7th Grade Matix: Algebra and Functions

Number Sense | Algebra and Functions | Measurement and Geometry | Statistics, Data Analysis, and Probability

AF 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:

AF 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).

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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AF 1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)

Expression Maze - Practice evaluating expressions with this printable and fun maze game from Harcourt.
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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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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
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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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AF 1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.

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.
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Commutative Property – BrainPop movie and interactive quiz
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Distributive Property – BrainPop movie and interactive quiz
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Properties Drill - use this Powerpoint properties drill to assess student understanding of additive, commutative, associative and distributive properties.
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Multiplication Properties - Students can test their knowledge of properties with this AAAmath.com practice game. Provides instant feedback and scroring.
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AF 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

Identifying qualitative graphs - This is a downloadable file in PDF format with a series of graphs. Students choose the graph that best describes the situation presented.
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Create A Graph – interactive site allows students to communicate information visually through construction of area, bar, line and pie charts with single or multiple data sets.
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Bar & Line Graphs - Video tutorial on creating bar & line graphs 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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Using Tables, Rules and Graphs – Explore Learning guided practice and exploration. Students compare the graph of a linear function to its rule and to a table of its values.
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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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Math Forum Web Unit on Graphs - everything you need to know about bar graphs, pie charts, pictographs and graphing linear, polynomial and exponential functions.
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AF 2.0 Students interpret and evaluate expressions involving integer powers and simple roots:

AF 2.1 Interpret positive whole number powers as repeated multiplication and negative whole number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents

Explore the Multiplication of Integers (Videotape Project). The concept of multiplication of positive and negative integers is cleverly presented using backward & forward motion of students walking and forward/reverse actions of a video camera to encourage understanding, not simply rote memorization of facts. Complete lesson plan and worksheets are included.
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Arithmetic Four - Practice with positive & negative whole number and integer addition, subtraction, multiplication and division. Two-player timed game with three levels of difficulty. Exploration questions are also offered as an extension of the activity.
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Rational Exponents - Rules for working with fractional (rational) exponents.
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Order of Operations with Exponents - Mrs. Glosser’s Lesson on order of operations with exponents. Gives a helpful mnemonic for remembering the order of operations. Includes examples and practice problems for this skill.
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Multiplying Exponential Expressions - Practice simplifying expressions with assessment questions.
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Dividing Exponential Expressions – guided practice simplifying expressions
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AF 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer component.

Rules of Exponents - Students learn the rules of exponents and solve easy, difficult or random problems.
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Multiplying Exponential Expressions - Students use tiles to simplify expressions. They are given expressions and asked to rewrite them with a single exponent. Tips are offered to further understanding. Multiple-choice questions follow for assessment.
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Dividing Exponential Expressions - Students must simplify exponential expressions as described above.
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AF 3.0 Students graph and interpret linear and some nonlinear functions

AF 3.1 Graph functions of the form y = nx and y = nx and use in solving problems.

Understanding linear equations - One-step, single-variable, first-degree linear equation, using a variety of methods.
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Quadratic and Absolute Value Functions - Exploration and guided practice
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AF 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.

Point-Slope Form of a Line – exploration and guided practice
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Rate of Change in Linear Functions Using Interactive Graphs
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Slope Slider - experiment with slope and y-intercept.
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AF 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

Exploring Linear Data - Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
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Zona Land - Experiment with changing the values for the slope and y-intercept and visualize how it affects the graph of the equation y=mx+b.
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AF 4.0 Students solve simple linear equations and inequalities over the rational numbers:

AF 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

Algebra Four Game - This activity is similar to Connect Four, and is designed for two players. The goal is to have four pieces of the same color connected either horizontally, vertically, or diagonally. To earn a piece, you need to correctly solve an algebraic equation. Solving an algebraic equation means finding the value of an unknown value in an equation that makes that equation true. For equations in the Algebra Four activity, you will be asked to find solutions to single variable equations.
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Equation of Mystery Game - Solve extraterrestrial math equations in the Cargo Bay with this shockwave version of Astro Algebra from Harcourt Brace and Edmark. Click and drag tiles to complete hidden equations.
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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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Modeling and Solving two-step equations – interactive math applet.
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Solve two-step equations - BrainPop movie and interactive quiz
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Solving Inequalities – BrainPop movie and interactive quiz
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Solving Linear Equations Tutorial & Practice
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Solving Inequalities - Students can read the tutorial, see examples and interactively practice solving equations and inequalities for the variables with a quiz.
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Two-Step Equations and Inequalities - Students learn to solve equations that have more than one operation, see examples and interactively practice solving equations.
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AF 4.2* Solve multi-step problems involving rate, average speed, distance, and time or a direct variation.

Distance, Rate & Time: Tim & Moby discuss the formulas for problems involving distance, rate & time and solve a traveling train problem. (Brainpop).
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Rate/Time/Distance Problem : Math TV Problem solving video. How long will it take a cyclist to catch up with her friend on her bike? Infinity Quick (IQ) leads students through word problems with step-by-step solutions, followed by an interactive word problem similar to the one in the video. Includes practice area, online calculator and notepad. (Click here for CTAP unpacking of this resource).
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Understanding Distance, Speed, and Time Relationships Using Simulation Software - Students control the speeds and starting points of runners, watch a simulated race, and examine a graph of the time-versus-distance. They analyze change that occurs as they manipulate the environment.
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Learn about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute
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Distance, Time and Speed Graphs – guided practice and exploration with two runners.
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Distance-Time Graphs – guided practice and exploration with two runners.
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Distance, Rate, Time Word Problems – teacher lesson plan with suggestions for guided and independent practice.
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Distance, Rate, Time - Prentice Hall tutorial with checks for understanding.
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Distance, Rate & Time - Practice Word Problems that involve distance, rate and time. Hints for up to five steps in the process are given.
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Last Updated ( Tuesday, 17 February 2009 17:03 )