Standard
1 - Number and Operations
Students will recognize, represent, model, and apply real numbers and operations and will demonstrate an understanding of properties and operations of the complex number system. |
| Level 1 |
order a given set of real numbers
|
- Comparing Seven Digit Numbers - practice area followed by an interactive game
- Rational and Irrational number review
|
identify the reciprocal of a real number |
- Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math
- How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
|
multiply two polynomials with each factor having no more than two terms. |
- Interactive Algebra Review - Multiplying Algebraic Expressions
- Multiplying Polynomials - a step-by-step explanation from PurpleMath
- Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial)
- Factoring Trinomials Self Quiz - Check your knowledge about factoring polynomials.
- 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.
|
Level 2 |
perform basic operations using complex numbers (i.e., addition, subtraction, and multiplication)
|
- A 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
|
select a graph that represents an absolute value equation on a coordinate plane |
- Absolute Value lesson from Purple Math
- Solving Absolute Value Equations - a lesson from Purple Math
|
identify the exponential form of a logarithmic expression and vice versa |
|
simplify expressions with rational and negative exponents |
- Converting Numbers to Scientific Notation - AAA Math lesson and practice problems &
- 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
- Scientific Notation - interactive practice
- 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
|
add, subtract, and multiply algebraic expressions. |
|
Level 3 |
determine the conjugate of a complex number |
|
Sample Task |
design and build a simple fractal from available materials |
|
Standard
2 Algebra
Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving, and will demonstrate an understanding of the behavior of a variety of functions and their graphs.
|
| Level 1 |
translate a verbal sentence into an algebraic equation and vice versa
|
- 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)
|
select the algebraic equation that generalizes the pattern represented by data in a given table |
|
solve multi-step (more than two steps) linear equations (one set of parentheses on each side of the equations and/or variables on both sides) |
-
Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
|
select the graph that represents a given linear function expressed in slope-intercept form |
- Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them
- 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.
-
 Slope Intercept Jeopardy review game in the form of a PowerPoint show
- Another Slope Intercept Jeopardy review game in the form of a PowerPoint show
|
select the graph that models a given real-world situation (i.e., linear and non-linear) |
|
identify the graphical representation of the solution to a one-variable inequality on a number line |
- Number Line Bounce - use all the arrows to bounce back and forth along the number line to reach a target number
- Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included
|
| Level
2 |
select functional notation to generalize a given numeric pattern
|
-
Calculating the nth Term - how to develop a formula that can be used to calculate these terms
- Multiple-Choice Questions – twenty (20) questions on Patterns & Functions
|
solve one-variable linear equations with rational expressions |
|
select the graph of a two-variable inequality |
|
determine the domain of polynomial, rational, square root, exponential and logarithmic functions |
- Simplifying Radical Expressions - Intermediate Algebra tutorial
- Simplifying Radicals - explanation and practice problems
|
determine the range of a wide variety of functions given a graph |
|
solve a system of linear equations with 2 variables (e.g. substitution, elimination, Cramer’s Rule, and graphing) |
|
apply properties of logarithms to simplify a logarithmic expression |
- Properties of Logarithms from SOS Math
- College Algebra - a tutorial on Logarithmic Properties with several examples and practice problems
- Basic Log Rules from Purple Math
|
identify matrices that model given real-world situations |
|
| Level
3 |
determine the inverse of a logarithmic function given its graph
|
- Exponential functions - a review of logarithms from SOS Math
- Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes
|
Sample Task |
examine patterns found in Pascal’s Triangle |
|
Standard 3 Geometry
Students will investigate, model, and apply geometric properties and relationships |
| Level 1 |
apply the given Pythagorean Theorem to real-world problems
|
- Animated Proof
of the Pythagorean Theorem
- Demonstrate
the Pythagorean Theorem - from NOVA
- 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.
- Nineteen
Pythagorean Theorem applets
-
Pythagorean theorem - In this session, you will look at a few proofs
and several applications of one of the most famous theorems in mathematics
- Proof
of the theorem is demonstrated through a Quicktime animation
- Pythagorean
Theorem - a java applet that allows students to investigate this
theorem
- Pythagorean Theorem
- This lesson will allow you to figure out the Pythagorean Theorem all
by yourself.
- Pythagorean
Theorem and its many proofs (43 to be precise)
- The Pythagorean
Theorem, Distance Formula and Intro to Trigonometry - other practice
activities
- Using
the Pythagorean Theorem Once you know the equation a2
+ b2 = c2 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 - In this investigation students will learn more about the
Pythagorean Theorem and see whether or not it works for triangles that
are not right triangles.
|
| Level 2 |
predict the graphical transformation that occurs when coefficients and/or constants of given function are changed (no trigonometric or logarithmic functions)
|
|
apply proportion and the concepts of similar triangles to solve real world problems |
- Geometry Java Applets - Similar Figures
- A Mathematical Droodle - Two Triples of Similar Triangles
- Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies
- Plane Math - Nine activities involving aviation and mathematic
- 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
- Virtual Manipulative - Similar Triangles
|
| Level
3 |
describe the transformation that has changed a “parent function” to the given related function (e.g., right shift of 3 units, reflection in the x-axis)
|
|
Sample Task |
use properties of similar triangles to determine the height of objects that are difficult to measure |
- Determining The Height Of A Waterfall - In research on waterfalls often the most confusing aspect has been determining the true height of a waterfall.
- How to use the distance formula to find distances between (x,y) points
- Object Height Calculator - Use the SCSA Object Height Calculator to calculate the height of tall shadow-casters, e.g., buildings, flagpoles, utility poles, trees, etc.
- Out of the Shadows: The Problem of Slopes - Knowing the sun's elevation is not enough to determine the height of an object from the length of its shadow; the slope of the surface on which the shadow is being cast must also be known.
- Measured Altitude of a Model Rocket - a simple way to determine the maximum altitude the rocket reaches at the end of the coasting flight
- Measured Altitude of a Kite - a simple way to determine the altitude of a flying kite
|
Standard 4 Measurement
The student will understand and be able to apply the units, systems and processes of measurement. |
| Level 1 |
select the area representation for a given product of two binomials
|
|
| Level 2 |
apply the given formula to find area and circumference of circles, area and perimeter of polygons, and volume of regular solids |
- Lesson on Circumference of a Circle - a quiz is included at the bottom of the page
- Lesson on the Area of a Circle
- Circle, Sphere & Cylinder Calculator
|
| Level
3 |
solve real world problems given logarithmic and exponential formulas (e.g. Ph scale, Richter scale.)
|
|
Sample Task |
Students construct designs using basic geometric constructions. Then they transfer the design to a piece of 8" X 11" pane of plexiglas and paint the pane to create a “stained glass.” Students construct one of the regular 3-dimensional solid and compute the volume and surface area.
|
|
Standard 5 Data Analysis and Probability
The student will collect, organize, represent, and interpret data; make and evaluate inferences and predictions; present and evaluate arguments based on data analysis; and model situations to determine theoretical and experimental probabilities. |
Level 1 |
make a prediction from the graph of a real-world data set
|
- Connecting Equations to Real-World Situations
- Graphs and charts - four different graphs and charts for you to consider
- 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
- Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem
- 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.
- 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.
|
determine the measures of central tendency for a given set of real-world data |
- 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
- Running and Weighted Averages - tutorial and examples
|
choose the matching linear graph when given a set of ordered pairs representing real-world data |
|
|
categorize the correlation of a scatter plot using real-world data (i.e., positive, negative, strong, or weak)
|
- 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
- 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
|
determine the number of possible outcomes for a given experiment (i.e. the multiplication counting principle, permutations, or combinations) |
|
determine the theoretical probability of a simple event for a given situation |
- 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.
|
determine the theoretical probability of a compound event (i.e., dependent or independent, union and intersection) |
|
Level 3 |
find the equation for the line of best fit given a scatter plot depicting real-world data |
- see a list above
|
Sample Task |
| Students analyze real-world data collected from the newspaper and explore and report the uses, misuses, and abuses of reported statistical data. Students search the internet to collect age and market value of a selected vehicle over a specific period of time. They use a graphing calculator to create a scatter plot and construct a line of best fit to predict the depreciation of the vehicle. |
- 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.
- List of Data Sources on the Internet4Classrooms Project page
- Review of tables, charts and graphs - an index of topics
- Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body - 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.
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