. They could be completed in any order. This is the type of summative assessment/evaluation task that will be given at the end of the course. To help organise the students’ work, a sample student recording sheet is provided in Appendix C.

· As a worksheet is completed and submitted, it could be:

· checked off on a class list as completed;

· placed in a student folder with a checklist on the front for tracking completed work.

· Determine at the start of this activity if students will use a portfolio, notebook, study sheet, etc. as support for completing the assignments.

· Prepare worksheets and record sheets.

· Students will need rulers, scissors, glue, calculators, centimetre square graph paper, and Bristol board.

· Encourage students to constantly judge the reasonableness of their answers.

· Prepare “Rubric for Assessing and Evaluating Worksheet A – Appendix B”.

Teaching/Learning Strategies

Teacher facilitation

· Organize supplies.

· Discuss Rubric for Assessing and Evaluating Worksheet A – Appendix B.

· Remind students of support materials that may be used.

· Worksheet A will need much of the allotted time.

· Reminders to keep organised and to complete all work may be helpful for some students.

· The teacher circulates around the room as students work to provide support and encouragement.

Assessment/Evaluation Techniques

Much of the assignment can be assessed for Knowledge/Understanding using an objective marking scheme. A rubric is included to assess Worksheet A for Knowledge/Understanding, Application and Communication, Worksheet D question 3 can be assessed for Communication and Worksheet F question 2 can be assessed for Problem Solving.

Sample Worksheets

Sample Worksheet A

You are designing an entertainment room for ____________________ (a family, a group of teenagers), fill in the blank with the name of the target group from the previous activity.

1. In your class survey, what were the top three items people said they wanted in an entertainment room?

(i) __________________________________

(ii) _________________________________

(iii) _________________________________

2. What three other items would you choose for an entertainment room? Why do you feel it is necessary to include these items?

Choice	Reason for Your Choice
1.
2.
3.

3. The room is 6 m long and 5 m wide. It has 2 doors 0.75 m wide. You decide where they are located. On a sheet of cm square graph paper, draw the outline of your room using the scale: 4 cm = 1 m.

Here are some dimensions and items that could be included in your room. Locate the ones that you listed in questions 1 and 2 and cut out scale templates for each. Decide how many of each you will need.

Item	Cost	Number of Items (templates required)	Dimensions of Item (floor space needed)	Dimension of Scale Templates (1 cm = 25 cm)
Sofa	$650		200 cm x 90 cm
Chair	$249		80 cm x 80 cm
Pool Table	$1 850		250cm x 130 cm
Entertainment Centre	$550		136 cm x 68 cm
Big Screen TV	$2 500		150 cm x 76 cm
Small TV & Stand	$650		70 cm x 40 cm
Games Table	$89		78 cm x 78 cm
Folding Chair	$45		40 cm x 40 cm
Coffee Table	$125		172 cm x 60 cm
Ottoman	$65		50 cm x 60 cm
Air Hockey Table	$450		120 cm x 90 cm

4. Using your scale diagram of the room, arrange the templates for the furniture in a variety of ways. When you have decided on the best arrangement, glue the templates in place.

5. Give three reasons to justify your choice of furniture arrangement within the room.

(i) ____________________________

(ii) ___________________________

(iii) ___________________________

Sample Worksheet B

1. From the list of items and prices given in Worksheet A, what is the total cost of the furniture you wish to purchase (This is the furniture you chose in Worksheet A)? Pay attention to the number of each item required.

Item	Cost of Item	Number of Items	Total Cost ($)
Sofa	$650	1
Chair	$249	4
		TOTAL

Sample Worksheet C

1. Carpet costs $32 per square metre. The underpad is $7 per square metre. The installation is $25 per hour. What is the area of the floor? Determine the total cost to carpet the entertainment room if it takes 1.5 hours to do the job.

Item	Rate	Amount Required	Cost ($)
Carpet
Underpad
Installation
		Subtotal
		Taxes (15%)
		Grand Total

Sample Worksheet D

1. You can buy a TV for $1200 (taxes included) or purchase it on the installment plan for $75 a month for 20 months. What is the total installment cost?

2. How much extra would you pay?

3. Why would someone buy a TV using the installment plan?

Sample Worksheet E

1. The Cable TV Company charges $65 to hook up the cable and monthly rates as follows:

Cable Package A $19/month

Cable Package B $22/month

Cable Package C $25.75/month

Choose a Cable Package and determine the total cost for one year.

Sample Worksheet F

1. A games table is rectangular and has a diagonal measure of 95 cm. One of the sides is 74 cm long. What is the length of the other side?

2. You want to do a jigsaw puzzle with a finished size of 70 cm by 65 cm. Will it fit on the games table in question 1? Explain. You may wish to sketch a diagram to include with your explanation.

APPENDIX A

Rubric for Assessing and Evaluating Scale Diagrams

Knowledge/Understanding

Criteria	Level 1 (50-59%)	Level 2 (60-69%)	Level 3 (70-79%)	Level 4 (80-100%)
Scale · accurate use of scale	- demonstrates limited understanding of use of scale	- demonstrates some understanding of use of scale	- demonstrates considerable understanding of use of scale	- demonstrates thorough understanding of use of scale
Labels · accurate display of scale, legends, title, dimensions	- limited use of labels	- some use of labels	- considerable use of labels	- thorough use of labels
Equipment · appropriate use of rulers, protractors, calculators, etc.	- demonstrates limited ability to use equipment appropriately	- demonstrates some ability to use equipment appropriately	- demonstrates considerable ability to use equipment appropriately	- demonstrates thorough ability to use equipment appropriately

Note: A student whose achievement is below level 1 (50%) has not met the expectations for this assignment or activity.

Appendix B

Rubric for Assessing and Evaluating Unit 3 Worksheet A

Criteria	Level 1 (50-59%)	Level 2 (60-69%)	Level 3 (70-79%)	Level 4 (80-100%)
Knowledge/ Understanding use of scale display of scale, legends, title, dimensions use of equipment – rulers, protractors, calculators, etc.	- demonstrates limited understanding of use of scale - limited use of labels - demonstrates limited ability to use equipment appropriately	- demonstrates some understanding of use of scale - some use of labels - demonstrates some ability to use equipment appropriately	- demonstrates considerable understanding of use of scale - considerable use of labels - demonstrates considerable ability to use equipment appropriately	- demonstrates thorough understanding of use of scale - thorough use of labels - demonstrates thorough ability to use equipment appropriately
Communication explanations of reasons in written and/or oral form	- explains with limited clarity	- explains with some clarity	- explains with considerable clarity	- explains with a high degree of clarity
Application use of results from class survey from previous activity	- applies the survey results with limited ability to solve the problem	- applies the survey results with some ability to solve the problem	- applies the survey results with considerable ability to solve the problem	- applies the survey results thoroughly to solve the problem

Note: A student whose achievement is below level 1 (50%) has not met the expectations for this assignment or activity.

Appendix C

Sample Student Record Sheet for Unit 3 – Activity 8 – Unit Summative Activity

Student name

Check off the work as it is completed and write in the date and time the assignment is handed in for marking.

Worksheet A	All choices are made for the entertainment room	q
	All reasons for the choices are clear and well written	q
	Room outline is drawn to scale	q
	Chart is filled in to determine the size of the templates for the items chosen	q
	Templates are arranged on the scale diagram and glued in place	q
	Reasons for placement are clear and well written	q
	*Before handing in Worksheet A, transfer the contents of the Chart on Worksheet A onto Worksheet B	q
	Date and time of submission ________________________
Worksheet B	The contents of the Chart on Worksheet A have been transferred to Worksheet B	q
	The total cost has been determined	q
	Double-checked all calculations	q
	Does my answer make sense?	q
	Date and time of submission ________________________
Worksheet C	The area of the room has been determined	q
	Entered all rates	q
	Calculated all costs	q
	Double-checked all calculations	q
	Does the answer make sense?	q
	Date and time of submission ________________________
Worksheet D	The total cost has been determined	q
	Reasons have been given for the question asked Double-checked all calculations	q q
	Does my answer make sense?	q
	Date and time of submission ________________________
Worksheet E	The total cost has been determined	q
	Double-checked all calculations	q
	Does my answer make sense?	q
	Date and time of submission ________________________
Worksheet F	The length of the side of the table has been determined	q
	The question has been answered	q
	Reason is clear and well written	q
	Double-checked all calculations	q
	Does my answer make sense?	q
	Date and time of submission ________________________

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