Course Profile Mathematics, Locally
Developed, Grade 10, Catholic
Unit 1: Making Sense of Numbers
Time: 27 hours
Students commence this unit by simulating a fund raising venture. The results of this venture enable students to solidify their knowledge of, and improve their skills in, using decimals, fractions, percent, rate and ratio, in situations drawn from everyday contexts. Activities in this unit investigate mathematical applications in the fields of finance and geography. Students discover that organizational strategies can simplify the completion of problems, as can technological tools such as calculators and spreadsheet software.
Ontario Catholic School Graduate
Expectations: CGE 2a, 2b, 2c, 2d, 3c, 4a, 4b, 4f, 5a, 5g.
Strand(s): Number Sense, Patterns and
Relationships
Overall Expectations: NSV.01, NSV.02,
PRV.02.
Specific Expectations: NS1.01, NS1.02,
NS1.03, NS1.04, NS1.05, NS1.06, NS1.07, NS1.08, NS2.01, NS2.02, NS2.03, NS2.06,
PR2.01, PR2.02, PR2.06.
|
Activity 1 |
Generating Funds [Numerical calculations, decimals, estimation, ratios, percent, sales tax, unit price] Follow-up Activities |
2.5 hours 1.5 hours |
|
Activity 2 |
On the Job [Wages, hourly rate, commission, overtime] Follow-up Activity |
2.5 hours 1 hour |
|
Activity 3 |
A Penny Saved is a Penny Earned [Interest, financial information] Follow-up Activity |
5.5 hours 0.5 hours |
|
Activity 4 |
Sharing the Wealth [Numerical calculations, decimals, sales tax] Follow-up Activity |
4.5 hours 0.5 hours |
|
Activity 5 |
Determining Our Speed [Ratio and rate] Follow-up Activities |
1.75 hours 0.75 hours |
|
Activity 7 |
Summative Assessment – Away We Go |
6 hours |
· apply strategies for mental mathematics and estimation
· illustrate the meaning of the concept of percent
· identify rates
· represent ratios
· use a scientific calculator effectively
· judge the reasonableness of answers
· make a hypothesis regarding a relationship between two variables
· understand the concept of a variable
· measure lengths accurately
· In the first activity, students do numerical calculations related to the cost of a school uniform. The teacher may wish to replace the clothing with other items such as sports equipment.
· Flyers or catalogues displaying toys and their cost are necessary for Activity 4, “Sharing the Wealth”.
· In the summative activity, students are required to plan a four day trip. Brochures describing bus trips would assist students in scheduling an itinerary and provide ideas for destinations.
· Activity 5, “Determining Our Speed”, and the summative activity, make frequent references to places in Ontario. The possibility also exists for students to explore the attractions in other provinces and states. It is recommended that the mathematics teacher make contact with the geography department for suggestions on resources to enhance the activities.
· Flyers or ads for school supplies are required for the first activity. The teacher may wish instead to have students do comparison shopping for groceries.
· The teacher may wish to invite a guest speaker from the financial industry to discuss interest rates and types of bank accounts.
· Although the activities, “Sharing the Wealth” and “Away We Go” include spreadsheet tasks, activities may be adapted for calculator use.
· Interspersed throughout this unit are activities requiring students to obtain information from charts and tables. These activities, and the portions in which students write procedures or reflections, while an integral part of the mathematical routines, also serve as practice sessions for the Grade 10 Test of Reading and Writing Skills.
· Many of the skills developed in this activity are necessary for completion of tasks in later activities. Frequent interaction of the teacher with the students during this activity will enable skills deficiencies to be noticed and remediation to occur.
· The skills will be reinforced through numerous activities throughout the unit.
· Flexibility when teaching this unit will permit less time to be devoted to acquired concepts and more time to be spent on activities focussing on concepts in which students are experiencing difficulty.
· Throughout this unit, many opportunities arise for students to work in pairs or small groups. As the summative activity involves considerable group interaction, the teacher should monitor group dynamics to ensure that choices for the final group formation are conducive to successful completion of the activity. Varying group members in the preceding activities is therefore recommended.
· A variety of assessment tools are to be used to evaluate student performance. Formative assessment occurs through the teacher conferencing with the student, teacher observation of the student in individual and group activities, and student self-assessment and peer-assessments.
· A diagnostic quiz may be administered at the beginning of the unit.
· Appropriate accommodations for identified students should be part of the planning of each unit activity. Suggested accommodations are included as part of each activity.
Calculators, stopwatches, concrete or manipulative materials as needed
Newspapers, catalogues and flyers
Licensed spreadsheet software
ClarisWorks
Microsoft Works
Corel WordPerfect Suite
http://www.bmo.com/
http://www.canadatrust.com/
http://www.cibc.com/
http://www.mortgagestore.com/laurent/eng_page_2.html/
http://www.royalbank.com/
http://www.scotiabank.ca/
http://www.tdbank.ca/index.html/
http://www.canadiandriver.com/testdrives/
http://maps.excite.com/address/
http://www.freetrip.com/
http://www.transontario.com./
http://www.transontario.com/chart.html/
http://aircanada.ca/
http://airontario.com/
http://www.greyhound.ca/
http://www.viarail.ca/
Time: 4 hours
In this activity, students manage the purchase of uniform and supply items for the beginning of school. During this simulation, they review operations with decimals, fractions, and percent. Estimation and mental computation are used to approximate answers to numerical problems. Numerical skills are also applied in solving questions dealing with unit price. Students use calculators and/or computers to perform tasks beyond the proficiency of pencil and paper operations.
Strand(s): Number Sense
Ontario Catholic School Graduate Expectations
CGE2a - listens actively and critically to understand and learn in light of gospel values;
CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;
CGE4a - demonstrates a confident and positive sense of self and respect for the dignity and welfare of others;
CGE4b - demonstrates flexibility and adaptability.
Overall Expectations
NSV.01 - use a variety of methods for calculation when solving problems (e.g. mental mathematics or estimation, calculator, paper and pencil computational method) and apply the method effectively;
NSV.02 - consolidate the meaning and use of proportionality through applications drawn from student experiences and broader contexts.
Specific Expectations
NS1.01 - use pencil/paper computational methods effectively to evaluate expressions involving fractions decimals, and exponents as they arise in problems through out the course;
NS1.02 - use a scientific calculator effectively to evaluate expressions involving fractions, decimals, percent, exponents, and square roots, as they arise in problems throughout the course;
NS1.03 - evaluate expressions involving the rules of operations, by hand and by using calculators;
NS1.04 - use estimation and mental computation to approximate and/or calculate answers to numerical problems as they arise throughout the course;
NS1.05 - apply percents in solving problems (involving aspects such as: discounts, sales tax, commissions, interest and ratios);
NS1.06 - solve problems involving fractions and decimals using appropriate strategies and calculation methods;
NS2.01 - demonstrate an understanding of the relationship between decimals, percent, rates and ratios;
NS2.02 - demonstrate an understanding of and apply unit rate in problem solving situations.
Number Sense
· apply strategies for mental mathematics and estimation
· use a scientific calculator effectively
· represent ratios
· judge the reasonableness of answers
Patterns and Relationships
· understand the concept of a variable
· The teacher may wish to administer a diagnostic test to determine the students’ background and knowledge in mathematics.
· Although the teaching strategies indicate that skills are being reviewed, it is realistic to expect that some students will have experienced significant difficulty with these skills in previous grades. Individual or whole class reiteration of methodology for some concepts may be necessary.
· The price list for uniform components may be substituted with items specific to the uniforms used in the teacher’s school. If uniforms are not required in a particular school, the activity could be introduced by stating, “Next year we may have uniforms in our school, …….”
· Students may use a spreadsheet for part of this activity. However, the introductory estimation assignment should be completed with pencil and paper. Some practice in calculating taxes should occur without computer assistance.
· In the first activity, students do comparison shopping and consider unit cost. Flyers or ads detailing the cost of school supplies are necessary. The teacher could collect such flyers at the commencement of the school year or develop mock ads. The teacher may wish to substitute the supply list with food items.
· The teacher may wish to expand on the segments in which students obtain information from the catalogue as a prelude to the Grade 10 Test of Reading and Writing Skills.
Teacher Facilitation: The teacher presents the following scenario to the class:
The school club to which you belong plans many fund-raising ventures this year. The purposes of the fund-raising ventures are to provide money for the Christmas Food and Toy Drive and to help subsidize an excursion for the club.
The class brainstorms both possibilities for fund raising and considerations that would enable the fund raising to be successful. Students make suggestions as to why charities need to fund raise. The teacher informs the class that the first venture consists of ordering and selling school uniforms. The students are provided with Worksheet 1.1 (Appendix A) that lists items, catalogue numbers and prices.
|
Item |
Cat. # |
Price |
|
Oxford style shirt, long sleeve, button down (60% cotton, 40% polyester) |
OSSL1 |
$23.25 |
|
Oxford style shirt, short sleeve, button down (60% cotton, 40% polyester) |
OSSS2 |
$18.75 |
|
Oxford style shirt, long sleeve, button down (100% cotton) |
OSSL3 |
$28.50 |
|
Oxford style shirt, short sleeve, button down (100% cotton) |
OSSS4 |
$25.50 |
|
Golf shirt, long sleeve (100% pre-shrunk cotton) |
GSL1 |
$25.00 |
|
Golf shirt, short sleeve (100% pre-shrunk cotton) |
GSS2 |
$20.50 |
|
Fleece vest |
FV |
$34.50 |
|
V-neck sweater, long sleeve |
VNS |
$33.00 |
|
Zipped-neck pullover, long sleeve |
ZNP |
$33.00 |
|
Sweatshirt, Crewneck, long sleeve |
SW |
$31.50 |
|
Cardigan, zippered front, long sleeve |
CZ |
$32.50 |
|
Cardigan, button front, long sleeve |
CB |
$29.50 |
|
Pants |
P |
$32.00 |
|
Walking shorts |
WS |
$22.00 |
|
Skirt |
SK |
$32.00 |
|
Knee socks (may be worn with skirts or walking shorts) |
KS |
$7.50 |
|
Socks |
SO |
$3.00 |
|
Note: Orders received and prepaid before June 15 for the following school year will receive a 5% discount. This discount will be taken off before calculating taxes. |
||
To ensure that students are discriminating among the items correctly, the teacher and students “place” various orders, making reference to the item, catalogue number, and price. The teacher, while discussing the clothing items, assists students in determining the ratio of cotton to polyester in some of the shirts. The class considers other possible ratios for the cotton to polyester content, and then converts the ratios back to percent. A brief dialogue on the fabric content of clothing items occurs and is used to reinforce the relationship between percent and ratios. During this discussion, the teacher reviews the method of reducing ratios or fractions to lowest terms.
The teacher enables students to practise estimation by presenting questions of the type: If 18 fleece vests are sold, approximately what amount of money should be collected? Prior to distributing the instructions for the activity, the teacher calculates the cost of purchasing a few items to review the rounding of decimals and percent applications (sales tax, discount).
Students, working in pairs, are presented with the following instructions:
1. After the first day of sales, you wish to complete a quick survey of how much money was obtained. You decide to estimate the amount for each quantity and then to obtain the approximate total. Show your steps for the estimation section. Display the final answer for the total.
|
|
Quantity |
Item / Catalogue Number |
Unit Price |
Estimation |
Total |
|
1 |
9 |
Oxford, long sleeve – OSSL1 |
$23.25 |
|
|
|
2 |
13 |
Oxford, short sleeve – OSSL2 |
$18.75 |
|
|
|
3 |
|
Oxford, long sleeve – OSSL3 |
$28.50 |
|
|
|
4 |
|
Oxford, short sleeve – OSSL4 |
$25.50 |
|
|
|
5 |
22 |
Golf shirt, long sleeve – GSL1 |
$25.00 |
|
|
|
6 |
15 |
Golf shirt, short sleeve – GSL2 |
$20.50 |
|
|
|
7 |
34 |
Fleece Vest – FV |
$34.50 |
|
|
|
8 |
18 |
V-neck sweater – VNS |
$33.00 |
|
|
|
9 |
|
Zipped neck pullover – ZNP |
$33.00 |
|
|
|
10 |
50 |
Sweatshirt – SW |
$31.50 |
|
|
|
11 |
12 |
Cardigan, zippered – CZ |
$32.50 |
|
|
|
12 |
3 |
Cardigan, buttoned – CB |
$29.50 |
|
|
|
13 |
35 |
Pants – P |
$32.00 |
|
|
|
14 |
19 |
Walking Shorts – WS |
$22.00 |
|
|
|
15 |
7 |
Skirt – SK |
$32.00 |
|
|
|
16 |
1 |
Knee Socks – KS |
$7.50 |
|
|
|
17 |
1 |
Socks – S |
$3.00 |
|
|
|
|
|
TOTAL |
|
|
|
2. The final tally for sales is displayed in the chart below. Calculate the actual amount for each item. Complete the order form to include the sub-total, taxes and final total.
|
|
Quantity |
Item/Catalogue Number |
Unit Price |
Total |
|
1 |
178 |
Oxford, long sleeve – OSSL1 |
$23.25 |
|
|
2 |
162 |
Oxford, short sleeve – OSSL2 |
$18.75 |
|
|
3 |
87 |
Oxford, long sleeve – OSSL3 |
$28.50 |
|
|
4 |
93 |
Oxford, short sleeve – OSSL4 |
$25.50 |
|
|
5 |
111 |
Golf shirt, long sleeve – GSL1 |
$25.00 |
|
|
6 |
156 |
Golf shirt, short sleeve – GSL2 |
$20.50 |
|
|
7 |
87 |
Fleece vest – FV |
$34.50 |
|
|
8 |
24 |
V-neck sweater – VNS |
$33.00 |
|
|
9 |
106 |
Zipped neck pullover – ZNP |
$33.00 |
|
|
10 |
137 |
Sweatshirt – SW |
$31.50 |
|
|
11 |
69 |
Cardigan, zippered – CZ |
$32.50 |
|
|
12 |
23 |
Cardigan, buttoned – CB |
$29.50 |
|
|
13 |
245 |
Pants – P |
$32.00 |
|
|
14 |
81 |
Walking shorts – WS |
$22.00 |
|
|
15 |
104 |
Skirt – SK |
$32.00 |
|
|
16 |
12 |
Knee socks – KS |
$7.50 |
|
|
17 |
8 |
Socks – S |
$3.00 |
|
|
|
|
the total cost before taxes |
Sub-total |
|
|
|
|
the GST |
GST-7% |
|
|
|
|
the PST |
PST-8% |
|
|
|
|
the total cost after taxes |
TOTAL |
|
3. If all items are purchased before June 15th, the customers receive a 5% discount. In this case, everyone paid before June 15th. You have to recount the sub-total, taxes and total to reflect the savings.
|
Final Calculations |
|
|
Previous Sub-total |
|
|
5% Discount |
|
|
Sub-total |
|
|
GST 7% |
|
|
PST 8% |
|
|
TOTAL |
|
4. a) Your club receives 18% of the sub-total. Calculate the amount of money that your club receives from this venture.
b) If your club had received 24% of the sub-total, how much more would the club have received?
Teacher Facilitation: The teacher leads the class in an analysis of the order form to develop skills in forming proportions, ratios, and fractions. Students commence the discussion by noting statistical facts of the form such as the item ordered most frequently and the item ordered least frequently. The discussion then focuses on proportionality. Questions such as, “What fraction of the Oxford shirts that were ordered are long sleeve? What is the ratio of pants ordered to walking shorts? What proportion of the total cost is devoted to the purchase of cardigans?” are proposed by the teacher. The teacher encourages students to challenge the class with their own questions.
|
Follow-up Activity |
|
Time: 0.75 hours |
|
Students complete questions to reinforce the skills developed in the investigation. The questions should be structured so that students are initially finding ratio and percent, including simple conversions among decimals, percent, and ratios, then progressing toward more difficult conversions within a problem-solving situation. |
Teacher Facilitation: The teacher leads a discussion of unit price, rounding (cent) and best buy. During this session, students relate considerations when determining the “best buy” (price, quantity, quality). The teacher reviews metric conversions while completing some examples. Students work in groups or work independently on the following activity.
It has been decided that throughout the year, the club will sell some school supplies during the lunches. You can obtain a discount on the items from local stores if you buy them in bulk.
· Develop a list of 6 school supplies that would be needed by the students in the school. Consider the courses that are offered to Grade 10 students. What supplies are needed for most courses? What items are needed for particular courses?
· Check catalogues or flyers to obtain 2 different prices for the articles. Record the name of the store, the price at the particular store and, the quantity at which it is priced.
· Determine the best buy. Display your calculations.
|
Follow-up Activity |
|
Time: 0.75 hours |
|
Students complete the following activity. |
|
A store is eager to obtain your business so has faxed prices for various items. Complete the following analysis. Round to the nearest cent. |
1. What
is the unit cost of each of the following?
a. 1
dozen pencils for $3.60
b. 3
rolls of Scotch tape for $2.97
c. 2
packages of 10 pens for $5.98
d. 4
packages of lined paper for $6.98
e. 5 highlighters for $3.59
2. If
you sell each of the above items, you will charge 10% more than you paid. How
much will you charge for the following?
a. 1
pencil
b. 1
roll of Scotch tape
c. 1
pen
d. 1
package of lined paper
e. 1
highlighter
3. In
each of these questions, determine whether (a) or (b) gives you the most for
your money by calculating the price per unit. (Round to the nearest cent.)
a. 100
sheets of paper for $1.89
500 sheets of paper for $9.98
Best Buy
b. 12 pens for $3.98
24 pens
for $6.89
Best Buy
a. 500
mL bottle of glue for $1.29
1 L
bottle of glue for $2.98
Best Buy
b. package of 12 pencil crayons for $2.49
package
of 24 pencil crayons for $4.98
Best Buy
Extension
· A guest speaker involved in the retail industry would provide insight into the determination of merchandise pricing. The speaker could also serve as a career link for students interested in retail.
· Students may wish to visit a charitable organization to become informed of its fund raising ventures and its use of funds.
· Blind or low vision students may need to have the chart introduced on an individual basis to ensure that they understand the format.
· A glossary of terms should be available for deaf or hard of hearing students.
· Knowledge and understanding may be assessed by checking the students’ work for accuracy.
· To assess thinking and communication, individual students should be asked to explain how they accomplished specific tasks with their calculators. (e.g., “Show me how you calculated the provincial sales tax? What did you do differently for the GST?” Why did you select that item as the ‘best buy’?)
· Three or four students per day could be assessed on their independent work habits, using Appendix J.
· All students complete the Self-Assessment, Appendix M, on the last day of the activity.
· The assessments completed by the teacher and the student could be compared in a student-teacher conference.
Flyers or ads detailing the cost of school supplies
Appendix A – Worksheet 1.1
Appendix J – Learning Skills Rubric
Appendix M – Self-Assessment
Time: 3.5 hours
The workplace environment serves as the context in which students extend their skills with decimals, fractions and percent. In this activity, students gain exposure to the mechanics of calculating salary, overtime hours, commission, and pay increases. They consider various salary options to make comparative judgments.
Strand(s): Number Sense
Ontario Catholic School Graduate Expectations
CGE2b - reads, understands and uses written materials effectively;
CGE2d - writes and speaks fluently one or both of Canada’s official languages;
CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;
CGE4f - applies effective communication, decision-making, problem-solving, time and resource management skills.
Overall Expectations
NSV.01 - use a variety of methods for calculation when solving problems (e.g. mental mathematics or estimation, calculator, paper and pencil computational method) and apply the method effectively.
Specific Expectations
NS1.02 - use a scientific calculator effectively to evaluate expressions involving fractions, decimals, percent, exponents and square roots, as they arise in problems throughout the course;
NS1.03 - evaluate expressions involving the rules of operations, by hand and by using calculators;
NS1.04 - use estimation and mental computation to approximate and/or calculate answers to numerical problems as they arise throughout the course;
NS1.05 - apply percents in solving problems (involving aspects such as: discounts, sales tax, commissions, interest and ratios).
· Students may work individually or in pairs throughout the activity.
· A mini-review on converting fractions to decimals can be conducted. Students should be able to perform this conversion by hand for simple fractions (1/2, 1/4, 1/10) and with the aid of a calculator for more complex fractions. Operations with fractions (addition, subtraction, multiplication and division) should be limited to two fractions. When more terms with fractions are involved, students should convert fractions to decimals.
· Questions incorporating the order of operations should, in general, be limited to two operations (e.g., adding terms in a bracket and then multiplying the sum by a number).
· The teacher should precede this activity with a review of addition and subtraction of fractions.
Number Sense
· apply strategies for mental mathematics and estimation
· use a scientific calculator effectively
· judge the reasonableness of answers
Teacher Facilitation: The teacher introduces the scenario of a music store open seven days a week with 15 employees. Some students from the club are involved in part-time jobs to raise money for the club’s excursion. Class discussion focuses on the efficient scheduling of the employees (full time and part time), hourly wages, and overtime requirements. Students may also discuss the benefits and deductions affecting full-time employees. Students relate considerations when having part-time employment while registered full-time in school. Students and the teacher define the meanings of average wage, overtime, and time and a half.
The teacher distributes the student activity and, with student input, completes the calculations for one or two employees. The teacher initiates the calculations by multiplying the hourly rate by the hours worked for one employee on one particular day. The teacher completes the calculation for the second day and queries students as to a faster method of doing the calculations. Students are led to realize that a first step of summing the weekly hours will simplify proceedings. The teacher completes the alternate method.
During these calculations, the teacher reviews the rules for the order of operations. The students assist the teacher in determining the hourly overtime rate for various employees. The teacher circulates around the classroom to assist and observe students during the subsequent activity.
The following chart shows the hours worked and hourly wage of seven of the employees. Employee “h” is left blank for you. Place your name and the hours you would work in a typical week in row “h”. Keep in mind your school and home responsibilities as the hours that you work should be reasonable. You are being paid $7.25 per hour.
A regular work week is 40 hours. Any hours over 40 hours are considered overtime. You are paid time and a half for overtime hours.
|
Employee MGM Music |
Mon. |
Tues. |
Wed. |
Thur. |
Fri. |
Sat. |
Sun. |
Hourly Wage |
|
a) Ms. Javier |
8 |
8½ |
8 |
9 |
10 |
— |
— |
$18.50 |
|
b) Mr. Pucci |
8 |
— |
— |
9 |
9 |
10 |
10 |
$15.25 |
|
c) Michele |
4¾ |
— |
4¼ |
4 |
5 |
— |
— |
$ 8.50 |
|
d) Benoit |
— |
3 |
4 |
4¼ |
4 |
6¼ |
— |
$ 8.00 |
|
e) Sandeep |
— |
— |
— |
4¾ |
8 |
8¼ |
4½ |
$ 7.50 |
|
f) Jodene |
4 |
4 |
4½ |
4 |
— |
— |
— |
$ 7.25 |
|
g) Bianca |
— |
— |
— |
— |
6¼ |
6¾ |
6 |
$ 7.25 |
|
h) |
|
|
|
|
|
|
|
$ 7.25 |
|
Totals |
|
|
|
|
|
|
|
XXXXX |
1. For each employee, calculate the total hours worked and the weekly wage, remembering to calculate the overtime hours as outlined above.
2. What is the store’s total wage payout for the week?
3. Use the total employee hours worked per day to determine:
a) Which day is the busiest day of the week?
b) Which day is the slowest day of the week?
4. If each employee receives a wage increase of 5%, what will each employee’s new weekly wage be?
5. What would be the new total wage payout for the week?
6. Why do you think Ms. Javier earns the most money per hour?
Teacher Facilitation: The teacher opens a discussion on the meaning of the term commission. Some of the students may have parents or relatives that work on commission and may be able to contribute more to the discussion.
The teacher poses scenarios to illustrate good and bad months for payment by commission: An employee in an electronic store receives commission on all sales he/she makes. The class discusses the employee’s earnings in December as compared to February. The class brainstorms the advantages and disadvantages of commissioned earnings.
Discussion then relates to the pros and cons of commission compared to a combination of salary plus commission. The discussion also examines how commission may, in a few instances, lead to unethical practices (pressure sales, dishonesty etc.).
The students imagine that they are new car salespeople. They indicate which of the following payment methods they would prefer and, they explain why they would choose the option.
a) straight 5% commission
b) $500 per week and 2.5% commission
c) $1000 per week
Students are to describe the advantages and disadvantages of each method to the owner of the new car dealership.
Ms. Javier seeks your advice. The owner of the music store has offered her a chance to change her wage structure. She may work at one of the following rates:
a) straight 5% commission on all sales
b) $400 per week and 2% commission on all sales
c) the same number of hours and hourly wage as outlined in the previous chart.
Complete the charts below to see how much money she would make under each of the three plans.
Include her salary from the previous chart in the last column.
|
Sales |
Option A pay (5% of sales) |
Option B pay ($400 + 2% of sales) |
Option C pay |
|
11 000 |
|
|
|
|
15 000 |
|
|
|
|
20 000 |
|
|
|
1. Which plan do you think Ms. Javier should take and why?
2. Create your own example of a commission problem like this one. You are to submit to your teacher, the problem, the options (with calculations) and your recommendation for the person’s payment plan. State why you would recommend the plan.
|
Follow-up Activity |
|
Time: 1 hour |
|
Students enter their thoughts on commission in a journal entry. |
|
Students complete teacher-complied questions on concepts developed in this unit, including the order of operations. |
Extension
Students perform the calculations to permit all employees to take advantage of the three plans. They graph three lines to represent the three plans and use the graphs to determine the best choice for various cases. Students format a spreadsheet to display the tables and graphs.
· Students may be provided with a model for the calculation of answers.
· The number of examples in the first worksheet may be reduced.
· The BEDMAS acronym should be posted on a wall of the classroom to assist students.
· The teacher may assess knowledge by checking the worksheets for accuracy.
· Learning skills may be assessed for one or two of the students using Appendix J.
· Communication may be assessed through students’ responses in class discussions and through entries in their math journal.
· A quiz on the mechanics of percent, rounding, and estimation would serve as formative information.
Appendix H – Sample Observational Checklist
Appendix I – Written Report Rubric
Appendix J – Learning Skills Checklist
Time: 6 hours
Students commence this activity by determining in what manner to save the money from the fund raising venture described in Activity 1.1. In the process, they explore the difference between simple and compound interest. They further consolidate their skills in operations with decimal, exponents, and percents. Students examine the Internet sites of banks to obtain financial information.
Strand(s): Number Sense
Ontario Catholic School Graduate Expectations
CGE2a - listens actively and critically to understand and learn in light of gospel values;
CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;
CGE4f - applies effective communication, decision-making, problem-solving, time and resource management skills.
Overall Expectations
NSV.01 - use a variety of methods for calculation when solving problems (e.g., mental mathematics or estimation, calculator, paper and pencil computational method) and apply the method effectively.
Specific Expectations
NS1.02 - use a scientific calculator effectively to evaluate expressions involving fractions, decimals, percent, exponents and square roots, as they arise in problems throughout the course;
NS1.03 - evaluate expressions involving the rules of operations, by hand and by using calculators;
NS1.04 - use estimation and mental computation to approximate and/or calculate answers to numerical problems as they arise throughout the course;
NS1.05 - apply percents in solving problems (involving aspects such as: discounts, sales tax, commissions, interest and ratios);
NS1.06 - solve problems involving fractions and decimals using appropriate strategies and calculation methods;
NS1.07 - judge the reasonableness of answers to problems by considering likely results;
NS1.08 - judge the reasonableness of answers produced by a calculator or computer, using mental mathematics and estimation.
· Students may not have had previous exposure to the power key (yx or ^) of their calculator. The teacher ensure that students know how to use this function if students choose to calculate compound interest using the formula, A = P(1 + i)n.
· Newspaper or magazine articles and ads on interest rates, RRSPs and savings plans underscore to the students the importance of budgeting one’s earnings. The teacher may wish to provide articles for student enrichment or request that each student find an article which discusses interest rates or savings plans.
· The teacher may wish to review with the students, in advance of the activity, the number of weeks and months in a year.
· The majority of the applications should be directed to annual time periods with only a few problems dealing with weekly and monthly time periods. This topic is further expanded in the grade 11 course, Mathematics for Everyday Life.
· During this activity, students are required to obtain information on types of bank accounts for youths. If the Internet is not available, the class could travel to a local bank or make arrangements for a bank official to visit the class.
· The suggested time for the Internet activity is 2 hours.
· The calculation of compound interest is developed in a series of steps due to the conceptual difficulty experienced by many students. The formula for compound interest is established in the “Extension” section of this Activity. However, teachers may choose to have students use the formula in place of the series of steps.
· Students should have ready access to the formula for simple interest throughout this unit. The objective is for students to understand when and how to use the formula.
Number Sense and Algebra
· apply strategies for mental mathematics and estimation
· use a scientific calculator effectively
· judge the reasonableness of answers
· apply rounding to decimal notation
· convert numbers from percent to decimal
Teacher Facilitation: The teacher initiates discussion by having students recall the first activity, “Generating Funds”. Students recall that in questions 4a, they obtained an amount equal to 18% of the subtotal. They are also informed that the money from selling school supplies amounts to $36.00 per week. All money will be used primarily for the Christmas food and toy drive and to subsidize the club’s trip in May. The teacher has students suggest other uses for the money. The students must determine in what manner to save the money. Students and teachers make suggestions regarding saving the money in the bank, in a Canada Savings Bond or in a GIC. In the process, the teacher explains financial terminology such as term deposit, savings bond, passbook, interest. The teacher has students reflect on why banks and other corporations are willing to give interest
Students, working individually or in pairs, employ the Internet to determine the financial services available to them as designated students or youth. They choose two financial institutions to search. For each institution, they are to determine (if available):
· the age requirement for the account.
· when interest is paid on the account.
· if there are any fees for withdrawals.
· if the person receives a passbook or monthly statement.
Students, individually, prepare an ad (for a bulletin board display) providing information on the account for young people, offered by one of the banks.
Teacher Facilitation: The teacher informs students that ¼ of the money from the uniform fund is to be used for the Christmas drive and the remainder will be used for the trip. The students calculate the amount for each purpose. The students also consider the income earned from part-time employment (the music store) and the amount which students could save weekly from such income. Students and teacher discuss the preferred types of savings plans for the various sources of income.
The teacher explains simple interest and the formula, I=PRT, to the students, noting that interest can be both paid to an individual and paid by an individual.
The teacher stresses that although interest and principal are stated in dollars, the interest rate is to be converted from a percent to a decimal and the time is converted to a portion of a year.
The teacher reinforces the fact that time is measured in years by having students determine the fraction of the year represented by various months, weeks, and days. For ease of calculation, the time is converted from a fraction to a decimal. With teacher direction, the students work through examples in which they calculate simple interest using the formula I=PRT with their calculators.
The explanation is supported by a mental mathematics activity in which students answer questions such as:
“What decimal value equals 10%?” or “What is the interest if you put $100 in the bank at 10% interest for one year?”
The students, working in groups, complete questions related to simple interest. To foster learning and allow early remediation, these questions should proceed from items in which students simply change percent to decimals and, in which they determine the fraction of a year for given times, to questions such as the following:
1. Jermaine deposits $1600 into an account to save for a new computer. He obtains a simple interest rate of 3% for 4 years. Calculate the interest earned.
2. Who earns the greater amount of interest?
a. Mr.
Johnson, with an investment of $8 500 for three years at 9 % per year.
b. Mrs. Yang, with an investment of $10 500 for three years at 8% per year.
3. Christian
borrows $3000 for 6 months at a rate of 5%. How much interest will he owe in 6
months? What is the total amount that he owes in 6 months?
Teacher Facilitation: The teacher refers to the amount of money for the Christmas drive,
raised from the sale of uniforms. Students are queried as to the value of the
money available after 6 months from a deposit at a simple interest rate of 4%
per year. The teacher introduces the formula for amount
(A = P+ I) and guides students through a series of questions.
Students determine the amount of money owed or received for the previous series of questions in the student activity.
Teacher Facilitation: The teacher investigates the following scenario with the class.
Five years ago, your favourite uncle inherited a million dollars. He gave you $8000 and put the money in a term deposit that paid 4% per year compounded annually. What is the value of the account now?
The teacher defines compound interest and with student assistance, detects the differences between compound and simple interest. Examples for compound interest are restricted to annual periods.
1. Complete the chart. For each time period, calculate the interest and then the amount. Place the ending amount for one year in the column for the beginning amount for the next year. The calculations for the first year have been done for you.
|
Year |
Amount |
Interest for the interest period |
Amount = Amount + Interest |
|
1 |
$8000 |
8000 x 0.04 x 1 = $320 |
$8000 + 320 = $8320 |
|
2 |
$8320 |
|
|
|
3 |
|
|
|
|
4 |
|
|
|
|
5 |
|
|
|
2. Calculate the amount if the $8000 had been deposited in an account, for 5 years, earning 4% per year simple interest.
Teacher Facilitation: The teacher assists the class in noting the benefits of compound interest. The teacher explains to the class that interest may be compounded semi-annually or quarterly.
Students complete practical questions related to compound interest. For each question, they are to construct a chart to display the interest and amount at each time interval. Thus, the period of investment should be relatively short. An example of a question is provided below:
Lina hopes to have saved $3000 in 3
years to use as a down payment on a car. She deposits $2 000 into a term
deposit, at 6% compounded annually for 3 years. Will she have enough money at
the end of 3 years for the down payment? If she will not have enough money,
what changes in her plan would you suggest?
|
Follow-up Activity |
|
Time: 0.5 hours |
|
In their journals, students describe the financial information, acquired during this activity, which has relevance to their present and/or future plans. They obtain articles or advertisements from magazines or newspapers to support their information. |
Extension
· The teachers instructs students on the use of the formula, A = P(1 + i)n to calculate compound interest. Student complete the assigned questions on compound interest by using this formula.
·
The teacher introduces questions on
compound interest when the period for which interest is compounded is less than
a year (quarterly, semi-annually). An example is provided below:
Which is the better investment: $1000 invested at 6% compounded annually for
5 years, or
$1000 invested at 6% compounded semi-annually for 5 years?
· Students continue their search of bank sites to determine the types of account offered for adults. They develop a chart comparing the benefits and service charges of each type of account.
· Learning disabled students have access to a sheet detailing the steps and formula for calculating simple interest.
· Key financial terminology should be reviewed with deaf and hard of hearing students prior to the commencement of the activity.
· Students complete a quiz on the mechanics of simple interest. The formula should be provided for their use. Students are evaluated for knowledge and problem solving.
· The Written Report rubric, Appendix I, may be modified to assess the journal entry.
· The problems on interest are assessed for accuracy.
· The ad for the bank’s service may be assessed with the Observational Checklist, Appendix, H, or the Communication segment of rubric, Appendix I (with appropriate modification).
Internet sites for Canadian banking establishments such as:
http://www.bmo.com/
http://www.canadatrust.com/
http://www.cibc.com/
http://www.mortgagestore.com/laurent/eng_page_2.html/
http://www.royalbank.com/
http://www.scotiabank.ca/
http://www.tdbank.ca/index.html/
Newspaper and magazines displaying information on financial services
Appendix H – Observational Checklist
Appendix I – Written Report Rubric
Time: 5 hours
In this activity, students expend the amount of money that was “raised” in Activity 1 for the Christmas food and toy drive. In completing this activity, they use spreadsheet software to track their expenses and total costs. Estimation techniques are practiced as they maintain a running total of their “purchases” to ensure that they have sufficient money to purchase the items that they desire.
Strand(s): Number Sense
Ontario Catholic School Graduate Expectations
CGE2b - reads, understands, and uses written materials effectively;
CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;
CGE4f - applies effective communication, decision-making, problem-solving, time and resource management skills.
Overall Expectations
NSV.01 - use a variety of methods for calculation when solving problems (e.g. mental mathematics or estimation, calculator, paper and pencil computational method) and apply the method effectively.
Specific Expectations
NS1.01 - use pencil and paper computational methods effectively to evaluate expressions involving fractions decimals, and exponents as they arise in problems through out the course;
NS1.02 - use a scientific calculator effectively to evaluate expressions involving fractions, decimals, percent, exponents, and square roots, as they arise in problems throughout the course;
NS1.04 - use estimation and mental computation to approximate and/or calculate answers to numerical problems as they arise throughout the course;
NS1.05 - apply percents in solving problems (involving aspects such as: discounts, sales tax, commissions, interest, and ratios);
NS1.06 - solve problems involving fractions and decimals using appropriate strategies and calculation methods;
NS1.08 - judge the reasonableness of answers produced by a calculator or computer, using mental mathematics and estimation.
· Although this activity incorporates a spreadsheet program, it can be completed with a calculator and paper and pencil.
· The accompanying worksheet has been written for use with Corel Quattro Pro 9. The worksheet may be modified for use with other versions of the program or for use with Excel.
· The teacher may wish to have a template loaded onto the computers with the column headings, age intervals for the children, and number of girls and boys in each interval. This adjustment would enable students to complete the activity in less time.
· A computer lab is required for this activity.
· The teacher should ensure that students understand that the cells of a spreadsheet are identified by row and column (e.g., A1).
· The students require catalogues or flyers displaying children’s toys and the prices of the toys.
· Sessions for which a computer lab are required are expected to take approximately 2.5 hours. Students will be entering their selections and modifying their selections to reach a total that is slightly less than $1300.
· The teacher may wish for students to choose toys from an appropriate Internet site.
Number Sense
· apply strategies for mental mathematics and estimation
· use a scientific calculator effectively
· judge the reasonableness of answers
· apply rounding to decimal notation
· convert numbers from percent to decimal
Sharing the Wealth
Teacher Facilitation: The teacher announces to the class that they are going to spend ¼ of the funds from the uniform sales on food and toys during the Christmas food drive. Students may wish to supplement the amount raised with personal donations. The class is to work in groups to develop a shopping list for toys for 50 children aged from under one year to 12 years of age.
Your group is to determine suitable toys for 50 children of age and gender as outlined below:
|
Age |
Boys |
Girls |
|
Under 1 |
3 |
4 |
|
1 – 2 |
5 |
3 |
|
3 – 6 |
6 |
9 |
|
7 – 9 |
7 |
3 |
|
10 – 12 |
4 |
6 |
· You have a total of $1300.00 to spend, including tax, on toys.
· The price of each gift must be between $8.00 and $30.00.
· You may not choose a gift that requires other equipment. Assume that batteries are included.
· The total cost of all gifts, including tax, should be as close as possible to $1300.00 but not greater than $1300.00.
· Each child in a particular group is to receive the same gift. For example, all 5 year old girls must receive the same gift. Since 5 year old girls are in the age interval 3-6, all girls between the ages of 3-6 will receive the same gift as 5 year old girls.
In order to make a shopping list, look through catalogues and flyers for suitable toys. Set up a spreadsheet to calculate the total cost, including 8% PST and 7% GST. On paper, keep an estimate of what you are spending so that your costs do not exceed $1300.00.
You and your partner are to produce:
· A shopping list of items to be purchased
· A picture, clipped from a catalogue or flyer, of 10 items, accompanied by the price of each item
· A spreadsheet printout displaying your calculations
· A report, explaining the reasons that you chose the 10 items for which you have the picture.
Use Worksheet 1.2, “Sharing the Wealth” (Appendix B) to do the calculations with the Spreadsheet. Before you begin working in the spreadsheet, select 5 toys to record immediately in the spreadsheet. Once these toys are entered, you can determine how much money you have spent and how much is remaining for the other toys. Keep a record of the toys and the price of the toys on paper to assist in estimation. Choose the next toy and enter it into the category. Continue in this manner. You can make changes to your selection at any time.
Teacher Facilitation: Prior to entering the computer lab, the teacher and students read the instructions on Worksheet 1.2, Appendix B. The teacher models the spreadsheet entries and estimation procedures on the blackboard for a few age intervals. This period of instruction clarifies some questions that students have regarding the use of the spreadsheet.
The teacher circulates among the students during the activity to insure that students have entered the correct formula into the proper cells of the spreadsheet. The teacher reminds students to continually estimate their subtotal.
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Follow-up Activity |
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Time: 0.5 hours |
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Students, working in pairs, will do question 1 or question 2 that follow. |
1. Joan lives in Marathon, Ontario. She is planning to attend a concert in Thunder Bay. Her costs are as follows:
· Ticket to the concert $34.50
· Bus (return fare) $62.00
· Taxis $24.00
· One night accommodation $65.00
· Meals, including snacks $42.00
a) Estimate the total cost if Joan goes alone.
b) Calculate the total cost of this trip.
c) Calculate the cost if 4 people go together with 2 people sharing a room.
d) Calculate the cost for one person if your church youth group charters a bus that holds 32 people. The cost of the bus is $1200.00 and is equally shared by the 32 people. There is no cost for a room because the bus will return home right after the concert. Taxi cost is also eliminated. Reduce the cost of individual meals by $12.00.
e) How much do you save by taking the bus trip with your youth group?
2. You are going to the movies with your best friend. Your costs will be:
· Tickets to the movie $9.00
· Popcorn $4.50 a box
· Drinks $2.50 each
· Bus – one way $1.50
a) Calculate the cost for you and your friend together.
b) Calculate the cost if you are taking a group of six children from the Children’s Liturgy group at church.
Note – Tickets for the children are $4.50. Each child will order one drink and one box of popcorn. How much will each child have to pay to attend?
Extensions
· Students who display facility with the spreadsheet may wish to add two more columns to their worksheet. The first column would be a running total of what they had spent and the second column would indicate the amount of money remaining in the fund.
· Students consider their expenses over a two week period. They use the spreadsheet to form a budget for two weeks and to track their actual expenses.
· Assistance from peer tutors or educational assistants would alleviate some of the anxiety for learning disabled students when working in the spreadsheet.
· The teacher may instead wish to modify the assignment such that headings and cell functions for the worksheet have been preset prior to the beginning of the class.
· Peer tutors or educational assistants should introduce this activity in advance to blind and low vision students. The students could then pre-select the toys prior to the commencement of the activity.
· A glossary of terms related to the spreadsheet should be prepared in advance and presented to the deaf and hard of hearing students. Students could then focus on the instructions and not on learning the meaning of terms.
· The completed project is assessed for knowledge/understanding; thinking/inquiry/problem-solving and communication using the written report rubric (see Appendix I for an example).
· The follow-up activity is assessed, by observation, for independence and initiative in applying knowledge of percents and decimals using Appendix J.
Licensed spreadsheet software
ClarisWorks
Microsoft Works
Corel WordPerfect Suite
Catalogues or flyers detailing toys and their prices
Appendix B – Worksheet 1.2
Appendix I – Written Report Rubric
Appendix J – Learning Skills Checklist
Time: 2.5 hours
Students explore relationships among distance, speed, and time as the base upon which to solidify their comprehension of rate. Through performing an experiment, and through paper and pencil activities, they obtain practice in solving problems involving rate. Students consider alternate conditions that may affect the results of their experiment.
Strand(s): Patterns and
Relationships
Ontario Catholic School Graduate Expectations
CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;
CGE4f - applies effective communication, decision-making, problem-solving, time and resource management skills;
CGE5a - works effectively as an interdependent team member.
Overall Expectations
NSV.02 - consolidate the meaning and use of proportionality through applications drawn from student experiences and broader contexts;
PRV.02 - collect and analyse data that will result in linear relationships.
Specific Expectations
NS2.01 - demonstrate an understanding of the relationship between decimals, percent, rates and ratios;
NS2.03 - solve problems involving ratio, proportion, and scale, drawn from familiar applications;
NS2.06 - communicate solutions to problems involving rates, proportion and scale and the results of these investigations using appropriate terminology, symbols and form;
PR2.01 - formulate an hypothesis about a relationship between two variables and express the relationships in words and/or symbols;
PR2.02 - collect data using appropriate equipment and/or technology;
PR2.06 - solve problems related to the design or the findings of an experiment.
· Problems in this activity should be situated in a realistic context to develop students’ awareness of the relevance of ratios and rates. Questions related to reducing ratios to lowest terms, or determining equivalent fractions, should written such that students would readily ascertain common factors.
· For the preliminary investigation, the distance to a particular site in the school, from the classroom, is required. The route should be one frequently traversed by students: to a locker, to the cafeteria, to the library. The teacher may wish to have the distance predetermined or to have the students actually measure the distance. The teacher may wish to have groups of students travel to different locations in the school rather than all travelling to the same location.
· The teacher may encourage students to measure the distance to the location by using a pedometer.
· Appendix C, a list of Ontario destinations measured from Toronto, may be replaced with a list of destinations measured from the secondary school or surrounding locale.
· An atlas of Ontario and an Ontario CAA booklet would serve as a resource to students who are recent residents of the province or to students who have not travelled to a large extent.
· A stopwatch or watch with a second hand is required for this activity.
· A suggested time interval for the initial investigation in which students determine the average rate of walking and, the subsequent discussion, is approximately one hour.
Number Sense
· identify rates
· use a scientific calculator effectively
· judge the reasonableness of answers
Patterns and Relationships
· make a hypothesis regarding a relationship between two variables
· understand the concept of a variable
Teacher Facilitation: Students are requested to reflect on possible destinations for the 4-day journey to be undertaken by the club. The discussion proceeds to considerations in determining the amount of time needed to arrive at the destination (distance, speed, mode of transportation, traffic congestions, stops en route). The teacher proposes to the students that they determine the average speed for an individual to travel from the classroom to a predetermined location, hereby referred to as Point X. The class reflects on the method of determining the average speed after recognizing that speed is calculated as distance/time or s = d/t. The teacher leads the class in a mini-review of average.
Students and the teacher develop a form to record the results of the experiment.
Students are grouped in threes and are designated as Group A or B. Students are provided with the following instructions:
You are to determine the average speed to travel by foot from the classroom to Point X.
1. One member of your group is to be the “traveller”. The traveller is to walk to Point X twice – once at a normal pace (N) and once at a fast pace (F).The order in which the traveller in your group completes the two walks is shown in the chart below:
Pacing Schedule
|
A |
B |
|
F |
N |
|
N |
F |
For example, if you are in group “B”, the traveller is to walk at a normal pace on the first journey. The second journey is to be walked at a fast pace.
2. One individual is to be the recorder. This individual records the amount of time that it took the traveller to reach the destination.
3. Someone in your group is to be the official timer and someone is the official starter. The timer is to be situated well ahead of the traveler. The official starter will signal when the traveler is to begin walking. At that point in time, the timer starts the stopwatch. The timer moves to the destination to await the traveller’s arrival. The timer stops the watch when the traveler arrives.
4. The traveller has a one-minute break after he/she returns to the class before beginning the next trip. The official recorder and starter switch roles.
5. After both journeys are completed, the group determines the average speed of travel. Why did you not time the return journey?
6. How far could the individual walk in 9 minutes at the average speed?
7. Consider repeating the experiment. What changes in the way that the experiment was conducted may result in a different average speed?
Teacher Facilitation: The teacher reconvenes the whole class and the groups present their findings. The class discusses the factors that may have led to differing rates of speed. The class determines an average rate of speed for the students in the class, based on all responses. The teacher and students provide examples of other situations when speeds are combined to determine an average speed (i.e., journeys in which the speed limit is not consistent).
The teacher initiates discussion on examples to determine distance or time. The teacher and students determine that d=s*t and t=d/s. During this discussion, the teacher should refer to the units in which each variable is measured.
Consider the city of Toronto as a destination for the club’s trip. However, there are many interesting sites outside the city of Toronto that could be visited. Appendix C lists various destinations in Ontario. The distance from Toronto to the site is provided as is the average speed in traveling from Toronto to the site.
· Form 6 columns in your notes as indicated below:
|
Destination |
Distance |
Speed |
Time |
Amount of Gas Needed |
Cost of Gas |
|
|
|
|
|
|
|
· Choose 5 interesting destinations to visit.
· Record the total distance (going and returning).
· Record the speed.
· Record the total time of the trip to travel to each destination.
· You must return to Toronto in time for dinner and a Blue Jay game at 7:05 pm. You do not wish to spend more than 4 hours in total on the road, to and from the destination. Are your choices acceptable or not? Place a 4(check mark) by the destination if it is acceptable, and an “X” if it is not.
Teacher Facilitation: The class reconvenes and discusses acceptable destinations.
The class brainstorms rates that are encountered in their daily environment: goals per game, litres of gas per 100 km. The class considers the problem of determining the amount of gas needed for a 385 km trip if the vehicle’s fuel consumption is 11.2L/100 km. To complete the problem, the students convert the fuel consumption to unit rate (0.112 L/1 km). They then multiply 385 by 0.112 to obtain the amount of gas. The cost of gas is determined based on the price of gasoline at the time of the activity.
· Determine the amount of gas needed for the 5 journeys and the cost of the gasoline using a fuel consumption of 11.2L/100km.
|
Follow-up Activity |
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Time: 0.75 hours |
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Students complete questions on rate, such as the following: |
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1. A train travels 667 km in 4 hours. What is its average speed? How far will it travel in 6 hours? |
|
2. A student rides a bike at a rate of 3.3 km/min. How far does she ride in 15 minutes? |
|
3. Your aunt has a sport utility vehicle. Its advertised fuel consumption for the city is 7.4 L/100 km. She drove 365 km with 26 L of gas. What is the fuel consumption of the car? |
Extension
· On the Internet site, http://www.canadiandriver.com/testdrives/, students may obtain information on the fuel consumption of various models of cars. Students may wish to develop a comparative analysis of the city and highway fuel consumption of cars based on the size of the car.
· Students, working in pairs, may consult a highway map of Ontario, surrounding provinces or surrounding states, and choose a destination that they would like to visit. They would plot a route, listing the highway(s), and distance to be traveled on the highway(s). Using the indicated speed for the highway, they would determine the approximate time required for the trip. Students would then be required to complete the exercise using an alternate route in attempt to find a more efficient itinerary.
· The formula for distance, d=s*t, and its variations (s=d/t and t=d/s) should be displayed to assist students in processing the terminology.
· A talking stopwatch would assist blind and low vision students in completing the first investigation.
· Students who have recently moved to the province may benefit from receiving Appendix C and an atlas or CAA book on Ontario in advance. They could then determine points of interest prior to the activity in which they choose 5 destinations.
· The teacher assesses some students with the Learning Skills Checklist, Appendix J, on their independent work habits, during completion of the destination chart.
· Some students are assessed with the Observational Checklist, Appendix H, to determine if they apply appropriate strategies during the investigation of student rate of walking.
· Student knowledge of the method for calculating speed, distance and time is evaluated with a mini- quiz.
Stop watches
Internet sites
http://www.canadiandriver.com/testdrives/
http://www.transontario.com/chart.html/
Appendix C – Destinations
Appendix H – Observational Checklist
Appendix J – Learning Skills Checklist
Time: 6 hours
In this activity, students apply numerical skills related to monetary matters. Students, working in groups of four, are required to plan a trip for the end of the school year. They are responsible for determining a destination, method of reaching the destination, itinerary and budgetary considerations for the journey. This activity affords an opportunity to incorporate geographical and mathematical skills.
Strand(s): Number Sense
Ontario Catholic School Graduate Expectations
CGE2b - reads, understands, and uses written materials effectively;
CGE2c - presents information and ideas clearly and honestly and with sensitivity to others;
CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;
CGE4b - demonstrates flexibility and adaptability;
CGE5g - achieves excellence, originality, and integrity in one’s own work and supports these qualities in the work of others.
Overall Expectations
NSV.01 - use a variety of methods for calculation when solving problems (e.g. mental mathematics or estimation, calculator, paper and pencil computational method) and apply the method effectively;
NSV.02 - consolidate the meaning and use of proportionality through applications drawn from student experiences and broader contexts.
Specific Expectations
NS1.02 - use a scientific calculator effectively to evaluate expressions involving fractions, decimals, percent, exponents and square roots, as they arise in problems throughout the course;
NS1.03 - evaluate expressions involving the rules of operations, by hand and by using calculators;
NS1.04 - use estimation and mental computation to approximate and/or calculate answers to numerical problems as they arise throughout the course;
NS1.05 - apply percents in solving problems (involving aspects such as: discounts, sales tax, commissions, interest, and ratios);
NS1.06 - solve problems involving fractions and decimals using appropriate strategies and calculation methods;
NS1.07 - judge the reasonableness of answers to problems by considering likely results;
NS1.08 - judge the reasonableness of answers produced by a calculator or computer, using mental mathematics and estimation;
NS2.01 - demonstrate an understanding of the relationship between decimals, percent, rates and ratios;
NS2.02 - demonstrate an understanding of and apply unit rate in problem solving situations;
NS2.03 - solve problems involving ratio, proportion, and scale, drawn from familiar applications;
NS2.06 - communicate solutions to problems involving rates, proportion and scale the results of these investigations using appropriate terminology, symbols, and form.
· The teacher is actively involved in leading discussions at the commencement of this activity. As the activity progresses, the students take ownership of their plans. However, it is recommended that the teacher closely monitor groups to ensure that interesting tangents do not lead them too far astray.
· Groups meet at various stages with the teacher to review their plans.
· An atlas with a map of Ontario as well as the surrounding provinces and states will assist students in choosing a destination. It would be useful to have at least one road map of Ontario that provides distances between communities in Ontario.
· Students should be afforded the opportunity to access the Internet for specific distances in Ontario. One method is to by log on to the Internet and, in the Search function, type “Travel Distances-Ontario”. From this site, distances can be found between any two communities in Ontario.
· Students or the teacher may contact travel agencies to acquire brochures on packages tours.
· Fares for bus, airplanes, or trains may be viewed through the Internet or by using a toll-free number.
· Rates for hotels or motels can be obtained from Internet sites, travel brochures or booklets from the CAA.
· The teacher may wish to simplify the activity by choosing a destination or to have students choose a destination from those listed in Appendix C.
· Worksheets 1.4a and 1.4b (Appendix D) provide, respectively, some driving distances and attractions for various localities. This appendix represents optional material.
· The resource section lists Internet sites which may be accessed to assist students in determining the mode of transportation to reach their destination.
Number Sense
· apply strategies for mental mathematics and estimation
· use a scientific calculator effectively
· judge the reasonableness of answers
Supplementary Skills
· read a map
Teacher Facilitation: The teacher presents the following scenario to the class.
The club has reconvened in a special meeting to determine the destination for the end of the year trip. In determining the destination for the four day trip, what budgetary and practical aspects need to be addressed?
In groups of four, students develop a list of considerations in planning the trip. One student is assigned the role of scribe for this segment of the investigation.
Teacher Facilitation: The class discusses what the groups have determined as considerations in planning a trip, such as cost of hotels, meals, transportation, tourist attractions, distance to destination. The class and teacher determine the amount of money remaining from the fund raising venture. The teacher informs students that they each obtained a term deposit, to be used for the trip, of $200 in September at 3% simple interest (per year) and will have the deposit for 8 months. This amount of money supplements costs over and above those costs covered by the fund raising activities and is to be used when determining the cost of the trip.
In their groups, students finalize their destination and plan a budget. They determine the amount of money available for each individual from the fund raising venture and the term deposit. Students must develop a chart or spreadsheet detailing probable expenses and total expenditure, including taxes. To complete the expense report, students must display the amount that students will have to individually provide for the trip. Students are required to report on tourist sites to visit at particular locations and to providing an itinerary of the trip. Entrance fees may be estimated.
Students co-operatively determine the function to be performed by each group member. The completed report will include:
a) Destination and mode of transportation (Meet with teacher)
b) Daily itinerary
c) Daily Cost worksheet (Meet with teacher)
d) Final Cost sheet
e) A list or statement as to what percent of the final cost is estimated for:
· Transportation
· Food
· Accommodation
· Entertainment (including visits to at least 2 tourist sites)
f) Self-assessment sheet (Appendix M)
At various intervals, as noted above, the group must confer with the teacher to obtain comments on their plan and suggestions for completing the activity.
Extensions
· Some students may wish to access Internet sites that provide maps and driving directions between specific points.
· Learning disabled students may require the assistance of a peer tutor or teaching assistant in searching web sites or reading a map.
· Tactile maps should be ordered in advance for blind and low vision students.
· The teacher may choose a destination and the mode of transportation for the students.
· The teacher may wish to provide students with bus, train or plane fares to the destinations that the students have chosen. This accommodation would simply the students’ tasks and, shorten the timeline for the activity.
· The teacher and students could develop a rubric for assessing the activity. The rubric would be designed as part of the initial discussion and enable students to become aware of all four categories being assessed throughout the course.
· Initiative and teamwork may be assessed throughout the activity using Appendix J.
· Each student completes a self-assessment using Appendix M.
· Peer evaluation can be completed using checklists and/or a modification of the Self-Assessment Rubric (Appendix M).
Maps, travel brochures, train schedules, bus schedules
Internet sites related to travel and distances such as:
http://maps.excite.com/address/
http://www.freetrip.com/
http://www.transontario.com./
Internet sites related to transportation such as:
http://aircanada.ca/
http://airontario.com/
http://www.greyhound.ca/
http://www.viarail.ca/
Appendix D – Worksheet 1.4a and 1.4b
Appendix J – Learning Skills Checklist
Appendix M – Self-Assessment