Sites to use to practice skills needed on the Algebra Gateway exam

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	Analyzing Numeric and Geometric Patterns of Paper Pool - an activity from Illuminations, the NCTM site. Multiple-Choice Questions - twenty (20) questions on Patterns & Functions
extend a numerical pattern	Calculating the nth Term - how to develop a formula that can be used to calculate these terms Mystery Operations - the computer makes up a mystery operation, and you have to figure out what the operation is Number Patterns - involving exchange of Valentines
translate a verbal expression into an algebraic expression or vice versa	Basic Algebra - Lesson 5 - Expressions from Sentences 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). 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) Taming Word Problems - a WebQuest on how to solve word problems 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)	Linear Equation Solvers - Practice Linear Equations! Improves your test scores! Linear Equations Solver Calculator - solves linear equations in the form; ax + b = cx + d Linear Equation Solver from Algebra.com Linear Equation Solver - a pop-up window allows users to specify the number of equations 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. Solving Linear Equation Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball on 9/4/08 Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball on 9/4/08
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	Mathematical problem solving. Linear equations, simple algebra. (Ignore the banner at the top of this page) 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. 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. Solving Math Word Problems - A Study Guides and Strategies web site posted by the University of St. Thomas 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)	Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball on 9/4/08 Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball on 9/4/08
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)	Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them Bell work PowerPoint show on Slope of a line 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. Equation of Lines - a PowerPoint show Find the graph that best matches the linear equation Linear Equation Test - Can you work out the answers? Use the multiple choice boxes or the radio buttons to select your answer. Linear Functions Part A: Basics: Slope and Intercept Part B: Finding the Equation of a Line Linear Function Jeopardy in the form of a PowerPoint show Linear Functions, Slope and Regressions - one example is the Kalamazoo Wal-mart Live or Die Scenario Slope Intercept Jeopardy review game in the form of a PowerPoint show Another Slope Intercept Jeopardy review game in the form of a PowerPoint show Using Slopes and Intercepts - a twenty-nine slide PowerPoint show
apply the concept of rate of change to solve real-world problems	Stressed Out - Slope as Rate of Change
select the appropriate graphical representation on the coordinate plane of a given linear inequality (given in standard form or slope-intercept form)	Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them 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. Slope Intercept Jeopardy review game in the form of a PowerPoint show Another Slope Intercept Jeopardy review game in the form of a PowerPoint show Graphing Linear Equations - an internet project Practice Converting Linear Equations Into Slope Intercept Form - an eleven slide PowerPoint show Slope of the Stairs - use this java applet to investigate the concept (written by someone in Japan, please overlook their spelling :-)
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	Line Jumper - [This link opens in a new window] Funbrain number line (choose Super Brain!) 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. 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!" Number Line Bounce - Instructions on how to play are included at the top of the window.
Level 3
solve multi-step linear inequalities in real-world situations	Inequalities Workout at Math.com 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. Practice with Solving Inequalities Rags to Riches Game - [This link opens in a new window] 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" Solving Inequalities: Overview - from Purple Math Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included
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	Domain, Range, Derivative, 1-D Kinematics - [This link opens in a new window] a Quia quiz Explore Families of Functions - Families of Functions you need to know This page opens in a new window. Close the window to return to this page. Families of Functions - includes a picture of the function family at home Families of Functions - graph-description match game Links to twelve other function family games Fam ilies of Functions and Curves - Four Basic Function Families - Function Machine Functions - There are different ways of looking at functions. This lesson from Purple Math will consider a few. Introduction to the Four Basic Function Families 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	Systems of Linear Equations - an introduction which considers three situations both algebraically and geometrically
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 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	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!" 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. Expressions, Equation Solving and Graphing in the Coordinate Plane - The Haunted house and many more coordinate plane practice problems Graphing Equations and Inequalities Unit Quiz Line Jumper - [This link opens in a new window] Funbrain number line (choose Super Brain!) Number Line Bounce - Instructions on how to play are included at the top of the window. 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.
Identify the opposite of a rational number	Interactive Algebra Review on the topic of real numbers 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. A proof that all square roots of primes are irrational
Determine the square root of a perfect square less than 169	Identify Perfect Squares - practice exercises at Math Pinball on 9/4/08 Simplifying Radical Expressions - Intermediate Algebra tutorial Simplifying Radicals - basic information about perfect square numbers Simplifying Radicals - explanation and practice problems Square Roots - Find the square root of a perfect square number. (a matching game like concentration) Squares and Square Roots - to understand square roots, first you must understand squares
Use exponents to simplify a monomial written in expanded form	Converting Numbers to Scientific Notation - AAA Math lesson and practice problems & Cube of a Number - AAA Math lesson and practice problems & Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems & 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. Exponents - Unit 3 from Ms. Glosser's Math Goodies Interactive Algebra Review on Integer Exponents Scientific Notation - interactive practice 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.
apply order of operations when computing with integers using no more than two sets of grouping symbols and exponents 1 and 2	Calculations Using Order of Operations - AAA Math lesson and practice problems & Evaluating Algebraic Expressions - Order of Operations/P.E.M.D.A.S. Evaluating Algebraic Expressions - from Regents Prep Order of Operations What's Wrong? - Order of Operations - Math Goodies from Ms. Glosser 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. Order of operations game from Funbrain.com (easier levels are available) Order of Operations Order of Operations - practice problems Order of Operations - a matching grid pattern game 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	Connecting Equations to Real-World Situations Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities. 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) Plane Math - Nine activities involving aviation and mathematic Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more 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	Comparing Seven Digit Numbers - practice area followed by an interactive game Rational and Irrational number review
Identify the reciprocal of a rational number	Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
add and subtract algebraic expressions	A concentration type game from Quia using algebraic expressions - If d=2 match the algebraic expressions to the correct answers. Interactive Algebra Review - Rational Algebraic Expressions
multiply two polynomials with each factor having no more than two terms	Factoring Trinomials - practice exercises at Math Pinball on 9/4/08 Factoring Trinomials Self Quiz - Check your knowledge about factoring polynomials. Interactive Algebra Review - Multiplying Algebraic Expressions Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial) Multiplying Polynomials - a step-by-step explanation from PurpleMath 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	Curious and Useful Math - Here you will find tricks and rules for quickly calculating certain types of math problems. Developing Estimation Strategies by Making Connections among Number, Geometry, Measurement, and Data Concepts: Estimating Scoops - NCTM lesson plan including video segments Every Breath You Take - worksheet to help students estimate the number of breaths they take in one hour K-12 Math Problems, Puzzles, Tips & Tricks from the Math Forum
select ratios and proportions to represent real-world problems	Connecting Equations to Real-World Situations Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities. 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) Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies Plane Math - Nine activities involving aviation and mathematic Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more Ratio and Proportion - four stage lesson includes examples and a set of workout problems 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	Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them Linear Functions, Slope and Regressions - one example is the Kalamazoo Wal-mart Live or Die Scenario 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. Slope Intercept Jeopardy review game in the form of a PowerPoint show 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.	Instructions for making a concept map using Excel Instructions for making a Venn Diagram using Excel 2007 Percent - graphical examples and practice problems Writing Fractions as Percent - unit 4 from Ms. Glosser's Math Goodies

Standard 3 - Geometry The student will investigate, model, and apply geometric properties and relationships.
Level 1
identify ordered pairs in the coordinate plane.	Practice from Math.com: The coordinate plane, Slope and y-intercept, and Graphing linear equations. Coordinate Geometry - use this PowerPoint show to teach the concept of ordered pairs [consider changing the text animation] (author Monica Yuskaitis) Battle Graph - teach your students about graphing on a coordinate plane. A PowerPoint show designed by Sarah Grabowski, University of Georgia, July 9, 2003 What's the Point? - [This link opens in a new window] a coordinate plane game from Funbrain.com (use the hardest level)
Level 2
apply the given Pythagorean Theorem to a real life problem illustrated by a diagram (no radicals in answer)	Animated Proof of the Pythagorean Theorem Demonstrate the Pythagorean Theorem - from NOVA Nineteen Pythagorean Theorem applets Pythagorean theorem - In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics Pythagorean Theorem - a java applet that allows students to investigate this theorem. Pythagorean Theorem - This lesson will allow you to figure out the Pythagorean Theorem all by yourself. 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. 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. Pythagorean Theorem and its many proofs (43 to be precise) Using the Pythagorean Theorem Once you know the equation a2 + b2 = c2 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	Geometry Java Applets - instructions for use ot the applet and a table of contents A Mathematical Droodle - Two Triples of Similar Triangles Pythagorean theorem and right triangle facts - given the length of three sides, determine if a right triangle is being described Ratio of the Sides of a Right Triangle 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. Virtual Manipulative - Similar Triangles
Level 3
calculate the distance between two points given the Pythagorean Theorem and the distance formula	How to use the distance formula to find distances between (x,y) points 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.

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	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. 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)	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. 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	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	Area and Volume from Ask Dr. Math - A simple way to think about area and volume Areas of Triangles, Trapezoids, and Kites - discover or demonstrate the formulas for the areas of triangles, trapezoids, and kites. (three activities) Challenge Exercises: Area of a Circle Circle, Sphere & Cylinder Calculator 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 How Are Things Shaping Up? Investigating Surface Area, Volume, and Properties of Shapes Introduction To Volume This lesson is a pure text document, but outlines an interesting experiment using popcorn. 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)	Comparing Properties of the Mean and the Median through the use of Technology and more. 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 Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem 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. Review of tables, charts and graphs - an index of topics 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. 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. What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment
interpret bar graphs representing real-world data	Using Data and Statistics - good graphs, however they are not interactive What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment
interpret circle graphs (pie charts) representing real-world data	Graphs and charts - four different graphs and charts for you to consider
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	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.
determine the median for a given set of real-world data (even number of data)	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.
Level 3
compute the probability of a simple compound event (2 independent events, no more than 6 possibilities per event)	Probabilistic Situations - a short slide show on the topic 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. 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. Coin Flipping - Click the Flip Coin button. Number of flips, number of heads, and probability of flipping heads is displayed. (one click per flip) Another coin flipping page 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. Interactive Probability Tutorials: Sample Spaces and Events, Estimated Probability, Empirical Probability, Abstract Probability and Conditional Probability and Independence
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.