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Instructional Plan Template
Mathematics Governor’s Institute 2004
(Download
as Microsoft word document: Gr 6-8 project 2004.doc)
Names of
group members: Dennis Garvin, Maureen Graver, Matt Lohr, Valery Melnick, Deb Wensel
Topic/Theme:
Introduction to the Relationship between Diameter and Circumference
Level:
7/8
Time Element: 2 hours
NCTM Standards Addressed:
Data
Analysis and Probability – “Select, create,
and use appropriate graphical representation of data, including histograms,
box-plots, and scatter plots.”
Measurement - “Develop and use formulas to determine the
circumference of circles and the area of triangles, parallelograms, trapezoid, and
circles and develop strategies to find the area of more complex shapes.”
PA Math
Standards Addressed:
2.3.8.A, “Develop
formulas and procedures for determining measurements.”
2.3.8.D – “Estimate, use, and describe measures of distance,
rate, perimeter, area, volume, weight, mass, and angles.”
Math
Assessment Anchors Addressed:
M.8.B.2.3.1 – “ Develop
and or use formulas and procedures to determine circumference, perimeter and
area of simple figures and complex figures.”
R8.A.2.7 “Evaluate text organization
including sequence, comparison/contrast, cause and effect, problem/solution,
headings, graphics and charts to derive meaning.”
R8.A.2.1 “Identify the meaning of vocabulary of various
subject areas.”
Objectives: Students
will be able to approximate the relationship between diameter and
circumference.
Instructional
Strategies and Plan (include strategies used to help different types of
learners, i.e. auditory, visual, etc): Hands-on activity with students working in
pairs. Large font used on handouts and
homework. Preprinted activity
worksheets.
Materials/Resources:
M&M’s,
pennies, handout with 5 pre-drawn circles, 2 blank data tables, graphing
calculators, 2 homework handouts, string measuring 30 inches for each pair,
centimeter rulers, and meter sticks
Procedure:
Day 1:
1) Have
students take one minute to draw a circle and label any parts they are familiar
with. Briefly share their ideas with the
class being sure to review key vocabulary.
2) Hand out
the circle sheet, data chart, and about forty pennies and put students in
pairs.
3) Review
and demonstrate the directions: Take
each circle (A through E) and lay pennies along the diameter line. Record the number of pennies used on the data
chart for circle “A”. Arrange pennies
around the circumference of the circle and record the number of pennies used on
the data chart for circle “A”. Repeat
for circles B through E. One student
should be recorder while the other handles the manipulative.
4) As one
partner turns in the pennies, the other partner records data on master chart
constructed on board or overhead.
5) Repeat
step three using “M & M’s” instead of pennies. Be sure to record data in appropriate section
of data chart. (Teacher needs to be circulating through the room to make sure
students are on task.)
6) As one
partner turns in the “M & M’s” and the circle sheets, the second partner
records the data on the master chart.
7) Have
students review data and discuss relationship that they observe.
8) Handout
and explain homework sheet.
Day 2:
1) Review
answers to homework and invite students to share their conclusions.
2) Ask
students, “Is there a more accurate method we could use to improve the
measurement in yesterday’s activity?” Lead students to the string and ruler method
of measuring diameter and circumference.
3) Hand out
Day 2, String Worksheet. Using circle
worksheets from previous day, assign different pairs a circle from A to E to
measure using string and ruler. Students
jot the measurement of diameter and circumference to the nearest tenth of a
centimeter.
4) Teacher
polls the groups to record the data of the diameter and circumference of the
circles on overhead or board. Students
complete their circumference and diameter charts along with the teacher. When all data is recorded, students calculate
the last column: Circumference divided
by diameter.
5) Stop and
discuss what students see in the final column of string worksheet.
Extension/Enrichment:
1) Using
graphing calculator, take data from string worksheet and put diameter data in
List 1, circumference data in List 2.
2) Create a
scatter plot of data and discuss.
3) Do linear
regression analysis of data and discuss.
Note that slope value is close approximation of pi.
Interdisciplinary
Connections:
·
o
Review vocabulary
o
Organizing and interpreting data
o
Extension Activity - Read Circumference
and the First Round Table: a Math Adventure , by Cindy Neuschwander.
·
Technology
o
Using graphing calculators for scatter
plots and line of best-fit calculation.
Assessment
Strategies:
·
Formative
Evaluation (checking student understanding during the lesson):
o
Observe pairs as they complete
activities and create tables
o
Check group responses as
displayed for class on overhead or board.
o
Reconnect with students
periodically during calculator segment
·
Summative
Evaluation (How will it be determined that the objectives were achieved?):
o
Complete Homework sheet with
circumference/diameter problems and answer questions demonstrating
understanding of the objective.
Correctives/Remediation:
o
Hands-on help as students
proceed through activity
Extensions/Enrichment:
o
Use alternate measuring devices
to more accurately define the diameter/circumference relationship.
o
To use graphing calculator to
analyze the collected data and further refine the relationship.
Special
Accommodations (special needs students)
·
Description
of the Special Needs student selected:
o
Jimmy is a student diagnosed
with Asperger’s syndrome. He is above grade level in decoding and
fluency in reading. Jimmy loves to read
anything that is fact based and quickly memorized and recites the facts. He has great difficulty with problem solving
and inferential thinking. Jimmy has poor
fine motor skills and has trouble writing within boundaries and organization of
his written work. He has strong rote
math facts but has severe difficulty with organization of multi-step sequences
and problem solving. When he is
presented with these types of math problems, he crawls under the desk and
refuses to come out.
·
Accommodations
to use with this student:
o Our accommodations for
our special needs student are made available for the entire class, so Jimmy
doesn’t feel singled out.
o Pair work is being
used to help Jimmy with the fine motor activity.
o Charts are pre-made
with lines to set boundaries and help Jimmy organize his work.
o Large fonts as well as
large spacing and pre-lined answer spaces are used as accommodations.
o Circle worksheet is
provided to accommodate the fine motor difficulties Jimmy has.
Circumference/Diameter
Relationship Worksheet (Day 1)
Materials:
·
Five circle worksheets (3 sheets)
·
Cup with pennies
·
Cup with M & M’s
Directions:
(Using pennies)
1. Place pennies around the circumference
of circle A
(Hint: Line up the pennies so that the center of
each penny is on the line)
2. Record the number in the
table below
3. Remove pennies from circle
before continuing
4. Place pennies across the diameter
of circle A
5. Record the number in the
table below
6. Remove pennies from circle
before continuing
7. Repeat steps 1-6 for circles
B, C, D, and E
Directions:
(Using M & M’s)
1. Use M & M’s in place of
pennies
2. Follow steps 1-7 from
directions for penny experiment
Pennies M & M’s
Circle |
Circumference
|
Diameter |
Circumference |
Diameter |
A |
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B |
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C |
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D |
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E |
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Circumference/Diameter
Relationship Worksheet (Day 2)
(String
Experiment)
Materials:
·
Five circle worksheets (3
sheets) – From Day 1 Experiments
·
One 30 inch piece of
string
·
Ruler
Directions:
1. Using the string and ruler, follow steps 1-6 from
yesterday’s lesson.
2. ONLY DO THE EXPERIMENT ON
3. As other groups finish, record their results in the
table
4. Use calculators to calculate the circumference
divided by the diameter
Circumference |
Diameter |
CircumferenceDiameter |
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Circumference and
Diameter Activity
Day 2
Independent Practice Name _____________________
Diameter |
Circumference |
|
5 in. |
|
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3 ft. |
|
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4 yd. |
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2 mi. |
|
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6 cm |
|
Using
the concepts learned in today’s activity, complete the following tables.
|
Diameter |
Circumference |
|
|
12 m |
|
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18 ft. |
|
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24 in. |
|
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9 yd. |
|
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21 cm |
Write
a minimum of 2 sentences telling comparing today’s results to yesterdays.
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Circumference and
Diameter Activity
Day 1
Independent Practice Name _____________________
Diameter |
Circumference |
|
5 in. |
|
|
3 ft. |
|
|
4 yd. |
|
|
2 mi. |
|
|
6 cm |
|
Using
the concepts learned in today’s activity, complete the following tables.
|
Diameter |
Circumference |
|
|
12 m |
|
|
18 ft. |
|
|
24 in. |
|
|
9 yd. |
|
|
21 cm |
Write
a minimum of 2 sentences telling what you learned about the relationship
between circumference and diameter.
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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