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Course Profile (for a locally developed course)

Essential Mathematics, Grade 9

Unit 4: Investigating the Marketplace

Activity 7 | Activity 8 | Activity 9 | Activity 10 | Activity 11

Time: 17 hours

Unit Description

In this unit, students are involved in various investigations and activities that allow them to use their knowledge of ratios and rates to understand and apply percent. They illustrate the meaning of percent and solve contextual problems. The marketplace is rich with applications as well as opportunities to use rates, ratios, and percents to solve problems that increase student awareness as consumers and decision-makers. Some activities provide opportunities to use previously developed methodologies and strategies for investigations. Technology is used to aid in the analysis of data. Students are further encouraged to use mental mathematics and estimation to ensure that their calculations, use of technology and problem solving strategies produce reasonable results.

Strand(s) and Expectations

Overall Expectations: NSV.01, REV.01, MGV.02.

Number Sense Strand Specific Expectations: NS1.01, .02, .03, .04, .05, .15, .16.

Relationships Strand Specific Expectations: RE1.03, .04, .05, .06.

Measurement and Geometry Strand Specific Expectations: MG2.02, 05.

Activity Titles

What follows is a suggested sequence, with timing, for teaching Unit 4. This profile not only develops typical pencil and paper activities but also those that lend themselves to more active involvement by students. These activities are designed to make sense of mathematics by working through concrete experiences to develop students' understanding of various mathematical concepts. The 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 further development of skills can be addressed as they arise within the activities.

An additional 60 minutes, outside of the activities, has been allotted for this purpose. The understanding and use of percent is particularly important for student success in the Grade 11 Workplace Course and it is therefore critical that the student master, with some degree of proficiency, the key concepts in this unit.

Activity 1	What is Percent?	75 minutes
Activity 2	Exploring Percent and Number Patterns	75 minutes
Activity 3	Floor Plans	135 minutes
Activity 4	Circle and Bar Graphs	75 minutes
Activity 5	Calculating with Percent	75 minutes
Activity 6	Commissions	75 minutes
Activity 7	Discounts and Mark-ups	90 minutes
Activity 8	Sales Tax	75 minutes
Activity 9	Applying Percent	75 minutes
Activity 10	What Makes a Friend?	90 minutes
Activity 11	Summative Assessment	120 minutes

*Time for: Activity completion and consolidation of the unit=s expectations: 60 minutes

Unit Planning Notes

· This unit incorporates numerous concrete materials that must be organized prior to each activity.

· There are opportunities to modify Activities 6, 7, 8, and 9 for spreadsheet use.

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. Teachers are working diagnostically with students to determine what type of support each student requires. Time has been built into the activities to allow for these opportunities and to further develop skills within a context.

Resources

Barry, B. and S. Wright. The Real Game. National Occupational Coordinating Committee and the National Life/Work Centre, 1998.

Bellheim, C., M. Cheverie, C. Danbrook, F. Leddy, T. Romiens, A. Sands, and M. Warren. Mathplus 7. Harcourt Brace Canada, 1994.

Bellheim, C., M. Cheverie, C. Danbrook, F. Leddy, T. Romiens, A. Sands, and M. Warren. Mathplus 8. Harcourt Brace Canada, 1994.

Ebos, F. D. McKillop, E. Milne, B. Morrison, B. Robinson, and K. Whelan. Math in Context 7. Nelson Canada, 1992.

Education Development Center Inc. Getting Down to Business. Creative Publications, 1998.

Flewelling, G., J. Routledge, J. Clark, and T. Brown. Making Mathematics 7. Gage, 1991.

Flewelling, G., J. Routledge, J. Clark, and T. Brown. Making Mathematics 8. Gage, 1991.

Knill, G., D. Dottori, E. Collins, and J. Cornwall. Mathpower 7. McGraw-Hill Ryerson Ltd., 1993.

Reys, B. Developing Number Sense in the Middle Grades. NCTM, 1991.

Activity 1: What is Percent?

Time: 75 minutes

Description

Students examine the meaning of percent and practise reading and drawing diagrams to represent percents.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .02, .15.

Planning Notes

· Each student requires a copy of the worksheets.

· Prepare overhead transparencies to demonstrate some of the work.

· Obtain articles from magazines and newspapers are also required.

Teaching/Learning Strategies

Student Activity

· Students gain an understanding of the meaning of percent as an amount out of 100 through a variety of exercises.

· Students investigate the use of percentages using magazines and newspapers.

· Students read percentages from diagrams and complete diagrams based on given percentages.

· Students determine what percentage of an ingredient is missing from a product list.

Teacher Facilitation

· Begin with a discussion regarding the use of percents and where they appear.

· Provide magazines and newspapers with highlighted statements that use percents.

· Prepare a chart, similar to the one below and have students complete it with you, as you complete it using an overhead projector.

Sample Chart

Statement	Where did you find it?	What does it mean?	Why was this statement given?
80% of all Canadians like to live in Canada	MacLean=s magazine June 1999	80 or 4 people like living in 100 5 Canada but 1 do not like it 5	- marketing purposes - information
50% polyester	jacket label
8%/a interest (8% per year interest)
20% chance of rain
etc.

· After completing the chart, provide the students with a number of pictorial representations of various percentages. For example, have a 10 by 10 grid with 50 squares shaded in one colour (e.g., red) and 25 squares shaded in another colour (e.g., blue) Discuss the percentages of each colour and also draw comparisons in both decimal and fraction form.

· Emphasize the notion of equivalent values displayed in different forms (e.g., 25% = 3 = 0.25). Also provide opportunities to discuss when one form may be preferred over the others.

· Provide worksheets with a number of shaded squares and have students determine the corresponding percentage. Provide worksheets with percentages given and have students shade the corresponding number of squares. Also provide opportunities to discuss the percentages in fraction form.

· Students complete a worksheet where they determine the percentage of the missing ingredient from a product list.

Sample Questions

Graham Crackers		Dried Minestrone Soup Mix		Cat Treats
Protein	8%	Protein	13%	Crude Protein	31%
Fat	? %	Fat	1%	Crude Fat	10%
Carbohydrate	80%	Carbohydrate	? %	Crude Fibre	4%
Other	5%	Other	18%	Moisture	? %
Calcium	1%	Other		43%

Sample student work

8 + 80 + 5 + 1 = 94

100 - 94 = 6

ˆ Fat comprises 6% of the total ingredients.

Assessment/Evaluation

Mark worksheets for completion and accuracy.

Activity 2: Exploring Percent and Number Patterns

Time: 75 minutes

Description

Students continue to examine the meaning of percent and practise reading and drawing diagrams to represent percents, fractions, and decimals. Students also examine number patterns in a number table for 1 to 100.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .02, .03, .15.

Planning Notes

· Provide overhead transparencies to allow students to check their estimates.

· Provide each student with the worksheets.

· Obtain a large chart of the numbers from 1 to 100 or an overhead transparency.

Teaching/Learning Strategies

Student Activity

· Students read and create more visual representations of percentages using grids of sizes 10 by 10, 10 by 20, and 10 by 5. The teacher initially needs to direct the students to complete a number of examples.

· Students estimate the percentage of a diagram that is shaded.

· Students investigate a chart containing the numbers 1 to 100 and look for number patterns in the chart. They relate these to fractions and percentages.

Teacher Facilitation

· Provide grids for students to interpret and also provide blank grids on which students shade specified percentages. (See sample worksheet.)

· Provide diagrams without the grid lines and ask the students to estimate what the percentages are for the shaded and unshaded areas. Acetate overlays can be provided to check the results.

· Apply proportional reasoning to determine the percentage shaded when a 10 by 20 grid is used, for example:

When 72 squares out of 200 are shaded;

· For this activity students should be given a 100's chart or asked to complete one.

Sample Worksheet

1. Write in the missing numbers and then discuss, with your teacher or another student, the patterns you see in the chart.

1. Complete the following chart.

Statement	Number of numbers that fit the statement	What is the number as a percent of all the numbers in the chart?	What is the number as a fraction of all the numbers in the chart? What is it in lowest terms?
example: numbers that are less than 50	49	49%	49 100
even numbers
1 digit numbers
(could include 20 to 25 other questions)

2. Teachers may wish to review reducing fractions to lowest terms and spend some time practising this skill.

3. Students should begin to commit to memory some common percentages in decimal and fraction form. A chart could be posted somewhere in the room and, as a common percentage is used, it could be added to the list (e.g., 75% , :, 0.75).

Assessment/Evaluation

Use Appendix 1 to observe a few students. The worksheets could be marked for completeness and accuracy.

Activity 3: Floor Plans

Time: 135 minutes

Description

Students examine a floor plan of a grocery store on a 10 by 10 grid and determine the percentage of floor space used for each department. They repeat the process for a bookstore with little or no assistance from the teacher. They design a park using a 20 by 10 grid. An opportunity for calculating areas and percentages is given using the floor plan of the school.

Strand(s) and Expectations

Strand(s): Number Sense and Relationships and Measurement and Geometry

Specific Expectations: NS1.02, .03, .13, .15, .16, RE1.06, MG2.02, .05.

Planning Notes

· Prepare worksheets.

· Provide blank grids for students to make their own floor plans.

Teaching/Learning Strategies

Student Activity

· Students examine the floor plan from a grocery store on a 10 by 10 grid overlay. They fill in a chart with the percentages of floor area designated for each department.

· Students could use the diagram to fill in a chart like the one below.

Sample Worksheet

FLOOR PLANS

Department	Number of squares covered	Fraction of the store=s floor area for that department	Percent of the store=s floor area for that department
bakery	example: 8	8 100	8%
meat
dairy
canned goods
etc.

· Students complete a similar activity using data from a bookstore. They organize the departments onto a 10 by 10 grid by shading in the appropriate number of squares and fill in a chart like the one for the previous example.

· Students repeat the process for a park design using a 20 by 10 grid and a chart like the one in the previous example.

·         Students may need some guidance to recognize that 1% is equivalent to 2 squares.
1   =   ?
100     200

· Measurements of areas in a part of the school (e.g., library) can be taken and percentages of floor space for each room or section are calculated.

Teacher Facilitation

· Provide students with a floor plan of a grocery store and chart as shown in the student activity section. Discuss how areas are arranged to allow for traffic flow, etc.

· Provide students with a 10 by 10 grid and the following information so they can create a floor plan for a bookstore. They also fill in a chart like the one above.

· Percentage of floor space used: 10% gardening books

20% children=s books

5% classics

5% cookbooks

20% fiction books

20% non-fiction books

20% walking space

· Provide students with a 20 by 10 grid and the following information so they can create a layout for a park.

· Percentage of ground used 5% sandbox

5% swings

15% swimming pool

15% mini putt

30% soccer field

15% picnic area

10% parking lot

5% pathways

· Students are instructed to construct a floor plan of a library or other area of the school (e.g., second floor, right wing, academic wing, tech wing). Within a library there could be a reference area, a sitting area, different types of books, computer room, circulation desk, etc. Students could calculate the area of these rooms and then calculate the percentage that each area occupies.

Sample Worksheet

Location in school	Length (m)	Width (m)	Area (length x width) (m²)	Percentage of area occupied
seminar room 1	8m	4m	8 x 4=32	32 x 100 total area =
computer lab
			Total Area:

Assessment/Evaluation

Mark the plans for accuracy and completeness and also for taking into account placement of areas to allow for traffic flow, etc.

Activity 4: Circle and Bar Graphs

Time: 75 minutes

Description

Students analyse and interpret a circle graph and a bar graph that have both been drawn using percentages. They construct a circle graph to show how they spend their time during an average school day.

Strand(s) and Expectations

Strand(s): Number Sense and Relationships

Specific Expectations: NS1.01, .02, .15, RE1.03, .04, .05, .06.

Planning Notes

· Prepare graphs for students to interpret.

· Students require two strips of paper that are the same length, one with 24 divisions and one with 100 divisions in order to construct the circle graph.

· Students also require a circle template with percentage increments. Refer to Unit 1.

Teaching/Learning Strategies

Student Activity

· Students examine graphs and interpret the information that has been displayed as percentages.

· Students create a circle graph from data gathered about how they spend their time during an average school day.

Estimating which fraction is closest to a specified percent and vice versa could be done here (e.g., is 45% closest to a, 3, 2?)

Teacher Facilitation

· Distribute the graphs to the students. Two examples are given here.

Areas of the Great Lakes as a percent of the total area of the 5 lakes (Lake Superior - 34%, Lake Michigan - 23%, Lake Huron - 24%, Lake Ontario - 8%, and Lake Erie - 11%) The second graph is a bar graph comparing the percentage of the population of Canada by ages 0-14 years 21%, 15-34 years 32%, 35-54 years 27%, over 55 years 20%.)

· Lead students through the process of creating a circle graph from their own data. Complete a chart (see sample worksheet). Fill in the corresponding strip with 24 divisions for each hour of the day. Then line up the two strips side by side and transfer the markings onto the 100 division strip. The hours are now percents. Transfer the percents to the chart. Form the 100 division strip into a circle and construct the circle graph as in unit 1.

Sample Chart

HOW DO YOU SPEND AN AVERAGE SCHOOL DAY?

Activity	Number of Hours	Fraction of the day	Fraction in lowest terms	Percent (from the paper strip)
Example: sleeping	8	8 24	1 3
school	6
after school job

Total	24	24 24	1	100%

sleeping

etc.

8 hours correspond to 33a divisions, so it is 33a %.

· A career component could be added here by examining the questions:

· How much leisure time do you have each day?

· What percent of your day is this?

· Consider the leisure time of certain careers? Which career people do you think have the most leisure time? How much do you think they have?

· Careers could be ranked from those with much leisure time to those with little. Data to support this activity can be obtained from “The Real Game”.

· For homework, students could construct a circle graph to show how they spend their time on a typical weekend. They would require more paper strips.

Assessment/Evaluation

Mark the chart for accuracy and completeness. The graph could be marked according to the rubric for assessing graphs in Unit 1-Activity 3.

Resources

Barry, B. and S. Wright. The Real Game. National Occupational Coordinating Committee and the National Life/Work Centre, 1998.

Activity 5: Calculating with Percent

Time: 75 minutes

Description

Students use some of the data collected in Unit 1 - Activity 2 to calculate percents and make comparisons. They learn a new method for calculating the percent of a number. Finally, students apply percents to calculate the costs of taking a ferryboat ride.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .04, .05, .13, .15, .16.

Planning Notes

· Prepare a worksheet using the data from Unit 1 - Activity 2.

· Prepare each student a Rocky Island Ferry worksheet.

Teaching/Learning Strategies

Student Activity

· Students discuss the results of the data from Unit 1, calculate percents, compare the values in percent, decimal form, and fractional form, and complete a worksheet examining the rates for a ferryboat ride.

Teacher Facilitation

· Using the data from unit 1, prepare a worksheet like the one shown and have the students make the comparisons.

Sample Worksheet

Question from Unit 1 - Activity 2	Number of students who agreed	Total Number of Students	Fraction form	Decimal form (agreed ) total)	Percent form (agreed ) total x 100)
example: students who are concerned about the environment	5	15	5 = 15	0.333....	33.3...% or 33⅓
favourite sports -baseball -basketball -volleyball -hockey -other
etc.

· Discuss the results and the various forms of the calculation and when it is suitable to use each type.

Include additional practice determining the percent one number is of another and calculating percent of a number. Provide questions in a context and practise straightforward examples (e.g., 30 out of 50 vehicles are trucks, 28 out of 70 dollars are deposited into a savings account, 10% of $24 is the discount).

· Complete the Ferry Prices worksheet. A sample is given.

Sample Worksheet for the Rocky Island Ferry

The Rocky Island ferry is a tourist attraction and keeps its fares low in order to attract business. If you wish to take a vehicle and group of people over to the island, you must pay before boarding.

ONE WAY FARES

Who is Travelling?	Price
car with driver	$5.00
each extra adult	$2.00
children under 10	Free

Special discounts -	Senior citizens	15% off
	Oct. - Dec.	¼ off
	Jan. - Apr.	⅓ off

How Much Will It Cost for Each of the Following Vehicles?

Number in Vehicle and month of trip	Car with Driver (always $5.00)	Adult Passengers (Number of adults x $2)	Senior Citizen Passengers (Number of seniors x $2)	Discount for senior citizens (15% x total from the previous column)	Total Cost (car with driver + total adults + total seniors - discount for seniors) (STOP HERE BETWEEN MAY AND SEPT)	Discount for the off season (fraction from chart x total cost)	Total Cost in the off season (Total cost - discount for the off season)
example: 2 adults July	$5.00	1 x $5.00 = $5.00	0	0	5 + 5 + 0 = $10.00	X	X
1 adult, 2 seniors Oct.	$5.00	0	2 x $2.00 = $4.00	15 ÷ 100 x $4.00 = $0.60	$5 + $4 - $0.60 = $8.40	¼ x $8.40 = 2.10	$8.40 - $2.10 = $6.30
etc.

At this time, you may wish to spend extra time recalling the method for reducing fractions to lowest terms, teaching about repeating decimals, and about basic decimal-fraction equivalencies
(e.g., ½ = 0.5 = 50%).

Assessment/Evaluation

Mark the worksheet for completeness and accuracy.

Activity 6: Commissions

Time: 75 minutes

Description

Students use percents to calculate commissions.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .04, .05, .13, .15, .16.

Planning Notes

· Students each need a copy of the worksheets.

· Check availability of computer lab if you intend to use spreadsheets to complete the assignment.

Teaching/Learning Strategies

Student Activity

Discuss the meaning of commissions and list jobs where employees are paid on a commission basis.

Complete worksheets. This work could be completed by using a spreadsheet.

Sample Worksheet 1

MY PAPER ROUTE

Newspaper carriers for the Daily Review are paid on a commission basis as follows.

COMMISSION RATES FOR PAPER CARRIERS

25% commission on Sunday papers

20% commission on Saturday papers

16% commission on weekday papers

Chris kept track of the paper deliveries for one month.

Sun.

Mon.

Tues.

Wed.

Thurs.

Fri.

Sat.

Totals

Weekday papers cost 754, Saturday papers cost $1.25, and Sunday papers cost $1.10.

4. Calculate the total money collected for Sunday papers, for Saturday papers, and finally for weekday papers.

Total Sunday sales x 1.10 =_____________

Total Saturday sales x 1.25 =_____________

Total Weekday sales x 0.75=_____________

5. Calculate the commission earned for Sunday papers, for Saturday papers, and finally for weekday papers.

Total Sunday earnings x 0.25 =____________

etc.

6. Calculate the total commission earned for the entire month.

· Discuss that some people are paid a salary and a commission on sales, and complete a worksheet such as the following.

Sample Worksheet 2

SHOES

Shoe salespeople, Armand, Jack, Marla, and Thomas (use names of students in the class) are paid by commission in addition to a monthly salary. Use the information in the following chart to determine their monthly earnings.

Name	Sales for the month	Rate of commission	Commission earned (rate of commission x sales)	Salary for the month	Total earnings for the month (salary + commission)
Armand	$10 000	6%		$100
Jack	$12 000	5%		$125
Marla	$22 000	2%		$200
Thomas	$7 200	8%		$75

Teacher Facilitation

· Work with the students to complete the first two or three examples on each page.

· Students should also be encouraged to estimate their answers before performing their calculations and checking their answers for reasonableness.

· Facilitate the discussions.

· Circulate around the room to help where required.

Assessment/Evaluation

· Mark the worksheets for completeness and accuracy. Use Appendix 1 and observe a few of the students for learning skills while they are working.

Activity 7: Discounts and Mark-ups

Time: 90 minutes

Description

Students calculate discounts and mark-ups for a variety of products.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .04, .05, .13, .15, .16.

Planning Notes

· Provide a copy of each handout for each student.

· Provide catalogues and sale flyers for students to use.

· Spreadsheets can be used. Arrange for availability of computer lab if you intend to complete this assignment using spreadsheets.

Teaching/Learning Strategies

Student Activity

· Students learn what discounts and mark-ups are and why retailers use them.

· Students complete a worksheet by calculating discounts, mark-ups and the resulting prices.

· Students use the catalogues to choose some items and calculate discount prices given a specified rate.

· Students use the sale flyers to calculate the percent discount for a variety of items.

Teacher Facilitation

· Facilitate the discussion about discounts and mark-ups.

· Encourage discussion that deals with the best way to do and show calculations. Encourage students to estimate their answers before performing their calculations and check their answers for reasonableness.

· Teach how to calculate discounts, mark-ups, and the resulting prices. Sample charts are provided for this purpose.

Sample Chart for Discounts

Item	Rate of Discount	List Price	Amount of Discount (rate of discount x list price)	Sale Price (list price - amount of discount)
example: sweater	25%	$44.00	25% x $44 =25 ) 100 x $44 =0.25 x $44 =$11	Sale Price = $44 - $11 = $33
jeans	30%	$63.00
etc.

Sample Chart for Mark-ups

Item	Rate of Mark-up	Wholesale Price	Amount of Mark-up (rate of mark-up x wholesale price)	Selling Price (wholesale price + amount of mark-up)
example: computer	85%	$1 600.00	85% x $1 600 or 85 ) 100 x $1600 = $1 360	$1 600 + $1 360 = $2 960 Selling Price is $2 960.00
jacket	90%	$75.00
etc.

The teacher may choose to spend some time reviewing the rules for rounding values when dealing with money.

· Have students select 10 items from a catalogue and randomly place them in the chart below. Students calculate the discount and sale price using the rates given in the chart. Rates are expressed in percent or fraction form.

Sample Chart

Item from catalogue	Price from catalogue	Rate of Discount	Amount of Discount (rate of discount x price)	Sale Price (price - amount of discount)
		50% off
		2 off
		40% off
		a off
		etc.

· Students choose 6-8 items from the sale flyers and record the regular price and the sale price and then they calculate the rate of discount. A chart like the one below could be used.

Sample Chart

DISCOUNT

Item from sale flyer

Regular Price from sale flyer

Sale Price from sale flyer

Rate of Discount

((regular price – sale price) ) regular price x 100) order of operations is important here

example: bike

$200.00

$150.00

(200 - 150) ÷ 200 x 100%

= (50) ÷ 200 x 100%

= 25%

The discount was 25% off.

etc.

Assessment/Evaluation

Mark the worksheets for completeness and accuracy. Appendix 1 can be used to observe a few students.

Activity 8: Sales Tax

Time: 75 minutes

Description

Students calculate PST and GST for a variety of taxable items. They also estimate and calculate the total tax for a purchase.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .03, .04, .05, .13, .15, .16.

Planning Notes

· Prepare worksheets.

· Arrange for availability of computer lab if you intend to complete this assignment using spreadsheets.

Teaching/Learning Strategies

Student Activity

· Students calculate PST and GST.

· Students estimate and calculate total sales taxes.

Teacher Facilitation

· Discuss that in Ontario the Provincial Sales Tax (PST) is 8% and the Goods and Services Tax (GST) is 7%, which are added to the price of the item to determine the final cost.

· The sample worksheet can be used to work through as an example for students to follow when calculating sales tax. The first one or two questions could be done as a whole class exercise and the students could finish the sheet with teacher assistance when necessary and by consulting their learning partner.

· This activity can be modified to be completed using a spreadsheet.

Sample Worksheet

SALES TAX

Here are 5 taxable expenses you might have as you travel from Toronto to Thunder Bay by car.

a)	accommodations	$90.00
	(a room)
b)	1 breakfast	$ 7.00
	2 lunches	$15.00
	1 dinner	$22.00
c)	1 tube of toothpaste	$ 1.99
d)	souvenirs	$48.25
e)	T-shirt	$19.00

Record your expenses in a table like the one below.

Item and Cost	Calculation of PST	Calculation of GST	Total Taxes (PST + GST)	Total Cost of Item (cost + total taxes)
room $90.00	0.08 x $90 = $7.20	0.07 x $90 = $6.30	$7.20 + $6.30 = $13.50	$90.00+ $13.50 = $103.50
Meals 1 breakfast $ 7 2 lunches $15 1 dinner $22 Total $59	0.08 x $59
etc.

This is an opportunity to explain that calculating 7% of $10 and 7% of $5 separately is the same as calculating 7% of $15.00. It is also an opportunity to discover that calculating 7% tax and 8% tax is the same as calculating 15% tax because they are both calculated on the same number.

· Create other scenarios where students are required to organize and calculate expenses incurred using an appropriate table.

· Introduce a method for mentally calculating the tax. Have students work the estimated total tax before using calculators to do the computation and then check for the accuracy of their estimate.

Sample Questions

Here are 4 taxable purchases you might have after shopping at Petrie=s Bike Shop.

a) a mountain bike	$857.00
b) a bicycle helmet	$ 79.00
c) a spandex suit	$109.00
d) a water bottle	$ 4.50

Estimate the tax for each item. For estimating 15%, take 10% first and then take half of that amount and add the two together.

example: $857 . $900 10% of $900 = $90

2 of $90 = $45

total tax = $135

Item

Estimated Tax

PST

GST

Total Tax

Total Cost

example: mountain bike

$135
(see above)

0.08 x $857

0.07 x $857

PST + GST

etc.

This exercise could be extended to calculating and estimating tips. It could also be pointed out that adding the PST and GST amounts shown on the bill gives the amount to leave for the tip.

Assessment/Evaluation

Mark the worksheets for completeness and accuracy. Use Appendix 1 to observe a few students.

Activity 9: Applying Percent

Time: 75 minutes

Description

Students determine the best buy when presented with two prices and two different discounts for the same item. They also complete multi-step problems involving mark-up, discount, and/or sales tax. There is also an exercise for purchasing pizza involving sales tax and discounts for pick-up orders.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .04, .05, .13, .15, .16.

Planning Notes

· Prepare worksheets.

· Check for availability of computer lab if you intend to complete this activity using a spreadsheet.

Teaching/Learning Strategies

Student Activity

· Students complete the worksheets for the multi-step problems.

Teacher Facilitation

· The teacher completes a few examples with the students and then circulates to assist where necessary.

· This lesson allows students to consolidate and practise skills learned in the previous few lessons.

· These worksheets could be modified to use a spreadsheet.

Sample Worksheet 1

MARK-UP

(Some students find it difficult to complete word problems. Arranging the questions in chart form like this one, instead of in sentence form, makes it easier for students to complete the work. For multi-step problems, a chart like the second one shown is a good way or organize the student solutions.)

Item and its wholesale price	This was the rate of mark-up.	After a period of time, the following discount was applied.	PST	GST	Final Cost
example: hat $10.00	75% mark-up	20% discount	8% PST	7% GST
bike	35%mark-up
etc.

Organize your solutions in the following table.

SOLUTIONS

Item and its whole-sale price

This is the mark-up.

This was the price after the mark-up.

This was the discount.

This was the price after the discount was subtracted.

PST

GST

Total Price

example: hat

$10.00

0.75 x $10

= $7.50

$10 + $7.50

= $17.50

.20 x $17.50

=$ 3.50

$17.50 - $3.50

= $14.00

0.08 x $14.00

= $1.12

0.07 x $14.00

= 0.98

$14.00

$1.12

+ $0.98

$16.10

etc.

· This exercise requires a substantial amount of teacher direction.

· Complete the pizza price list and order worksheet.

Sample Worksheet 2

CHUNKY CHEESE PIZZA

MENU

SMALL (cheese & sauce)	$ 5.75	each additional Topping $ 1.05
MEDIUM (cheese & sauce)	$ 7.99	each additional Topping $ 1.39
LARGE (cheese & sauce)	$ 9.89	each additional Topping $ 1.65
JUMBO (cheese & sauce)	$13.95	each additional Topping $ 2.65

Toppings:

Mushrooms Pepperoni Bacon Meatballs Green Peppers

Onions Pineapple Ham Tomatoes Ground Beef

Hot Peppers Black Olives Feta Cheese Anchovies Extra Cheese

10% off of all Pick-up orders.

7. Carmen works at Chunky Cheese Pizza. She filled the following pick-up orders. Complete the chart to find out the exact money Carmen should have collected.

Quantity	Kind of Pizza	Size	Unit Price (cost for one pizza)	Total Cost of Pizzas Ordered	10% Off Pick-up Orders	Discount Price	Total Tax 15%	Total Cost of Order
	Pepperoni	Large	$9.89 + $1.65 = $11.54	$11.54	$1.15	$11.54 - $ 1.15 = $ 10.39	$10.39 x 0.15 = $ 1.56	$10.39 + $ 1.56 = $ 11.95
1	Black Olive and Feta Cheese	Jumbo	$13.95 + 2 x $2.65 = $19.25	$19.25	$1.93	$17.32	$2.60	$19.92
2	Mushrooms, Bacon, Onions and Ham	Large	$9.89 + 4 x $1.65 = $16.49	$32.98	$3.30	$29.68	$4.45	$34.14
3	Pineapple, Ham and Onions	Small
2	Green Peppers, Bacon, Meatballs, Tomatoes and Extra Cheese	Medium
etc.

Assessment/Evaluation

Mark the worksheets for completeness and accuracy. Appendix 1 could be used to observe a few students.

Activity 10: What Makes a Friend?

Time: 90 minutes

Description

Students examine given data and calculate the percent of a number. They then collect data from their classmates and use percents to draw conclusions and make comparisons. The results are displayed graphically.

Strand(s) and Expectations

Strand(s): Number Sense and Relationships

Specific Expectations: NS1.01, .05, .13, .15, .16, RE1.03, .04.

Planning Notes

· Prepare worksheets.

· Students require circle templates (marked with increments on the circumference to draw circles), coloured pencils and rulers to construct graphs.

Teaching/Learning Strategies

Student Activity

· Complete calculations for percent of a number using a worksheet.

· Survey classmates to determine the attributes most prized in a friend.

· Gather the data in chart form and construct a bar graph and/or a circle graph using percentages.

· Students think about the needs of their community and how they could allocate a $100 000 donation and display allocation in a bar graph and/or a circle graph.

Teacher Facilitation

· Elicit the qualities of a good friend from a class discussion.

· Provide students with a sample of a large survey in the form of a chart showing percentages of each category (see sample worksheet).

· Work with the students to calculate the first few answers and have them finish the list.

· From the class, fill in the tally chart to see which attributes they feel are most important. Calculate the percentages and display the results graphically.

Sample Worksheet 1

ATTRIBUTES THAT ARE MOST PRIZED IN A FRIEND

Two thousand five hundred (2500) people were asked which one of the following attributes were the most desirable in a friend.

Attribute	% of people	Number of people
Honesty	15%	example: 0.15 x 2500 = 375
Loyalty	4%
Sense of Humour	14%
Reliability	21%
Kindness	12%
Supportive	16%
Likes the same things I do	18%

Now conduct the same survey with your classmates (or other students in the school if your class is very small).

Gather the data in a frequency table like the one outlined below.

Attribute	Tally	Number of people	% of people
Honesty
Loyalty
Sense of Humour
Reliability
Kindness
Supportive
Likes the same things I do

Display one table using a bar graph and the other using a circle graph using percentages.

Facilitate a discussion with the students. You are part of a committee that has received a $100 000 donation to improve your community. How would your committee allocate the funds? It is important to get students to think beyond their own needs and desires. This is another opportunity to promote proportional thinking (e.g., 5% of 100 000 = $5 000).

Assessment/Evaluation

Mark the worksheet for accuracy and completeness. Use Appendix 1 to observe a few students as they work. Assess the construction of the graph(s) using the appropriate part of the rubric from Unit 1 - Activity 3.

Activity 11: Summative Assessment

Time: 120 minutes

Description

Students use their skills with percent to complete this summative assessment. They read a floor plan, design a garden, and use mark up, discounts, and taxes to ascertain the costs associated with a plant sale in a greenhouse.

Strand(s) and Expectations

Strand(s): Number Sense

Specific Expectations: NS1.01, .02, .03, .04, .05, .13, .15, .16.

Planning Notes

· Prepare worksheets, grids, and floor plan.

· Have rulers, coloured pencils, graph paper, and blank paper available.

· Prior to assigning the task, have students organize their workbooks or prepare a study sheet so it can be used as a reference.

· This assessment tool can be given as a series of short exercises in order to minimize task anxiety for the student.

Teaching/Learning Strategies

Student Activity

· Students are given information for planting a show garden and produce a diagram following given percentages.

· Students are given the floor plan of a greenhouse and interpret and analyse the drawing.

· Students calculate the wages.

· Students are given wholesale prices for plants along with the mark-up percentages, discounts and taxes in order to calculate final price.

Teacher Facilitation

Part I

· Provide students with large 10 x 10 grids and the directions for planting a show garden.

· It may be necessary for them to try a few diagrams before they are satisfied with the results.

· Provide a worksheet similar to the one outlined below.

Sample Worksheet

SHOW GARDEN

Your job is to plant a show garden at the front of the greenhouse. It is the first thing that the customers see when they arrive to shop. You must plant according to the following instructions.

40% of the garden is to be planted with red flowers.

20% of the garden is to be planted with only green plants.

15% of the garden is to be planted with yellow flowers.

15% of the garden is to be planted with tall pink flowers.

10% of the garden is to be unplanted soil.

On the grid provided, draw your garden according to the percentages given. Make sure all areas can be easily accessed.

Part II

· Provide students with a floor plan of a greenhouse and have them estimate the floor space for annuals, perennial, vegetables, trees, other garden supplies and walking space.

· Provide students with a 10 x 20 grid overlay and have them determine the areas by counting the squares. This gives them a fraction out of 200 and they must change this to a percent.

Sample Floor Plan

Part III

· Students could fill in a chart for a number of salespeople who are paid a commission on sales.

Sample Worksheet for Commission Sales

Name of Employee	Rate of Commission	Amount of Sales	Commission Earned
Julia	5%	$850.00	0.05 x $850.00 =
Sanjit	4%	$1300.00
etc.

Part IV

· Provide a worksheet for students to do calculations for mark-up, discount and taxes.

Sample Worksheet

GREENHOUSE SALES

The greenhouse owners paid for seeds, soil, heat, etc.. They calculated the cost price and added a mark-up to the price to decide how much to charge for each item. Some items had a greater mark-up. Later in the season, they wanted to sell off some of the plants by discounting the price. PST and GST were charged for all plant sales.

Use the examples in your workbook to help you do the calculations and complete the worksheet.

Item

Cost Price

Rate of Mark-up

Mark-up

Price after Mark-up

Rate of Discount

Discount

Price after Discount

example: Petunia

$0.50

90%

0.90 x $0.50

= $0.45

$0.50 + $0.45

= $0.95

10%

0.10 x $0.95

= 0.10

$0.95 - $0.10

= $0.85

etc.

· The worksheet should include fractional mark-ups and discounts.

Price after discount from last chart

PST

GST

Total Price

0.85

0.08 x 0.85 =

0.07 x 0.85 =

0.85 + PST + GST

etc.

Assessment/Evaluation

Use a variety of assessment tools. Mark student work for accuracy and completeness. Use the rubric from Appendix 1 to assess initiative and work habits. Use the following rubric for problem solving.

Problem Solving Rubric

Level 1

Level 2

Level 3

Level 4

Ability to solve problems

- can solve problem with coaching for each step.

- solves the problem but requires regular assistance from the teacher.

- can solve the problem after some review or discussion, occasionally checks with the teacher for assistance.

- is able to decide on the necessary procedure to solve the problem independently and solves it correctly.

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