Different Acceleration of Gravity?
Title: Acceleration
of Gravity
Topic: Mathematics
(Algebra) and Physics
Grade: 9th - 12th
Lesson Summary:
The main goal of this lesson is to let students have the ability to use appropriate instruments or technology, such as calculators or CBL ( calculator- based lab), to collect data, represent information, and connect with appropriate mathematics concepts to solve problems, like this question- different mass have different acceleration of gravity ?
IL
Learning Standards
NCTM
Standards
Lesson
Alignment
Goals
1. Be able to use graphing calculators and other equipment to collect,
analyze, and organize data.
2. Connect with algebra- function (e.g., parabola and quadratic function)
and graph- and apply these concepts to describe and judge the meanings
of data students collect.
3. Be able to use the same or similar equipment to solve other problems
in real world.
Material
1 Graphing Calculators
(e.g., TI-83, 85)
2 CBL Machine
3 Motion Sensor
4 Books and papers
Lesson
Plan
Assessment
Summarizing
Statement
Lesson
Plan
Day 1 - Introduction and class discussionDay 1
Day 2 - Group activity to collect and analyze data
Day 3 - Group discussion, analysis, sharing, and conclusion
The instructor asks an interesting question to let students think: Are the values of their final velocity the same when different objects which have different mass fall to the ground from the same height? How do you find these values if they are different? Discuss students' thought and other relative questions. Then, students should turn toward to play and test CBL devices and discuss how to collect data, analyze the graphs, and find their answer of the question by using these devices. The instructor also need to review some concepts about quadratic function, parabola, for students.
Day 2
Have 4- 5 students form a group team to work.
Setup the devices as picture #1.
Questions:
1. Are the graphs different when you use one, two, or three books to
test? That is, are the values of acceleration of gravity different
when when the mass of the free falling objects are different?
2. Is the graph a calculator plots quadratic function (parabola) when
X-axis is time and Y-axis is meter (distance)? Why?
2.1 Have students use worksheet#1 to
investigate the relationship between distance and time to find the function
of the graph.
3. Do you know what is the function to represent the graph? D= A*t^2
+ Bt+ C? Does it represent the graph calculators draw? (D is the falling
distance; t is the falling time; The values of A, B, and C are constant.)
Are the values of B and C equal to 0 ? Why ? Explain it. Picture
#2 [Hint: vertex]
4. How can you estimate the value of acceleration?
5. What is the value of acceleration of gravity? That is, what is the
value of g? (g= 2*A. Why? )
6. What will happen in a graphing calculator if you use a paper
to replace a book in this test?
Day 3
In this class, students offer their results to discuss
and share among groups and make the final conclusion for the question in
day 1 class and find the acceleration of gravity. Discuss other examples
in our real life that are similar to this project and their implementation.
Explanation (Use Calculus)
Relative Web Sites: On
Motion
Assessment
Q1:
(a) If we did the same test in the moon, what was
the graph compared with the graph you did in the earth? Did the graph (parabola)
you did in the moon open bigger than that in the earth? Explain it.
(b) If we put the motion sensor on the ground and
let books fall freely from the same height, what is the difference of graph
compared with the graphs on day 2 class?
Q2:
There are some graphs from graphing calculators.
Could you explain how the objects move?
Q3:
Suppose you know a graph passes three points. They are (1,2), (2, 8),
and (3, 26). Could you find the value of acceleration of the graph?
Summarizing statement:
Strength:
Using technology to get hand on experience is helpful students' learning
in mathematics. By using CBL devices and graphing calculators in this lesson
plan, students can "see" mathematics because technology change the essence
of mathematics, from abstract to concrete, and create images for students.
Students can feel the function of mathematics in real life world and closer
mathematics.
Weakness:
It would be better to let students draw the graph of function of object
motion in person.
Any Comment: Yi-wen Chen ychen17@uiuc.edu