Download MAT 161 Math for Elementary Teachers II

MAT 161
Math for Elementary Teachers II
Course Package
Approved
December 4, 2009
MCC Form EDU 0007 (rev. 12/04/09)
COURSE PACKAGE FORM
Contact Person (s)
Laurel Clifford, Eric Aurand
Date of proposal to Curriculum Sub-committee:
12-04-09
Purpose:
___New
If this is a change, what is being changed?
(Check ALL that apply)
___
___
_X_
_X_
___
Effective Semester/Year
Fall 20______
x Change
Update Prefix
Title
Learning Units
Competencies
Format Change
Spring 2010_
__ Delete
__ Course Description
__ Course Number
_X Textbook (EDITION)
__ Credits
__ Prerequisite
Summer 20_____
COURSE INFORMATION
Prefix & Number:
MAT 161
Catalog Course Description:
Title:
Math for Elementary Teachers II
Mathematics for Elementary Teachers II is designed to aid prospective elementary teachers to
understand and apply the mathematical principles and processes underlying current and evolving
programs of mathematical instruction, grades K-8. This course emphasizes problem solving,
reasoning, statistics and probability, geometry, and measurement. Credit Hours: 3.0
Lecture Hours: 3.0
Lab Hours:
Prerequisite(s)
MAT 160 with a grade of “C” or better.
Co-requisite(s)
Does this course need a separately scheduled lab component? ____Yes
__x_No
Does this course require additional fees? If so, please explain. ____Yes
__x No
Is there a similar course in the course bank? ___Yes (Please identify.) _x_No
Articulation: Is this course or an equivalent ___No
offered at other two and four-year
_x Yes (Identify the college, subject, prefix,
universities in Arizona?
number and title:
ASU: MTE 181; NAU: MAT 155; UA: Dept.
Elective (UA equivalent course is a 300-level
course; transferability is decided on a case
by case basis); This course is offered at
every CC in the state; see
www.aztransfer.org for CEGs.
MCC Form EDU 0007 (rev. 12/04/09)
Writing Across the Curriculum Rationale:
Mohave Community College firmly supports the idea that writing can be used to improve
education; students who write in their respective content areas will learn more and retain
what they learn better than those who don’t. Courses in the core curriculum have been
identified as “Writing Across the Curriculum” courses.
Minimum standards for the Writing Across the Curriculum component are:
1. The writing assignments should total 1500 – 2000 words.
For example, a single report which is 1500 words in length
OR
a series of essay questions and short papers (example: four 375-word
assignments) which total 1500 words could meet the requirement.
2. The writing component will represent at least 10% of a student’s final grade in
the course.
Is this course identified as a Writing Across the Curriculum course? __x _Yes ____No
(See addendum for writing rubrics)
Intended Course Outcomes/Goals
By the end of the semester, students will be able to:
1. Apply diverse problem solving strategies to solve a variety of problems, following
Polya's four step problem solving process (Understand the Problem, Devise a Plan,
Carry Out the Plan, Look Back).
2. Understand and apply the basic concepts of experimental and theoretical probability
to find probabilities of simple and compound events.
3. Select and use appropriate graphical and numerical statistics techniques to
summarize, analyze, and interpret data, and evaluate the use and possible misuse of
these techniques in examples of data analysis.
4. Using various inductive and deductive investigational techniques such as
constructions, coordinate systems, and transformations, analyze characteristics and
define properties of two- and three-dimensional geometric shapes, develop
mathematical arguments and solve problems about geometric relationships
5. Understand measurable attributes of objects and the units, systems, and processes
of measurement and apply appropriate techniques, tools, and formulas to determine
measurements.
Course Competencies and Objectives
By the end of the semester, students will be able to:
Competency 1 Understand and interpret basic concepts of probability, and apply these
concepts to solve problems.
Objective 1.1 Express the experimental and theoretical probability of simple and
compound events in ratio, decimal, and percent form
Objective 1.2 Apply the concepts of complementary events, geometric probability, tree
MCC Form EDU 0007 (rev. 12/04/09)
diagrams and the “AND” and “OR” rules to find probabilities of multi-stage events, including
independent and dependent events (with replacement, without replacement, etc.).
Objective 1.3 Recognize when a condition is applied to the event (“given that…”) and
determine the conditional probability.
Objective 1.4 Explain how to use a random number table or other representation to
simulate an experiment, and interpret the results of a simulation.
Objective 1.5 Express probability in ODDS form, in favor and against, and be able to
translate between probability and odds.
Objective 1.6 Find the expected value (mathematical expectation) of an experiment and
determine whether or not the experiment is “fair.”
Objective 1.7 Use counting principles, permutations, and combinations to determine the
number of outcomes possible for an experiment and apply these concepts to find probability
of an event and solve problems.
Competency 2 Collect, organize, display, summarize relevant data to answer questions,
selecting and applying appropriate graphical and numerical data analysis concepts.
Objective 2.1 Recognize and use the vocabulary of statistics and data analysis
appropriately in interpreting given data analyses, and formulating questions that can be
addressed with data analysis.
Objective 2.2 Collect, organize, and summarize data into an appropriate statistical display
(graph, table, etc.) for the type of data collected, and interpret what the display reveals about
the data.
Objective 2.3 Collect, organize, and summarize data with an appropriate numerical value
(averages, percentages, dispersion, position), and interpret what the values reveal about the
data.
Objective 2.4 Use graphical and numerical data analysis techniques to compare sets of
data,
Objective 2.5 Evaluate statistical displays or values for possible bias, misuse, or other
misleading implications.
Competency 3 Discover, define, and analyze characteristics and properties of two- and
three-dimensional shapes, including points, lines, planes, angles, and polygons, use these
properties to define and classify geometric figures and solve problems.
Objective 3.1 Recognize, name, build, compare, and sketch geometric figures, using
correction notation, and identify real-world models and examples of these figures.
Objective 3.2 Identify, compare, classify, and analyze two dimensional shapes according
to their properties and use inductive and deductive reasoning to create definitions of classes
of shapes from examples and non-examples, and also be able to create their own examples
and non-examples that would allow someone else to determine similar definitions.
Objective 3.3 Discover and apply angle relationships to solve problems, including
MCC Form EDU 0007 (rev. 12/04/09)
supplementary and complementary angles, vertical angles, parallel line angles, triangle angle
sum, remote interior angles vs. exterior angle of a triangle, polygon angles, polygon exterior
angle sum, and angles in regular polygons.
Objective 3.4 Make and test conjectures about geometric properties and relationships, and
develop logical arguments to justify conclusions.
Competency 4 Use construction techniques, visualization, spatial reasoning, coordinate
systems, and geometric modeling to solve problems, describe spatial relationships, and
create and evaluate mathematical arguments about these relationships.
Objective 4.1 Recognize and apply the congruent triangle “short cuts” (SSS, SAS, etc.) to
determine if triangles are congruent and problem solve/create arguments about congruent
parts of figures based on congruent triangles.
Objective 4.2 Use a variety of construction techniques, including compass and
straightedge, paper folding, tracing paper, ruler and protractor, MIRA reflector, and geometry
software (Geometer’s Sketchpad) to draw geometric objects with specified properties, such
as side lengths or angle measures, and interpret properties of these geometric objects from
the construction.
Objective 4.3 Discover and apply the properties of various quadrilaterals and determine
the type of quadrilateral given from its properties.
Objective 4.4 Determine if figures are similar, and if so, use proportional reasoning to find
their measurements and develop models to solve problems.
Objective 4.5 Use coordinate geometry to represent and examine properties of geometric
shapes.
Competency 5 Understand measurable attributes of objects and the type of unit appropriate
for the dimension of the object, and apply standard and nonstandard systems and formulas
to determine the measurements, including distance, area, surface area, volume, mass, and
temperature.
Objective 5.1 Use standard English, metric, and nonstandard units to measure distance
around plane polygons, circles and other figures, and solve problems.
Objective 5.2 Explore areas on a geoboard (or dot paper grid), and develop and apply
formulas for finding the area of quadrilaterals, regular polygons, circles, and other related
shapes to solve problems.
Objective 5.3 Understand, prove, and apply the Pythagorean Theorem to find distance,
including lengths of special right triangles, and use the Pythagorean theorem and its
converse to solve problems.
Objective 5.4 Visualize a three dimensional object as its two dimensional net, and use this
net to find and develop formulas for surface area of prisms, cylinders, pyramids, cones, and
other three dimensional shapes, and solve problems involving surface area.
Objective 5.5 Visualize the volume of a three dimensional object and develop formulas for
volume of prisms, cylinders, pyramids, cones, and other three dimensional shapes and solve
MCC Form EDU 0007 (rev. 12/04/09)
problems involving volume of these shapes.
Objective 5.6 Apply dimensional analysis to convert between different units of measure,
and express the relationships among metric units of volume, capacity, and mass.
Objective 5.6 Apply concepts of measurement for mass and temperature to solve
problems.
Competency 6 Apply motion geometry and transformations using different construction tools,
and use symmetry to analyze properties of geometric figures, and solve problems.
Objective 6.1 Predict and describe sizes, positions, and orientations of shapes under
transformations such as translations, rotations, reflections, glide reflections, and dilations,
using a variety of tools including the rectangular coordinate system, MIRA reflectors, paper
folding, tracing paper, dot paper, geoboards, computer software, etc.
Objective 6.2 Evaluate congruence, similarity, and line or rotational symmetry of objects
using transformations, and describe a transformation or series of transformations that will
demonstrate that two shapes are congruent or similar.
Objective 6.3 Recognize and identify line and rotational symmetry in designs, patterns,
and everyday objects, and determine properties of these objects, classify objects, and solve
problems via this symmetry.
Objective 6.4 Determine which regular and irregular polygons will tile the plane, and
create their own tessellations based on these polygons.
Teacher’s Guide
Course Textbook, Materials and Equipment
Textbook(s)
(same texts
used in MAT
160)
Software/
Equipment
Title
Author(s)
Publisher
ISBN
Problem Solving Approach to Mathematics for Elementary School
Teachers, A
Billstein, Libeskind, and Lott
Addison-Wesley
ISBN-10: 0321570553; ISBN-13: 9780321570550
Title
Mathematics Activities for Elementary School Teachers, 10/E
Author(s)
Dolan, Williamson, and Muri
Publisher
Addison-Wesley
ISBN
ISBN-10: 0321575687; ISBN-13: 9780321575685
The instructor should have a copy of The Geometer’s Sketchpad software from
Key Curriculum Press. Ideally, students should have access to the software as
well, which is available in various multi-user packages from Key Curriculum
Press. Labs that correlate to the text are available for free instructor download at
http://www.pearsonhighered.com/mathstatsresources/
Note: Package ISBN-10: 0321649273 | ISBN-13: 9780321649270 includes the
text, the activity book, the MyMathLab student access code, and Geometer’s
Sketchpad software
Course Assessments
MCC Form EDU 0007 (rev. 12/04/09)
Description of Possible Course Assessments
(Essays, multiple choice, etc.)
Exams standardized for this course? No
__ Midterm
__ Final
__ Other (Please specify):
Where can faculty members locate or access
the required standardized exams for this
course? (Contact Person and Location)
Example: NCK – Academic Chair Office
Quizzes, Exams, Readings, Activities from
activity book, Class presentations,
Comprehensive final exam; Homework
assigned from the required textbook is also
mandatory.
Writing across the curriculum can be
addressed by a series of at least fifteen 100word responses to questions selected by the
instructor from the Mathematical Connections
section at the end of each textbook section.
Are exams required by the department?
_x_Yes ___No
If Yes, please specify:
Midterm and Final Exams
Learning Units
Learning Unit Topic 1: Probability
Competency: 1
Objectives: 1.1 to 1.7
Text: Chapter 9
Overview: This chapter can be very difficult for students, and so a lot of hands-on practice is
important (use the activity book!), with continual emphasis on the basic concept of probability as a
ratio of “part to whole” and the experimental and theoretical definitions necessary throughout the
chapter. Students need many examples of the terminology used, such as mutually exclusive and
complementary events. It also helps to include activities that have two outcomes that are not
equally weighted (like “tossing tacks,” where point up vs. point down is not 50% each way). Having
students make spinners out of paper plates that match various probabilities (see activity 2 in
chapter 9 of the activity book) as a way to emphasize the basics of probability can be helpful.
When working with multi-stage events, students have difficulty creating tree diagrams. Begin with
examples using hands-on events and partially constructed trees that they can fill out (see activity 7
in the activity book) until they build confidence in creating their own. A solid understanding of treediagrams can help them visualize complex probabilities, so spend adequate time on the
construction of these trees.
Simulations are often new to them. A fun and effective introduction is the “world” beach ball
simulation outlined in the Instructor’s Resource Guide. In addition, usually they have not used a
random number table before, so spend time demonstrating its use, and have them work in groups
on a simulation.
For odds, be sure to contrast the difference with probability as “part to whole” and odds as “part to
part” (or “not part” to “part”). Give students a hands-on activity using two-colored objects where
they count them, and give the probability of choosing each color, and then the odds in favor and
odds against. This simple activity takes only a small amount of time and is extremely effective.
For conditional probability, do many examples, and have the students connect the condition to the
sample space prior to introducing the formal definition.
MCC Form EDU 0007 (rev. 12/04/09)
Students understand counting principles if the are developed carefully from the basic counting
principle (choosing one item from distinct sets of m, n, etc. items) to permutations (arranging items
in one set) to combinations (choosing items where order doesn’t matter). A simple flow chart
(which they can help create) can help them discern between permutations and combinations.
Activity 10 in chapter 9 of the activity book is particularly helpful in motivating combinations in a
hands-on manner. Be sure to reemphasize the definition of the probability ratio to help students
understand how to use combinations to find probability. Peppermint Patty’s problem in section
9.5 can lead to the binomial probability formula, if you choose to develop it.
Activities from Activity Book: Chapter 9: Activities 1, 2, 3, 7, 10, 11
Suggested Reading/Other: NCTM Standards: Data Analysis and Probability
ADJUSTABLE SPINNER at http://shodor.org/interactivate/activities/ explores probability with
spinners
EXPERIMENTAL PROBABILITY at http://shodor.org/interactivate/activities/ explores probability
with spinners, dice, coins, etc. and compares experimental and theoretical probability
MONTY HALL at http://shodor.org/interactivate/activities simulates that famous quandary.
Learning Unit Topic 2: Data Analysis/Statistics: An Introduction
Competency: 2
Objectives: 2.1 to 2.5
Text: Chapter 10
Overview: Activity 1 Graphing M&Ms is a great way to introduce statistical graphs to students.
Follow up with the other activities, where each group works on one and presents their ideas to the
class on when it is appropriate, what it tells you, its advantages and disadvantages, etc. Be sure to
emphasize that if the scale on the graph is a number line (like histograms, which they are less
familiar with) it needs to be a number line: consistently spaced, uniform scale.
As you follow with numerical techniques, students are often familiar with the basic averages but
are less familiar with measures of position and variation. Be sure to spend enough time on these
with real-world data examples. Work out a variation and standard deviation problem with simple
data (such as number of green m&ms in a snack size package of m&ms collected as class data) by
hand, so students understand how this measure works, and follow up with how to use a calculator
to find these measurements. Be sure to spend an adequate time with the normal curve, and
compare and contrast the use of percentiles and quartiles, and their relationship to the normal
curve and standard deviation.
The last section of ch. 10 covers statistical misuses, and can be assigned as out-of-class reading
and homework (be sure to follow up with classroom discussion). It can be helpful to have groups of
students choose a problem and explain the misuse to the rest of the class.
If you choose to have students do a statistical project, another text section on statistical design is
available online at the publisher’s website.
Activities from Activity Book: Chapter 10: Activities 1, 10, 3, 4, 6, 7 and 9 (9 can be assigned as a
homework project)
Suggested Reading/Other: NCTM Standards: Data Analysis and Probability
Shodor also has about every graphic display covered in the text at
http://shodor.org/interactivate/activities/ under their STATISTICS submenu, and
the National Library of Virtual Manipulatives also has graphers and probability activities at
http://www.nlvm.usu.edu/en/nav/topic_t_5.html
Learning Unit Topic 3: Introductory Geometry
Competency: 3
Objectives: 3.1 to 3.4
Text: Chapter 11
MCC Form EDU 0007 (rev. 12/04/09)
Overview: Students come with different levels of experience in geometry, some having it in high
school, and some with very little exposure. One of the difficulties is the quantity of vocabulary
involved. Spend time having students explore the different shapes, using examples and
nonexamples to compare and contrast prior to defining them, and have students create their own
glossary with illustrations (similar to the tables in the book in section 11.1) to keep track of the
terms and definitions. Point out examples of parallel, perpendicular, and skew lines throughout the
room. Emphasize the notation used for the various geometric figures as that may also be
unfamiliar to students, especially those who are used to using capital and lower case letters
interchangeably. Depending on student experience, you may need to supplement the exercises
throughout chapter 11 and 12 with additional practice worksheets that are more basic until they
are familiar with the concepts.
Tracing paper is a great tool to quickly explore relationships among angles created by intersecting
and parallel lines, which can then be reinforced with protractor use (it’s cheap and easy to print
protractors on transparency film for students to use). The Geometer’s Sketchpad creates simple,
dynamic, and powerful examples for the angle and line relationships as well as triangles and
polygons. After inductively exploring the relationships, encourage students to deductively prove
them, although a two-column proof is not introduced in this section. Review of the logic section
(1.3) from MAT 160 can be helpful in reminding students about valid arguments.
Section 11.4 deals with geometry in three dimensions, and can be covered here, or covered just
prior to doing surface area and volume later on. Activity 9 is helpful to encourage students to
develop their spatial visualization skills prior to further work with three dimensional figures.
Activities from Activity Book: Chapter 11: Activities 1, 3, 4, 5, 6
Suggested Reading/Other: NCTM Standards: Geometry; Reasoning and Proof
GSP Labs (Lab 1, 2, 3)
http://shodor.org/interactivate/activities/ has ANGLES activity for practicing with angle
identification
http://www.nlvm.usu.edu/en/nav/topic_t_5.html has geoboard, pattern block, and other geometry
manipulatives online.
Learning Unit Topic 4: Constructions, Congruence, and Similarity
Competency: 4
Objectives: 4.1 to 4.5
Text: Chapter 12
Overview: Constructions are the core of this unit. Traditional compass and straightedge
constructions can be a real challenge to those less skilled with their hands. Other construction
techniques can be just as effective and less frustrating, such as paper folding, tracing paper, a
MIRA reflector, geoboards, and the Geometer’s Sketchpad. Choose the appropriate construction to
the ability of your students and the concept covered. It is helpful to walk students through copying
a segment, and copying an angle using a compass, then after they have done these basic
constructions, have them write down directions to help others do them. These basic constructions
allow them to show the triangle inequality and the SSS and SAS congruence postulates as they
copy a triangle. Although finding the midpoint and angle bisector constructions are not too
difficult, paper folding or using a MIRA is far more efficient and easier for these investigations. The
ASA postulate can also be shown using the basic constructions of copying segments and angles,
and the disproof of SSA is very effective in this manner as well.
It is also helpful to follow up these activities with practice identifying from given figures if
postulates apply, especially for figures with overlapping angles or sides that students may not see.
Encourage students who struggle with this concept to draw the figures separately, especially when
working later in the chapter on similar triangles.
MCC Form EDU 0007 (rev. 12/04/09)
Quadrilateral properties can be explored nicely with rulers and protractors, or more efficiently with
the Geometer’s Sketchpad program. Give students examples of the quadrilaterals with a table of
possible properties, and have them investigate and mark off if that quadrilateral has the particular
property (this can then be followed up with more formal proof).
The Activities manual has a similar triangle activity, or you can create your own using the drawing
tools of a computer program to give students triangles they can measure and conjecture what
“similar” means; this is a case where the math word is much different from the English term, so
emphasize that! The Side-splitter theorem is nicely explored using the Geometer’s Sketchpad (lab
7).
Students are familiar with the Cartesian plane from previous algebra classes, and also with
equations of lines. It is fun to explore the concept of parallel and perpendicular lines first with a
geoboard and have them notice the slope relationships on the geoboard that they remember from
geometry.
If you have time, you can cover right triangle trigonometry (or assign it as a student presentation)
as an extension of similar figures. This section is available online at the publisher’s website.
Activities from Activity Book: Chapter 12: Activities 1, 2, 3, 5, 6
Suggested Reading/Other: NCTM Standards: Geometry; Reasoning and Proof
NCTM e-examples: 4.2 Investigating the Concept of Triangle and Properties of Polygons
http://standards.nctm.org/document/eexamples/index.htm
GSP Labs (Lab 4, 7, 8)
CONGRUENT TRIANGLES activity at http://www.nlvm.usu.edu/en/nav/topic_t_5.html explores
congruent vs. similar triangles
Learning Unit Topic 5: Concepts of Measurement
Competency: 5
Objectives: 5.1 to 5.6
Text: Chapter 13
Overview: Most students actually have little experience working directly with measurement, and
may not even know how to use a ruler. One activity is to create your own ruler out of a strip of
paper (by folding it in halves repeatedly, and labeling the smallest unit whatever you’d like: like “1
goober,”) and measuring objects in the room with this ruler, to emphasize that we create the
measurement tools ourselves, and discuss the history of English measurements. Activity 1, units
of measure, is also helpful. Practice with dimensional analysis and conversions throughout the
unit. Emphasizing the relationship between metric unit prefixes and place value can help students
with the conversion among those units.
Students are also used to using formulas with measurement, and may often have no clue which
formula is the right one to use, so emphasize concepts over formulas, and develop formulas from
concepts. The activity book has many activities that build on concepts to create the formulas. This
section also emphasizes more on circles, which students are often less familiar with. Be sure to
discuss the vocabulary of circles thoroughly. Develop the concept of pi from measuring circles’
circumference vs. diameter and graphing the ordered pairs to see the slope is pi. This can be
quickly reinforced or demonstrated with the Geometer’s Sketchpad. Once students understand
that pi = C/d, they are less likely to confuse the formulas for area vs. perimeter. In developing the
formula for area of a circle, there are nice animations available on the internet that show the
process on p. 867 of the text.
Use tangrams to explore area (see activity book) and students are more likely to see ways to
calculate area of irregular shapes as the sum of its parts, and also understand the difference
MCC Form EDU 0007 (rev. 12/04/09)
between area and distance/perimeter. It also helps students to see area as literally “square”
units. Geoboard explorations help with this as well (see activity book).
Students have experience working with the Pythagorean Theorem, but less with its converse. The
activity 11, “Right or Not?” is an excellent activity to reinforce the theorem as well as investigate
the converse (and students like it, so don’t skip this one!). Connect the Pythagorean Theorem to
the distance formula (help students see how they are the same!) through examples where you can
“count squares” to find lengths of sides. The formula for the area of a circle will them follow more
easily if students can see how the Pythagorean Theorem “fits” on the coordinate plane. Be sure to
include examples where students use the Pythagorean Theorem to solve for one of the legs rather
than just the hypotenuse, and follow up with investigating the “special triangles” as students enjoy
seeing these patterns, and they help with area formulas for the area of an equilateral triangle.
In visualizing surface area, work first with building nets for solids. Once students can visualize a
shape “unfolded” they can more easily see the surfaces and thus calculate the area without relying
on a formula they don’t understand (and thus will use incorrectly). Students also need help when
working with pyramids and cones to understand the difference between slant height and the actual
height (that will be used with volume). You may also wish to review the 3-D shapes from section
11-4 as you discuss surface area and volume.
Use blocks or cubes to motivate and explain what volume is and its measurement in cubic units.
Bring plastic models of various shapes and have students identify the shape by name and describe
what its surface area would look like (as a net) and what the volume would be to help clarify the
difference between volume and surface area. It is easily demonstrated with water that the volume
of a pyramid or cone is 1/3 the volume of the related cylinder or prism (it’s an “AHA” moment for a
student to guess how many cones it will take to fill the cylinder, for example).
It also helps to have students discuss many different problems and determine if volume or surface
area is involved, even if they don’t solve the problem itself, to help recognize the appropriate
concept.
The interrelationship among the cubic centimeter, millimeter, and gram can be fascinating. Try
having students calculate the volume of a soda can in cubic centimeters, then display a cubic
centimeter, and read the volume in millimeters off the can.
Activities from Activity Book: Chapter 13: Activities 1-4, 7-13
Suggested Reading/Other: NCTM Standards: Measurement
NCTM e-examples: 6.5 Understanding the Pythagorean Relationship Using Interactive Figures
http://standards.nctm.org/document/eexamples/index.htm
GSP Labs 9, 10 (Sketchpad also comes with some good sample sketches proving the Pythagorean
Theorem)
*Very nice* dimensional analysis practice tool at
http://www.nlvm.usu.edu/en/nav/frames_asid_272_g_4_t_4.html
AREA EXPLORATION at http://shodor.org/interactivate/activities compares and contrasts
perimeter and area
SURFACE AREA AND VOLUME at http://shodor.org/interactivate/activities/ compares and
contrasts surface area and volume
TANGRAMS, geoboards, the Pythagorean Theorem are also explored at
http://www.nlvm.usu.edu/en/nav/topic_t_5.html
Learning Unit Topic 6: Motion Geometry and Tessellations
Competency: 6
Objectives: 6.1 to 6.4
Text: Chapter 14
MCC Form EDU 0007 (rev. 12/04/09)
Overview: This unit is best explored hands-on first, then more formally. The activity manual has
several activities that are really helpful in doing transformations. It also helps to work with
geoboards and dot paper prior to the formal Cartesian system methods. The MIRA and paper
folding are excellent tools for reflections, and tracing paper can be used for all the rigid
transformations. Tracing paper is especially effective for movement along the vector, where the
student can trace the pre-image, and the vector, then slide the vector down itself and see where the
image lands. The Geometer’s Sketchpad also has great transformation tools that can demonstrate
which are isometries and which are not.
With size transformations, you can revisit simple compass and straightedge constructions as an
exploration tool, as well as use the Geometer’s Sketchpad’s dilation tool. Activity 2 in the activity
manual provides a guide for this exploration.
This pattern of explore first, then formalize is helpful to do for each transformation as well as
explore the properties of the shape that results.
The MIRA and folding paper are simple and cheap tools for exploring line symmetry. Tracing paper
is helpful for rotational symmetry as the students can hold the paper to the center of rotation with
their pencil or compass stylus, then turn the paper to see the traced shape line up with the preimage.
For tessellations, students can explore with pattern blocks as well as online manipulatives
(www.nlvm.usu.edu) to determine which shapes tessellate and why. Have students create their
own triangle and quadrilateral tessellations to show that they tile the plane, then follow up with
creating Escher-type tessellations, which students enjoy. Online resources at www.shodor.org are
also helpful in exploring tessellations.
Activities from Activity Book: Chapter 14: Activities 1 - 5
Suggested Reading/Other: NCTM Standards: Geometry; Reasoning and Proof;
NCTM e-example 6.4 Understanding Congruence, Similarity, and Symmetry Using Transformations
and Interactive Figures, http://standards.nctm.org/document/eexamples/index.htm
GSP Labs 11, 12
FLOOR TILES at http://shodor.org/interactivate/activities/ explores tessellations with
quadrilaterals
TESSELLATE! at http://shodor.org/interactivate/activities/ is an awesome online tool for quickly
exploring tessellations… don’t miss this one!
TRANSMOGRAPHER at http://shodor.org/interactivate/activities/ explores transformations on the
coordinate plane
Each transformation is also nicely explored at http://www.nlvm.usu.edu/en/nav/topic_t_5.html
MCC Form EDU 0007 (rev. 12/04/09)