Project AMP Dr. Antonio Quesada – Director, Project AMP
LEARNING LAB 1
SNEAKING UP ON SLOPE & INTERCEPT
Kathy Miceli (Hudson) & Karen Kapes (Cuyahoga Falls)
PROJECT AKRON WEB
SUBJECT Algebra
GRADE 9
STRAND Algebra and Functions
TOPIC Slope and Intercept
OBJECTIVES Students will intuitively and inductively determine / clarify meaning of slope and intercept from graphs generated from standard form linear equations
Students will generalize observations and results
Students will recognize the significance of slope and intercept in algebraic and practical examples
MATERIALS Worksheet (p. 3-4); graph paper and straight edge; graphing calculators; if available, computers with graphing software
EXPECTED 2-3 days
TIME
Project AMP Dr. Antonio Quesada – Director, Project AMP
LEARNING LAB 1
SNEAKING UP ON SLOPE & INTERCEPT
Kathy Miceli (HudsonHigh School) & Karen Kapes (Cuyahoga Falls High School)
PROJECT AKRON WEB
June 22, 2000
CONCEPT Slope and intercepts can be determined by graphically interpreting standard form linear equations
(OPO, Mathematics: Gr 9 - #12; Gr 12 - #6, 13, 18; Ohio HSGQE #4, 5, 7, 12, 15, 16; Summit County Academic Standards: Mathematics: Gr 11 - #10, 11, 18, 20, 34, 39, 40, 41)
LEARNING Students will intuitively and inductively determine / clarify
OBJECTIVES meaning of slope and intercept from graphs generated from standard form linear equations
Students will generalize observations and results
Students will recognize the significance of slope and intercept in algebraic and practical examples
ASSUMED It is assumed that students doing this lab can
SKILLS plot points
solve a linear equation for a specified variable
It is assumed that students have not yet discussed the slope-intercept
form of linear equations
It is assumed that students doing this lab have developed some
cooperative learning skills
PROJECT 1) Given 10 standard form linear equations on worksheet (see pg 3-4)
TASKS graph each equation using, graph paper, or computer
complete included table with data based on observation of
each graph, including
-- where graph cross
y-axis
x-axis
-- description of the slant of the line
-- equation solved for y
2) Graph the equation (solved for y) from last column of chart
using graphing calculator, if possible, and compare with original
graph
3) Write 3 - 5 observations based on graphs and completed chart
4) Discuss results with class
5) Generalize slope-intercept form
Project AMP Dr. Antonio Quesada – Director, Project AMP
LEARNING This lesson is designed to be a 2 - 3 day or single block
STRATEGIES self-contained lesson with a worksheet.
Worksheet sections A and B are done during the 1st class period and can be completed either during the second day or as an assignment. Students are encouraged to find sources of appropriately graphed
data. The lesson concludes with a generalization to the slope-
intercept form (y = mx + b) and it is used in graphing.
Students might require instruction in using the graphing calculator.
Student grouping can be according to pre-assigned cooperative
learning groups or can be either assigned or student selected for this assignment.
The teacher prompts and/or assists groups as requested and/or as needed.
CLASSROOM / Cooperative group work followed by class discussion and
INFORMATION generalization
MANAGEMENT
ASSESSMENT Observation of student time and focus on task
Cooperation within the groups
Accuracy of student graphs and chart from worksheets that are turned-in, either 1 summary worksheet per group or individually, according to teacher preference.
Student observations and notes from discussion
TOOLS & Worksheet (p. 3-4); graph paper and straight edge; graphing
RESOURCES calculators; if available, computers with graphing software
RESULT Among members of each group in performing tasks
SHARING
Between groups in sharing observations
Whole class summary and generalizations regarding slope-intercept form
Project AMP Dr. Antonio Quesada – Director, Project AMP
GRAPHING LAB Name ______
STUDENT WORKSHEET Group member(s):
In this lab you and your partner(s) will be graphing some equations and making observations and generalizations about your graphs.
A) Graph each equation using graph paper and a straight edge or a computer and then complete chart with data based on your observation of each graph.
X + Y = 5 2X + 5Y = -20
X + 2Y = 8 4X - 3Y = -18
X - Y = -3 5Y = -25
6X + Y = 9 2X = 12
5X + 3Y = 15 -3X + 2Y = -12
EQUATION / crosses x-axis at / crosses y-axis at / describe slant of line / solve equation for y(y = ...)
Project AMP Dr. Antonio Quesada – Director, Project AMP
B) Graph the equation (solved for y) from last column of chart using a graphing
calculator, if possible, and compare this graph with your original graph. Write
your conclusions.
C) Write 3 - 5 observations based on graphs and chart
1.
2.
3.
4.
5.
List any other observations that you have about this lab
D) Cite at least 2 examples / uses of this kind of graph in your other courses.
Cite at least 2 examples / uses of this kind of graph in work or daily life.
(Suggestion: ask your parents, etc.)
E) Discuss your groups results with your class and write your notes from the class
discussion here.