Algebra Matrix

STANDARD

1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.

1.1 Students use properties of numbers to demonstrate whether assertions are true or false.

Interactive Number Theory - From Learning Wave Online. Learn about order of operations, commutative and associative properties of addition and multiplication, distributive property, and additive property of zero. Practice Problems. Numerous interactive challenges provide motivation and give students a rigorous workout.
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Associative Property – BrainPop movie and quiz. Choose math, associative property.
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Commutative Property – BrainPop movie and interactive quiz. Choose math, commutative property.
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Distributive Property – BrainPop movie and interactive quiz. Choose math, distributive property.
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Algebraic Problem Solving Using a spreadsheet moving from numerical to symbolic representation. This unit takes four days: formulas on a spreadsheet, setting up a spreadsheet, solving problems on a spreadsheet and follow-up.
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2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

Order of Operations - The user reviews the rules for the order of operations for a given expression. After viewing examples, users can interactively practice evaluating expressions following the rules for the order of operations.
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Order of Operations - mathcasts by students simplying expressions using the correct order of operations.
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Order of Operations - Exploration guide, interactive applets and assessment questions.
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Order of Operations - Brainpop Movie and Interactive Quiz. Choose math and then order of operations
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Order of Operations - Video tutorial from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. You may need to set up a free user account to access this site and see all topics. Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages.
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Lesson on Order of Operations - Tutorial on the Order of Operations followed by a set of problems.
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Expression Maze - Practice evaluating expressions with this printable and fun maze game from Harcourt.
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Negative Exponents - PurpleMath.com tutorial.
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Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 6: Exponents
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Exponents - Brainpop adventure with Tim and Moby. Choose math and then Exponents. Students discover how far it is to Mexico as they learn to convert numbers between standard and exponent form. Includes video and interactive quiz. Choose math, exponents.
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Working With Exponents - Video tutorial from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. You may need to set up a free user account to access this site and see all topics. Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed.
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Working With Negative Exponents - Video tutorial from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. You may need to set up a free user account to access this site and see all topics. Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed.
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Exponents (Multiplication, Division, Negative Exponents) - The user reviews the basic rules of working with exponents in algebra. After viewing examples of the rules, users can interactively practice solving problems with exponents.
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Multiplying Exponential Expressions – Explore Learning guided practice in simplifying expressions using multiplication. Students choose the correct steps to multiply exponential expressions and use the feedback to diagnose incorrect steps.
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Dividing Exponential Expressions - Explore Learning guided practice in simplifying expressions using division. Students choose the correct steps to divide exponential expressions and use the feedback to diagnose incorrect steps.
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An online project by students for students - Math for Morons like Us - a ThinkQuest Project. Have you ever been stuck on math? If it was a question on algebra, geometry, or calculus, you might want to check out this site. It's all here from pre-algebra to calculus. You'll find tutorials, sample problems, and quizzes.
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AAA Math has a series of resources for scientific notation with explanation, practice, play and explore.
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Equation Match - Shockwave game from the BBC. Students match pairs by working out the values in each equation. Includes help file of “key ideas” in solving an expression.
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Purple math – tutorial on solving radical equations
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Exploring Exponents and Scientific Notation - Junior High Interactive resource. Includes a video that illustrates how math is used by paleontologists in the study of dinosaurs. An interactive activity allows students to sort and then order numbers that are expressed in scientific notation. A print activity about exponents can be downloaded.
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Scientific Notation - Brainpop video explains how to write scientific notation using planet distances as an example. It walks students through the process of converting positive and negative numbers into scientific notation. Can be paused or replayed. Includes an interactive quiz.
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Converting Numbers to Scientific Notation - Video tutorial from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. You may need to set up a free user account to access this site and see all topics. Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed.
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Quick Math Scientific Notation – Very cool JavaScript tool from Quick Math that lets you plug in numbers and then it walks the user through steps that it took to arrive at the conversion to scientific notation. Eight types of problems are covered.
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Fact Monster Tutorial on scientific notation.
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Scientific Notation Conversions – Write a whole number in scientific notation and vice versa. Follow the directions to learn how to convert from scientific notation to whole numbers using an online scientific calculator, then make your own examples. Uses Macromedia flash.
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Scientific Notation Problem Generator – JavaScript program that lets you convert basic numbers to scientific notation
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Writing Algebraic Equations - Tutorial and practice
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Balance Beam Activity - Solve simple linear equations using a balance beam representation. (Click here for CTAP unpacking of this resource).
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Balance Beam – Solving equations
Interactive text (itext) from Prentice Hall. Includes a teacher QuickTime video explaining the process of balancing equations. Could be used with previous activity.
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The Language of Algebra - The user can practice their understanding of algebraic terms, the correct order of operations, and how to write equations and inequalities as they take an online interactive quiz. (Math.com)
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Writing Inequalities - Students learn how to write inequalities from sentences. After viewing examples, users can interactively match sentences to the equivalent inequality. (Math.com)
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Using Algebraic Equations – Explore Learning gizmo. Students translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation .guided practice and exploration.
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3.0 Students solve equations and inequalities involving absolute values.

Motivating Math –Interactive Algebra practice with an interactive tool. Students are given a problem, ask to solve the problem on paper. They can choose to see individual steps to check their work and the solution to the problem. Choose lessons 5-8
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Mathulator - an online tool that can help students understand the concept by explaining sample problems and by evaluating whether statements are true or false. The graphing component is simple to use and can plot single functions or overlay them on previous functions.
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Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 4: Inequalities and section 5: absolute value.
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Absolute Value Inequalities - a tutorial on solving absolute value inequalities by providing some examples and going through each one step by step. Purplemath
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Purplemath Absolute Value - has extensive explanation of the absolute zero concept offers timelines for visual aids and also provides different kinds of problems where absolute value might appear.
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Math Wizz: Absolute value problems - get a question and solve it. You can also get an answer with detailed explanations.
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Regents Math A: Absolute value - includes a basic review, practice section and a whiteboard drill of absolute value.

4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.

Distributive Property – BrainPop movie and interactive quiz. Choose math and then distributive property.
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Shodor: Algebra Quiz Game - Students have an on line quiz where the score and time elapsed is recorded on various level of solving equation problems.
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5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

Equation Match - a BBC game where students have to match two equations that will give the same answer. There are three levels of play.
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Interactive mathematics – algebra balance scale
This virtual manipulative allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, you can choose to perform any arithmetic operation, as long as you DO THE SAME THING TO BOTH SIDES, thus keeping the beam balanced. This e-mail address is being protected from spambots, you need JavaScript enabled to view it
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Shodor: Algebra Four - A game for two players to for a connect four type of game where students solve equations (several difficulty levels of quadratic and/or linear equations)to drop a chip.

Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 2: Equations.
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Quia Mathematics – Easy Algebra equations – Rags to Riches Students solve algebraic equations. For each correct answer the student moves up the money ladder. Can be played in html or Java
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Tutorial - Linear equations in two variables – graphing
After completing this tutorial, the student should be able to:
1. Recognize when an equation in two variables is a linear equation.
2. Graph a linear equation.
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Figure this! - solving word problems concerning linear equations and percents
Includes 80 math challenges that reinforce the math middle school students do in school. As the student proceeds through the problems, they are given more difficult problems to solve.
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Math Challenge 17
Math Challenge 08

Lesson - Buy or Lease a car
Each student will come with information on 3 NEW cars they would like to drive. Then for each car the student will use the Buy/Lease calculator to see which option, buy or lease is best.
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Word Problems - Mystery Numbers
Students are given a problem and are shown how to solve it. Then, they are asked to solve a similar problem. Finally, they are given the opportunity to write their own problem and submit it to the website.
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Calculating Discounts - Check the Roll ‘em archives for Percentage problems (Episode 3) Students follow along as their TV host (IQ) works through step-by-step solutions of a word problem; then they are invited to solve an interactive word problem of their own. They can replay the video as needed. The practice area is equipped with a notepad and calculator. Whole numbers, fractions, percentages, ratios, probability, algebra and geometry topics are explored.
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Election Night with Percent - A graphing calculator activity in which the students will work primarily with the concept of % of a number. They will calculate the number of people expected to vote when given the population and % of registered voters along with historical data on percentage of voter turnout. They will then use polls to graph predictions.
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Percent Tricks - Teach your student how to calculate percentages using the Percent Tricks method. (Handout and Lesson Plan)
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Finding Percents – Brainpop video and interactive quiz on how parts of the day are spent.
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Practice Using Percent Proportion
Tutorial for three types of questions and practice problems.
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Percentages – (Virtual Manipulative) Discover relationships between fractions, percents, and decimals by specifying two of the three quantities (part, whole or percent) and computing results.
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Percentage Converter - Virtual manipulative that lends itself to a discussion of relations among fractions, decimals, ratios and percentages.
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How students spend parts of their day.
(Spreadsheet activity)
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How Do You Manage Your Time? - Similar activity with extensive handouts, activities and web resources.
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A Conceptual Model for Solving Percent Problems - Students use a 10 x 10 grid to represent given information and solve various percentage problems. Lesson plan from Illuminations/nctm.org is included.
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“Percent of” Word Problems – PurpleMath tutorials and practice problems on markup and markdown.
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Percent of Increase & Decrease – Learningwave.com tutorials and colorfully illustrated interactive math challenges help students learn how to use formulas to solve percent problems.
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Word Problems: Percent Increase & Decrease - Excellent tutorial from Algebra Lab on solving problems that deal with increase or decrease. Includes practice problems and the ability to check your answers.
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Word Problems involving Percents – WebMath.com resource lets students find a word problem below that resembles the one they need help with, fill in the blanks, then click "Solve" to find the answer. Some coaching help is offered, based on input.
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Glencoe Online Self-Check Quiz on Percent of Change
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Perplexing Percentages - Everyday real-world math challenge from Figure This! site for the classroom or for families to do together. Students must determine if multiple successive discounts on clothing yield a lower price than one larger discount. They are given hints, things to think about and additional problems. Bilingual web site, indexed according to challenges and math strands. Each problem also contains bonus "interesting facts" related to the topic.
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The Discount is Right – Web activity from Mississippi Regional Educators for calculating original price, sales price and rate of discount. Includes student handouts.
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Let’s Go Shopping – Lesson plan and worksheets from Technology Innovation Challenge Grant site. Students spend $500, determine discounts, convert percents and fractions to decimals, and calculate 7.5% tax amounts on purchases. They use ads from newspapers, catalogues and magazines to locate sale items. Could also be done as a spreadsheet activity.
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Calculating Discounts - Students follow along as their TV host (IQ) works through step-by-step solutions of a word problem; then they are invited to solve an interactive word problem of their own. They can replay the video as needed. The practice area is equipped with a notepad and calculator. Whole numbers, fractions, percentages, ratios, probability, algebra and geometry topics are explored. (Click here for CTAP unpacking of this resource).
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Calculating Simple Interest – Learningwave tutorials and practice on calculating simple interest, calculating sales tax and tipping.
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Markup Tutorial - Triple A Math tutorial and practice samples.
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Discounts Tutorial - Triple A Math tutorial and practice samples.
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6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., sketch region 2x + 6y < 4).

Motivating Math –Interactive Algebra practice with an interactive tool. Students are given a problem, ask to solve the problem on paper. They can choose to see individual steps to check their work and the solution to the problem. Choose lessons 5-8
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Cell Phone Plans - using an Excel Spreadsheet
Students investigate cell phone plans using a spreadsheet. Many math teachers are familiar with an electronic spreadsheet, but may not be using it for instruction. It can be a powerful tool for exploring many math concepts, including graphing equations.
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WebMath - This page shows students how to graph an inequality.
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PurpleMath Solving Inequality, Linear and Non-linear - This is a student tutorial on solve inequalities.
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Graphing Linear Inequalities - This video demonstrates how to graph linear inequalities
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ExploreLearning –interactive
There are three gismos for slope, three gismos for points in a coordinate planes, three for slope-intercept, 2 for point-slope, one for standard form and one for defining a line with 2 points. You can do one activity (gismo) per day without paying a fee
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Graphing Calculator Lesson - This is a step-by-step guide for using the TI-85 Graphing Calculator to do scatter plots using data obtained from sources on the Internet. Some information will model linear functions and some will be models of exponential functions.
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Make a Rule - This interactive activity from PBSTeacherLine Interactives demonstrates the relationship between a real-life situation, the values it presents and the mathematical equation that generates those values. This activity could be used in combination with a graphing activity.
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Slope and Y Intercept - Tutorial on graphing equations and inequalities, followed by examples and practice problems. Student gets immediate feedback if they answer incorrectly.
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7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

Slope - using GraphIt, a tool for plotting points, graphing and exploring functions. Graphit is a tool for plotting points, graphing and exploring functions.
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Slope Slider
This activity allows the user to explore the relationship between slope and intercept in the Cartesian coordinate system. The applet allows the manipulation of a linear function of the form f (x) = mx + b. Using slider bars one can manipulate the line and a point along the line.
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Linear Function Machine- Each activity comes with supplementary What, How, and Why pages. What: gives background on the activity; How: gives instructions for the activity;
Why: gives curriculum context for the activity.
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Algebra Cruncher - Cool Math Algebra practice problems in various topics. Choose the first four categories.
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Area, Peas, and Linearity - This is a graphing calculator activity in which students will receive a circle and determine how many dried peas will fit on that circle. They will also calculate the area of the circle, and using the data of the entire class, determine if there is a linear association.

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Equation Jeopardy Game - A PowerPoint Jeopardy game to review linear equations in standard form, point-slope form, slope-intercept form.

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8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

Parallel and Perpendicular lines - A single page tutorial on parallel and perpendicular lines.
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Paralell and Perpentiduclar lines - Oswego City School District Regents Exam prep with tutorials, practice and teacher resources.
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Algebra Cruncher - Cool Math Algebra practice problems in various topics. Choose the parallel and perpendicular lines practice.
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9.0 Students solve a system of 2 linear equations in 2 variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of 2 linear inequalities in 2 variables and to sketch the solution sets.

Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 13: Systems of Linear Equations.
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Finding your way around solving systems of equations.
Step-by-step use of a graphing calculator to solve the system by graphing
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Practice graphing systems of equations.
Students practice graphing systems of equations without a graphing calculator.
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Algebra in the Bakery - Students are given a problem to solve and are shown how to solve it. Then, they are asked to solve a similar problem, using build-in tools. Finally, they are given the opportunity to write their own problem and submit it to the website.
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10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.

Polynomials - using Digital Math
Students will add, subtract, multiply, and divide monomials and polynomials, solve a multi-step problem involving operations with monomials and/or polynomials, and solve word problems involving operations with monomials and/or polynomials
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Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 7: Polynomials
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Exploring Polynomials - a short video clip focusing on the use of math concepts in every day life. This episode deals with polynomial equations.
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Virtual Manipulative allowing students to use Algebra tiles to multiply and factor binomials
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11.0 Students apply basic factoring techniques to second- and simple third-degree equations.

YouTubeVideos - a series of videos describing the various processes to factor different types of polynomials. it also includes other Algebra topics.
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Understanding Algebraic Factoring - A lesson from the Math Forum to show the geometric basis of algebraic factoring.
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Math Tools at Math Forum - factoring A series of java applets and lessons on factoring with ratings and discussions on factoring.
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Factor Practice - an applet designed to provide practice factoring polynomials.
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Factor Trail Game -Students play this Illuminations game and they have to identify the factors of a number to earn points.
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Mathcasts - Students and teachers demonstrate how to factor, using various techniques. There are over 30 videos/podcasts.
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Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 8: Factoring
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12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

Cool Math - A tutorial and practice for simplifying fractions with polynomials in the numerator and denominator.
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Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 8: Factoring
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13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.

Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 9: Rational Expressions
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Algebra Cruncher - Cool Math Algebra practice problems in various topics. Choose the Algebraic Fractions section.
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Cat and Mouse
Concepts of direct variation and inverse variation can be taught using a familiar brainteaser-type math problem. Method given reinforces the concepts, while preparing the students for the algebra involved.
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PBS mathsource: Students will use the graphing calculator to explore general patterns of polynomial and rational functions, and a real-world application of a polynomial function. In this lesson, students explore relationships between x-intercepts, factors, and roots of polynomial functions using the graphing calculator. Students also investigate rational functions, identifying the roots and the asymptotes as well as holes in the graphs.
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14.0 Students solve a quadratic equation by factoring or completing the square.

Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 15: Quadratics
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15.0 Students apply algebraic techniques to solve rate, work, and percent mixture problems.

Rate and Work - Students are given a problem and are shown how to solve it. Then, they are asked to solve a similar problem. Finally, they are given the opportunity to write their own problem and submit it to the website.
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Mixture Problems This United Streaming video has good visuals to help students understand how to break down mixture problems involving percents. Instructors could use the video as part of a PowerPoint presentation.
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Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 16: Applications
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16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 12: Functions
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ExploreLearning Gismos – interactive tool with exploration ideas - three activities for exponential functions
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PBS Mathline - This activity involves two simulations with M&M's® to explore population growth and decay
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PBS Mathline -This activity builds on the population decay M&M activity, introduces NOW-NEXT or recursive equations, and uses calculators as an efficient tool for exploring population models
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Seating in a theater - Students view the solving of a problem about seating in a theater. Then they solve a similar problem and given the opportunity to
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17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

Spreadsheet – Graphs to go – An engaging sports-related problem to work with statistics as related to the algebraic Standards. After looking up specific statistical data, students represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph. Students collect, organize, and represent data sets that have one variable and identify relationships within a data set by hand and through the use of an electronic spreadsheet software program.
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ExploreLearning Gismos – interactive tool with exploration ideas with three activities for exponential functions with an exploration guide, Assessment Questions, and Accessibility Options
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Simple and Compound Interest – An overview of interest. After reviewing some basic facts about interest and the way it is calculated, students link to other sites on the Internet to try out a variety of financial calculators to experiment with the concepts introduced here. Through this activity, students will look at the basic concepts of savings and investing, and see how money can actually make more money.
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Simple and Compound Interest - Interactive gizmo, exploration guide and assessment questions. Great resource to accompany investment simulation project. Good follow-up activity to direct instruction. Real world application of math. Could be used with overhead to provide visual representation of key concepts.
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Compound Interest and Exponential Growth - Math.com tutorial
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18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

Algebasics - White board solutions to algebraic topics. Good for test review and exams. Choose section 12: Functions
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Compound Interest and Exponential Growth - Math.com tutorial
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19.0 Students know the quadratic formula and are familiar with its proof by completing the square.

20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

21.0 Students graph quadratic functions and know that their roots are the x-intercepts.

Quadratic Equations - The students will view an episode of the Standard Deviant videos to begin their study of quadratic equations. Adventurous World of Algebra, The, Program 4: Quadratic Equations
This video is a four minute introduction to the world of graphing quadratic functions. It includes visual as well as auditory clues to the vocabulary that is introduced.
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22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

24.0 Students use and know simple aspects of a logical argument.

24.1 Students explain the difference between inductive and deductive reasoning and identify and provide examples of each.

24.2 Students identify the hypothesis and conclusion in logical deduction.

Pythagorean Theorem - using Squaring the Triangle
Pythagorean Theorem - using Pythagorean Explorer
By manipulating the sides of a right triangle, students can repeatedly prove the Pythagorean Theorem by comparing the length of the sides and by viewing the area of the three squares formed by using the sides of the right triangle.
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BrainPop movie and interactive quiz
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Project Mathematics – the theory of Pythagoras
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Pythagorean Theorem - a short video clip, from LearnAlberta, focusing on the use of math concepts in every day life.
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24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.

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25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.

25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

25.2 Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

Web Fun Brain - Try the medium & hard problems
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Order of Operations The user reviews the rules for the order of operations for a given expression. After viewing examples, users can interactively practice evaluating expressions following the rules for the order of operations.

25.3 Given a specific algebraic statement involving linear, quad, or abs value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.

Last Updated ( Tuesday, 14 April 2009 14:56 )

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