Mathematics 10C: Module 41Assignment
Module 4Assignment
Lesson 4 Assignment
Math Lab: Slope of a Staircase
The following diagram is a profile of a staircase with the run of each stair (tread width) equal to 10 in and rise of each stair equal to You will use this diagram to answer questions 1, 2, and 3.
Remember the following terms:
- Rise: the height of a step’s riser
- run: the depth of the step’s tread (not including the nosing)
Procedure
1.Study the diagram above. State the rise and run of a step.
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2.Divide the rise by the run of a step. Record this as the “steepness of one step.”
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3.Divide the total rise by the total run. Record this value as the “steepness of staircase.”
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4.Look at the following diagrams. The relationship between the rise and the run determines the steepness of the staircase.
a.Which staircase has a steeper slope?
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b.Which has a gentler slope?
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c.How can you tell?
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5.Find a staircase in your school or your home that you can measure.
a.Measure the run. If the tread has a nosing, don’t include it in your measurement. Record your calculation.
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b.Measure the rise. Record your calculation.
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c.Calculate the steepness of the stairs by dividing the rise by the run.
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Analysis
6.How does the rise and run of a single step compare with the rise and run of the entire staircase?
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7.How do you think the rise and run calculation for several consecutive steps compares with the rise and run of a single step? Show the calculation of the steepness of several steps (choose two or more) to check your hypothesis.
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8.a.How do the stairs that you measured compare with the stairs in the diagram?
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b.How can you tell which set of stairs is steeper?
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Note:You will refer to this Math Lab again later in the lesson.
Once you have completed Math Lab: Slope of a Staircase, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Try This
TT 1. Many buildings have ramps for people in wheelchairs. The illustration below shows two ramps with different dimensions. Predict which ramp is steeper. Support your reasoning without using a calculator. Save your work to your course folder.
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Once you have completed TT 1, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Try This
Study the lines in the following graph. You will use this graph to answer TT 2, TT 3, and TT 4.
TT 2.
a.How are the lines in this graph different?
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b.How are they the same?
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TT 3.
a.Which line is the steepest?
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b.Which line is the least steep?
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TT 4. Describe how the value for the slope of each line could be determined.
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TT 5. Would a calculated value for the slope help you verify your answers to question 2? Explain your answer.
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Study the lines in the next graph. You will use this graph to answer TT 6.
TT 6.
a.Consider the Line E and Line H. How are these lines different?
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b.How are Line E and Line Hsimilar?
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TT 7. How would you describe to someone the slope of Line F so that he or she would not think you were describing Line G?
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Once you have completed TT 2 to TT 7, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Share
1.Create a revised copy of your work for TT 2 to TT 7 based on the feedback you receive from other students.
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Once you have completed the Share activity, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Try This
TT 8. What if you wanted to start at a different point on the graph?Would it make a difference in the value of the slope? Why or why not?
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TT 9. What if you started at a point that was higher up on the graph and counted down to the next point?Would that make a difference in the value of the slope? Why or why not?
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TT 10. Suppose the slope is an integer. How do you identify the rise and the run?
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Once you have completed TT 8 to TT 10, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Share
2.Respond to the answers to TT 8 to TT 10 posted by another student. Indicate in your response whether you agree or disagree with the explanation. If you agree, state a supporting example. If you do not agree, respond with an example which is not supported by the explanation.
Answer:
Once you have completed the Share activity, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Try This
Use the “Slope of a Line Segment” to explore the slopes of line segments. Notice that you can drag both ends of the line segment.
You may want to drag the bottom of the line segment to (0,0), and then you can drag the upper part of the line to wherever you like.
Keep your eye on the slope so you can see how it changes as you change the line.
As you explore with this applet, try to determine the following:
TT 11. How are all line segments with positive slope similar?
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TT 12. How are all line segments with negative slopes similar?
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TT 13.
a.What is the slope of a horizontal line segment?
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b.Does the slope change as its length increases?
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TT 14.
a.What is the slope of a vertical line segment?
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b.Does the slope change if the line segment is located in another part of the graph?
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Once you have completed TT 11 to TT 14, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Try This
Go to your textbook to practise applying the concepts that you have learned. Show work to support your answers. The work may be descriptive or mathematical. You may want to check the solutions in the back of the textbook to make sure you are doing the questions correctly. You may also want to review relevant parts of the lesson as you work through the problems.
The questions you answer will depend on which textbook you are using to complete this course.
Math 10 (McGraw-Hill Ryerson)
TT 15. Complete “Check Your Understanding” questions 1, 2, 3.b), 3.c), 3.e), 3.f), 8.a), 8.b), and 9 on pages 325 to 327.
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OR
Foundations and Pre-calculus Mathematics 10 (Pearson)
TT 15. Complete “Exercises” questions 4, 5, 6, 13, and 16 on pages 339 to 341. Note: For question 13, use the slope formula.
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Once you have completed TT 15, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.
Reflect and Connect
RC 1. What other words are used to describe slope?
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RC 2. How can the steepness of a line be determined besides calculating the rise/run ratio?
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RC 3. How can you remember whether a slope is positive, negative, zero, or undefined?
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RC 4. What errors could be made when applying the slope formula? What strategies can be used to avoid those errors?
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Once you have completed the Reflect and Connect activity, save the Lesson 4 Assignment to your course folder. You will submit the Lesson 4 Assignment to your teacher for marks.