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Course Profile   Principle of Mathematics, Grade 9 academic, Catholic

 

Unit 4:  Making Connections

Time:  10 hours

Description

Students engage in activities that reflect the content and procedures of the course, in preparation for final assessment activities which may include a performance assessment and a final exam.

Strand(s) and Expectations

Ontario Catholic School Graduation Expectations:  CGE 2b, CGE 5a, CGE 5b.

Overall Expectations:  all

Specific Expectations:  all

Unit Planning Notes

Ten hours are allotted for preparation and carrying out of the final assessment activities.  It is recommended that these activities include both a performance assessment and a final examination.

Four sample activities are included that might be used as part of the preparation for the exam or performance assessment.  It is recommended that teachers supplement these activities with material drawn from the student textbook or other sources.

The activities are embedded within the following context:

A local organization has donated a piece of land to be used as a community park.  The land and a small wading pool have been donated, and the community has come together to do the necessary preparation work.  Students from the local schools are very involved. 

The activities are found on the following worksheets.

 

Student Worksheet – The Paper Chase

You have been put in charge of “Advertising” for the grand opening of the Community Park and have contacted two local newspapers to inquire about their rates for placing an ad. The Lake Graphit Gazette charges $ 15 per day for the ad that you want to place, regardless of how many days you wish to place the ad. Another local paper, The Mount Slope Reporter charges a flat rate of $ 100 plus $5 per day for the same ad.

 

1.       Write an equation to represent the relationship between total cost (C) and number of days (n) for:

a)   The Lake Graphit Gazette

b)   The Mount Slope Reporter

 

1.       a)   Construct a table of values for each relation. Pay special attention to which variable is the independent variable.

b)   Construct the graph of each relation on the same set of axes.

c)   Which line is steeper? Why?

d)   State the slope of each relation.

e)   Explain the meaning of the slope within this application.

 

2.       a)   At what point do the two lines cross?

b)   Interpret the point of intersection in the context of this application.

c)   Under what circumstances would you choose to advertise in each publication? Explain how you reached your conclusions.

 

3.       You discover a third local publication, which would charge $ 137.50 for 5 days and $ 162.50 for 15 days. Assume that there is a linear relation between the cost of the ad and the number of days that it would run.

a)   Determine the cost per day for the ad in this publication.

b)   Determine the flat fee charged.

c)   Write the equation of the linear relation.

d)   Add this line to your graph. Explain which publication is now the better choice.

 

Student Worksheet – A Pool Is Cool!

In one corner of the park, a section has been fenced off to enclose an in-ground wading pool for younger children. The section is in the shape of a trapezoid, having height 14 m and base lengths 25 m and 18 m. The wading pool is cylindrical in shape, having a diameter of 8 m and a height of 50 cm. The area outside the pool, but inside the fence, is planted in lawn.

A group of students has assumed responsibility for preparing the play area..

4.       Draw a diagram to represent the situation.

 

5.       One part of the preparation is the painting of the fence, which is 1.5 m high and constructed of closely packed boards. A local merchant is donating paint that requires 4 L for every 65 m2 of coverage. To put two coats of paint on both sides of the fence, how many 4L cans are needed?

 

6.       The wading pool is to be filled to a depth of 30 cm. A hose is available that flows water at a rate of 9 L/min. How long will it take to fill the pool to the required height?

 

7.       Before opening the area, the lawn is to be topped with top soil and then re-seeded. If the top soil is to be applied at a constant depth of 2 cm, how many m3 of top soil are required?

 

8.       There is a planter in the shape of a “frustum” on each side of the entrance to the play area. As shown in the diagram, a frustum is a cone that has been truncated (cut) parallel to its base. The dimensions of the planter are shown in the diagram. If each planter is filled to the brim with potting soil, how much soil is needed?

 

Student Worksheet: Something for the Gardeners

Another group of students has been assigned the task of designing a garden area for the park.  It is to be surrounded by a low hedging plant and enough plants are available to create a perimeter of 60 m. 

The group has been asked to identify the shape (e.g., triangle, quadrilateral, pentagon, ...) that would provide the maximum enclosed area for a perimeter of 60 m.

 

Design an investigation to identify the required shape.  Prepare a written report that includes:

an explanation of the design process

all diagrams, calculations, tables, graphs used as part of the investigation

a statement of the final shape identified, along with the dimensions that yield maximum area

an explanation of how you reached your conclusion and your thoughts on why the identified shape yields the maximum area

a description of other factors that might influence the choice of shape for the garden

 

Student Worksheet:  Water, Water, Everywhere!

All of the students brought along water because the day was warm and the work quite strenuous. One student had a sealed plastic bottle filled with water. A leak opened in the bottle and the water drained out at a constant rate.

 

Time t (seconds)

Height (h) of water in bottle (cm)

0

25

10

22

20

19

30

16

40

14

50

12

60

8

70

6

80

4

90

2

100

0

 

The table above identifies the height (in cm) of water in the bottle at time t seconds after the draining began.

a)   Recopy the table and extend to calculate the finite differences.

 

b)   Is this relation linear or non-linear? Explain.

 

c)   Construct a graph for the data.

 

d)   Using the shape of the graph and values of the finite differences, sketch a possible shape for the bottle. Explain your reasoning.

 

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