End-of-Course - Foundations II

Sites to help students practice skills needed for the Foundations II exam

Links verified 4/14/2026

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

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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	Prime Factorization Chart - click on a number to see its prime factorization The 1000 smallest Prime Numbers How to Find the Prime Factorization of a Composite Number Using the Ladder Method Prime Factorization - how to find the prime factorization of a number
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
multiply a fraction by a multiple of its denominator (denominator less than or equal to 25)	Dividing fractions - Fraction Bar -This is a very versatile tool that can be used to illustrate a variety of number operations. How to Divide a Fraction by a Whole Number - Video Multiply Fractions with Different Denominators | Steps & Examples - Video explaining how to multiply fraction. Multiplying Fractions Using Cancellation - Video helping multiplying fractions with cross cancellation.
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 with Exponents - Math Goodies from Ms. Glosser
Level 2
identify the opposite of any rational number	Identifying Opposites and Absolute Value of Rational Numbers - Video Interactive Algebra Review on the topic of real numbers Identifying Opposites and Absolute Value of Rational Numbers - This is a PowerPoint show created by a teacher. You may pick and choose which slides you wish to work with in your classroom. Math Opposites of Rational Numbers - Video 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
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	Making Sense of Remainders when Dividing - Video - This lesson models 4 different types of problems that involve remainders when solving division word problems. Interpreting Remainders in Division Word Problems - Video - The lesson walks students through examples of each option and includes concrete modeling to increase conceptual understanding of interpreting remainders
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)	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.	10 Careers for People Who Love Math - Mathematicians have strongly developed logical skills and decomposition skills, they’re very organized, and they can more easily attack big-picture problems. Careers Using Math - Hundreds of careers use skills learned in high school math on a daily basis. The truth is virtually every career you could choose will build on the basic skills learned in High School Math. Routine Numeracy Skills in the Workplace - Video Real-life Applications of Numbers - Numbers are not only used in mathematics class, but they are also an important part of our daily lives.

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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.

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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	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)	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 An Interactive Proof of Pythagoras' theorem - This Java applet was written by Jim Morey. It won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995. Pythagorean Theorem and its many proofs (43 to be precise) Pythagorean theorem and right triangle facts - given the length of three sides, determine if a right triangle is being described
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.]

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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.

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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)
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)	Probabilistic Situations - a short slide show on the topic
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
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

AAAMath 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