Slopes of Cincinnati

Grade Level & Duration:

/ 9th Grade
2-50 minute /

Subject:

/

Algebra-Dawn Williams

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Prepared By:

/ Kelly J Cross

Analyze Learners

Overview & Purpose (STEMcinnati theme)

What will be learned and why it is useful.
The objective for the first day of the lesson will be to have the students build sand hills and to change the slope of the hill with varying amounts of water. Handout directions will specify the height and base of the hill. Each group will calculate the slope of sand hill.The lecture will include an in depth description of the factors that effect the slope of landslides.
The objectives of the 2nd day of lesson are to determine the slope of various Cincinnati locations from a contour map and investigate the relationship between the sand hill slopes and landslides. Also students will identify functions as linear or nonlinear equations and using graphing calculators to creategraphical displays. /

Education Standards Addressed

Ohio Benchmark Math 9-10: Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations
Ohio Benchmark Math 8-9: Identify functions as linear or nonlinear based on information given in a table, graph or equation.
ISTE Standard: Students demonstrate a sound understanding of technology concepts, systems, and operations. Students should transfer current knowledge to learning of new technologies.
Select Goals and Objectives /

Teacher Guide

/

Student Guide

Goals and

Objectives

(Specify skills/information that will be learned.) / Day 1
1. Build sand hills with a specified height and base.
2. Determine the slope of the sand hill
3. Introduce factors such as slope that lead to a landslide
Day 2
1. Use contour map to determine the slope of various locations in Cincinnati
2. Describe the relationship between the slope of a hill and landslides.
3. Identify linear vs. non linear equations. / -Instructions on handout
-Instructions on the handout
-Discuss factors that lead to a landslide and sand slope
-Graph non linear examples /

Materials Needed

  • Handout
  • Pencil
  • Graphing Calculators
  • Laptop
  • Projector
  • Sand
  • Plastic containers

Select Instructional Strategies –

Information

(Give and/or demonstrate necessary information) / Day 1
AG: Pre Assessment Questions
(5 minutes)
Teacher lead direct instruction to outline objectives and provide background info.
(5 minutes)
Activity 1-Group Activity to build sand hills(20 minutes)
Activity 2- Clean up sand(5 minutes)
Activity 3- Direct instruction
(10-12 minutes, EQ1)
Activity 4- Review
Discuss EQ1, EQ2
(5 minutes)
Day2
AG: Review of Day 1 (EQ1 and EQ2)
(5 minutes)
Teacher lead direct instruction to outline objectives and provide background info.
(5 minutes)
Activity1- Group activity to calculate the slope.(15 minutes)
Activity 2-Teacher lead demonstrations of non linear examples.
(20 minutes, EQ3)
Activity 4- Review group discussion
Discuss EQ1, EQ2, and EQ3 Misconceptions 1 and 2
(5 minutes)
Activity 5- Post Assessment
(5 minutes) / -Students will work in collaborative groups pre-assigned by Ms. Williams
-Handouts to record data
EQ = Essential Questions
EQ1: Explain the factors that lead to a landslide
EQ2: Describe the method to estimate slope of a hill (I.e. the sand hills)
EQ3: Compare linear vs. non linear equations.
Utilize Technology / Computer with Office
TI digital projector
Graphing calculators /

Other Resources

(e.g. Web, books, etc.)

Require Learner Participation

Activity

(Describe the independent activity to reinforce this lesson) / Day 1
AG: Pre Assessment Questions
(5 minutes)
Teacher lead direct instruction to outline objectives and provide background info.
(5 minutes)
Activity 1-Each group will build sand hills and use the Pythagorean theorem to determine the slope of a sand pile. Build a hill with the sand and use water to change the slope.
(20 minutes)
Activity 2- Clean up sand(5 minutes)
Activity 3-Teacher lead discussion of translation vs. rotational landslides and the effect of slope. Explain the factors that affect a landslide such as weather and soil properties.
(10-12 minutes, EQ1)
Activity 4- Review
Discuss EQ1, EQ2(5 minutes)
Day2
AG: Review of Day 1 (EQ1 and EQ2)
(5 minutes)
Teacher lead direct instruction to outline objectives and provide background info.
(5 minutes)
Activity1- Read and record various Cincinnati heights on handout. Calculate the slope.(15 minutes)
Activity 2-Teacher lead demonstration of non linear examples. Demonstrate data input and graphing functions. Each group will use group calculator to graph the non linear equations
(15 minutes, EQ3)
Activity 3- Review
Discuss EQ1, EQ2, and EQ3 Misconceptions 1 and 2(5 minutes)
Activity 4- Written Post Assessment
(5 minutes) / -Each group will be provided normal sand in a plastic container with a lid
-Instructions and triangle on handout
Formative Assessment: Could you use this method to determine the slope of where you live?
-Slides with examples ofCincinnati landslide
Formative Assessment: How do you think the slope will affect the landslide?
Formative Assessment: Which factors affect the slope of a possible landslide the most?
-Contour map, handout, and pencil
-Determine slope of various heights in with TI-Nspire CAS graphing calculator
-Examples below in lecture notes
Formative Assessment: What are some differences between linear vs. non linear equations?
Review questions below
-Handout

Evaluate (Assessment)

(Steps to check for student understanding) / Post Assessment attached / Reflection
The Slopes of Cincinnati lesson was executed over 2 fifty minute class periods. The sand activity went really well and the students were engaged and responded positively to building the sand pyramids. The students were trying to build complex structures with the sand. The plastic tub housed the sand very nicely and effectively cut down the clean up time. It was a challenge to get the students to transition from the group sand activity to the direct instruction with the powerpoint slides with the lesson content. The slides described the types of landslides and 4 main factors that cause an unstable slope that leads to landslides in Cincinnati. Translational landslides were compared to linear equations and the rotational landslides were described by non linear equations. The students had strong emotional reactions to the dramatic pictures of landslides in Cincinnati. Once the lesson was started the lesson plan was executed as planned. The 2nd day of the lesson did not follow the plan. I over estimated the students familiarity with depth perception and their ability to read contour maps. I only allocated 15 minutes for that activity that took nearly the entire instructional period. The students did not respond positively to the contour maps because they were not familiar with information being presented in this manner. Although the same topic of slope was introduced with a different application, the students felt very lost. Also students that were absent on the first day struggled to grasp the applications of the slope being presented on the second day. I ran out of handouts for the additional students as I only brought 2 or 3 extras. During the implementation of the lesson, I was unable to minimize the student’s anxiety about the contour map. I thought the instructions were simple and clear enough. I was overwhelmed trying to answer the student’s individual questions regarding the procedure to read the contour map. I was unable to graph the non linear examples in the lesson due to time constraints. I adjusted the lesson during the execution to ensure that the review and post assessment were performed at a comfortable pace. The classroom set up made the lesson a little more difficult to execute. I needed more room on the white board to write example calculations. Including sample calculations in the lecture slides would be the first modification to the lesson. Suggestions for adjustments to the lesson included using an interactive 3-D contour map to provide the students with a better depth perception of the contour map. The apprehension of the new concept was often expressed by the students. In the lesson, I attempted to start with the idea of linear equations that the class was familiar with and expand that base knowledge to a practical engineering application. Another possible adjustment to the lesson would include allowing more time for the 2nd activity with contour maps to allow students to become more comfortable with the new information. One of the significant aspects that I learned as a novice teacher, is to take great care to ensure that even the weaker students can grasp the primary point of the lesson. The post assessment indicated that ¾ of the students were able to identify 2 of the 4 main factors that lead to an unstable slope which could lead to a landslide. Enjoying the hands on sand activity and unclear about the contour map were the primary feedback comments stated by the students. A final finding from the lesson was that most students were able to describe an example when the slope could be effect them directly. /

Additional Notes

Post Assessment

  1. Write an example of a linear and a non linear equation
  1. Estimate the slope of Cincinnati if the area of the city is 78 square miles and the height is 869 feet above sea level?

draw the triangle!!)

  1. Explain two (2) factors that create landslides in Cincinnati (Answer: ground water, soil properties, vegetation, weather, slope, levee)
  1. Give a real life example when the slope of a hill will be important (Answer: handicap ramps, highway ramps, rock climbing)

Misconceptions

  1. Level or smooth ground. Vegetation and other factors make the actual slope of a hill vary a little bit. We will assume a smooth level ground for the calculation of the slope.
  1. Only 1 point needed to calculate slope of a line. We will use multiple points to calculate the slope.

Review Questions

  1. List the properties of a linear equation?
  2. Give an example of a non linear equation?
  3. How does the slope of a hill affect a landslide?
  4. How can a slope affect you?

Lecture Notes

AG: Pre Assessment and Introduction

Introduction

  1. Who has been to a beach and played with sand? Did you ever build a sand castle? If you wanted to build a sand castle how would you do it?
  2. What is the general form/equation of a line? What is the slope and why is it important?
  3. How would determine the slope of the street you live on?
  4. What would happen if the slope of hill was increased?

Examples of Cincinnati Landslides

Recent 2008 example

Slopes of Cincinnati- Day 1

Objectives: Each group will build two (2) sand hills with different slopes. Record the height and base of the sand hill on the handout. Each group will calculate the slope of sand hill based on the triangle below.

  1. Introduction
  2. Instructions for finding the heights of Cincinnati

Each Group must build sand hill and record base and height!

-Sand Pile 1: Base at least 4 inches and Height at least 3 inches

-Record your actual base and height

-Show first sand hill to the instructor to verify the dimensions

-Sand Pile 2: Base at least ____ inches and Height at least ____ inches

-Record your actual base and height

-Use triangle and equation below to estimate the slope of each sand pile

Sand Pile / Base (in) / Height (in) / Slope (in)
1
2

Slopes of Cincinnati- Day 2

Objectives: To determine the slope of various Cincinnati locations from a contour map and investigate the relationship between the sand hill slopes and landslides. Be able to identify functions as linear or nonlinear equations and use graphing calculators to create graphical displays.

  1. Introduction
  2. Instructions for finding the heights of Cincinnati

A topographical or contour map is a detailed graphical representation of the earth’s surface

1 inch = 1.33 miles or 1 inch ≈ 7000 feet

-Identify locations on the contour map

-Find the contour line closest to the location to determine the height

-Measure the distance with a ruler in inches from WUHS to the location

-Use calculator to convert from inches to feet

-Use triangle and equation below to estimate the slope of each location

A = B = C2 = A2 + B2 C=

Location / Dist (ft) / Height (ft) / Slope (ft)
WUHS / X
R / The Rhine
PB / Paul Brown Std.
UC / Univ. of Cincy
Ohio River

Slopes of Cincinnati- Day 2

  1. Linear and non linear examples

Time (s) / Cell Cts
10 / 2.718282
30 / 7.389056
60 / 54.59815
90 / 403.4288
150 / 2980.958
240 / 22026.47

a)Cell growth: Input data and graph data

b)Graph y=x3 (list properties)

c)Graph y = 2x + 3 (R2 values)