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Cynthia Mathis
Cynthia Mathis
(Reno - United States)

Math Simulations

Pythagorean Theorem Battleship

 

It's a battle of wits against the computer. Remember that a²+b²=c²

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Arithmetic

For the most up-to-date version and related activities, see http://phet.colorado.edu/simulations/sims.php?sim=Arithmetic

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Adding Integers (Positives and Negatives)

This activity uses Instructional Architect and a variety of web resources to help students learn to add integers.

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National Library of Virtual Manipulatives

 

Interactive and online virtual manipulatives for mathematics.

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Equation Grapher from PhET

Family of Functions

Introduction:
In this Math I/Math I Support course, students will explore specific aspects of the six Family of Functions and be able to graph and identify each by key characteristics.

Group Size: Any

Learning Objectives:
A. Identify functions by graph and equation
B. Identify critical points and slope
C. Identify characteristics: Domain and range, zeros and intercepts, max and min, end behavior, and increase and decrease
C. Graph equation
D. Write equations from graph
E. Identify parent graphs.


 

Guiding Question:

How do we identify and graph each of the family of functions?

Materials:

Presentation materials: PowerPoint & Promethean flipscharts from Valdosta High School Math I Team, graph paper, colored pencils, construction paper for graphic organizer,  
 

Additional materials. Textbook:  Georgia High School Mathematics 1.  McDougal Littell, 2008.Workbook:  Math 1: Georgia Notetaking Guide. McDougal Littell, 2008.Test Prep:  Georgia Mathematics 1: Test Preparation and Practice. McDougal Littell, 2008.Coach:  Georgia GPS Edition Standards Based Instruction. Triumph Learning. 2009. Procedures:
What do students need to learn to be able to answer the Essential Question? Answer Assessment Prompts: Assessment Prompt #1: White Board: Identify family of function equations:  x1, x2, │x│, x3, √x, 1/x  (Math I Concept 2 Promethean Flipchart page 12.)Assessment Prompt #2: White Board/Promethean: Identify parent graphs (Math I Concept 2 Promethean Flipchart page 80.)Assessment Prompt #3:  Graph the parent graphs by completing a graphic organizer.
Assessment:

Quiz: Math I Concept 2 PowerPoint or Promethean Flipchart  

Day One     Ticket out the Door:  Georgia Mathematics 1: Test Prep and Practice (McDougal Littell, 2007. ISBN-13: 9780-618-92023-5).

Day Two     3-2-1  Draw 3 linear graphs, Draw 2 quadratic graphs, Draw 1 Absolute Value graph

Day Three (if necessary): Find the critical points on samples of each type of graph

Answer Key or Rubric:
Answer Key: Included within Promethean charts, text and resource materialsAP #1: Math I Concept 2 Promethean Flipchart page 14AP # 2: Math I Concept 2 Promethean Flipchart page 80

Benchmark or Standards:   Georgia Performance Standards for Math I/Math I Support

MM1A1.a: How do we represent functions using function notation?
MM1A1.b: How do we graph and write equations for each of the Family of Functions?      
MM1A1.c: How do we graph transformations of functions?
MM1A1.d:
What are the characteristics of a function and how do you use them?
MM1A1.e: How do we use graphs and tables to investigate behavior of functions?

MM1A1.f: How do we recognize sequences as functions with domains that are whole numbers?
MM1A1.g: How do constant rates of change compare to variable rates of change within the Family of Functions?
MM1A1.h: How do we determine graphically and algebraically whether a function has symmetry and whether it is odd, even, or neither?
MM1A1.i: How do we interpret an equation in x, and its solutions as f(x) = g(x) and show where they intersect?

Attached Files:
 

    Unit1GeneralgraphsandIdentifyingVertexandslopeofAbsoluteValue.doc 
    ModelLessonFunctionFamilies.doc 
    Unit1GraphingQuadraticFunctions.doc 
    Unit1GraphingAbsoluteValueFunctions.doc 
    Unit1MatchingCubicequationwithCubicgraph.doc 
    Unit1MatchingRadicalequationswiththeirgraphs..doc 
    Unit1MatchingRationalequationswiththeirgraphs.doc 

Area of Circle

Lesson 2
Step 1
Watch it!

During the previous lesson you learned about pi and the circumference of a circle. Review how to measure the circumference of a circle with this animation.

Step 2
Watch it! Now you will learn how to measure the area of a circle. Try these activities and watch an animation .

Step 3: Think back and connect
forest

Do you remember your "Which Method" project?
What difference would it make to choose the circumference method as opposed to the area method?

Step 4: e-Notebook
eNotebook

Calculate the area of combined shapes.

Note: Save the e-Notebook to your desktop. After you have completed it, print it out and submit it to your teacher.

Step 6: Homework
homework Don’t forget to print out your homework.

© 2004, Education Development Center. All rights reserved.

Interactive Tutorial for Integer Addition/Subtraction

 

Provides step-by-step feedback for students as they learn to model integer addition and subtraction with pictures. A hands-on experience that allows students to master the reasoning behind the "add the opposite" method for subtracting integers while developing fluency with addition.

Interactive Simulation: Bar Grapher

 

An interactive to create a custom bar graph with your own data or display a bar graph from an included set of data.

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Interactive Excel Spreadsheets: Examples for Use in the Classroom and How to Develop

 

This is a collection of interactive Excel spreadsheets or Excelets for use in mathematics and general chemistry. Many of the spreadsheets come with discovery-based activities. A number of Excelets support the introduction of mathematical modeling concepts. The user changes a variable and the spreadsheet changes in numerical, graphical, and/or even symbolic form (equations). Through the use of numerical experimentation and "what if" scenarios, we have a powerful learning tool for students using readily available off-the-shelf software. All of this is done computationally with no use of programming, no macros or Visual Basics for Applications, VBA.

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Turing Machine Simulation

 

In 1936 Alan Turing, a British Mathematician, came up with an idea for an imaginary machine that could carry out all kinds of computations on numbers and symbols. He believed that if you could write down a set of rules describing your computation his machine could faithfully carry it out. Turing's Machine is the cornerstone of the modern theory of computation and computability even though it was invented nine years before the creation of the first electronic digital computer.

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Simulation: Circle Grapher

 

An interactive to create a custom pie chart with your own data or display a pie chart from an included set of data.

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