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Instructional Plan
Mathematics Governor’s Institute 2004
(Download
as Microsoft word document: Handshake Circuit.doc)
Names
of group members: Marjorie
Graeff, Joan Horwatt,
Anna
Marie Mako, and Josh Woolsey
Topic/Theme: The Handshake Circuit
Statistics
and data collection using scatterplots and
a line of best - fit
Level: 8th grade
Time
Element: 120-150 minutes
NCTM
Standards Addressed:
Algebra Standard
·
represent,
analyze, and generalize a variety of patterns with tables, graphs, words, and, when
possible, symbolic rules
·
identify
functions as linear or nonlinear and contrast their properties from tables,
graphs, or equations
·
model and
solve contextualized problems using various representations, such as graphs,
tables, and equations
·
use graphs
to analyze the nature of changes in quantities in linear relationships
Data
Analysis and Probability Standard
·
select,
create, and use appropriate graphical representations of data, including
histograms, box plots, and scatterplots
·
make conjectures
about possible relationships between two characteristics of a sample on the
basis of scatterplots of the data and approximate lines of fit
Problem
Solving Standard
Reasoning
and Proof Standard
·
Develop
and evaluate mathematical arguments and proofs
Communication
Standard
Connections
Standard
Representation
Standard
PA
Math Standards Addressed: 2.6.8.C,
2.6.8.F
2.7.8.B, 2.7.8.C,
2.7.8.E
Math
Assessment Anchors Addressed: M8.E.1.1, M8.E.4.1
M8.E.4.1.1,
M8.E.4.1.2
Objectives: Students will be able to:
·
collect
and record data in a table
·
create a
scatterplot on graph paper from recorded data
·
draw a
line of best - fit and describe any correlation of the variables
·
use line of
best - fit to make predictions
·
develop a
method of extrapolation
·
write an
argument justifying prediction methods
·
use
graphing calculator to create
scatterplots
·
use the
graphing calculator to create a line of best - fit
·
use the
graphing calculator to make predictions
Instructional Strategies and Plan (include strategies used to help different types of learners, i.e. auditory, visual, etc):
Handshake Circuit
Lesson Plan
In statistics many
problems require analysis of two variables.
We ask if these variables are related, how are they related, and are
they correlated. Mathematics allows
predicting the behavior one variable has on the other. Linear correlation analysis measures the
strength of how this correlation relates to the two variables. Vocabulary used is as follows: input,
independent variables, output, dependent variables, scatterplot, positive
correlation, no correlation, negative correlation, and line of best - fit.
Task:
Students will
systematically collect, organize, and graph a progression hand squeeze circuit
Roles:
Student recorder, timer, and start/stop person are designated.
Directions:
- Timer signals “go” and simultaneously
starts stopwatch.
- Start/stop person squeezes right wrist
of person to immediate left.
- When squeeze reaches the right arm of
the start/stop person, timer is notified to stop and recorder records the
time.
- Second person is added to the circuit
and procedure is repeated with this time recorded. A third person is added, a fourth and so
on, until all students have been added to the circuit and data has been
recorded.
** Option: You may decide to average a couple of circuit time trials for your recorded data for the same size circuit.
Day 1: Conducting the experiment
Large Group
- Create data table using recorder’s
data; this data should be displayed on the overhead for class viewing.
Small Group
- Construct scatterplot
- Discussion of appropriate scales,
independent, dependent variables.
- Draw line of best - fit
Large Group
- Summarization: Discussion of the
following:
- Correlation between two variables
(positive, negative, or no)
- Line of best – fit
i.
Identify
points
ii.
Why
are data points found outside the line of best - fit, is this ok?
iii.
Y
intercept; what des this represent
Day 2: Completing
the experiment
Large Group
- Review and expand vocabulary and key
concepts while continuing summarization.
Small Group
- Discuss and complete question
worksheet.
- Work for 1976 student’s circuit is
organized and placed on transparency to prepare for group’s presentations.
Day3: Graphing Calculator and group presentations
Large Group
- Graph scatterplot
- Create linear regression
- Graphing calculator results compared
to manual predictions
- Question session to assess and expand
student understanding
- Group presentations of results and
methods used for 1976 student’s circuit.
Instructional strategies for the:
- kinesthetic and tactile learner:
physically forming the circuit and the use of technology
- visual learner: vocabulary
word wall, story and questions are written
- auditory learner: story
will be read aloud, questions will be discussed in small groups
- all learners: use of
individual, small, and large group settings
Materials/Resources:
Stopwatch, scatterplot grid
paper, data collection sheet, clear ruler, pencil, graphing calculator and
overhead projection panel, question worksheet, extension worksheet, large
sheets of paper for vocabulary wall
Interdisciplinary
Connections:
·
·
Technology: Graphing
Calculators
·
Other(Writing): Writing
an argument to persuade
others that your method of prediction is valid
·
Other(Social
Studies)
Assessment
Strategies:
·
Formative
Evaluation (checking student understanding during the lesson): Monitor
group work, assess understanding by leading small group discussions, and
concept development with individuals.
·
Summative
Evaluation (How will it be determined that the objectives were achieved?): Graded
response to question sheet with a focus on the validity question. Group presentation is graded.
Correctives/Remediation:
·
Self-reflections
or journal entries on what you understand well and on your individual needs
·
Teacher
and peers work with individuals while others work on the bonus
·
Support
materials as needed
Extensions/Enrichment: World
Circuit of Peace question
Special
Accommodations (special needs students)
·
Description
of the Special Needs student selected:
Margaret is functioning three years below grade level. She is receiving learning support services for
language arts and math and has difficulty following direction in all
instructional areas. Margaret has
difficulties in language comprehension, vocabulary, direction following,
event-sequencing and working memory. She
can answer literal comprehension questions in all content areas and usually
answers 1 out of 5 inferential questions correctly. She tends to jump into reading tasks without
previewing material but has success when instructions are broken down and accompanied
by modeling. She has difficulty with
basic math facts for multiplication and division as well as problems involving
multiple steps.
·
Accommodations
to use with this student:
o Teacher will organize groups in advance to best meet
the needs of this student
o Small group work
o Vocabulary wall
o Questions given in advance to review with resource
teacher
o Calculator permitted
o Work will be accessed according to her ability
o Options for working with materials in resource room
or at home with parents
o Small group presentation allows for a verbal response
option
o All materials to be kept in math notebook
o When working is small group, teacher will circulate
to provide feedback when needed
o Peers can also provide support
Name:
__________________
Date: __________________ Day 2
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There has been a
lot of discussion about conflict in the world and peace issues. You might remember “Hands Across America”;
the idea was to spread goodwill and peace across a chain of people. Wouldn’t it be wonderful if everyone around
the world supported peace by sharing a gesture of goodwill with neighbors? Suppose you had people form a circle around
the equator and by shaking your neighbor’s hands you spread the feeling of
peace across the earth. How long do you
think it will take to complete this circuit of peace?
***Hints:
Do you know the circumference of the earth?
How much space would an average person occupy?
1. Predict how much time 30 people, would need
to complete the handshake circuit. Use the line of best fit and a scatter plot
to mark this predicted value,
2. How accurate is your prediction with 30
students? What factors could cause
errors in your prediction?
3. Develop a method to determine how long it would
take the entire student body (approximately 1976 students) to complete the
circuit? Show all work.
4. How accurate is your prediction with 1976
students? What factors could cause
errors in your prediction?
5.
Write a paragraph to explain your method of prediction for 1976
students. Please include the reason why
your prediction is mathematically valid.
Bonus
How long do you
think it would take to complete the world circuit of peace around the
equator. Set up your answer in the form
of a PSSA Free Response Question.
***Hints:
Do you know the circumference of the earth?
How much space would an average person occupy?
Handshake Circuit Data Sheet
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Number of People in Circle |
Time to Complete Circuit(seconds) |
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