Technology Twenty-Five



Technology Twenty-Five

Name Marjorie Economopoulos Date 6/30/03

Idea # 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. | 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. |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 Date 7/1/03

Idea # 2

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, )

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. | 7th |

|NCTM Illuminations | |

| | |

|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. |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 Marjorie Economopoulos Date 7/1/03

Idea # 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 | 7th |

| | |

|QCCs Addressed |Math Topic: |

|31 Topic: Number Theory |primes, and composites |

|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 Date 7/5/03

Idea # 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 | 7th |

|PowerPoint on computers in a lab setting | |

|Computer, Presentation device for classroom (a TV adapter or video projector) | |

|QCCs Addressed |Math Topic: |

|2 Topic: Communication, Reasoning |Many and varied. Depends on |

|Standard: Describes orally and in writing, using the appropriate mathematical vocabulary, mathematical |the mathematician selected. |

|concepts and procedures, such as solving a word problem or computing. | |

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.



Mathematics History Index of ThinkQuest materials. Includes multicultural and historical links as well as present day mathematics.



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.



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.



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.



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.



Mesopotamian Mathematics. A link for a History of Mathematics class. Is updated since 2003. Has links to other history sites. Mostly text.



Women in Mathematics Project. Professor at University of Oregon maintains this page. Useful links with a focus on women.



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 Available Earned Points

Points (Student Self) (Teacher)

Power Point with 5 or more slides 5 _____ _____

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 2 _____ _____

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 20 _____ _____

Technology Twenty-Five

Name Marjorie Economopoulos Date 7/05/03

Idea # 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 |geometry transformations; |

|Standard: Compares and contrasts geometric figures with respect to congruency and similarity (scaling, |translations, reflections, |

|dilations) |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 Marjorie Economopoulos Date 7/4/03

Idea # 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 | 7th |

|Help screen under Help, Statistics, Creating a Histogram | |

|QCCs Addressed |Math Topic: |

|3   Topic: Technology, Calculator Skills, Computer Skills, Problem Solving, Reasoning |Tables and bar graphs, |

|Standard: Uses scientific calculator and computer skills to solve problems, to discover patterns and |Histogram |

|sequences, to investigate situations and to draw conclusions. | |

| | |

|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 |0 |1 |2 |

|1 |No answer or no connection to data |Loosely describes, shows a connection |Clearly articulates connection of x-axis to |

| | |to the lowest and highest grades or |the data, lowest and highest grades are taken|

| | |focus is on frequency of grades |in account with some “margin” added in. |

| | |(y-axis) |Y-axis is related to frequency of grades. |

|2 |No answer, blank or a decision that would|The graph is mostly visible. Maybe |The entire graph is observable. Decision on |

| |not allow a graph to be observed |some of the top of a bar is missing or|x- and y- axis is appropriate. |

| | |some other minor error | |

|3 |Blank, or impossible scale such as a |Some number that produces a result, |Increments of 10 are recommended. Connect to|

| |negative number |but not the required grade increments.|grading scale in problem description. |

|4 |No answer or limited description |Tells about changes but cannot relate |Explains the connection of the input, |

| | |the input to the result. |(increment) to the width of the intervals, to|

| | | |the width of the bars. |

|5 |No connection shown or missed the concept|Most of the grades A= , B= , given and|Number of each of the grades are correct and |

| | |explained. Minor counting error or no|related to height of bars. |

| | |connection to graph given. | |

|6 |No graph attached |NA |Table & Graph is attached |

|7 |No response |Selects a preferred technology but |Selects a technology and tells a reason. |

| | |gives no reason. | |

Technology Twenty-Five

Name Marjorie Economopoulos Date 7/4/03

Idea # 7 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 |Tables and bar graphs, |

|Standard: Uses scientific calculator and computer skills to solve problems, to discover patterns and |Histogram |

|sequences, to investigate situations and to draw conclusions. | |

| | |

|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 Marjorie Economopoulos Date 7/5/03

Idea # 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: |Grade Level |

|Computer with spreadsheet | 7th |

|Word Processing. | |

|QCCs Addressed |Math Topic: |

|41 Topic: Charts, Tables, Graphs, Distributions |Data collection, graphs, |

|Standard: Collects, organizes data, determines appropriate method and scale to display data, and constructs |interpreting, making |

|frequency distributions, bar graphs, line graphs, circle graphs, tables, and charts. |conclusions |

|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. | |

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 Marjorie Economopoulos Date 7/5/03

Idea # 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. |Area, perimeter, fractions, |

|Standard: Solves problems, reasons, and estimates throughout mathematics. |sums, patterns |

|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. | |

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 Date 7/5/03

Idea # 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 TI-83, 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 |Coordinate plane, graphing |

|Standard: Uses scientific calculator and computer skills to solve problems, to discover patterns and |points and regions. |

|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. | |

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 Date 7/05/03

Idea # 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: |Grade Level |

|TI-handheld with Sierpinski Triangle program | 7th |

|Geometer’s Sketchpad with Sierpinski script file | |

|QCCs Addressed |Math Topic: |

|1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental Computation. |Probability, measurement, |

|Standard: Solves problems, reasons, and estimates throughout mathematics. |patterns |

|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. | |

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 Marjorie Economopoulos Date 7/5/03

Idea # 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. |Estimation, mental math, |

|Standard: Solves problems, reasons, and estimates throughout mathematics. |decimal values, role of powers|

|16 Topic: Mental Computation Strategies |of 10 in multiplication & |

|Standard: Performs computations mentally using strategies such as multiples of ten, powers of ten, |division |

|compensation, breaking apart numbers, or compatible numbers. | |

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 Date 7/05/03

Idea # 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) |Slope, y-intercept, graphing |

|Topic: Graphing Models, Algebra, Geometry, Problem Solving |linear equations |

|Standard: Graphs points in the coordinate plane, identifies coordinates of points, graphs linear equations, | |

|and solves problems using these concepts. | |

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 Date 7/05/03

Idea # 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 TI-APP 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 |Simple probability |

|Standard: Identifies possible outcomes of simple experiments and predicts or describes the probability of a |experiments, outcomes, sample |

|given event expresses as a rational number from 0 through 1. |space, predictions, |

|37 Topic: Compound Probability |simulations |

|Standard: Conducts and interprets a compound probability experiment. | |

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 Marjorie Economopoulos Date 7/05/03

Idea # 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 |Graphing points in a |

|Standard: Identifies and graphs an ordered pair of integers on a four-quadrant coordinate plane. |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

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