AUTHORS: Richard Morris and Katrina Carbone
GRADE LEVEL: 9/10
SCHOOL ADDRESS: 1335 Washington Street Watertown, NY 13601
PHONE/FAX: 785-3810/785-3733
SUBJECT AREA: Mathematics
CONTENT KNOWLEDGE
Declarative
Terminology/vocabulary
Slope as a rate of change
Y Intercept as a constant or starting point
Verbal relationships
The relationship between data points of a line and the equation that represents them.
Procedural
Collect data - Internet, Survey
Create a graph (to plot) Hand Graph Graphing Calculator, Spreadsheet
Read/Interpret Graph
Find the rate of change
Determine the line of best fit - Graphic calculator, or manually
Write an equation that represents the line of best fit
Determine whether a point is on a line
Given an x value, determine the y value (vise versa)
Define a new line with same rate of change and different y intercept and describe a situation where this would occur.
Make a prediction based on the results of the graph.
ESSENTIAL QUESTION
Describe a situation in real life that can best be represented by a linear function.
INITIATING ACTIVITY
"THE WAVE" - Arrange students in classroom in a semi-circle. One student is the initiator. The teacher or another student can be the stopwatch timer. Have students perform the wave by standing up from their seats and raising arms up over head and down again. Students will continue one after the other until the last person in the semi-circle. Choose a set number of students to begin the wave and time how long it takes for the initiator to walk across the room to start the first person in the wave. Continue to increase the number of students performing the wave and the record each time. Once the data is collected, use the attached Wave Worksheets to plot, graph and answer questions.
LEARNING EXPERIENCES
Extending and Refining
Model and guided practice
Understanding Qualitative Graphs
The Journey worksheet
Snow accumulation worksheet
Bike Race worksheet
Interpret and Describe Graphs
Sunburst Communications worksheet 1 p. 8
Sunburst Communications worksheet 2 p. 9
Investigating Functions Through Motion
Take a Hike worksheets
Teach the Line of Best Fit
Discuss Y Intercept
Discuss Slope
Discuss Slope as a Rate of Change
Find Slope Given Two Points
Notes on Linear word Problems
Using Graphic Calculators and/or Spreadsheets
Circumference and diameter of a circle relationship
Number of sides of a polygon and sum of interior angles (also use sum of exterior angles)
Review Slope as a Rate of Change and Y Intercept
Notes
With the Same Rate of Change, but Different Y Intercepts
With the Same Slope but Different Y Intercepts
Model a Given Situation that Represents a Linear Equation
Can specify passing through a given point
Discuss X Intercepts
Refer to previous line activities (extending line through x axis)
Discovery of what the x intercept means
Use technology to check if lines are the same
Find Distance and Midpoint Given Two Points
Groups of 2 or 3 Students Will Choose 2 or 3 Projects to be completed
Identify Slope, X and Y Intercepts
Make a Prediction Based on the Graph
Graph Lines to Solve Problems
Find the Point of Intersection
What Does the Point of Intersection Mean
Make a Prediction on Your Graphs
CULMINATING PERFORMANCE
Students will choose and collect data from the Internet and/or a survey that demonstrates a real life situation represented by a linear equation. Students will create a graph, finding the line of best fit. An equation of the line of best fit must be identified. The students will use the equation to make a prediction.
CONNECTIONS TO STANDARDS
Standard one - MATHEMATICAL ANALYSIS
Benchmarks: Use algebraic and geometric representations to describe and compare data.
Use deductive reasoning to construct and evaluate conjectures and arguments, recognizing that patterns and relationships in mathematics assist them in arriving at these conjectures and arguments.
Apply algebraic and geometric concepts and skills to the solution of problems.
Standard one - SCIENTIFIC INQUIRY
Benchmarks: Develop and present proposals including formal hypothesis to test explanations.
Carry out their research plan for testing explanations, including selection and developing techniques, acquiring and building apparatus, and recording observations as necessary.
Use various means of representing and organizing observations and insightfully interpret the organized data.
Standard two - INFORMATIONS SYSTEMS
Benchmarks: Understand and use the more advanced feature of word processing, spreadsheets and data-base software.
Standard three - MEASUREMENT
Benchmarks: Relate the absolute value, distance between two points, and the slope of a line to the coordinate plane.
Standard three - PATTERN/FUNCTIONS
Benchmarks: Represent and analyze functions using verbal descriptions, tables, equations, and graphs.
Translate among the verbal descriptions, tables, equations and graphic forms of functions.
Model real world situations with the appropriate function.
Use computers and graphing calculators to analyze mathematical phenomena.
CULMINATING EXPERIENCE RUBRIC
| Rubrics |
1 |
2 |
4 |
5 |
| -Data Collected -Accurately represents real life situation |
Data obviously not reliable |
Data is questionable |
Source and Method Somewhat Fair and Reliable |
Source and Method Fair and Reliable |
| Graph -accurate -appropriate intervals -size and shape |
Needs work |
Partially Accurate, some axes & data identified |
Accurate, Appropriate intervals, some axes & data identifies |
Accurate, Appropriate intervals, all axes & data identified |
| Appropriate Technology Used |
None |
Spreadsheet or graphing calculator used but not accurate |
Some implication that spreadsheet or graphing calculator used. |
Spreadsheet or graphing calculator used and shown |
| Text and Graphics |
None |
Little |
Good |
Graphics used do a great deal to clarify information |
| Identified and Understandable Information |
Not identified |
Semi-identified Not understandable |
All identified but not understandable |
All identified and all understandable |
| Predictions made |
None |
Unable to evaluate equations correctly to predict |
Both future and past. Partially realistic and sensible. |
Both future and past. Realistic and sensible based on graph. |
| Overall organization |
Needs more work |
Only partially completed, hard to follow. |
Easy to follow. More details would ass clarity. |
Well thought out and put together. |