Analytic Geometry

Analytic Geometry: Grade 9

Overall Expectations

By the end of Grade 9, students will:

determine, through investigation, the relationships between the form of an equation and the shape of its graph with respect to linearity and non-linearity;
determine, through investigation, the properties of the slope and y-intercept of a linear relation;
graph a line and write the equation of a line from given information.

Related Web Pages

Site Name

Online
Description

Analytic Geometry (in a plane)

This site has examples and instructions on analytic geometry, including circles hyperbolas, lines, ellipses, parabolas, and many more. There is a good investigation of relationships between the equation of a relation and the shape of its graph.

The Geometry of Computer Graphics

[Sketchpad]The recent field of computer graphics nicely merges many elegant and simple geometric ideas with concerns about function, realism, and aesthetics. In so doing, it provides a stimulating context for exploring many traditional topics of an introductory geometry course. In this paper, which is based on my after-dinner presentation at the St. Olaf conference, I develop a number of problems and activities drawn from the field of computer graphics, and illustrate them with dynamic sketches from The Geometer's Sketchpad.

Geometer's Sketchpad Materials

[Sketchpad] We have placed some materials related to Geometer's Sketchpad (GSP) on the Web for your reference. It is suggested that you read these materials to help you gain familiarity with the potential of GSP as well as some of the geometry topics in the middle school curriculum where GSP may be useful. Excellent for grades 9 & 10.

The Geometer’s Sketchpad Online Activity Guide

[Sketchpad] These links take you to other sites discussing Sketchpad or presenting Dynamic Geometry activities, lessons, and ideas. For information about print-based resources, consult the Bibliography.

High School Math Lessons

Lessons written by a retired teacher on a variety of items for grade nine and ten. Topics for Geometry include Basic Postulates, Angle Sum in Triangles, Congruence, Similarity, Pythagorean Theorem. good teacher resource.

ICSE Maths

This site provides a large number of math problems with answers intended to supplement your course and textbook. Excellent quick resource for mathematics facts and theorems. Each topic has three levels although much of the third level is incomplete at this time.

Interactive Mathematics Online - Geometry

Direct connection to the Geometry section of Interactive Mathematics Online. Wide variety of Geometry resources. Topics include Introduction, Angles & Lines, Conditionals, Unions, and Intersections, Measurement Formulas, Constructions, and much more.

Let's Drive the Best Bargain

This site uses several situations using the costs of renting cars to illustrate a linear modelling process to choose the best deal.

Jim Loy’s Mathematics Page

Contains many articles on algebra and geometry. Topics are somewhat advanced but many would be useful to Grade 9 and 10 students.

Math for Morons Like Us

A web site that contains multiple lesson plans for almost all topics covered in grades nine and ten written in easy to read language. To run this page from the cd be sure you do not have a live connection to the internet.

Olympic Games ... Historical Results

This site lists Olympic event statistics. Students use these to create scatterplots and develop an equation of the line of best fit.

Resource Room at Math Central

A Saskatchewan site that covers a variety of topics in the grade 9 and 10 curriculum. Various lessons and activities. Many lessons for both grade 9 & 10 Geometry.

S.O.S. Mathematics

S.O.S. MATHematics is your free resource for math review material from Algebra to Differential Equations!

Stressed out-slope as rate of change

The site is a series of graphs and questions that illustrate the meaning of slope in the context of applications such as stress level and athletic performance. The slope of straight lines is reviewed and the slope of curves is discussed.

Teachers Helping Teachers

Dr. Mandel's Mathematics "Teachers Helping Teachers" website designed to share ideas that can be immediately implemented into the classroom and to provide new ideas in teaching methodologies.

Jim Wilson’s Home Page

[Sketchpad] Set of worksheets for Geometer’s sketchpad. Many of these examples support the grade 9 & 10 Geometry Curriculum.

The AIMS Puzzle Corner

The goal of the AIMS Puzzle Corner is to provide teachers with a variety of interesting puzzles that can be used to create a learning environment where students engage in doing mathematics just for the fun of it! With the proper encouragement and enthusiasm on the part of the teacher, students can learn to enjoy puzzles and the mathematics behind them.

Data Analysis Lab

[Calculator] This activity involves graphing Olympic results, determining a line of best fit, interpolation and extrapolation. The graphing calculator is used.

Data Collection

[Calculator] The site is a description of a simple data collection exercise that results in data that can be fitted with a linear equation. The experiment and discussion illustrates the meaning of slope and the use of slope in making predictions from data.

Dave’s Math Tables

This site contains helpful hints on geometry, algebra, fractions, graphing, vectors and basic math.

Direct and Partial Variations

Investigations illustrating/discovering the differences between direct and partial variation.

The Discount Problem

[Calculator] The activity gives to possible discount formulas for a CD player. The student must determine the best discount plan. The graphing calculator is used.

Math Activities for Grades 9 - 12

Terrific collection of lessons with data from a variety of sources.

GSP Lessons

[Sketchpad] These are examples of using GSP to present lessons/problems using "show/hide" buttons. The links are to your GSP helper application.

Get Into Line

A complete unit on linear equations. Aspects of graphing, properties of a straight line, scatterplots, etc. are developed through lessons and investigations.

Houghton Mifflin Math Education Place

The Mathematics Center: math-related resources that include Data Place, Brain Teasers, textbook support, math links, and projects

How Many Drivers?

The site contains an investigation of the slope-intercept form of a line using the TI-83 calculator. Topics include the effect of m and b on a line and fitting a line to data. The 10 page handout includes practice questions and an investigation of the number of driver’s on US roads per state.

IMO: Interactive mathematics Online

This site has instructions and examples for Algebra, Geometry and trigonometry.

Interactive Mathematics Online - Geometry

This site has instructions and many interactive examples for Algebra, Geometry and Trigonometry. Create your own stereograms online! Some of the examples require Java to be enabled in your browser.

The Internet Mathematics Library

[Calculator, Sketchpad] This link takes you to the Swarthmore Math Forum with a huge reference for mathematics topics that cover all areas of secondary school math.

Introduction to Slope for Middle Years Mathematics

A collection of activities to develop concept of slope, y-intercepts, the equation of a line, parallel and intersecting lines.

Investigation: Airline Schedules:

[Calculator] This activity data from an airline company recording time and distance of flights. Students graph data, line of best fit, as well as interpret the meaning of x and y intercepts. The TI-83+ can be used.

Understanding Algebra

The complete contents of this algebra textbook are available here online.

Linear Regression Applet

This applet allows a person to add up to 50 points onto its green viewing screen. After each point is added by clicking on the screen with the mouse, a best fit line can be created. The slope of the best fit line is provided, as well as the equation of the line of best fit.

Lesson Plans for the Geometer's Sketchpad

[Sketchpad] Collection of Lesson Plans for use with the Geometer’s Sketchpad

Jim Loy’s Mathematics Page

Contains many articles on algebra and geometry. Topics are somewhat advanced but some may be useful to Grade 9 and 10 students.

Math.com

Variety of resources for explaining ideas, along with quizzes to accompany the material

Math Forum - High School Student Center

[Calculator, Sketchpad] This link takes you to the Swarthmore Math Forum High School area with a huge reference for mathematics topics that cover all areas of secondary school math.

Math Home

This site has hints and examples to help students learn algebra, geometry, trigonometry, calculus, and statistics.

Math Planet: Where Math Is Universal

Math Planet features preparing, exploring, interacting, and collecting of information and resources for Algebra and Geometry. Many links to math activities and events to pique student interest.

The Maths File Game Show

This BBC site features a game wheel powered by shockwave, printouts for class use, and teacher tips.

Mathematics at BCIT

Links basic mathematical principles to everyday technology and occupations. Good for making lessons relevant to students.

Mathworld Interactive

MathWorld is dedicated to helping educators and parents motivate their students to solve open-ended word problems, communicate mathematically, and share cultural and geographical information.

MegaMath

Mathematics is a live science with new discoveries being made every day. The frontier of mathematics is an exciting place, where mathematicians experiment and play with creative and imaginative ideas. Many of these ideas are accessible to young children.

Pass The Book

[Calculator] This is a data collection activity that leads to graphing and using linear regression to find the line of best fit. The graphing calculator is used.

Pre-Calculus Lab ... Data Analysis

[Calculator] This activity involves graphing Olympic results, determining a line of best fit, interpolation and extrapolation. The graphing calculator is used.

Score Mathematics Lessons

These SCORE Mathematics Lessons have been written by teachers selected to participate in SCORE Mathematics workshops.

Solving Linear Regression Problems Using the TI83 Graphing Calculator

[Calculator] This lesson plan gives a set of real-life data values for students to graph. Instructions are given on how to use the TI-83 graphing calculator to graph the points, as well as calculate and then graph the line of regression. Data in regards to the distance from the sun and orbit times of asteroids is provided. Two additional data sets are provided for assessment purposes. (Temperature and chirping of crickets and High School and College GPA’s.)

Spring Lab

[Calculator] A version of the length of spring vs. mass activity using the graphing calculator.

Stressed to the Breaking Point

This activity uses spaghetti to create bridges to test their strength in terms of the bridge length and its width.

What’s My Line

[Calculator] This activity gives the student a number of lines graphed using the calculator. The student must determine the equation of the line from the graph.

Welcome to Zona Land...

In Zona Land you will find educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general.

Site Name	Online	Description
Analytic Geometry (in a plane)		This site has examples and instructions on analytic geometry, including circles hyperbolas, lines, ellipses, parabolas, and many more. There is a good investigation of relationships between the equation of a relation and the shape of its graph.
The Geometry of Computer Graphics		[Sketchpad]The recent field of computer graphics nicely merges many elegant and simple geometric ideas with concerns about function, realism, and aesthetics. In so doing, it provides a stimulating context for exploring many traditional topics of an introductory geometry course. In this paper, which is based on my after-dinner presentation at the St. Olaf conference, I develop a number of problems and activities drawn from the field of computer graphics, and illustrate them with dynamic sketches from The Geometer's Sketchpad.
Geometer's Sketchpad Materials		[Sketchpad] We have placed some materials related to Geometer's Sketchpad (GSP) on the Web for your reference. It is suggested that you read these materials to help you gain familiarity with the potential of GSP as well as some of the geometry topics in the middle school curriculum where GSP may be useful. Excellent for grades 9 & 10.
The Geometer’s Sketchpad Online Activity Guide		[Sketchpad] These links take you to other sites discussing Sketchpad or presenting Dynamic Geometry activities, lessons, and ideas. For information about print-based resources, consult the Bibliography.
High School Math Lessons		Lessons written by a retired teacher on a variety of items for grade nine and ten. Topics for Geometry include Basic Postulates, Angle Sum in Triangles, Congruence, Similarity, Pythagorean Theorem. good teacher resource.
ICSE Maths		This site provides a large number of math problems with answers intended to supplement your course and textbook. Excellent quick resource for mathematics facts and theorems. Each topic has three levels although much of the third level is incomplete at this time.
Interactive Mathematics Online - Geometry		Direct connection to the Geometry section of Interactive Mathematics Online. Wide variety of Geometry resources. Topics include Introduction, Angles & Lines, Conditionals, Unions, and Intersections, Measurement Formulas, Constructions, and much more.
Let's Drive the Best Bargain		This site uses several situations using the costs of renting cars to illustrate a linear modelling process to choose the best deal.
Jim Loy’s Mathematics Page		Contains many articles on algebra and geometry. Topics are somewhat advanced but many would be useful to Grade 9 and 10 students.
Math for Morons Like Us		A web site that contains multiple lesson plans for almost all topics covered in grades nine and ten written in easy to read language. To run this page from the cd be sure you do not have a live connection to the internet.
Olympic Games ... Historical Results		This site lists Olympic event statistics. Students use these to create scatterplots and develop an equation of the line of best fit.
Resource Room at Math Central		A Saskatchewan site that covers a variety of topics in the grade 9 and 10 curriculum. Various lessons and activities. Many lessons for both grade 9 & 10 Geometry.
S.O.S. Mathematics		S.O.S. MATHematics is your free resource for math review material from Algebra to Differential Equations!
Stressed out-slope as rate of change		The site is a series of graphs and questions that illustrate the meaning of slope in the context of applications such as stress level and athletic performance. The slope of straight lines is reviewed and the slope of curves is discussed.
Teachers Helping Teachers		Dr. Mandel's Mathematics "Teachers Helping Teachers" website designed to share ideas that can be immediately implemented into the classroom and to provide new ideas in teaching methodologies.
Jim Wilson’s Home Page		[Sketchpad] Set of worksheets for Geometer’s sketchpad. Many of these examples support the grade 9 & 10 Geometry Curriculum.
The AIMS Puzzle Corner		The goal of the AIMS Puzzle Corner is to provide teachers with a variety of interesting puzzles that can be used to create a learning environment where students engage in doing mathematics just for the fun of it! With the proper encouragement and enthusiasm on the part of the teacher, students can learn to enjoy puzzles and the mathematics behind them.
Data Analysis Lab		[Calculator] This activity involves graphing Olympic results, determining a line of best fit, interpolation and extrapolation. The graphing calculator is used.
Data Collection		[Calculator] The site is a description of a simple data collection exercise that results in data that can be fitted with a linear equation. The experiment and discussion illustrates the meaning of slope and the use of slope in making predictions from data.
Dave’s Math Tables		This site contains helpful hints on geometry, algebra, fractions, graphing, vectors and basic math.
Direct and Partial Variations		Investigations illustrating/discovering the differences between direct and partial variation.
The Discount Problem		[Calculator] The activity gives to possible discount formulas for a CD player. The student must determine the best discount plan. The graphing calculator is used.
Math Activities for Grades 9 - 12		Terrific collection of lessons with data from a variety of sources.
GSP Lessons		[Sketchpad] These are examples of using GSP to present lessons/problems using "show/hide" buttons. The links are to your GSP helper application.
Get Into Line		A complete unit on linear equations. Aspects of graphing, properties of a straight line, scatterplots, etc. are developed through lessons and investigations.
Houghton Mifflin Math Education Place		The Mathematics Center: math-related resources that include Data Place, Brain Teasers, textbook support, math links, and projects
How Many Drivers?		The site contains an investigation of the slope-intercept form of a line using the TI-83 calculator. Topics include the effect of m and b on a line and fitting a line to data. The 10 page handout includes practice questions and an investigation of the number of driver’s on US roads per state.
IMO: Interactive mathematics Online		This site has instructions and examples for Algebra, Geometry and trigonometry.
Interactive Mathematics Online - Geometry		This site has instructions and many interactive examples for Algebra, Geometry and Trigonometry. Create your own stereograms online! Some of the examples require Java to be enabled in your browser.
The Internet Mathematics Library		[Calculator, Sketchpad] This link takes you to the Swarthmore Math Forum with a huge reference for mathematics topics that cover all areas of secondary school math.
Introduction to Slope for Middle Years Mathematics		A collection of activities to develop concept of slope, y-intercepts, the equation of a line, parallel and intersecting lines.
Investigation: Airline Schedules:		[Calculator] This activity data from an airline company recording time and distance of flights. Students graph data, line of best fit, as well as interpret the meaning of x and y intercepts. The TI-83+ can be used.
Understanding Algebra		The complete contents of this algebra textbook are available here online.
Linear Regression Applet		This applet allows a person to add up to 50 points onto its green viewing screen. After each point is added by clicking on the screen with the mouse, a best fit line can be created. The slope of the best fit line is provided, as well as the equation of the line of best fit.
Lesson Plans for the Geometer's Sketchpad		[Sketchpad] Collection of Lesson Plans for use with the Geometer’s Sketchpad
Jim Loy’s Mathematics Page		Contains many articles on algebra and geometry. Topics are somewhat advanced but some may be useful to Grade 9 and 10 students.
Math.com		Variety of resources for explaining ideas, along with quizzes to accompany the material
Math Forum - High School Student Center		[Calculator, Sketchpad] This link takes you to the Swarthmore Math Forum High School area with a huge reference for mathematics topics that cover all areas of secondary school math.
Math Home		This site has hints and examples to help students learn algebra, geometry, trigonometry, calculus, and statistics.
Math Planet: Where Math Is Universal		Math Planet features preparing, exploring, interacting, and collecting of information and resources for Algebra and Geometry. Many links to math activities and events to pique student interest.
The Maths File Game Show		This BBC site features a game wheel powered by shockwave, printouts for class use, and teacher tips.
Mathematics at BCIT		Links basic mathematical principles to everyday technology and occupations. Good for making lessons relevant to students.
Mathworld Interactive		MathWorld is dedicated to helping educators and parents motivate their students to solve open-ended word problems, communicate mathematically, and share cultural and geographical information.
MegaMath		Mathematics is a live science with new discoveries being made every day. The frontier of mathematics is an exciting place, where mathematicians experiment and play with creative and imaginative ideas. Many of these ideas are accessible to young children.
Pass The Book		[Calculator] This is a data collection activity that leads to graphing and using linear regression to find the line of best fit. The graphing calculator is used.
Pre-Calculus Lab ... Data Analysis		[Calculator] This activity involves graphing Olympic results, determining a line of best fit, interpolation and extrapolation. The graphing calculator is used.
Score Mathematics Lessons		These SCORE Mathematics Lessons have been written by teachers selected to participate in SCORE Mathematics workshops.
Solving Linear Regression Problems Using the TI83 Graphing Calculator		[Calculator] This lesson plan gives a set of real-life data values for students to graph. Instructions are given on how to use the TI-83 graphing calculator to graph the points, as well as calculate and then graph the line of regression. Data in regards to the distance from the sun and orbit times of asteroids is provided. Two additional data sets are provided for assessment purposes. (Temperature and chirping of crickets and High School and College GPA’s.)
Spring Lab		[Calculator] A version of the length of spring vs. mass activity using the graphing calculator.
Stressed to the Breaking Point		This activity uses spaghetti to create bridges to test their strength in terms of the bridge length and its width.
What’s My Line		[Calculator] This activity gives the student a number of lines graphed using the calculator. The student must determine the equation of the line from the graph.
Welcome to Zona Land...		In Zona Land you will find educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general.