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# End-of-Course - Foundations II

## sites to help students practice skills needed for the Foundations II exam

Item sampler from the state of Tennessee [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
Standards Number & Operations | Algebra | Geometry | Measurement | Data Analysis & Probability site for teachers | PowerPoint show | Acrobat document | Word document | whiteboard resource | sound | video format | interactive lesson | a quiz | lesson plan | to print

 Standard 1 Number and Operations Students will recognize, represent, model, and apply real numbers and operations verbally, physically, symbolically, and graphically and will compute fluently and make reasonable estimates in problem solving. Level 1 choose the correct prime factorization of a two-digit composite whole number Factoris - Remember Tetris? To complete this game students must select a block size which would represent factors of the given number and then stack them using left and right arrows. Prime factorization of a number - a lesson on the concept and seven practice problems Prime factorization of the first 1000 integers - from SOS Math The Prime Machine - The applet on this page lets you explore the set of prime numbers. Prime Factorization Chart - click on a number to see its prime factorization The 1000 smallest Prime Numbers compare a fraction to a decimal using less than, greater than, and equals symbols Fraction Decimal Match-up - a concentration type game Comparing Decimals and Fractions [values < 1] lesson followed by a practice session then a quiz Comparing Decimals and Fractions [values > 1] lesson, practice session , and quiz Fraction to Decimal Calculator Multiple-Choice Questions - twenty (20) questions on Mathematical Reasoning multiply a fraction by a multiple of its denominator (denominator less than or equal to 25) Multiply fractions - circles, mixed number times a whole number Divide fractions - using circles, will show visually how the divisor will fit into the dividend a whole number of times Dividing fractions - Fraction Bar -This is a very versatile tool that can be used to illustrate a variety of number operations. Fractional Distances - Find Grammy by entering a fractional distance. (includes mixed numbers and various fractions) Rename Fractions in Lowest Terms - practice renaming fractions Word problems - online quiz adding and subtracting fractions Multiplying and Dividing Fractions - online quiz apply order of operations to evaluate numerical expressions (whole numbers only; no exponents or grouping symbols 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 [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] 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 - lesson [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Order of Operations - practice problems [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Order of Operations - a matching grid pattern game [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Order of Operations - a sixteen-slide show with plenty of examples Order of Operations - two problems used review of PEMDAS, followed by three equations for students to solve Order of Operations with Exponents - Math Goodies from Ms. Glosser Level 2 identify the opposite of any 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 Digits of Irrational Numbers - for example: the first 10 million digits of the number e select the best estimate for the coordinate of a given point on a number line (rationals) 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 Number Line Bounce - Instructions on how to play are included at the top of the window. choose an equivalent exponential form of a one-variable monomial given in factored form (only first-degree variables with positive integral coefficients) multiply an integer by a one-variable binomial select a reasonable solution for a real-world division problem in which the remainder must be considered Multiple-Choice Questions - twenty (20) questions about Operations apply order of operations to evaluate numerical expressions containing whole numbers, exponents, and no more than two sets of grouping symbols (no power larger than two) 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. An order of operations game from Funbrain.com (easier levels are available) Evaluating Algebraic Expressions - Order of Operations/P.E.M.D.A.S. Level 3 select ratios and proportions to represent real-world problems such as scale drawings and samplings (all ratios are positive integers to positive integers) Multiple-Choice Questions - thirty-one (31) questions about Ratios and Measurement Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies 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 Sample Task Search the newspapers for various uses of numbers and, in writing, justify the representations chosen (i.e., percent, fraction, and decimal). Investigate the applications of numbers and computations in the workplace. Percent - graphical examples and practice problems Writing Fractions as Percent - unit 4 from Ms. Glosser's Math Goodies
 Standard 2 Algebra Students will describe, extend, analyze, and create a wide variety of patterns and solve real-world problems using appropriate materials and representations. � Level 1 extend a pattern of geometric figures Spy Guys Interactive - Summarizing/Extending Patterns -  extend a numerical pattern using only whole numbers Calculating the nth Term - how to develop a formula that can be used to calculate these terms What Number Comes Next? - a FunBrain game with four levels (try SuperBrain) Level 2 solve a one-step linear equation with a variable on only one side of the equation (integral coefficients and constants) solve a two-step linear equation with a variable on only one side of the equation (integral coefficients and constants) translate a one-variable verbal expression into an algebraic expression (no more than two operations) evaluate a first-degree algebraic expression given the values for the variables (up to three variables) select the appropriate linear graph that models a real-world situation Level 3 select the number line graph that models a given one-step linear inequality (variables may not have negative coefficients) simplify a first-degree algebraic expression by combining like terms (integral coefficients and constants) Sample Task Use the internet or daily newspaper to find information regarding the stock results of one to five companies. Graphically demonstrate the histories of the companies for five to thirty days. Using the information found, predict the status of the company five to thirty days from now. Develop a range of the companies' stock values for the last five to thirty days, using inequalities. Write a scenario explaining why a company's stock changed drastically.
 Standard 3 Geometry Students will investigate, model, and apply geometric properties and relationships. Level 1 determine the perimeter of any geometric figure Level 2 identify the coordinates for a given point Simple Coordinates Game - Students investigate the first quadrant of the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted. General Coordinates Game - Students investigate the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted. Simple Maze Game - Students investigate the first quadrant of the Cartesian coordinate system by directing a robot through a mine field laid out on the plane. Maze Game - Students use their knowledge of points on a graph to move a robot to the target, while avoiding mines. Spy Guys Interactive - Using Ordered Pairs -  Worksheet Generator - print your own blank coordinate plane worksheets, and much more Other coordinate grids can be found at Data Illustrated (also look at their index of other printable resources ) Practice from Math.com: The coordinate plane , Slope and y-intercept , and Graphing linear equations . What's the Point? - a coordinate plane game from Funbrain.com (use the hardest level) Graphing Equations and Inequalities Unit Quiz 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 find the missing length of a side given two similar triangles Virtual Manipulative - Similar Triangles A Mathematical Droodle - Two Triples of Similar Triangles Level 3 use the Pythagorean Theorem to determine the length of a missing side of a right triangle (no radicals) Pythagorean theorem - In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics Demonstrate the Pythagorean Theorem - from NOVA Using the Pythagorean Theorem Once you know the equation a 2 + b 2 = c 2 is true, then you can use it to solve all kinds of problems. Try the Pythagorean theorem with two other examples given on this page Pythagorean Theorem - a java applet that allows students to investigate this theorem. 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. Proof of the theorem is demonstrated through a Quicktime animation. Pythagorean Theorem and its many proofs (43 to be precise) 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. Sample Task Students choose tessellating polygon shapes to design a quilt pattern. Students use the properties of similar triangles to investigate the height of trees, flagpoles, and other structures. Use Paint to Create a Tesellation - step by step instructions [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
 Standard 4 Measurement Students will become familiar with the units and processes of measurement in order to use various tools, techniques, and formulas to determine and estimate measurements in problem solving. Level 1 apply the given formula to determine the area of a rectangular figure with rational dimensions Level 2 calculate the cost per unit to determine the best buy (no more than three samples) Level 3 choose the correct area representation of the product of an integer and a one-variable first-degree binomial Sample Task Provide students a scale drawing of a room and have them calculate the amount and cost of various floor-covering. Give students a blow pop and have them measure the circumference. Have students rotate the blow pop in their mouths for two minutes. Measure the circumference again. Repeat this process five times. Plot time versus circumference and explain the change.
 Standard 5 Data Analysis and Probability Students will interpret a given set of data, including analyzing the use, misuse, and abuse of data; choose, construct, and analyze appropriate graphical representations for a data set; use technology in data collection and analysis; and apply theoretical and experimental probability to analyze the likelihood of an event. Level 1 determine the mean of a given set of data (no more than five two-digit numbers) 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. determine the number of possible outcomes for a simple experiment using a list, tree diagram, or the multiplication counting principle Working with Tree Diagrams [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] determine the probability of a single event (i.e. rolling a die and using a spinner) Coin Toss - The results of the coin tosses will appear in a pop-up window. If you have pop-ups disabled, you might have to check to see if another window opened in the background. Coin Toss - Simulation of a coin toss allowing the user to input the number of flips. Toss results can be viewed as a list of individual outcomes, ratios, or table 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. 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. Interactive Probability Tutorials: Sample Spaces and Events , Estimated Probability , Empirical Probability , Abstract Probability and Conditional Probability and Independence Level 2 interpret bar graphs representing real-world data Bar Graphs from the National Center for Education Statistics interpret circle graphs (pie charts) representing real-world data Pie Graphs from the National Center for Education Statistics determine the median from a given stem-and-leaf plot Stem & Leaf Plotter Level 3 determine the median of 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. select the measure of central tendency that best describes the given real-world situation Central Tendency - explanation of this concept and related concepts Measures of Central Tendency - tutorial and examples Measuring Central Tendency - explanation, examples and a large number of links to related topics [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Running and Weighted Averages - tutorial and examples Sample Task Survey 100 people on political candidates, favorite shows, etc. Create a frequency table and display the data.� Randomly sample the school population and survey those students to predict the opinions of other students on certain topics.

 Multiple Review Activities SOS Mathematics - Algebra lessonsAAAMath offers a large number of math review topics Practical Algebra Lessons from PurpleMath - The lessons give practical tips, hints, and examples, and point out common mistakes. National Library of Virtual Manipulatives - Virtual manipulatives Practice Tests from Virginia State Standards of Learning - Select Algebra I or II , and then select 10, 20, or 40 questions. Algebra Help - in-depth algebra help through algebra history, an online textbook, and various articles covering everything from basic algebra fundamentals to the latest-and-greatest algebra software help available Internet4classrooms is a collaborative effort by Susan Brooks and Bill Byles. 