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Algebra Gateway Exam Practice

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Gateway - Algebra I


Interactive sites to help students practice skills needed for the Algebra Gateway exam
Links verified 10/14/2009 - older version of this page
Number & Operations | Algebra | Geometry | Measurement | Data Analysis & Probability | Multiple Review Activities
Practice Tests
Links open on a new page
A resource for the teacher to use in planning their lessons site for teachers | A PowerPoint show related to this standard PowerPoint show | An Adobe Acrobat document in .pdf format Acrobat document | A Microsoft Word document to be downloaded Word document | This interactive site would work well on an interactive whiteboard whiteboard resource | This resource includes voice instructions for students sound | A video is available through this link video format | This site is interactive and allows students to play a game or input or collect data interactive lesson | This site includes questions for your students to check their understanding a quiz | A lesson plan can be found at this site lesson plan | This link includes something for the teacher to print to print
Standard 1 - Number and Operations
The student will recognize, represent, model, and apply real numbers and operations verbally, physically, symbolically, and graphically.
Level 1
Select the best estimate for the coordinate of a given point on a number line
  1. Comparing two numbers on a number line from Web Math. Learn how to compare two numbers using a number line. Type each number into the boxes provided, then click "Show Me!" This site is interactive and allows students to play a game or input or collect data
  2. Create a Haunted House.....if you dare! - Follow directions to sharpen your graphing skills, create a cool haunted house and then morph it using math. A lesson plan can be found at this site
  3. Expressions, Equation Solving and Graphing in the Coordinate Plane - The Haunted house and many more coordinate plane practice problems
  4. Graphing Equations and Inequalities Unit Quiz - an eight question multiple-choice quiz This site includes questions for your students to check their understanding
  5. Line Jumper - Funbrain number line ( choose Super Brain ! ) This site is interactive and allows students to play a game or input or collect data
  6. Number Line Bounce - Instructions on how to play are included at the top of the window. This site is interactive and allows students to play a game or input or collect data
  7. Number Line: Comparing and Ordering Integers - practice with an Interactive Adventure with Deep Sea Carl . Carl is diving in the Great Barrier Reef off the coast of Australia. These waters are shark infested. Keep Carl safe by determining how many feet below sea level Jaws Daddy is. This site is interactive and allows students to play a game or input or collect data
Identify the opposite of a rational number
  1. Interactive Algebra Review on the topic of real numbers This site includes questions for your students to check their understanding
  2. Rational Number Tutorial - This tutorial will help you understand the significance of the minimum and maximum integers in a rational number system and the meaning of overflow. This site is interactive and allows students to play a game or input or collect data
  3. A proof that all square roots of primes are irrational
Determine the square root of a perfect square less than 169
  1. Identify Perfect Squares - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
  2. Simplifying Radical Expressions - Intermediate Algebra tutorial
  3. Simplifying Radicals - explanation and practice problems
  4. Square Root Calculator - simple calculator from Calculator Geek - the site also offers square root instruction and worksheets to download
  5. Square Roots - Find the square root of a perfect square number. (a matching game like concentration) This site is interactive and allows students to play a game or input or collect data
  6. Square Roots Worksheets - square root worksheet generator from Home School Math
  7. Squares and Square Roots - to understand square roots, first you must understand squares
  8. Squares and Square Roots - four page lesson; introduction, in-depth, examples, and practice problems
  9. Squares and Square Roots - tables of squares and square roots and a video on simplifying the square root of a perfect square [2:26] A video is available through this link
  10. A PowerPoint show related to this standard Squares and Square Roots - 28 slides including practice at estimating square root
  11. Table of Squares and Square Roots - Use this table to find the squares and square roots of numbers from 1 to 100
Use exponents to simplify a monomial written in expanded form
  1. Converting Numbers to Scientific Notation - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  2. Cube of a Number - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  3. Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  4. Exponent Practice - Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again. This site is interactive and allows students to play a game or input or collect data
  5. Exponents - Unit 3 from Ms. Glosser's Math Goodies
  6. Interactive Algebra Review on Integer Exponents This site is interactive and allows students to play a game or input or collect data
  7. Powers of Ten - illustrating powers of ten this site zooms from 10^23 to 10^-16, moving from million light years away from the Milky Way galaxy to a quark
  8. Scientific Notation - interactive practice This site is interactive and allows students to play a game or input or collect data
  9. Simplifying - Expressions that have had their like terms combined. Match each expression on the left with an expression on the right. Type the letter of the correct expression in the box. This site includes questions for your students to check their understanding
apply order of operations when computing with integers using no more than two sets of grouping symbols and exponents 1 and 2
  1. Calculations Using Order of Operations - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  2. Evaluating Algebraic Expressions - Order of Operations/P.E.M.D.A.S.
  3. Evaluating Algebraic Expressions - from Regents Prep This site is interactive and allows students to play a game or input or collect data
  4. A PowerPoint show related to this standard Order of Operations What's Wrong? -
  5. Order of Operations - Math Goodies from Ms. Glosser
  6. Order of Operations - Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again. This site is interactive and allows students to play a game or input or collect data
  7. Order of operations game from Funbrain.com ( easier levels are available) This site is interactive and allows students to play a game or input or collect data
  8. Order of Operations A lesson plan can be found at this site
  9. Order of Operations - practice problems This site includes questions for your students to check their understanding
  10. A resource for the teacher to use in planning their lessons Order of Operations - a matching grid pattern game This link includes something for the teacher to print
  11. Order of Operations with Exponents - Math Goodies from Ms. Glosser
select a reasonable solution for a real-world division problem in which the remainder must be considered
  1. Connecting Equations to Real-World Situations This site is interactive and allows students to play a game or input or collect data
  2. Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities.
  3. Moneyopolis - A challenging math game, which requires you to demonstrate your math skills in the context of some real life money matters. Created by the national accounting firm Ernst & Young ( free registration required) This site is interactive and allows students to play a game or input or collect data
  4. Plane Math - Nine activities involving aviation and mathematic This site is interactive and allows students to play a game or input or collect data
  5. Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more
  6. Real World Mathematics - One of the challenges facing mathematics teachers is convincing their students that there is a place for mathematics in the real world. The goal of this page is to collect examples of those applications. This is a SCORE (Schools of California - Online Resources for Educators) page.
Level 2
Order a given set of rational numbers
  1. Comparing Seven Digit Numbers - practice area followed by an interactive game This site is interactive and allows students to play a game or input or collect data
  2. Rational and Irrational number review
Identify the reciprocal of a rational number
  1. Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math
  2. How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
add and subtract algebraic expressions
  1. A concentration type game from Quia using algebraic expressions - If d=2 match the algebraic expressions to the correct answers. This site includes questions for your students to check their understanding
  2. Interactive Algebra Review - Rational Algebraic Expressions This site is interactive and allows students to play a game or input or collect data
multiply two polynomials with each factor having no more than two terms
  1. Factoring Trinomials - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
  2. Factoring Trinomials Self Quiz - Check your knowledge about factoring polynomials. This site includes questions for your students to check their understanding
  3. Interactive Algebra Review - Multiplying Algebraic Expressions This site is interactive and allows students to play a game or input or collect data
  4. Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial ) This site is interactive and allows students to play a game or input or collect data
  5. Multiplying Polynomials - a step-by-step explanation from PurpleMath
  6. Solving Polynomial Equations - In algebra you spend lots of time solving polynomial equations or factoring polynomials (which is the same thing). This paper ties them all together in a coherent whole.
use estimation to determine a reasonable solution for a tedious arithmetic computation
  1. Curious and Useful Math - Here you will find tricks and rules for quickly calculating certain types of math problems.
  2. Developing Estimation Strategies by Making Connections among Number, Geometry, Measurement, and Data Concepts: Estimating Scoops - NCTM lesson plan including video segments A lesson plan can be found at this site
  3. Every Breath You Take - worksheet to help students estimate the number of breaths they take in one hour An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  4. K-12 Math Problems, Puzzles, Tips & Tricks from the Math Forum
select ratios and proportions to represent real-world problems
  1. Connecting Equations to Real-World Situations This site is interactive and allows students to play a game or input or collect data
  2. Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities.
  3. Moneyopolis - A challenging math game, which requires you to demonstrate your math skills in the context of some real life money matters. Created by the national accounting firm Ernst & Young ( free registration required) This site is interactive and allows students to play a game or input or collect data
  4. Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies
  5. Plane Math - Nine activities involving aviation and mathematic This site is interactive and allows students to play a game or input or collect data
  6. Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more
  7. Ratio and Proportion - four stage lesson includes examples and a set of workout problems
  8. Real World Mathematics - One of the challenges facing mathematics teachers is convincing their students that there is a place for mathematics in the real world. The goal of this page is to collect examples of those applications. This is a SCORE (Schools of California - Online Resources for Educators) page.
Level 3
Apply the concept of slope to represent rate of change in a real-world situation
  1. Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them This site is interactive and allows students to play a game or input or collect data
  2. Linear Functions, Slope and Regressions - one example is the Kalamazoo Wal-mart Live or Die Scenario
  3. Equation of a Line: Slope-Intercept Form - An interactive applet that will help you visualize how changing the values for the slope, m, and the y-intercept, b, will affect the graph of the equation y = mx + b. This site is interactive and allows students to play a game or input or collect data
  4. A PowerPoint show related to this standard Slope Intercept Jeopardy review game in the form of a PowerPoint show
  5. A PowerPoint show related to this standard Another Slope Intercept Jeopardy review game in the form of a PowerPoint show
Sample Task
Students design a concept map that illustrates the relationship among decimals, fractions, and percents. Students summarize in writing their concept maps and discuss how equivalent fractions, decimals, and percents can be flexibly interchanged. Students justify the selection of fraction, decimal, or percent notation in specific situations.
  1. Instructions for making a concept map using Excel
  2. Instructions for making a Venn Diagram using Excel 2007
  3. Percent - graphical examples and practice problems
  4. Writing Fractions as Percent - unit 4 from Ms. Glosser's Math Goodies

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Standard 2 - Algebra
Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real world problem solving.
Level 1

extend a geometric pattern

  1. Analyzing Numeric and Geometric Patterns of Paper Pool - an activity from Illuminations, the NCTM site. This site is interactive and allows students to play a game or input or collect data
  2. Multiple-Choice Questions - twenty (20) questions on Patterns & Functions This site includes questions for your students to check their understanding
extend a numerical pattern
  1. Calculating the nth Term - how to develop a formula that can be used to calculate these terms
  2. Mystery Operations - the computer makes up a mystery operation, and you have to figure out what the operation is This site is interactive and allows students to play a game or input or collect data
  3. Number Patterns - involving exchange of Valentines This site is interactive and allows students to play a game or input or collect data
translate a verbal expression into an algebraic expression or vice versa
  1. Basic Algebra - Lesson 5 - Expressions from Sentences A lesson plan can be found at this site
  2. Learn to Solve Word Problems - (a collection of word problem solvers that solve your problems and help you understand the solutions) All problems are customizable (meaning that you can change all parameters).
  3. Ms. Lindquist: The Tutor - A free, web-delivered, intelligent tutoring system for tutoring students in writing expressions for algebra word problems. This site is sponsored by NSF. (the New Ms. Lindquist )
  4. Taming Word Problems - a WebQuest on how to solve word problems Internet4Classrooms
  5. Word Problems For Kids - This is a set of carefully selected problems (grade 5 to Grade 12) which can help you improve your problem solving skills.
evaluate a first degree algebraic expression given values for one or more variables

 

solve one- and two-step linear equations using integers (with integral coefficients and constants)
  1. Linear Equation Solvers - Practice Linear Equations! Improves your test scores! This site is interactive and allows students to play a game or input or collect data
  2. Linear Equations Solver Calculator - solves linear equations in the form; ax + b = cx + d This site is interactive and allows students to play a game or input or collect data
  3. Linear Equation Solver from Algebra.com This site is interactive and allows students to play a game or input or collect data
  4. Linear Equation Solver - a pop-up window allows users to specify the number of equations This site is interactive and allows students to play a game or input or collect data
  5. Solving addition and subtraction equations - Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again. This site is interactive and allows students to play a game or input or collect data
  6. Solving Linear Equation
  7. Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
  8. Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
Level 2

select the algebraic notation which generalizes the pattern represented by data in a given table

 

translate a verbal sentence into an algebraic equation or vice versa
  1. Mathematical problem solving . Linear equations, simple algebra. ( Ignore the banner at the top of this page ) This site is interactive and allows students to play a game or input or collect data
  2. On Valentine's Day, every friend gives a valentine to each of the other friends. How many valentines are exchanged? solve a simple problem, and keep track of how you did it, in order to solve a more complex problem. This site is interactive and allows students to play a game or input or collect data
  3. Translating Word Problems - The hardest thing about doing word problems is taking the English problem and translating it into math. A lesson from Purplemath, a great Algebra resource.
  4. Solving Math Word Problems - A Study Guides and Strategies web site posted by the University of St. Thomas
  5. Algebra - Fun with Calendars
select the graph that represents a given linear function expressed in slope-intercept form
 
solve multi-step linear equations (more than two steps, variables on one side of the equation with no use of parentheses)
  1. Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
  2. Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
solve multi-step linear equations (more than two steps, with variables on both sides of the equation with no use of parentheses)
 
solve multi-step linear equations (more than two steps, with one set of parentheses on each side of the equation)
 
select the linear graph that models the given real-world situation described in a narrative (no data set given)
 
select the linear graph that models the given real-world situation described in a tabular set of data or vice versa
 
evaluate an algebraic expression given values for one or more variables using grouping symbols and/or exponents less than four
 
determine the slope from the graph of a linear equation (no labeled points)
  1. Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them This site is interactive and allows students to play a game or input or collect data
  2. A PowerPoint show related to this standard Bell work PowerPoint show on Slope of a line
  3. Equation of a Line: Slope-Intercept Form - An interactive applet that will help you visualize how changing the values for the slope, m, and the y-intercept, b, will affect the graph of the equation y = mx + b. This site is interactive and allows students to play a game or input or collect data
  4. A PowerPoint show related to this standard Equation of Lines - a PowerPoint show
  5. Find the graph that best matches the linear equation This site includes questions for your students to check their understanding
  6. Linear Equation Test - Can you work out the answers? Use the multiple choice boxes or the radio buttons to select your answer. This site includes questions for your students to check their understanding
  7. Linear Functions Part A : Basics: Slope and Intercept Part B : Finding the Equation of a Line This site is interactive and allows students to play a game or input or collect data
  8. A PowerPoint show related to this standard Linear Function Jeopardy in the form of a PowerPoint show
  9. Linear Functions, Slope and Regressions - one example is the Kalamazoo Wal-mart Live or Die Scenario
  10. A PowerPoint show related to this standard Slope Intercept Jeopardy review game in the form of a PowerPoint show
  11. A PowerPoint show related to this standard Another Slope Intercept Jeopardy review game in the form of a PowerPoint show
  12. A PowerPoint show related to this standard Using Slopes and Intercepts - a twenty-nine slide PowerPoint show
apply the concept of rate of change to solve real-world problems
  1. Stressed Out - Slope as Rate of Change A lesson plan can be found at this site
select the appropriate graphical representation on the coordinate plane of a given linear inequality (given in standard form or slope-intercept form)
  1. Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them This site is interactive and allows students to play a game or input or collect data
  2. Equation of a Line: Slope-Intercept Form - An interactive applet that will help you visualize how changing the values for the slope, m, and the y-intercept, b, will affect the graph of the equation y = mx + b. This site is interactive and allows students to play a game or input or collect data
  3. A PowerPoint show related to this standard Slope Intercept Jeopardy review game in the form of a PowerPoint show
  4. A PowerPoint show related to this standard Another Slope Intercept Jeopardy review game in the form of a PowerPoint show
  5. Graphing Linear Equations - an internet project This site is interactive and allows students to play a game or input or collect data
  6. A PowerPoint show related to this standard Practice Converting Linear Equations Into Slope Intercept Form - an eleven slide PowerPoint show
  7. Slope of the Stairs - use this java applet to investigate the concept (written by someone in Japan, please overlook their spelling :-) This site is interactive and allows students to play a game or input or collect data
select the non-linear graph that models the given real-world situation or vice versa
 
identify the graphical representation of the solution to a one variable inequality on a number line
  1. Line Jumper - Funbrain number line ( choose Super Brain ! ) This site is interactive and allows students to play a game or input or collect data
  2. Number Line: Comparing and Ordering Integers - practice with an Interactive Adventure with Deep Sea Carl . Carl is diving in the Great Barrier Reef off the coast of Australia. These waters are shark infested. Keep Carl safe by determining how many feet below sea level Jaws Daddy is located. This site is interactive and allows students to play a game or input or collect data
  3. Comparing two numbers on a number line from Web Math. Learn how to compare two numbers using a number line. Type each number into the boxes provided, then click "Show Me!" This site is interactive and allows students to play a game or input or collect data
  4. Number Line Bounce - Instructions on how to play are included at the top of the window. This site is interactive and allows students to play a game or input or collect data
Level 3

solve multi-step linear inequalities in real-world situations

  1. Inequalities Workout at Math.com This site includes questions for your students to check their understanding
  2. Linear Equation Solver - You type in the equation. The equation solver will solve it for you with an explanation of how the problem was done. This site is interactive and allows students to play a game or input or collect data
  3. Practice with Solving Inequalities This site includes questions for your students to check their understanding
  4. Rags to Riches Game - a fun practice for 1-step, 2-step and multi-step equations. The game is similar in nature to "Who Wants to Be a Millionaire" This site is interactive and allows students to play a game or input or collect data
  5. Solving Inequalities: Overview - from Purple Math
  6. Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included This site is interactive and allows students to play a game or input or collect data
recognize the graphical transformation that occurs when coefficients and/or constants of the corresponding linear equations are changed
 
determine the domain and/or range of a function represented by the graph of real-world situations
  1. Domain, Range, Derivative, 1-D Kinematics - a Quia quiz This site includes questions for your students to check their understanding
  2. Explore Families of Functions - This site is interactive and allows students to play a game or input or collect data
  3. An Adobe Acrobat document in .pdf format Families of Functions you need to know This page opens in a new window. Close the window to return to this page.
  4. Families of Functions - includes a picture of the function family at home
  5. Families of Functions - graph-description match game This site is interactive and allows students to play a game or input or collect data
    1. Links to twelve other function family games
  6. Fam ilies of Functions and Curves -
  7. Four Basic Function Families -
  8. Function Machine This site is interactive and allows students to play a game or input or collect data
  9. Functions - There are different ways of looking at functions.  This lesson from Purple Math will consider a few.
  10. Introduction to the Four Basic Function Families
  11. A PowerPoint show related to this standard What is a Function? - a thorough examination of the concept in the form of a PowerPoint show
select the system of equations that could be used to solve a given real-world problem
  1. Systems of Linear Equations - an introduction which considers three situations both algebraically and geometrically This site is interactive and allows students to play a game or input or collect data
find the solution to a quadratic equation given in standard form (integral solutions and a leading coefficient of one)
 
select the solution to a quadratic equation given solutions represented in graphical form (integral solutions and a leading coefficient of one)
 
select one of the factors (e.g., x + 3) of a quadratic equation (integral solutions and a leading coefficient of one)
 
select the discriminant of a quadratic equation (integral solutions and a leading coefficient of one)
 
Sample Task
Use an almanac or the internet to find the area and the average depth of the world's ten largest bodies of salt water. Draw a scatterplot showing the relationship between these two sets of data. Describe the relationship and determine if it is a functional relationship.
 

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Standard 3 - Geometry
The student will investigate, model, and apply geometric properties and relationships.
Level 1
identify ordered pairs in the coordinate plane.
  1. Practice from Math.com: The coordinate plane , Slope and y-intercept , and Graphing linear equations .
  2. A PowerPoint show related to this standard Coordinate Geometry - use this PowerPoint show to teach the concept of ordered pairs [consider changing the text animation] (author Monica Yuskaitis)
  3. A PowerPoint show related to this standard Battle Graph - teach your students about graphing on a coordinate plane. A PowerPoint show designed by Sarah Grabowski, University of Georgia, July 9, 2003
  4. What's the Point? - a coordinate plane game from Funbrain.com (use the hardest level) This site is interactive and allows students to play a game or input or collect data
Level 2

apply the given Pythagorean Theorem to a real life problem illustrated by a diagram (no radicals in answer)

  1. Animated Proof of the Pythagorean Theorem This site is interactive and allows students to play a game or input or collect data
  2. Demonstrate the Pythagorean Theorem - from NOVA This site is interactive and allows students to play a game or input or collect data
  3. Nineteen Pythagorean Theorem applets This site is interactive and allows students to play a game or input or collect data
  4. Pythagorean theorem - In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics A lesson plan can be found at this site
  5. Pythagorean Theorem - a java applet that allows students to investigate this theorem. This site is interactive and allows students to play a game or input or collect data
  6. Pythagorean Theorem - This lesson will allow you to figure out the Pythagorean Theorem all by yourself.
  7. Pythagorean Theorem - In this investigation students will learn more about the Pythagorean Theorem and see whether or not it works for triangles that are not right triangles. This site is interactive and allows students to play a game or input or collect data
  8. An Interactive Proof of Pythagoras' theorem - This Java applet was written by Jim Morey. It won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995. This site is interactive and allows students to play a game or input or collect data
  9. Pythagorean Theorem and its many proofs (43 to be precise)
  10. Using the Pythagorean Theorem Once you know the equation a 2 + b 2 = c 2 is true, then you can use it to solve all kinds of problems. Try the Pythagorean theorem with two other examples given on this page
apply proportion and the concepts of similar triangles to find the length of a missing side of a triangle
  1. Geometry Java Applets - instructions for use of the applet and a table of contents This site is interactive and allows students to play a game or input or collect data
  2. A Mathematical Droodle - Two Triples of Similar Triangles This site is interactive and allows students to play a game or input or collect data
  3. Pythagorean theorem and right triangle facts - given the length of three sides, determine if a right triangle is being described This site includes questions for your students to check their understanding
  4. Ratio of the Sides of a Right Triangle
  5. Solving a right triangle - This example illustrates how finding the height of the pyramid is equivalent to solving the right triangle. The virtual reality media can help students visualize the interrelation between the 3-dimensional pyramid and the 2-dimensional right triangle. This site is interactive and allows students to play a game or input or collect data
  6. Virtual Manipulative - Similar Triangles This site is interactive and allows students to play a game or input or collect data
Level 3
calculate the distance between two points given the Pythagorean Theorem and the distance formula
  1. How to use the distance formula to find distances between (x,y) points
  2. The Pythagorean Theorem, Distance Formula and Intro to Trigonometry - practice activities
Sample Task
Approximate the value of pi (π) by looking at the relationship between the diameter and circumference of various circular objects after measuring using a string or a tape measure. Students research and write about how various geometric properties are used in careers such as construction, drafting, and surveying.
 

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Standard 4 - Measurement
The student will apply appropriate tools and units of measurement to produce reasonable results
Level 1

estimate the area of irregular geometric figures on a grid

  1. Square Skate - Divide this figure into four identical parts (of the same shape and size) which may form the square as shown in the figure. This link includes something for the teacher to print
  2. Other geometric dissections on the web - A geometric dissection is a cutting of one or more figures into pieces that can be rearranged to form other figures. Dissections are often cast as puzzles, in which the object is to use as few pieces as possible. These geometrical puzzles fall under the category of mathematical recreations
calculate rates involving cost per unit to determine the best buy (no more than four samples)
  1. Global Grocery List Project - Students share local grocery prices to build a growing table of data to be used in social studies, science, health, mathematics, and other disciplines.
  2. Uncle Vito's New York Pizza has an online menu and sizes all in one place. This would be a good source of data to practice unit cost.
apply the given formula to determine the area or perimeter of a rectangle
  1. Challenge Exercises: Perimeter & Area of Polygons
Level 2
apply the given formula to find the area of a circle, the circumference of a circle, or the volume of a rectangular solid
  1. Area and Volume from Ask Dr. Math - A simple way to think about area and volume
  2. Areas of Triangles, Trapezoids, and Kites - discover or demonstrate the formulas for the areas of triangles, trapezoids, and kites. (three activities) This site is interactive and allows students to play a game or input or collect data
  3. Challenge Exercises: Area of a Circle
  4. Circle Calculator - Cylinder Calculator - Sphere Calculator
  5. Circle, Sphere & Cylinder Calculator [This expired page is from the Internet Archive known as the Wayback Machine.] This site is interactive and allows students to play a game or input or collect data
  6. Estimating How Much Your Fish Weighs - two suggestions that depend upon figuring out the volume of a fish ( A free site that may occasionally exceed its allocated data transfer
  7. How Are Things Shaping Up? Investigating Surface Area, Volume, and Properties of Shapes A lesson plan can be found at this site
  8. A resource for the teacher to use in planning their lessonsIntroduction To Volume This lesson is a pure text document, but outlines an interesting experiment using popcorn. A lesson plan can be found at this site
  9. Lesson on Circumference of a Circle
Level 3
select the area representation for a given product of two one-variable binomials with positive constants and coefficients

 

Sample Task
Place students in small groups giving each group a different length of string. Have each group form a rectangle with the string. Ask each group to measure the sides of their rectangle and find its area. Using the string, direct each group to construct the rectangle with the greatest possible area. Give each group the opportunity to justify their solution.
 

Standard 5 - Data Analysis and Probability
The student will collect, organize, represent, and interpret data and model situations to determine theoretical and experimental probabilities.
Level 1

determine the mean (average) of a given set of real-world data (no more than five two-digit numbers)

  1. Comparing Properties of the Mean and the Median through the use of Technology A lesson plan can be found at this site
  2. and more.
  3. Finding Data on the Internet - You'll soon be checking facts and downloading reputable data on everything from public safety to education to agriculture to crime to economics ... you name it. This site is intended as a resource for journalists, but why not make this a source for projects. Your students can find raw data related to: aviation, demographics, weather, energy, health, immigration
  4. Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem A lesson plan can be found at this site
  5. Hand Squeeze - (a data collection and analysis class experiment) - Pass a "hand squeeze" around a circle and measure the amount of time that it takes for the hand squeeze to complete the circle. A lesson plan can be found at this site
  6. Review of tables, charts and graphs - an index of topics
  7. Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body - This three-part example illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. A lesson plan can be found at this site
  8. What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome. This site is interactive and allows students to play a game or input or collect data
  9. What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment A lesson plan can be found at this site
interpret bar graphs representing real-world data
  1. Using Data and Statistics - good graphs, however they are not interactive
  2. What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment A lesson plan can be found at this site
interpret circle graphs (pie charts) representing real-world data
  1. Graphs and charts - four different graphs and charts for you to consider This site is interactive and allows students to play a game or input or collect data
Level 2

choose the matching linear graph given a set of ordered pairs

 

make a prediction from the graph of a real-world linear data set
  1. Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body: Graphing the Situation This three-part example illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. A lesson plan can be found at this site
determine the median for a given set of real-world data (even number of data)
  1. Comparing Properties of the Mean and the Median through the use of Technology - Using interactive software, students can compare and contrast properties of measures of central tendency, specifically the influence of changes in data values on the mean and median. A lesson plan can be found at this site
Level 3
compute the probability of a simple compound event (2 independent events, no more than 6 possibilities per event)
  1. Probabilistic Situations - a short slide show on the topic
  2. What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome.
  3. Probability Theory: The Layman's Guide to Probability - An in-depth but easily readable guide on probability theory, covering various aspects of the theory with a bias to gambling games and strategies. Includes working examples in an excel spreadsheet.
  4. Coin Flipping - Click the Flip Coin button. Number of flips, number of heads, and probability of flipping heads is displayed. ( one click per flip ) This site is interactive and allows students to play a game or input or collect data
  5. Another coin flipping page This site is interactive and allows students to play a game or input or collect data
  6. Ken White's Coin Flipping page - flip up to 100 coins and see the total number of heads and tails. Excellent for teaching about probability. This site is interactive and allows students to play a game or input or collect data
  7. Interactive Probability Tutorials: Sample Spaces and Events , Estimated Probability , Empirical Probability , Abstract Probability and Conditional Probability and Independence This site is interactive and allows students to play a game or input or collect data
Sample Task
Students research the age of each Tennessee governor at the time of his/her inauguration. The students organize their information and will determine which measure of central tendency is the best description of the data. Students explain their decision.
 
Practice Tests
  1. Tennessee item sampler | Tennessee Practice Test An Adobe Acrobat document in .pdf format Indiana Item Sampler | Analysis of Incorrect Responses - Indiana
  2. Released tests - Texas Assessment of Academic Skills (TAAS) Spring 2002 | Spring 2001 | Spring 2000
  3. Virginia SOL 2000 | 2001 | 2002 | 2003 | 2004 | 2005 An Adobe Acrobat document in .pdf format
  4. FCAT Sample Test Book - [2008] sample questions and test taking tips An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  5. FCAT Sample Answer Book - [2008] sample questions and test taking tips An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  6. Virginia Standards of Learning - Select Algebra I and 10, 20 or 40 questions - Repeat for a new set of questions This site includes questions for your students to check their understanding
  7. SOL Algebra I & II resources - posted by Rockingham County Public Schools

Howe-Two Online Gateway Skills Assessment - Quiz questions based on a quiz prepared by Anderson County Teachers based on Gateway Performance Objectives modified by Leslie Howe, a Farragut High School math teacher. (Note: the results page offers software for sale, but students may take this test as many times as needed without a purchase.) This site includes questions for your students to check their understanding
Multiple
Review
Activities
  1. Interactive online End of Course Algebra Review -
  2. SOS Mathematics - Algebra lessons
  3. 28 E-Lab Activities for eighth grade level mathematics from Harcourt School Publishers This site is interactive and allows students to play a game or input or collect data
  4. Take a Gateway Practice Test - This nine-page test was prepared by Anderson County teachers An Adobe Acrobat document in .pdf format This site includes questions for your students to check their understanding
  5. AAAMath offers a large number of math review topics , each one supported by an interactive practice page (8th grade level)
  6. Practical Algebra Lessons from PurpleMath - The lessons give practical tips, hints, and examples, and point out common mistakes.
  7. National Library of Virtual Manipulatives - Virtual manipulatives related to the NCTM Number & Operations standard. (9-12 at the bottom of the page)
  8. Practice Tests from Virginia State Standards of Learning - Select Algebra I or II , and then select 10, 20, or 40 questions. This site includes questions for your students to check their understanding
  9. Algebra Help - in-depth algebra help through algebra history, an online textbook, and various articles covering everything from basic algebra fundamentals to the latest-and-greatest algebra software help available

Internet4classrooms is a collaborative effort by Susan Brooks and Bill Byles.
 

  

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