Uses of Java Applets in Mathematics Education
|
|
- Beatrix Richardson
- 2 years ago
- Views:
Transcription
1 Uses of Java Applets in Mathematics Education Christopher P. Mawata Mathematics Department University of Tennessee at Chattanooga Abstract: This paper illustrates different ways in which Java applets can enhance on-line lessons. We discuss and give instances of the following uses of applets: Applets to generate examples. Instead of a single image with a picture that gives an example of the concept being taught an applet allows us to have very many examples without the need for a lot of space. Applets that give students simple exercises to make sure that they have understood a definition or concept. Applets that generate data. The students can then analyze the data and try to make reasonable conjectures based on the data. Applets that guide a student through a sequence of steps that the student performs while the applet is running. Applets that present ''picture proofs''. With animation it is possible to present picture proofs that one could not do without a computer. An applet can also be in the form of a mathematical puzzle. Students are then challenged to explain how the applet works and extract the mathematics from the puzzle.this also helps with developing problem solving skills. An applet can set a theme for a whole course. Different versions of an applet can appear at different stages of a course to illustrate aspects of the problem being studied. Introduction: Java applets began to appear in web pages in Apart from applets used as decorative pieces on web pages, most "serious" applets are used in business, particularly the financial industry. In the education community we need to explore pedagogical uses to which we can put applets. This paper aims to demonstrate that applets are very powerful as a medium of instruction. Examples of several ways in which applets can improve mathematics instruction will be given. The reader, however, should not be left with the impression that these applets are all that can be done. The hope is that the reader
2 will think of instances where an applet would be appropriate in his or her teaching. The level of the material to be learned can be anywhere from elementary school to tertiary level. Many of the same ideas can also be used in other disciplines of instruction as well. Applets to generate examples: We start with applets used to generate examples and instances of the objects under discussion. These are applets that replace the standard picture of one instance of an object. The applet below, for example, is inserted in a web page just after acute and obtuse angles have been defined. Rather than one or two pictures of acute and obtuse angles the terminal side sweeps through angles from 0 to 180 degrees. You will find that even people who are quite familiar with acute and obtuse angles will patiently watch the applet as the angles change. What this applet is doing is holding the students attention and reinforcing the definition. Many students watch carefully to see if at 90 degrees it does say right angle. It is desirable to have a start/stop button so that students can stop the animation when they are done with it. That way the applet does not become a distraction. Here is another applet that provides examples, this time of triangles. When the applet runs the sides and angles of the triangle change size as the student watches. We can use this applet to practice estimation. The student can try to stop the applet when one of the angles is a given size, say 45 degrees, without watching the figures.
3 Applets for simple multiple choice questions: We can use applets to generate simple yes/no or multiple choice questions so that students can get immediate reassurance that they have understood a concept. Since there is a "random" number generator in Java the questions can vary. The applet below can be used by elementary school children, given instructions like "Click on the button with the fraction that represents the part of the pie that is shaded." There are many ways to provide feedback using applets. In the applet below the student is supposed to click on the appropriate button when the measure of an angle is displayed in the textbox. An incorrect answer will prompt the applet to put up a frame with a brief explanation as to why the response was incorrect. One can also have the applet take the student to another web page anywhere on the internet where a more detailed explanation can be given. The picture below is of the situation just after an incorrect button is clicked.
4 Applets to generate data: Applets can be used as quick ways to generate data for students to analyze. There are times when it is desirable for students to analyze data using graphs and calculators and to make conjectures as to what the explanation for the data is. One could, for instance, have students construct right angled triangles and measure the sides and hopefully after some analyzing come up with a formulation of the Pythagorean Theorem. While it is definitely instructive to draw a few right angled triangles it would require a lot of time to draw enough of them to get a table with sufficient data to analyze. We can use an applet to generate data as in the example below. The red dots can be dragged using the mouse and the figures written in a table for analyzing later.
5 Applets to show a sequence of steps: Applets can guide a student through a sequence of steps with the student performing the activities at each step as the applet runs. The applet below tries to convince the student that the sum of the measures of the angles in a triangle is 180 degrees by having him or her cut up a triangle and rearrange the angles to form a 180 degree angle. The animation makes the experience more memorable than it would be if presented in a textbook. The picture shows one of the phases in the animation. The next applet is one of a sequence of applets for teaching compass and straight edge constructions. At this point the student has already used an applet that teaches how to construct a perpendicular and is learning how to construct a right triangle given the length of one of the legs and that of the hypotenuse.
6 Applets that show animated picture proofs: A popular use of applets is in animated picture proofs. Here is an applet that gives a picture proof of the Pythagorean Theorem. At this point the blue triangles are being moved to new positions. Applets with mathematical puzzles: An applet can be in the form of a mathematical puzzle. Students are challenged to explain how the applet works. If the level of difficulty of the puzzle is appropriate the students can extract the underlying mathematical concepts. The applet below was written for an undergraduate discrete structures class. It tiles a deficient 2 n by 2 n grid using right trominos. It is a good introduction to the principle of mathematical induction. It also helps students to develop problem solving skills.
7 Applets that are the center of a course: The final applet I will present is an example of what I call a "theme applet". This is the most ambitious type of project where a whole course revolves around an applet that appears and reappears in different contexts. In this example the applet presents an "overhead photograph" of a forest. Green dots are healthy trees and red ones are diseased trees. The light green patches are grass. The applet is meant for an elementary statistics class. The version of the applet I show takes a sample, gives you the statistics and you (the student) are expected to estimate confidence intervals for the proportion of the trees that are diseased. One can find many educational applets by using a search engine. The applets referred to in this article can be seen in context at the author's site, Math Cove. There is a large collection of very good applets at the IES Inc. site, Manipula Math
8 with Java. Other places to look are the Mathematics Section of Gamelan and The Java Repository. Asian Technology Conference in Mathematics, 1998.
Problem 3.2 A Proof of the Pythagorean Theorem
Problem 3.2 A Proof of the Pythagorean Theorem Use the puzzles your teacher gives you. Puzzle frames Puzzle pieces A. Study a triangle piece and the three square pieces. How do the side lengths of the
G E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY. Notes & Study Guide
G E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY Notes & Study Guide 2 TABLE OF CONTENTS SIMILAR RIGHT TRIANGLES... 3 THE PYTHAGOREAN THEOREM... 4 SPECIAL RIGHT TRIANGLES... 5 TRIGONOMETRIC RATIOS...
Law of Cosines TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System
Math Objectives Students will be able to state the Law of Cosines Students will be able to apply the Law of Cosines to find missing sides and angles in a triangle Students will understand why the Law of
Answer Key. Lesson 7.1. Study Guide
Answer Key Lesson 7.1 Study Guide 1. leg; 30 2. hypotenuse; 3 Ï } 13 3. hypotenuse; 52 4. leg; 20 Ï } 6 5. leg; 5 Ï } 3 6. hypotenuse; 39 7. 1452 yd 2 8. 540 mi 2 9. 5, 12, 13; 130 cm 10. 7, 24, 25; 96
Math Mammoth Geometry 1 Contents
Math Mammoth Geometry 1 Contents Introduction... 4 Review: Area of Rectangles... 8 Review: Area and Perimeter... 13 Lines, Rays, and Angles... 17 Measuring Angles... 22 Drawing Angles... 27 Angle Problems...
Pythagorean Theorem. Inquiry Based Unit Plan
Pythagorean Theorem Inquiry Based Unit Plan By: Renee Carey Grade: 8 Time: 5 days Tools: Geoboards, Calculators, Computers (Geometer s Sketchpad), Overhead projector, Pythagorean squares and triangle manipulatives,
Mathematics Task Arcs
Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number
Unit Lesson Plan: Modeling Pythagoras Theorem
1 Unit Lesson Plan: Modeling Pythagoras Theorem Grade Level: 8 Unit: Measurement SCO: Students should be able to demonstrate an understanding of the Pythagorean relationship using models. Prior Knowledge:
Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom
Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom Grade Level: Seven Time Span: Four Days Tools: Calculators, The Proofs of Pythagoras, GSP, Internet Colleen Parker Objectives
Discovering Math: Exploring Geometry Teacher s Guide
Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional
Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter
Heron s Formula Lesson Summary: Students will investigate the Heron s formula for finding the area of a triangle. The lab has students find the area using three different methods: Heron s, the basic formula,
NEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
LESSON PLAN #1: Discover a Relationship
LESSON PLAN #1: Discover a Relationship Name Alessandro Sarra Date 4/14/03 Content Area Math A Unit Topic Coordinate Geometry Today s Lesson Sum of the Interior Angles of a Polygon Grade Level 9 NYS Mathematics,
Grade 8 Math Pythagorean Theorem
Grade 8 Math Pythagorean Theorem By Joy Clubine, Alannah McGregor & Jisoo Seo Teaching Objectives For students to discover and explore the Pythagorean Theorem through a variety of activities. Students
Geometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
Unit 6 Coordinate Geometry
Mathematics I Frameworks Student Edition Unit 6 Coordinate Geometry 2 nd Edition Table of Contents Introduction:... 3 Video Game Learning Task... 6 New York Learning Task... 11 Quadrilaterals Revisited
Geometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
Right Triangles Long-Term Memory Review Review 1
Review 1 1. Is the statement true or false? If it is false, rewrite it to make it true. A right triangle has two acute angles. 2 2. The Pythagorean Theorem for the triangle shown would be a b c. Fill in
Unit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
1 Math 116 Supplemental Textbook (Pythagorean Theorem)
1 Math 116 Supplemental Textbook (Pythagorean Theorem) 1.1 Pythagorean Theorem 1.1.1 Right Triangles Before we begin to study the Pythagorean Theorem, let s discuss some facts about right triangles. The
In a triangle with a right angle, there are 2 legs and the hypotenuse of a triangle.
PROBLEM STATEMENT In a triangle with a right angle, there are legs and the hypotenuse of a triangle. The hypotenuse of a triangle is the side of a right triangle that is opposite the 90 angle. The legs
THE PROOF IS IN THE PICTURE
THE PROOF IS IN THE PICTURE (an introduction to proofs without words) LAMC INTERMEDIATE GROUP - 11/24/13 WARM UP (PAPER FOLDING) Theorem: The square root of 2 is irrational. We prove this via the mathematical
Lesson 19. Triangle Properties. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 19 Triangle Properties Objectives Understand the definition of a triangle Distinguish between different types of triangles Use the Pythagorean
Trigonometry. Week 1 Right Triangle Trigonometry
Trigonometry Introduction Trigonometry is the study of triangle measurement, but it has expanded far beyond that. It is not an independent subject of mathematics. In fact, it depends on your knowledge
Proving Pythagoras. Lesson Plan
Proving Pythagoras Lesson Plan Cube Fellow: Kenneth A. Macpherson Goal: Get 10th Graders to understand and prove the Pythagorean Theorem Grade and Course: tenth grade geometry KY Standards: Geometry: MA-11-2.1.3
GeoGebra Workshop for the Initial Teacher Training in Primary Education
GeoGebra Workshop for the Initial Teacher Training in Primary Education N. Ruiz natalia.ruiz@uam.es Facultad de Formación de Profesorado y Educación (Faculty of Education) Universidad Autónoma de Madrid
Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:
Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button
EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan
1 EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan Tangrams Geoboards Equation Grapher Green Globs AlphaShapes Protractor Compass Created by Sandra Metzler 2 OVERALL OBJECTIVES 1- Students will increase
10.2 45-45 -90 Triangles
Page of 6 0. --0 Triangles Goal Find the side lengths of --0 triangles. Key Words --0 triangle isosceles triangle p. 7 leg of a right triangle p. hypotenuse p. Geo-Activity Eploring an Isosceles Right
Knowing and Using Number Facts
Knowing and Using Number Facts Use knowledge of place value and Use knowledge of place value and addition and subtraction of two-digit multiplication facts to 10 10 to numbers to derive sums and derive
CLIL MultiKey lesson plan
LESSON PLAN Subject: Mathematics Topic: Triangle Age of students: 16 Language level: B1, B2 Time: 45-60 min Contents aims: After completing the lesson, the student will be able to: Classify and compare
The Not-Formula Book for C1
Not The Not-Formula Book for C1 Everything you need to know for Core 1 that won t be in the formula book Examination Board: AQA Brief This document is intended as an aid for revision. Although it includes
Factoring Patterns in the Gaussian Plane
Factoring Patterns in the Gaussian Plane Steve Phelps Introduction This paper describes discoveries made at the Park City Mathematics Institute, 00, as well as some proofs. Before the summer I understood
Algebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
Types of Angles acute right obtuse straight Types of Triangles acute right obtuse hypotenuse legs
MTH 065 Class Notes Lecture 18 (4.5 and 4.6) Lesson 4.5: Triangles and the Pythagorean Theorem Types of Triangles Triangles can be classified either by their sides or by their angles. Types of Angles An
Area of Parallelograms and Triangles
Context: Grade 7 Mathematics. Area of Parallelograms and Triangles Objective: The student shall derive the formulas for the area of the triangle and the parallelogram and apply these formulas to determine
*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
The Dot and Cross Products
The Dot and Cross Products Two common operations involving vectors are the dot product and the cross product. Let two vectors =,, and =,, be given. The Dot Product The dot product of and is written and
A Correlation of Pearson Texas Geometry Digital, 2015
A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations
Specimen Entrance Examination. Mathematics Entry to Year 6. Time: 1 hour. You will need a ruler, but you must not use a calculator.
Specimen Entrance Examination Mathematics Entry to Year 6 Time: 1 hour You will need a ruler, but you must not use a calculator. Answer as many questions as you can. Write your answers in the spaces provided
Unit 6: Pythagorean Theorem
Approximate Time Frame: 2 weeks Connections to Previous Learning: In Unit 1, students learned to evaluate expressions and equations with exponents and solved equations of the form worked with triangles
is the area of the polygon. Pick s Theorem says that A=I+B/2-1. Here is an example B = 7 I = 0 A = I + B/2 1 = = 2.5
I chose Pick s Theorem to do as a part of a Math Magic block of math circles. I have used this formula as a party trick for several years. The next section introduces the properties of polygons and explains
Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website
Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 5-50 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra
Assignments and Activities Topic 8: Explicit Instruction
Activity 8.1: Identifying Explicit Instruction Assignments and Activities Topic 8: Explicit Instruction Learning Outcomes Learning Outcome 1: Explain the similarities, differences, and benefits of explicit
Pre-Calculus Math 12 First Assignment
Name: Pre-Calculus Math 12 First Assignment This assignment consists of two parts, a review of function notation and an introduction to translating graphs of functions. It is the first work for the Pre-Calculus
Exploring Geometric Mean
Exploring Geometric Mean Lesson Summary: The students will explore the Geometric Mean through the use of Cabrii II software or TI 92 Calculators and inquiry based activities. Keywords: Geometric Mean,
Geometry Mathematics Curriculum Guide Unit 6 Trig & Spec. Right Triangles 2016 2017
Unit 6: Trigonometry and Special Right Time Frame: 14 Days Primary Focus This topic extends the idea of triangle similarity to indirect measurements. Students develop properties of special right triangles,
Geometry. Unit 1. Transforming and Congruence. Suggested Time Frame 1 st Six Weeks 22 Days
Geometry Unit 1 Transforming and Congruence Title Suggested Time Frame 1 st Six Weeks 22 Days Big Ideas/Enduring Understandings Module 1 Tools of geometry can be used to solve real-world problems. Variety
Roofing and Right Triangles Lesson Plan
Roofing and Right Triangles Lesson Plan Concept/principle to be demonstrated: The Pythagorean Theorem is used extensively in designing and building structures. This lesson demonstrates the relationship
Audience Response System (Turning Point) A Quick Start Guide
Audience Response System (Turning Point) A Quick Start Guide What is Turning Point? Turning Point is an audience response system and by downloading a plug-in for PowerPoint it enables you to add interactivity
Background Knowledge
Background Knowledge Precalculus GEOMETRY Successful completion of the course with a grade of B or higher Solid understanding of: Right Triangles Congruence Theorems Basic Trigonometry Basic understanding
G r a d e 8 M a t h e m a t i c s. Number
G r a d e 8 M a t h e m a t i c s Number Number and Shape and Space (Measurement) 8.N.1, 8.N.2, 8.SS.1 Enduring Understandings: The square roots of perfect squares are rational numbers. The square roots
Pythagorean Theorem. Overview. Grade 8 Mathematics, Quarter 3, Unit 3.1. Number of instructional days: 15 (1 day = minutes) Essential questions
Grade 8 Mathematics, Quarter 3, Unit 3.1 Pythagorean Theorem Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Prove the Pythagorean Theorem. Given three side lengths,
Using Sketchpad to Demonstrate the Pythagorean Theorem
Using Sketchpad to Demonstrate the Pythagorean Theorem 1. Start Sketchpad if it isn t already running. If it is running, choose New Sketch from the file menu. A new, blank sketch window appears. 2. Choose
TryAngle? A c t i v i t y 2. Objective. Materials
. Objective To investigate properties of triangles and learn how to classify the various types of triangles A c t i v i t y 2 TryAngle? Materials TI-73 calculator 12 6-inch straws with about 40 twist ties
If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
Looking for Pythagoras: Homework Examples from ACE
Looking for Pythagoras: Homework Examples from ACE Investigation 1: Coordinate Grids, ACE #20, #37 Investigation 2: Squaring Off, ACE #16, #44, #65 Investigation 3: The Pythagorean Theorem, ACE #2, #9,
Introduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test
Introduction The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are
The Most Widely Used. Mathematics Textbook Series in Japan is Now in English! Introducing Tokyo Shoseki s. and
The Most Widely Used Mathematics Textbook Series in Japan is Now in English! Introducing Tokyo Shoseki s Mathematics International (Elementary School, s 1 to 6) and Mathematics International (Lower Secondary
Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook
Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Objectives Use the triangle measurements to decide which side is longest and which angle is largest.
Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3
Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels
Multiplying Fractions by a Whole Number
Grade 4 Mathematics, Quarter 3, Unit 3.1 Multiplying Fractions by a Whole Number Overview Number of Instructional Days: 15 (1 day = 45 60 minutes) Content to be Learned Apply understanding of operations
Module 3 Congruency can be used to solve real-world problems. What happens when you apply more than one transformation to
Transforming and Congruence *CISD Safety Net Standards: G.3C, G.4C Title Big Ideas/Enduring Understandings Module 1 Tools of geometry can be used to solve real-world problems. Variety of representations
Objective. Materials. Discover the Pythagorean Theorem. Determine if a triangle is acute, right, or obtuse.
. Objective To find the lengths of sides of right triangles Activity 8 Materials TI-73 Student Activity page (p. 90) Right Triangles are Cool Because of Pythag s Rule In this activity you will Discover
Teaching Pre-Algebra in PowerPoint
Key Vocabulary: Numerator, Denominator, Ratio Title Key Skills: Convert Fractions to Decimals Long Division Convert Decimals to Percents Rounding Percents Slide #1: Start the lesson in Presentation Mode
Grade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse
Lesson 1 Section 2.5 Angle Relationships
Creator: Heather McNeill Grade: 10 th grade Course: Geometry Honors Length: 50 minutes Lesson 1 Section 2.5 Angle Relationships 1. Prior Knowledge, Skills, and Dispositions: In this lesson, students should
Q1. Here is the start of a spiral sequence of right-angled triangles. Draw accurately the next right-angled triangle on the diagram.
Q. Here is the start of a spiral sequence of right-angled triangles. Draw accurately the next right-angled triangle on the diagram. You may use an angle measurer. 2 marks Use an angle measurer to find
NOT AN OFFICIAL SCORE REPORT. Summary of Results
From SAT TEST MARCH 8, 214 Summary of Results Page 1 of 1 Congratulations on taking the SAT Reasoning Test! You re showing colleges that you are serious about getting an education. The SAT is one indicator
A polygon with five sides is a pentagon. A polygon with six sides is a hexagon.
Triangles: polygon is a closed figure on a plane bounded by (straight) line segments as its sides. Where the two sides of a polygon intersect is called a vertex of the polygon. polygon with three sides
Pythagorean Theorem: Proof and Applications
Pythagorean Theorem: Proof and Applications Kamel Al-Khaled & Ameen Alawneh Department of Mathematics and Statistics, Jordan University of Science and Technology IRBID 22110, JORDAN E-mail: kamel@just.edu.jo,
The Sampling Distribution of the Mean Confidence Intervals for a Proportion
Math 130 Jeff Stratton Name The Sampling Distribution of the Mean Confidence Intervals for a Proportion Goal: To gain experience with the sampling distribution of the mean, and with confidence intervals
App Inventor Tutorial 4 Cat & Mouse Game
App Inventor Tutorial 4 Cat & Mouse Game This is an app that will let you get familiar with using image sprites, canvas, sound, clock and the accelerometer (Movement Sensor) within a Game in App Inventor.
Polygon of the Day Discovering Area Formulas
Polygon of the Day Discovering Area Formulas Utilizing Technology and Manipulatives Cuisenaire pop-cubes Geometry tiles GSP triangles tool Trapezoid magnets Sixth Grade 6-day Unit Plan (40 minute classes)
The program also provides supplemental modules on topics in geometry and probability and statistics.
Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students
Maths Toolkit Teacher s notes
Angles turtle Year 7 Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles. Use a ruler and protractor
6.1 Basic Right Triangle Trigonometry
6.1 Basic Right Triangle Trigonometry MEASURING ANGLES IN RADIANS First, let s introduce the units you will be using to measure angles, radians. A radian is a unit of measurement defined as the angle at
Domain: Geometry (G) Cluster: Understand and apply the Pythagorean Theorem.
Domain: Geometry (G) Cluster: Understand and apply the Pythagorean Theorem. Standard: 8.G.6. Explain a proof of the Pythagorean Theorem and its converse. MP.3. Construct viable arguments and critique the
Geometry and Spatial Reasoning
Mathematics TEKS Refinement 2006 6-8 Tarleton State University Geometry and Spatial Reasoning Activity: TEKS: Creating Venn Diagrams with Quadrilaterals (6.6) Geometry and spatial reasoning. The student
MI314 History of Mathematics: Episodes in Non-Euclidean Geometry
MI314 History of Mathematics: Episodes in Non-Euclidean Geometry Giovanni Saccheri, Euclides ab omni naevo vindicatus In 1733, Saccheri published Euclides ab omni naevo vindicatus (Euclid vindicated om
Wentzville School District Curriculum Development Template Stage 1 Desired Results
Wentzville School District Curriculum Development Template Stage 1 Desired Results Unit Title: Radicals and Radical Expressions Course: Middle School Algebra 1 Unit 10 Radicals and Radical Expressions
1 Investigation of Right-angled Triangles
1 Investigation of Right-angled Triangles Answering this investigation Some tasks in this investigation require you to use Geogebra (www.geogebra. org). All the files are viewable online, so you will not
Geometry: Classifying, Identifying, and Constructing Triangles
Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral
Circles in Triangles. This problem gives you the chance to: use algebra to explore a geometric situation
Circles in Triangles This problem gives you the chance to: use algebra to explore a geometric situation A This diagram shows a circle that just touches the sides of a right triangle whose sides are 3 units,
Maths Area Approximate Learning objectives. Additive Reasoning 3 weeks Addition and subtraction. Number Sense 2 weeks Multiplication and division
Maths Area Approximate Learning objectives weeks Additive Reasoning 3 weeks Addition and subtraction add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar
CGE 3b 2 What s My Ratio? The Investigate the three primary trigonometric ratios for right-angled MT2.01 triangles. Summarize investigations.
Unit 2 Trigonometry Lesson Outline Grade 10 Applied BIG PICTURE Students will: investigate the relationships involved in right-angled triangles to the primary trigonometric ratios, connecting the ratios
Geometry and Measurement
Geometry and Measurement Geometry Most Missed Questions According to the analysis of GEDTS data, geometry is an area with which students have difficulty. The data indicates that GED candidates often lack
In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
UNCORRECTED PROOF. Unit objectives. Website links Opener Online angle puzzles 2.5 Geometry resources, including interactive explanations
21.1 Sequences Get in line Unit objectives Understand a proof that the angle sum of a triangle is 180 and of a quadrilateral is 360 ; and the exterior angle of a triangle is equal to the sum of the two
Family Letters. Assessment Management. Playing Fraction Of
Formula for the Area of a Parallelogram Objectives To review the properties of parallelograms; and to guide the development and use of a formula for the area of a parallelogram. www.everydaymathonline.com
SIOP Lesson Plan: 8 th grade Math
Topic: Angles in Triangles SIOP Lesson Plan: 8 th grade Math Content Objectives: TEKS: (8.15.A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical,
Scores and Commentary: Flagpole Spotlight, Paper #E-28 Making Sense of the Task (MS) Representing and Solving the Task (RS) Communicating Reasoning (CR) Accuracy (AC) Reflecting and Evaluating (RE) 2 3
Instructions for SA Completion
Instructions for SA Completion 1- Take notes on these Pythagorean Theorem Course Materials then do and check the associated practice questions for an explanation on how to do the Pythagorean Theorem Substantive
Pythagorean Theorem with Hippocrates Lunes
Spreadsheets in Education (ejsie) Volume 8 Issue 2 Article 5 8-1-2015 Pythagorean Theorem with Hippocrates Lunes Gunhan Caglayan New Jersey City University, gcaglayan@njcu.edu Follow this and additional
Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?)
Name Period Date Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?) Preliminary Information: SOH CAH TOA is an acronym to represent the following
Unit 3 Circles and Spheres
Accelerated Mathematics I Frameworks Student Edition Unit 3 Circles and Spheres 2 nd Edition March, 2011 Table of Contents INTRODUCTION:... 3 Sunrise on the First Day of a New Year Learning Task... 8 Is
Jump-Start Tutorial For ProcessModel
Jump-Start Tutorial For ProcessModel www.blueorange.org.uk ProcessModel Jump-Start Tutorial This tutorial provides step-by-step instructions for creating a process model, running the simulation, and viewing
CURRICULUM VITA. Michael J. Tammaro. Department of Physics University of Rhode Island Kingston, RI 02881 (401) 874-2079 tammaro@uri.
CURRICULUM VITA Michael J. Tammaro Department of Physics University of Rhode Island Kingston, RI 02881 (401) 874-2079 tammaro@uri.edu EDUCATION Ph.D., August 1997, Theoretical Condensed Matter Physics,
The Straight Line I. INTRODUCTORY
UNIT 1 The Straight Line I. INTRODUCTORY Geometry is the science of space and deals with the shapes, sizes and positions of things. Euclid was a Greek mathematician of the third century B.C. who wrote
Extra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.
Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson