Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date
6/30/03
1
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Sieve of Eratosthenes.
Students will explore prime and composite numbers.
A computerized version of the old favorite. Students will work with an interactive
“Eratosthenes Sieve” program where they can define the size of the number grid and
interact with the software to produce the effect of “graying out” multiples of primes on
the number grid. Pairs of students at computers with Internet access.
Advantages include individual instantaneous response. Grid can be small or enlarged.
Primes, composites, and patterns can be introduced. Have students play with it and
come up with characteristics of the numbers left in the sieve. What about grayed out
numbers? Expand size of grid from 50 cells to 100, further. Encourage conjectures.
How many numbers do you need to check? For prime or composite? Maybe make a
“rule,” then test it out. Extensions are possible. Part of a lesson on primes &
composites. Also a handy tool if you need to know if a number is composite. Fun in
any case.
Technology Required:
Grade Level
Computer with Internet access.
http://www.vex.net/~trebla/numbertheory/eratosthenes.html
QCCs Addressed
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving,
Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to
discover patterns and sequences, to investigate situations and to draw
conclusions.
7th
Math Topic:
Primes,
composites, &
patterns.
31 Topic: Number Theory
Standard: Identifies factors, multiples, primes, and composites.
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Marjorie Economopoulos
Idea #
2
Date 7/1/03
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students explore and use prime and composite numbers in a game format.
Have students play in pairs the “Factor Game” from the NCTM Illuminations web site.
Reinforces concepts of prime and composite numbers in a game format. Some
strategies are required. Experience can point out prime numbers (no factors other than
itself and 1) or no factors left that have not been selected. Distinguishing between
primes and composites is key to making good strategy choices.
“The Factor Game engages students in a friendly contest in which winning strategies
involve distinguishing between numbers with many factors and numbers with few
factors. Students are then guided through an analysis of game strategies and
introduced to the definitions of prime and composite numbers. “ (Illuminations Teacher
notes, http://illuminations.nctm.org/imath/6-8/FactorGame/index.html)
Part of a lesson or as a warm-up or anytime. Guiding questions on the Illumination web
site provide suggestions to the teacher and/or help for the student. Questions extend
the concepts of number theory to real life experiences and events. For example,
choices about measuring time are introduced. Why are there 24 hours in a day? What
if there were 23? Or 25?
Technology Required:
Grade Level
Computer with Internet access.
NCTM Illuminations
http://illuminations.nctm.org/imath/68/FactorGame/student/index.html
QCCs Addressed
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving,
Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to
discover patterns and sequences, to investigate situations and to draw
conclusions.
7th
Math Topic:
Primes,
composites, &
patterns.
31 Topic: Number Theory
Standard: Identifies factors, multiples, primes, and composites.
Does your selection make interdisciplinary connections? Explain. YES, extensions
include questions relating to applications of composite numbers with many factors.
Students are requested to think about time and increments of 24 hours. Compare to 23
or 25 hour days.
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date
7/1/03
3
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Miss Glosser’s Math Goodies. Grid of lessons
Lesson: Factors and Greatest Common Factor
Lesson: Prime & Composite Numbers
Continuing (or introducing) prime and composites. Lessons use a geometric model to
initiate thinking about prime and composite numbers. There are student notes,
examples, and some questions on the web to give immediate feedback to students who
might be unsure. The lesson is very procedural. Multiple choice selections may not be
the best questions, but the feedback is immediate and students can try until they get it
correct. This might be a good use of technology for a student who was absent or for a
center activity. It is not very interactive, but could have a place in the classroom. (A
varied approach rather than textbook.)
Technology Required:
Grade Level
Computer with Internet access
http://www.mathgoodies.com/lessons/toc_vol3.shtm
7th
QCCs Addressed
Math Topic:
31 Topic: Number Theory
Standard: Identifies factors, multiples, primes, and composites.
primes, and
composites
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/5/03
4
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students will create a Power Point presentation about a famous mathematician in
history (living or dead). They will research in the library or on the Internet to find their
person. Students will need to identify the person (and a second choice) and let the
instructor know before beginning the project to avoid too much repetition. Possible web
sites will be provided, but students are not limited. Students will be provided a grading
checklist so they know the required and optional components. A short biography of the
person, the math topic that person worked in, other disciplines related to this work or
research, and more
Class time will be provided to do the research and to plan the presentation (on paper)
and then to create the Power Point. At least two class days or equivalent will be
devoted to computer time (one or more to research, one to create Power Point.)
Students will present their Power Point to their class over a couple of weeks time (two
or three a day). Assigned times will be determined based on math topics so that there
is a historical connection to their math topics when possible. Reports on other
mathematicians will be scheduled as convenient. This could be varied as needed.
Another option is to take a couple of days just to do the presentations.
Source: Observation several years ago of one of our student teachers in a math
classroom at McCleskey Middle School, 7th grade. Was an amazing lesson. The kids
really loved it.
Technology Required:
Grade Level
Internet access
PowerPoint on computers in a lab setting
Computer, Presentation device for classroom (a TV adapter or
video projector)
QCCs Addressed
7th
Math Topic:
2 Topic: Communication, Reasoning
Standard: Describes orally and in writing, using the appropriate mathematical
vocabulary, mathematical concepts and procedures, such as solving a word
problem or computing.
Many and varied.
Depends on the
mathematician
selected.
Does your selection make interdisciplinary connections? Explain. YES. Most of the
mathematicians will have other content topics as well as mathematics. Students will be
encouraged to see the interdisciplinary connections.
Have you included (attached) an effective rubric? (Necessary for at least five). YES
Famous Mathematician Project (Activity # 4)
Research a famous mathematician and use Power Point to make a presentation for the
class. The scoring sheet lists the required elements. Be sure to refer to this sheet often
as you work. You want to earn the maximum possible points. You can work at home,
in the library or in class during specified times. Some helpful web sites can get you
started.
http://library.thinkquest.org/22584/index.html
Mathematics History Index of ThinkQuest materials. Includes multicultural and historical
links as well as present day mathematics.
http://www-history.mcs.st-and.ac.uk/~history/
History of Mathematics topics. Extensive resource. Some interactive Java applications
accompany text. A good quick spot to find graphs as well as biographies of
mathematicians and mathematical topics.
http://www.michielb.nl/maya/math.html
Maya Mathematics. Display of the Mayan Mathematical symbols. Has an interactive
field where you can type a number and see the Maya equivalent. Then you can
increment or decrement by one to see the basic numeration properties of their system.
http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Mathematics.html
Ancient Science and its Modern Fates. Links to Greek and more Greek mathematics.
Mostly text, but there are some photos of original works in Greek and Latin. Interesting.
http://www.mathforum.org/isaac/mathhist.html
Famous Problems in the History of Mathematics. A Math Forum project. Included are
the Bridges of Konigsberg, Puzzling Primes, the Value of Pi, Famous Paradoxes, and
more.
http://it.stlawu.edu/~dmelvill/mesomath/
Mesopotamian Mathematics. A link for a History of Mathematics class. Is updated
since 2003. Has links to other history sites. Mostly text.
http://darkwing.uoregon.edu/~wmnmath/
Women in Mathematics Project. Professor at University of Oregon maintains this page.
Useful links with a focus on women.
http://www.math.buffalo.edu/mad/wmad0.html
Black Women in Mathematics. Short summaries of African American women who
are/were mathematicians and links to other historical sites. Opening paragraph has
some shocking attention grabbing statements.
Famous Mathematician Project (Activity # 4) Scoring Sheet
Required Elements
Power Point with 5 or more slides
Available
Points
5
Earned Points
(Student Self) (Teacher)
_____
_____
Person is a mathematician
1
_____
_____
Math topic identified with brief description
2
_____
_____
Other disciple area identified with topic
2
_____
_____
Biography highlights include
5
When mathematician lived
Where mathematician lived and worked
What contributions did he/she make?
Any other facts of interest to share (at least two)
_____
_____
Organization—flow is logical and smooth
_____
_____
Presentation and delivery
3
_____
Student can explain facts and tell about math content
Student has practiced and is confident
Student answers questions from the class appropriately
_____
Total Points
_____
2
20
_____
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/05/03
5
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Student creates figures in Geometer’s Sketchpad and investigates them under specific
conditions. Student explores the concepts of transformations (slides, flips, turns),
scaling (similarity) and stretches (dilations). Key Curriculum Press has some structured
and open-ended lessons to investigate such properties for middle schoolers. Many
more advanced lessons also exist in a wonderful resource designed particularly for
middle grades students and teachers.
Source: Wyatt, K., Lawrence, A., Foletta, G., Geometry Activities for Middle School
Students, Key Curriculum Press, 1998.
Technology Required:
Grade Level
Computer with Geometer’s Sketchpad software
7th
QCCs Addressed
Math Topic:
20 Topic: Geometric Figures
Standard: Compares and contrasts geometric figures with respect to
congruency and similarity (scaling, dilations)
geometry
transformations;
translations,
reflections,
rotations,
congruence,
scaling, similarity
and dilations.
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date
7/4/03
6
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students will create a histogram from a set of data about grades. Sample worksheet
can be found in TI-Interactive Help screen as described below. Some modification
would be necessary, but not much. Groups of two to a computer in either a center
format of whole class depending on availability of computers. Centers could work with a
couple of computers. Next calculator activity addresses same content, so could be
center 1 & 2.
Students follow directions on entering Lists and a graph into TI-Interactive. Have them
experiment with the graph, changing domain & range to “see” the graph come into view.
Some questions regarding interval size and numbers of letter grades guide the activity
and provide a method of assessment.
Technology Required:
Grade Level
Computer with TI-Interactive software
Help screen under Help, Statistics, Creating a Histogram
7th
QCCs Addressed
Math Topic:
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving,
Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to
discover patterns and sequences, to investigate situations and to draw
conclusions.
Tables and bar
graphs,
Histogram
41 Topic: Charts, Tables, Graphs, Distributions
Standard: Collects, organizes data, determines appropriate method and scale to
display data, and constructs frequency distributions, bar graphs, line graphs,
circle graphs, tables, and charts.
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). YES
Assessment for Activities 6 & 7
Fill out this form for each of the technologies you use (Computer with TI-Interactive, TI
handheld calculator).
Tell which one you are describing ____________________________
(Some of the answers may be the same on both sheets.)
As you work on building the Histogram for the Class Grades, please think about and
answer the following.
1.
How did you decide on the scale for the x-axis and y-axis?
2.
What did you decide?
X-axis scale is from _______ to _________ Y-axis scale is from _______ to
________
Why did you make this choice?
3.
What increment did you use for the x-axis scale? ___________
Tell why you chose that?
4.
Try changing the increment to see the impact on the graph. Tell what you did
and what happened.
5.
How many grades of each letter did the class earn?
How does your graph help you know this?
6.
Please print your table of data and best graph and attach to this sheet (only for
the computer technology.)
7.
After you compete the questions for both technologies (computer and handheld),
tell which one you liked better and one reason why.
Rubric to grade assessment for Activities 6 & 7
Item
1
0
No answer or no
connection to data
1
Loosely describes,
shows a connection to
the lowest and highest
grades or focus is on
frequency of grades
(y-axis)
2
No answer, blank or a
decision that would not
allow a graph to be
observed
3
Blank, or impossible
scale such as a
negative number
4
No answer or limited
description
The graph is mostly
visible. Maybe some
of the top of a bar is
missing or some other
minor error
Some number that
produces a result, but
not the required grade
increments.
Tells about changes
but cannot relate the
input to the result.
5
No connection shown or Most of the grades A=
missed the concept
, B= , given and
explained. Minor
counting error or no
connection to graph
given.
No graph attached
NA
No response
Selects a preferred
technology but gives
no reason.
6
7
2
Clearly articulates
connection of x-axis to the
data, lowest and highest
grades are taken in
account with some
“margin” added in. Y-axis
is related to frequency of
grades.
The entire graph is
observable. Decision on
x- and y- axis is
appropriate.
Increments of 10 are
recommended. Connect
to grading scale in problem
description.
Explains the connection of
the input, (increment) to
the width of the intervals,
to the width of the bars.
Number of each of the
grades are correct and
related to height of bars.
Table & Graph is attached
Selects a technology and
tells a reason.
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
7
Date
7/4/03
Version of # 6 above with Calculator instead of computer software
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students will create a histogram from the same set of data about grades. This
calculator activity uses the TI-83 or TI-73 calculator. The activity could be done in a
whole class setting or as a part of a center activity where students move from one
technology to another. Students will take the data set and fill in lists on the calculator,
adjust the window, selecting x- and y-axes, and increments. They will turn on Plots and
select Histogram. Their goal will be to display a graph and answer the same set of
questions as Activity # 6.
Have them experiment with the graph, changing domain & range to “see” the graph
come into view. Some questions regarding interval size and numbers of letter grades
guide the activity and provide a method of assessment.
Technology Required:
Grade Level
TI-83 or TI-73 handheld calculators
7th
QCCs Addressed
Math Topic:
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving,
Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to
discover patterns and sequences, to investigate situations and to draw
conclusions.
Tables and bar
graphs,
Histogram
41 Topic: Charts, Tables, Graphs, Distributions
Standard: Collects, organizes data, determines appropriate method and scale to
display data, and constructs frequency distributions, bar graphs, line graphs,
circle graphs, tables, and charts.
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). YES,
see above for both activity 6&7
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/5/03
8
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students collect data, organize, and form conclusions as part of a large community
project. Interdisciplinary teaming of language arts, social studies, math, and science
teachers make this a project to remember. Mathematics becomes an integral tool to
analyze and present data. Students collect data, organize it in a spreadsheet and use
graphs as well as word processing to create a report that is eventually presented to the
school board for action. The article referenced here has elaborate descriptions of the
details and excitement of all involved. Two projects are described. One is Create a
Country and the other a Community Problems Project. Modification for the community
project would be appropriate depending on the local conditions or needs. The project
described in this article related to a school area traffic problem.
Source: Olson, J.C., “Interdisciplinary Projects Enhance Teaching and Learning,”
Mathematics Teaching in the Middle School, Vol. 8, No. 5, Jan 2003, pp. 260-266.
Technology Required:
Computer with spreadsheet
Word Processing.
Grade Level
7th
QCCs Addressed
Math Topic:
41 Topic: Charts, Tables, Graphs, Distributions
Standard: Collects, organizes data, determines appropriate method and scale to
display data, and constructs frequency distributions, bar graphs, line graphs,
circle graphs, tables, and charts.
43 Topic: Charts, Tables, Graphs, Distributions
Standard: Reads and interprets data in frequency distributions. diagrams,
charts, tables, and graphs; and makes predictions or conclusions based on this
data.
Data collection,
graphs,
interpreting,
making
conclusions
Does your selection make interdisciplinary connections? Explain. YES. This is a
fabulous interdisciplinary project. Combines LA, Math, SS, Science and the community.
Have you included (attached) an effective rubric? (Necessary for at least five). YES
Scoring Guide for the Oral Presentation (Activity 8)
This is a point system suggested in the article. It is part of a longer description of
expectations and criteria. Students know before the presentation how it will be graded.
Content is graded separately. This is about delivery.
Oral Presentation: 20 points (maximum 2 points for each skill)
Enthusiasm
Eye contact—looked at the audience
Posture—stood erect yet relaxed
Pauses—for effect and punctuation
Gestures—appropriately placed movements or facial expressions
Fluency—smoothness of delivery; no stumbles
Rate—not too fast or slow
Volume—loud enough to be heard without shouting
Clarity—each word is clear and understandable
Expression—rising and falling tone; emphasis
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/5/03
9
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students explore relationships of area and perimeter using pictures, models, diagrams,
and tables in a handheld calculator. Students are encouraged to predict, find patterns,
make conjectures, visualize infinite sums of fractions, and more. The calculator
technology is a tool to make access to patterns easy and accessible to middle school
learners.
Questions regarding various figures lead to extended thinking. “What happens to the
perimeter as the length of the side of the square is doubled?” “What happens to the
area as the length of the side of the square is doubled?” “If the table is extended, what
values would you see in the next column?”
The article describes an extensive collection of tasks and questions. The author
introduces Zeno’s paradox, at least conceptually. Nice treatment and great ideas.
Source: Chavez, O. & Reys, R. “Do you see what I see?” Mathematics Teaching in the
Middle School, Vol. 8, No. 3, Nov. 2002, pp. 162-168.
Technology Required:
Grade Level
Handheld calculator TI 73 or TI-83
7th
QCCs Addressed
Math Topic:
1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental
Computation.
Standard: Solves problems, reasons, and estimates throughout mathematics.
24 Topic: Circles, Polygons, Geometric Solids, Formulas
Standard: Finds the perimeter (circumference) and area of polygons and circles,
and the volume and surface area of geometric solids using formulas. (Uses
student development of formulas when possible.
28 Topic: Fractions, Decimals, Integers, Percent
Standard: Compares and orders whole numbers, integers, fractions, decimals,
and percents.
Area, perimeter,
fractions, sums,
patterns
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/5/03
10
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Drawing pictures on the TI-83 handheld. Student will learn drawing features of the TI83, become familiar with some of the features such as the Draw command, grid
systems and how to store a picture. Students will combine geometry skills with
calculator functions to create designs and pictures. Holiday pictures, illusions, logos,
other graphics are described and referenced in the “Reflections” source. Extensions
include drawing of cartoons, scaled up class projects and more. A fun activity with
some geometric rewards.
I personally did a similar activity ages ago on the TI-81 calculator with a group of middle
school students in a math/science camp at Kennesaw State. Went over well once they
got familiar with calculator.
Source: Clemmons, R.L., “Creating Geometric Displays,” Reflections, A publication of
GCTM, Volume XLVIII, Number 3, Fall 2002, pp. 14-15, 20.
Technology Required:
Grade Level
TI-83 handheld calculator
7th
QCCs Addressed
Math Topic:
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving,
Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to
discover patterns and sequences, to investigate situations and to draw
conclusions.
22 Topic: Graphing, Integers
Standard: Identifies and graphs an ordered pair of integers on a four-quadrant
coordinate plane.
Coordinate
plane, graphing
points and
regions.
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/05/03
11
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students will play the “Chaos Game” to explore organized patterns and fractals in
nature and science. The rules are found in many web sites on Fractals, as well as at
the Transitions Math web site at KSU. Students produce patterns of dots on overhead
transparencies based on a set of rules which include rolling a die and a measuring and
placing a dot. There is a predictable set of consequences within the randomness.
Collections of student work on the multiple overheads create the Sierpinski Triangle, a
famous fractal pattern. There is a TI-calculator program that produces the same results
in a short time. In addition, it is fun to show the students an interactive script available
in Geometer’s Sketchpad to build the same Sierpinski Triangle. Further investigations
lead students to see patterns in a fern, on a beach coast, on a leaf, and relate concepts
of chaos with perceived order.
Source: Student teacher in class at E. Cobb Middle School, circa 1996, various
presentations by me and others at workshops, NCTM, etc., + Transitions Math web site,
transitions.kennesaw.edu
Technology Required:
TI-handheld with Sierpinski Triangle program
Geometer’s Sketchpad with Sierpinski script file
Grade Level
7th
QCCs Addressed
Math Topic:
1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental
Computation.
Standard: Solves problems, reasons, and estimates throughout mathematics.
36 Topic: Simple Probability
Standard: Identifies possible outcomes of simple experiments and predicts or
describes the probability of a given event expresses as a rational number from 0
through 1.
Probability,
measurement,
patterns
Does your selection make interdisciplinary connections? Explain. YES. Science and
mathematics topics intertwine in this lesson. Patterns in nature are often of fractal form.
Many extensions are also possible including writing and fractals in multiple forms. Web
sites abound taking students into many discipline areas.
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/5/03
12
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
A game on the TI-83 plus. Application, Decimal Defender (DecDfend) by Jonah Cohen.
“While exploring a strange and distant galaxy, your ship is surrounded by hostile
decimal numbers. Your mission is to destroy them as quickly as possible and return
safely to earth. The onboard computer will create multiplication and division problems.
The location of the decimal point in each answer reveals the enemy’s vulnerable spot.”
Students play the game by moving a missile and firing at the appropriate decimal point
in the number. Problems include multiplication, division and mixed. Each problem is a
number times or divided by a power of ten, so place value and concept of decimal is
practiced. A pretty quick game, but time is sufficient to get going and succeed. If you
miss, you are smashed, but still alive, so there are many chances. Top scoring games
are recorded. A nice variation on mental math and drill in a game format.
Technology Required:
Grade Level
TI-83 plus with App DecDfnd (class set or small groups)
7th
QCCs Addressed
Math Topic:
1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental
Computation.
Standard: Solves problems, reasons, and estimates throughout mathematics.
16 Topic: Mental Computation Strategies
Standard: Performs computations mentally using strategies such as multiples of
ten, powers of ten, compensation, breaking apart numbers, or compatible
numbers.
Estimation,
mental math,
decimal values,
role of powers of
10 in
multiplication &
division
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/05/03
13
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Student will find the values of m and b in a function y=mx+b by viewing a graph of the
line. Students will interactively play a game on the TI-83 plus called “Guess my
Coefficients,” a Concept APP programmed by Sebastian Theiss.
Options include:
1. Linear
2. Quadratic
3. Absolute value
4. Linear & quadratic
5. All
For middle grades, Linear and possibly Absolute value are appropriate. Two forms of
linear are available. My preference is y=mx+b. The student sees a graph and enters
values for m= and b=. The application gives great feedback, showing an immediate
graph of the selected line. If it falls on the graph of the line, the student knows
immediately. If it does not, it also is apparent immediately. If the response is correct, a
screen says so, if incorrect, same with hints and a second chance. Very reinforcing and
student can do some self correction before asking for help. A nice way to visualize and
practice without pencil and paper. High scores are recorded. Student can compete
with self (or others) for improvement.
Teacher or student can vary some settings. Very user friendly with instructions.
Technology Required:
Grade Level
TI-83 plus with APP GuesCoef
7th or 8th
Pre-Algebra
QCCs Addressed
Math Topic:
30 (Pre-Algebra)
Topic: Graphing Models, Algebra, Geometry, Problem Solving
Standard: Graphs points in the coordinate plane, identifies
coordinates of points, graphs linear equations, and solves problems
using these concepts.
Slope, yintercept,
graphing linear
equations
Does your selection make interdisciplinary connections? Explain. NO
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/05/03
14
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students conduct simulations and discover patterns and make conjectures. This TIAPP could be used for multiple lessons during an entire unit on probability. The
possibilities are quite extensive. The simulations are accompanied by rather
sophisticated graphics so that when you simulate “toss a coin,” you can see a virtual
coin toss. Similarly for a die toss, an urn problem, spinner, and card draw. Fabulous
and entertaining as well as quick way to get large samples.
Choices in the Application include:
Toss Coin
Roll Dice
Pick Marbles
Spin Spinner
Draw Cards
Random Numbers
Wow, hard to imagine this is all in the handheld APP Probability Simulation written by
Corey Taylor. Fabulous!
Extend to real-world applications. Discuss the lottery, probability of rain and other
weather reports, politics, and more.
Technology Required:
Grade Level
TI-83 plus with App Prob Sim (class set or small groups)
7th
QCCs Addressed
Math Topic:
36 Topic: Simple Probability
Standard: Identifies possible outcomes of simple experiments and predicts or
describes the probability of a given event expresses as a rational number from 0
through 1.
37 Topic: Compound Probability
Standard: Conducts and interprets a compound probability experiment.
Simple
probability
experiments,
outcomes,
sample space,
predictions,
simulations
Does your selection make interdisciplinary connections? Explain. YES. Applications
can range from social science to meteorology. Interdisciplinary connections to
probability are many and varied.
Have you included (attached) an effective rubric? (Necessary for at least five). NO
Technology Twenty-Five
Name
Idea #
Marjorie Economopoulos
Date 7/05/03
15
Brief Description of different plans for using technology to teach mathematics more
effectively. Include source. (Attach any worksheets or handouts if they should be
included)
Students will interpret a graph of temperatures over a twenty-four hour period. Teacher
collects data using a temperature probe, CBL, graphing calculator. Teacher displays
the data for the class and students are asked guiding questions about the data. What
do you think this could represent. Trace key and exploration of the data, time along the
x-axis, numbers along the y-axis, … Students will ask questions, as will teacher to
“uncover” the mystery of the data. The x-axis represents 24 hours, y is temperature in
Fahrenheit (or Celsius, depends on setup). This lesson should coincide with a science
lab of temperatures or earth science, or maybe just measuring temperatures.
A worksheet of guiding questions summarizes the students’ understandings of the
graph.
Source is TI-experiments book that either comes with the CBL or can be purchased
separately. Kim & I did this one years ago in an interdisciplinary lab. Quite nice with
Kim asking the Q’s.
Technology Required:
Grade Level
TI-83, CBL with temperature probe
7th & 8th
& Pre-Algebra
QCCs Addressed
Math Topic:
22 Topic: Graphing, Integers
Standard: Identifies and graphs an ordered pair of integers on a four-quadrant
coordinate plane.
Graphing points
in a coordinate
plane,
interpreting data
points and
graphs
Does your selection make interdisciplinary connections? Explain. YES Data collection
of natural science phenomena of temperatures over a twenty four hour period. Can
connect to science lab, weather, clouds, day/night, depends on what’s going on in
team/school.
Have you included (attached) an effective rubric? (Necessary for at least five).
Technology Twenty Five, 16-25 is a modified assignment to create
Staff development workshop on Web Pages for the MGE faculty
See other work