Mathematics

These attached documents are GEOSS activities, created to use open source software to teach to mathematics GEs. The activities were initially Logo activities. These were field tested. The activities have been adapted to use Scratch instead of Logo. The Scratch adaptations have not been field tested.

Scratch is available as a free download at the MIT website:

Geometry From Scratch is a classic activity that is normally done using Logo to draw and rotate a square. What's the Point has students use Cartesian Coordinates to draw shapes. Exploring Polygons From Scratch is an adaptation of the Logo program, Poly, that will draw any regular polygon.

This site is dedicated to connect mathematics, science, technology and engineering to the real world of careers and achievement, so that students can envision a context and purpose for what they are learning allowing them to envision their own successful futures.

There are online movies to demonstrate some excellent ways for students to learn and apply math to solving real problems. For example there is a unit on Designing Stronger Skateboards and another called The Bakery that addresses all the measurements and mathematics that go into baking successful products.

This is a very useful website for a teacher of elementary and middle school mathematics and or science.

Descriptors: coin toss, probability, theoretical probability, spinner, Maththematics, mathematical model

Title of resource: Spreadsheet Model of a Coin Toss or Binary Spinner

Author: Bob Sargent

Purpose: Enrichment of probability unit in MathThematics Book 2 demonstrating a mathematical model.

Audience: students grades 7-10

Resource Requirements: I have attached an excel spreadsheet.  You will need a compatible application.

Abstract:

Simulating coin tosses is a classic example of an educational computer program modeling an event.  The attached spreadsheet graphs simulated trials of some sort of 50/50 binary event, a coin flip or a spinner with two equal sides, using the random function.  I am not suggesting that students should not flip real coins or spin real spinners.  The lesson is about the mathematical model.  The question the students must answer is this; “In what ways does the model behave like what is being modeled, and how is it different?”  The lesson assumes the students already know about probability.  The model does not look like a coin flip or a spinner, yet it yields a similar table of results.  Getting students to articulate this, and elaborate on it, is the hoped for outcome of the lesson.  By repeatedly recalculating the spreadsheet (pressing F9 in Excel) it is possible to have many trials in rapid succession.  By comparing the graphs of 10 coins to the graphs of 100 coins in this way one can see that 100 coins more closely approximate the expected result of 50/50 more often than do 10 coins.  This is a graphic way to get at this idea.

Justification:

Mathematical modeling is one of the Vermont Standards that can be difficult to convey to students.  The spreadsheet is part of an enrichment exercise using a simple model of a simple event to illustrate the idea of mathematical modeling.  The spreadsheet could be part of a station among a group of stations in a unit on probability.  Coin flips and spinners is part of the curriculum in MathThematics, Book 2.  Probability and modeling are Vermont Standards.

 This site includes a multitude of ideas, samples, lessons, templates, instructions, and links to other resources, including data banks for gathering data, to help elementary teachers build lesson plan ideas around graphing and using Excel. 

 Intensive application of mathematical concepts including content and practice.  The site is broken up into math strands and grade level.  Great site for parents and students who need some extra practice.

Intended Purpose:  to show how technology can be used for ordinary classroom tasks

Intended Audience: (grade level/curricular area, etc.)  4th grade

Resource Requirements: (include, file type, platform, cost, user level, etc.)

Microsoft  Excel

Abstract:   The 4th grade teacher approached me about teaching her students how to use technology (Excel) to present a combination problem.  I created this problem to use to practice what I taught them before they did an actual portfolio problem.

Justification: (why/how is this a quality resource?)  Too many teachers think of technology integration as this whole big “other” thing that they have to do in addition to their already full plate.  Activities like this one can show them that technology can be used to improve ordinary classroom tasks..

Intended Purpose: I use this website everyday in my math class as a learning center. My students finish their work and go to this website to work on and build math concepts. This website is even better if you have a Smartboard as it allows you to really interact with the different topics.

Abstract: Learning and understanding mathematics, at every level, requires student engagement. Mathematics is not, as has been said, a spectator sport. Too much of current instruction fails to actively involve students. One way to address the problem is through the use of manipulatives, physical objects that help students visualize relationships and applications. We can now use computers to create virtual learning environments to address the same goals.

Justification: Every classroom in the Vermont is required to teach math. This is just one more tool available to teachers.

Intended Purpose:  Show how students can use technology to present math portfolio problems

Intended Audience: (grade level/curricular area, etc.)  middle school

Resource Requirements: (include, file type, platform, cost, user level, etc.)  Microsoft Excel

Abstract: Students were shown how to use Excel to present a math portfolio problem.  The narrative is not included

Justification: (why/how is this a quality resource?)  What better way to show technology integration than using a spreadsheet to present a math portfolio problem.

Author: (NCTM) National Council of Teachers of Mathematics

Intended Purpose: To provide mathematic activities, problems and ideas for grades K-12.

Intended Audience: Teachers

Resource Requirements: Internet access, A ton of free resources without signing up for a paid membership.

Abstract:  This site offers classroom resources based on principles and standards.

Justification: To access to learn is to learn to access.

Intended Purpose: to show students how to determine the most likely numbers to be rolled with two 6-sided dice and using 50 rolls to check the prediction

Intended Audience: (grade level/curricular area, etc.)  6th grade

Resource Requirements: (include, file type, platform, cost, user level, etc.) Microsoft Excel and a computer lab

Abstract: This is an exercise that I put together for the 6th grade before probability was taught in their math class.  I don’t teach terms like theoretical or experimental probability.  We just do the activity.  When the classroom teacher taught the terminology the students were immediately able to make a connection to what they had done in my classroom.  Their teacher said that she thought they had a better understanding of probability by learning it this way.

Justification: (why/how is this a quality resource?)

I think that this is a quality resource because it integrates technology into the math curriculum and it provides a guide for teachers to use to do it themselves.