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Geometry and Probability
Objectives:
§
Students will identify geometric
two-dimensional shapes and apply geometric terms.
§
Students will be able to make a
prediction based on chance and determine the likelihood of an event.
§
Students will be able to design
their own spinner to use in probability.
Download
as Microsoft Word Documents:
Instructional Plan Template
Mathematics Governor’s Institute 2005
Names
of group members:
Pat
Miller (
Marge Bittner (
Kathy Herman (
Tricia Livingood (
Topic/Theme:
Geometry and Probability
Level:
Third Grade
Time
Element:
Two math periods (approximately 2
hours) enrichment activities may need extended times.
NCTM
Standards Addressed:
Geometry- Analyze characteristics and
properties of two-and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships. Grade 3-5
Data Analysis and Probability Standard –
Formulate questions that can be addressed with data and collect, organize, and
display relevant data to answer them.
Grade 3-5
PA
Math Standards Addressed:
2.7A Predict and measure the likelihood of events and
recognize that the results of an experiment may not match predicted outcomes.
2.6.3A Gather, organize, and display data using pictures,
tallies, charts, bar graphs, and pictographs.
2.6.3C Predict the likely number of times a condition will
occur based on analyzed data.
2.9.3A Name and label geometric
shapes in two- and three-dimensions.
Math
Assessment Anchors Addressed:
M3.C.1 Analyze characteristics
and properties of two- and three-dimensional geometric shapes and demonstrate
understanding of geometric relationships.
M3.C.1.1 Identify and/or describe two- and
three-dimensional objects.
M3.E.1 Formulate or answer questions that can be addressed
with data and/or organize, display, interpret, or analyze data.
M3.E.1.1 Answer questions based on
data shown on tables, charts, bar graphs, or pictographs.
M3.E.3 Understand and/or apply basic concepts of
probability or outcomes.
M3.E.3.1 Predict and/or measure the likelihood of
events.
R3. A.1 Understand fiction texts appropriate to grade
level.
R3. A.1.1 Identify the meaning of vocabulary.
R3. A. 1
Understand fiction text appropriate to grade level.
R3. A. 1.3 Make inferences and draw conclusions based on
texts.
R3. A.2 Understand nonfiction text appropriate to grade
level.
R3. A.2.3
Make inferences and draw conclusions based on texts.
Objectives:
Students will identify geometric two-dimensional shapes and
apply geometric terms.
Students will be able to make a prediction based on chance
and determine the likelihood of an event.
Students will be able to design their own spinner to use in
probability.
Instructional
Strategies and Plan (include strategies used to help different types of
learners, i.e. auditory, visual, etc):
- Conduct
an oral review of geometric shapes with pattern blocks on each child’s
desk. Review geometric terms such
as right angle, shape names, symmetrical…
- Hand
out activity sheet #1 and have students complete the activity sheet
independently. Students pair up and
discuss the results as a whole group.
Review with students and ask them thought provoking questions such
as:
What shape is this? Why is it a _______? How are a rhombus and a square alike? Can you find any other shapes that are
similar? How are they similar? Can you find any shapes that are very different? How are they different?
- Introduce
students to the vocabulary words likely, certain, impossible, unlikely,
equally likely by using real life situations.
- Hand
out activity sheet #2 and introduce students to the spinner which is a
tool used in probability.
- Students
work with a partner or in a group and complete activity #2. Follow up this activity with a discussion
about their answers.
- Hand
out activity #3 and students will design spinners according to the
directions. Students will share their solutions by displaying them on the
board. Discuss their reasoning for
their design.
- Enrichment
activities included as needed. Hand
out activity sheet #4 and students will design their very own
spinners. Students will write
three predictions about their spinner.
They will then test their predictions and write an explanation of
their results.
Strategies
to implement with different types of learners.
Do an additional
assignment using colored cubes which includes a visual and kinesthetic learning
style.
- Give
students 10 red cubes and place them in a bag. Ask students if it is possible to pull a
blue cube out of the bag. No, because all of the cubes are red.
- If you
have a student who is color blind, the cubes can be numbered.
- Add one blue cube to the bag. Ask students if it is possible to pull
one blue cube out of the bag. Is it likely? Is it certain? It
is possible, but not likely. It is
not certain.
- Have a
one-to-one discussion with students about how adding one blue cube changed
the outcome.
- Add 25 blue cubes to the bag. How does this change the outcome
now? It is likely to pull a blue cube.
- Continue
this activity until students demonstrate an understanding.
Materials/Resources:
Overhead spinner, pattern blocks,
overhead pattern blocks, paper, pencil, and activity papers.
Interdisciplinary
Connections:
·
Instead of having geometric shapes
on the spinner replace them with reading vocabulary words, parts of speech,
spelling words…
·
Technology
Design a spinner on a computer
Overhead pattern blocks and spinner
Assessment
Strategies:
·
Formative
Evaluation (checking student understanding during the lesson):
Assessment Rubric – used during the
lesson
4 Full Accomplishment
● Student is able to make
predictions based on the likelihood of an outcome.
3 Substantial Accomplishment
● Student is able, with
prompting, to make predictions based on the likelihood of an outcome.
2 Partial Accomplishment
● Student is able to make a prediction
but is not always based on the likelihood of an outcome.
1 Little Accomplishment
● Student is unable to make
predictions based on the likelihood of an outcome.
·
Summative
Evaluation (How will it be determined that the objectives were achieved?):
Activity 1 and activity 2 will be
used to determine if the objectives were achieved.
Correctives/Remediation:
Please refer to the activities listed under strategies to
implement with different types of learners.
Extensions/Enrichment:
●Enrichment Activity Sheet 4
●Good websites
–
http://illuminations.nctm.org/tools/patchtool.asp
http://illuminations.nctm.org/index.aspx
●Good
children’s literature
The Greedy Triangle by: Marilyn Burns
Three Pigs, One Wolf, and Seven Magic Shapes
by: Grace Maccarone
Do You Wanna Bet? By: Jean Cushman
Probably Pistachio by: Stuart J. Murphy
Round Table Geometry
Sir Cumference and the First
Round Table
Special
Accommodations (special needs students)
·
Description
of the Special Needs student selected:
Male – This student is very active in class. He has difficulty sitting in his seat. He often uses abusive language. He is often known as a “bully”. He hits other students and is often very
provocative.
·
Accommodations
to use with this student:
This student will receive priority seating in the
classroom. He will have the task of
handing out needed materials to offset his activity levels. If the student has a behavior contract he may
be allowed to select his math partner for the activity.
Name
_________________________ Date
___________________
Activity 4
Enrichment Activity
Design a spinner using
geometric shapes. After completing your
spinner write three predictions for your spinner using the terms likely,
unlikely, certain, impossible, and equally likely.
Now take a paperclip and
pencil to try your spinner. Spin your spinner 20 times and record your
results using tally marks. Did your
results match your predictions?
Explain your results. Make three predictions
for your spinner. 1. 2. 3.
Name _____________________________ Date __________________
Tally Chart
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Explanation of results
____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Probability and Geometric Shapes
Name _____________________ Date
_____________
Activity 1 The spinner above has
geometric shapes on it. Identify
these shapes by their geometric name. Draw and identify three
additional shapes.
= __________________
= ____________________
=
___________________
= _____________________
Probability and Geometric Shapes
Name _____________________ Date
_____________
Activity 1 The spinner above has
geometric shapes on it. Identify
these shapes by their geometric name. Draw and identify three
additional shapes. Answer Key
= hexagon
= trapezoid
= rhombus
= triangle
Name _____________________ Date _____________
Activity 2 Answer the following
questions using the probability terms: certain, likely, unlikely, impossible,
or equally likely for the spinner above. 1. What is the probability of
spinning a six-sided figure? __________ 2. What is the probability of
spinning a five-sided figure? __________ 3. What is the probability of
spinning a quadrilateral?_____________ 4. What is the probability of
spinning a circle? _____________ 5. What is the probability of
spinning a polygon? ____________ 6. What is the probability of
spinning a shape that is symmetrical? _____________ 7. What is the probability of
spinning a shape with a right angle? ______________ 8. What is the probability of
spinning a shape that has an odd number of sides? ______________ 9. What is the probability of
spinning a shape that has an even number of sides? _____________ 10. What is the probability of
spinning a two-dimensional shape? ____________
Name _____________________ Date _____________
Activity 2 Answer the following
questions using the probability terms: certain, likely, unlikely, impossible,
or equally likely for the spinner above. 1. What is the probability of
spinning a six-sided figure? unlikely 2. What is the probability of
spinning a five-sided figure? impossible 3. What is the probability of
spinning a quadrilateral? Equal likely 4. What is the probability of
spinning a circle? impossible 5. What is the probability of
spinning a polygon? certain 6. What is the probability of
spinning a shape that is symmetrical? likely 7. What is the probability of
spinning a shape with a right angle? impossible 8. What is the probability of
spinning a shape that has an odd number of sides? unlikely 9. What is the probability of
spinning a shape that has an even number of sides? likely 10. What is the probability of
spinning a two-dimensional shape? certain Answer Key
Name ___________________________ Date ___________
Activity 3
Design a spinner following the instructions listed
below.
1. Make a
spinner that has an equal chance of landing on a triangle as it does on a
hexagon.
2.
Make a spinner that is very likely to land on a
rhombus and not very likely to land on a triangle.
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