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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.
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)
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
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.
Standard
2Algebra 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.
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.
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
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.
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.
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
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.
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 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
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
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.
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.
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
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.
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