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Mathematics Curriculum Standards
3102 - Algebra I
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Internet Resources |
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Develop meaning for mathematical vocabulary.
3102.1.1 |
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Use the terminology of mathematics correctly.
3102.1.2 |
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Understand and use mathematical symbols, notation, and common mathematical abbreviations correctly.
3102.1.3 |
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Write a rule with variables that expresses a pattern.
3102.1.4 |
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Use formulas, equations, and inequalities to solve real-world problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems.
3102.1.5 |
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Use a variety of strategies to estimate and compute solutions, including real-world problems.
3102.1.6 |
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Identify missing or irrelevant information in problems.
3102.1.7 |
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Recognize and perform multiple steps in problem solving when necessary.
3102.1.8 |
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Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality).
3102.1.9 |
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Use algebraic properties to develop a valid mathematical argument.
3102.1.10 |
- 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.
- 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.
- Learn to solve word problems - This is a collection of word problem solvers that solve your problems and help you understand the solutions.
- Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
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Use manipulatives to model algebraic concepts.
3102.1.11 |
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Create and work flexibly among representations of relations (including verbal, equations, tables, mappings, graphs).
3102.1.12 |
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Change from one representation of a relation to another representation, for example, change from a verbal description to a graph.
3102.1.13 |
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Apply graphical transformations that occur when changes are made to coefficients and constants in functions.
3102.1.14 |
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Apply arithmetic concepts in algebraic contexts.
3102.1.15 |
- Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
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Understand and express the meaning of the slope and y-intercept of linear functions in real-world contexts.
3102.1.16 |
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Connect the study of algebra to the historical development of algebra.
3102.1.17 |
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Translate syntax of technology to appropriate mathematical notation.
3102.1.18 |
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Recognize and practice appropriate use of technology in representations and in problem solving.
3102.1.19 |
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Estimate solutions to evaluate the reasonableness of results and to check technological computation.
3102.1.20 |
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Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.
SPI 3102.1.1 |
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Write an equation symbolically to express a contextual problem.
SPI 3102.1.2 |
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Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.
SPI 3102.1.3 |
- 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
- 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.
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Translate between representations of functions that depict real-world situations.
SPI 3102.1.4 |
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Recognize and express the effect of changing constants and/or coefficients in problem solving.
SPI 3102.1.5 |
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Determine and interpret slope in multiple contexts including rate of change in real-world problems.
SPI 3102.1.6 |
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Mathematics Curriculum Standards
3102 - Algebra I
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Internet Resources |
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Recognize and use like terms to simplify expressions.
3102.2.1 |
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Operate with and simplify radicals (index 2, 3, n) and radical expressions including rational numbers and variables in the radicand.
3102.2.3 |
- 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
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Operate efficiently with both rational and irrational numbers.
3102.2.4 |
- Proof that all square roots of primes are irrational
- Rational and Irrational number review
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Perform operations with numbers in scientific notation (multiply, divide, powers).
3102.2.5 |
- Converting Numbers to Scientific Notation - AAA Math lesson and practice problems &
- Scientific Notation - interactive practice
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Use appropriate technologies to apply scientific notation to real-world problems.
3102.2.6 |
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Identify the subsets in the real number system and understand their relationships.
3102.2.7 |
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Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line.
3102.2.8 |
- Proof that all square roots of primes are irrational
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Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical
expressions including radicands involving rational numbers and algebraic expressions.
SPI 3102.2.1 |
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Multiply, divide, and square numbers expressed in scientific notation.
SPI 3102.2.2 |
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Describe and/or order a given set of real numbers including both rational and irrational numbers.
SPI 3102.2.3 |
- Comparing Seven Digit Numbers - practice area followed by an interactive game
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National Library of Virtual Manipulatives |
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Number & Operations [Grades 9-12]
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Mathematics Curriculum Standards
3102 - Algebra I
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Internet Resources |
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Recognize and extend arithmetic and geometric sequences.
3102.3.1 |
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Explore patterns including Pascal’s Triangle and the Fibonacci sequence.
3102.3.2 |
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Justify correct results of algebraic procedures using extension of properties of real numbers to algebraic expressions.
3102.3.3 |
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Simplify expressions using exponent rules including negative exponents and zero exponents.
3102.3.4 |
- 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
- 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.
- Use the Equation Calculator from Algebra Help
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Add, subtract, and multiply polynomials including squaring a binomial.
3102.3.5 |
- 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.
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Find the quotient of a polynomial and a monomial.
3102.3.6 |
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Use various models (including area models) to represent products of polynomials.
3102.3.7 |
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Find the GCF of the terms in a polynomial.
3102.3.8 |
- Factoring out the Greatest Common Factor - practice exercises at Math Pinball on 9/4/08
- Finding the Greatest Common Factor of 2 or 3 Numbers - practice exercises at Math Pinball on 9/4/08
- Finding the Greatest Common Factor of Variable Expressions - practice exercises at Math Pinball on 9/4/08
- LCM and GCF - To find either the Least Common Multiple (LCM) or Greatest Common Factor (GCF) of two numbers, you always start out the same way
- Investigating LCM and GCF Using Rods
- GCF & LCM - enter two values and this site will solve for GCF and LCM
- Interactive Algebra Review - Factoring Algebraic Expressions
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Find two binomial factors of a quadratic expression.
3102.3.9 |
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Add, subtract, multiply, and divide rational expressions and simplify results.
3102.3.10 |
- Concentration type game from Quia using algebraic expressions - If d = 2 match the algebraic expressions to the correct answers.
- Interactive Algebra Review on Integer Exponents
- 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 - Rational Algebraic Expressions
- 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.
- Use the Equation Calculator from Algebra Help
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Solve multi-step linear equations with one variable.
3102.3.11 |
- 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
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Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions.
3102.3.12 |
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Solve multi-step linear inequalities with one variable and graph the solution on a number line.
3102.3.13 |
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Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line.
3102.3.14 |
- Absolute Value lesson from Purple Math
- 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.
- Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- 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.
- Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- Solving Absolute Value Equations - a lesson from Purple Math
- Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included
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Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.
3102.3.15 |
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Determine if a relation is a function from its graph or from a set of ordered pairs.
3102.3.16 |
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Recognize “families” of functions.
3102.3.17 |
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Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions. Use technology where appropriate.
3102.3.18 |
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Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.
3102.3.19 |
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Understand that a linear equation has a constant rate of change called slope and represent slope in various forms.
3102.3.20 |
- Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them
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 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
- Graphing Linear Equations - an internet project
- 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
- Practice Converting Linear Equations Into Slope Intercept Form - an eleven slide PowerPoint show
- Practice from Math.com: The coordinate plane, Slope and y-intercept, and Graphing linear equations.
- Slope Intercept Jeopardy review game in the form of a PowerPoint show
- Slope of the Stairs - use this java applet to investigate the concept (written by someone in Japan, please overlook their spelling :-)
- Another Slope Intercept Jeopardy review game in the form of a PowerPoint show
- Stressed Out - Slope as Rate of Change
- Using Slopes and Intercepts - a twenty-nine slide PowerPoint show
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Determine the equation of a line using given information including a point and slope, two points, a point and a line parallel or perpendicular, graph, intercepts.
3102.3.21 |
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Express the equation of a line in standard form, slope-intercept, and point-slope form.
3102.3.22 |
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Determine the graph of a linear equation including those that depict contextual situations.
3102.3.23 |
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Interpret the changes in the slope-intercept form and graph of a linear equation by looking at different values of the parameters, m and b.
3102.3.24 |
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Find function values using f(x) notation or graphs.
3102.3.25 |
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Graph linear inequalities on the coordinate plane and identify regions of the graph containing ordered pairs in the solution.
3102.3.26 |
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Determine the number of solutions for a system of linear equations (0, 1, or infinitely many solutions).
3102.3.27 |
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Solve systems of linear equations graphically, algebraically, and with technology.
3102.3.28 |
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Solve contextual problems involving systems of linear equations or inequalities and interpret solutions in context.
3102.3.29 |
- 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
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Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle.
3102.3.30 |
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Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.
3102.3.31 |
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Recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions.
3102.3.32 |
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Recognize data that can be modeled by an exponential function.
3102.3.33 |
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Graph exponential functions in the form y = a(bx) where b ≠ 0.
3102.3.34 |
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Apply growth/decay and simple/compound interest formulas to solve contextual problems.
3102.3.35 |
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Express a generalization of a pattern in various representations including algebraic and function notation.
SPI 3102.3.1 |
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Operate with polynomials and simplify results.
SPI 3102.3.2 |
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Factor polynomials.
SPI 3102.3.3 |
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Operate with, evaluate, and simplify rational expressions including determining
restrictions on the domain of the variables.
SPI 3102.3.4 |
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Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.
SPI 3102.3.5 |
- Absolute Value lesson from Purple Math
- Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- Solving Absolute Value Equations - a lesson from Purple Math
- 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
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Interpret various relations in multiple representations.
SPI 3102.3.6 |
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Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.
SPI 3102.3.7 |
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Determine the equation of a line and/or graph a linear equation.
SPI 3102.3.8 |
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Solve systems of linear equation/inequalities in two variables.
SPI 3102.3.9 |
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Find the solution of a quadratic equation and/or zeros of a quadratic function.
SPI 3102.3.10 |
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Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.
SPI 3102.3.11 |
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National Library of Virtual Manipulatives |
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Algebra [Grades 9-12]
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Data Analysis, Statistics, & Probability
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Mathematics Curriculum Standards
3102 - Algebra I
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Internet Resources |
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Identify patterns or trends in data.
3102.5.1 |
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Develop a meaning for and identify outliers in a data set and verify.
3102.5.2 |
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When a set of data is changed, identify effects on measures of central tendency, range, and inter-quartile range.
3102.5.3 |
- Central Tendency - explanation of this concept and related concepts
- 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.
- Measures of Central Tendency - tutorial and examples
- Measuring Central Tendency - explanation, examples and a large number of links to related topics
- Running and Weighted Averages - tutorial and examples
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Explore quartiles, deciles, and percentiles of a distribution.
3102.5.4 |
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Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables).
3102.5.5 |
- Analyzing Blood Pressure with Scatter Plots (Best-fitting Line) - lesson plan (Algebra 1)
- Creating an Excel XY (Scatter) Plot - simple explanation
- Creating a Scatter Plot in Excel - two elaborate examples of scatter plots; Beer's law scatter plot and linear regression, and creating a scatter plot of titration data
- Explanation of Scatter Plots from the Engineering Statistics Handbook
- Review of tables, charts and graphs - an index of topics
- Scatter Plot Applet - This applet draws a scatter plot of points (a,b), where the data is taken from an input table. The table is on the left side of the applet and can be edited by the user.
 Using Excel to create a Scatter Plot - an Internet4Classrooms module - Weather and Spreadsheets - Java applet which allows you to enter data and display a scatter plot or a column chart of the data entered
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Draw qualitative graphs of functions and describe a general trend or shape.
3102.5.6 |
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Compare two data sets using graphs and descriptive statistics.
3102.5.7 |
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Examine real-world graphical relationship (including scatter-plots) to determine type of relationship (linear or nonlinear) and any association (positive, negative or none) between the variables of the data set.
3102.5.8 |
- Connecting Equations to Real-World Situations
- 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 and more.
- Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem
- Graphs and charts - four different graphs and charts for you to consider
- 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.
- 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
- 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.
- Using Data and Statistics - good graphs, however they are not interactive
- 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.
- What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment
- 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.
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Determine an equation for a line that fits real-world linear data; interpret the meaning of the slope and y-intercept in context of the data.
3102.5.9 |
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Using technology with a set of contextual linear data to examine the line of best fit; determine and interpret the correlation coefficient.
3102.5.10 |
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Use an equation that fits data to make a prediction.
3102.5.11 |
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Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.
3102.5.12 |
- Probabilistic Situations - a short slide show on the topic
- 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)
- 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
- 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.
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Determine the complement of an event and the probability of that complement.
3102.5.13 |
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Determine if two events are independent or dependent.
3102.5.14 |
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Explore joint and conditional probability.
3102.5.15 |
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Identify situations for which the Law of Large Numbers applies.
3102.5.16 |
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Perform simulations to estimate probabilities.
3102.5.17 |
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Make informed decisions about practical situations using probability concepts.
3102.5.18 |
- Probabilistic Situations - a short slide show on the topic
- 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)
- 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
- 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.
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Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).
SPI 3102.5.1 |
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Identify the effect on mean, median, mode, and range when values in the data set are changed.
SPI 3102.5.2 |
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Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.
SPI 3102.5.3 |
- Analyzing Blood Pressure with Scatter Plots (Best-fitting Line) - lesson plan (Algebra 1)
- Creating an Excel XY (Scatter) Plot - simple explanation
- Creating a Scatter Plot in Excel - two elaborate examples of scatter plots; Beer's law scatter plot and linear regression, and creating a scatter plot of titration data
- Explanation of Scatter Plots from the Engineering Statistics Handbook
- Review of tables, charts and graphs - an index of topics
- Scatter Plot Applet - This applet draws a scatter plot of points (a,b), where the data is taken from an input table. The table is on the left side of the applet and can be edited by the user.
- Using Excel to create a Scatter Plot - an Internet4Classrooms module
- Weather and Spreadsheets - Java applet which allows you to enter data and display a scatter plot or a column chart of the data entered
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Generate the equation of a line that fits linear data and use it to make a prediction.
SPI 3102.5.4 |
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Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.
SPI 3102.5.5 |
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National Library of Virtual Manipulatives |
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Data Analysis & Probability [Grades 9-12]
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a site for teachers | 
a Word document
sound | 
video format | 