Resources

**Fractions/Decimals/Percents**

Fraction Model



This resource enables students to see the connection between fractions, decimals, and percents. Students are able to use alter the numerator and denominator of a fraction and transform the representation to a decimal, percent, or mixed number. Students also have the potential to save numbers in a chart on the left with the purpose of comparing stored numbers. This applet relies on the use of multiple representations and student centered learning to further student understanding of numbers of various forms.

Resource Evaluation

** Free Ride **



The applet revolves around understanding how to add and subtract fractions in a real world situation. Students are pedaling a bicycle with the task of stopping on a number of different flags, each positioned on the number line. To land exactly on a flag the bike must move a specified distance. Students determine the distance by manipulating the bicycle gears. The ratio of the front gear to the back gear is the fraction with which the bicycle will move. The settings can be changed so that the flags are on fractions with different denominators or the same denominator. In both cases students need to be able to recognize the distance the bicycle needs to travel (by subtracting fractions), and determine the how to select the correct gear (often requiring students to recognize equivalent fractions).

Resource Evaluation

**Evaluating Expressions**

Evaluating Expressions with 2 Variables



This applet tests users on their ability to evaluate algebraic expressions with two variables. An expression is presented along with values for two varibales. Students are expected to substitute the values into the expression, simplify, and type the answer in the field provided. There is one example provided before the applet to remind students of the process. Also, there is immediate feedback provided for the students. Incorrect answers are deemed incorrect and the correct process is presented. Another key feature of this resource is that it tracks the percentage of correct answers and the amount of time spent completing problems. Reports can be created for keeping records of progress.

**Solving Equations**

Algebra Balance Scales



"Algebra Balance Scales" presented users with the opportunity to input a problem and model the step by step actions of solving the problem. Students are able to create and input a problem with one constant and one coefficient on each side of the equation. By dragging variables and numbers to each side of the balance scale the equation can be represented visually. Once the problem is modeled there is an option to continue to solve the equation. The applet presents the user with the option of adding, subtracting, multiplying, or dividing an amount from both sides of the equation. Once this is entered the balance scales will reflect the step taken. This allows students to understand if their step progressed the problem towards a solution or was unnecessary. When the equation is solved the applet will notify the user that the solution is correct. The steps are kept displayed at the top of the balance scales which allows students to see the order of all of the steps taken to arrive at the solution.

Resource Evaluation

Algebra Quiz



This “Algebra Quiz” offers differentiated instruction for students of all abilities. Users are able to customize the time limit for each question or determine to not set a time limit at all. Also, students are able to select the difficulty of the questions (relating to the complexity of numbers used). The applet also enables students to specify the types of problems with which they wish to focus. The problem types include variables on both sides, distributive property, quadratic, two step equation, and one step equation. Once the quiz begins randomized questions arise and students are given immediate feedback on their accuracy. If a user is incorrect the correct answer is given, yet there is no rationale given for the correct answer. Instead, there are links to activities that demonstrate to students how to solve the various types of equations. The applet also allows users to track their overall progress through a “scoreboard” which breaks down their overall accuracy by topics and difficulty.

Absolute Value Quiz



The resource quizzes users on absolute value equations. Equations of varying difficulty are presented. Some equations have absolute value expressions on both sides, others have constants within the absolute value, and others have constants outside of the absolute vale. Students enter the possible answers in the spaces provided. Equations with no solution are also presented and students are instructed to leave the answer field blank in this case. The applet keeps track of the number correct and incorrect. Below the applet there are links to notes on solving absolute value equations, which contain multiple examples and written directions.

Distance, Rate, and Time



This resource presents students with a bank of application problems involving distance, rate, and time. The applet takes the students step by step through the problems. Each problem begins with the given. Next, the applet describes the symbolic representation of two aspects of the real world phenomena alongside written rationale. Finally, the applet constructs an equation and solves for the missing information. After following through this process several times students become aware of the steps and work towards predicting the next step and the rationale before it is provided by the applet. The major aim is enabling students to decode application problems and construct expressions and equations that lead to a solution. Following the applet there is a link to another page which explains distance, rate, time, and their connectedness in greater depth.

Resource Evaluation

**Graphing Linear Equations**

Point Plotter



This resource quizzes a user on plotting points in the coordinate plane. Three ordered pairs are presented and the user is required to plot the three points on the graph by clicking on the graph. Once the points are on the graph, students will be able to drag them around. Once all three points are plotted students are able to check their answers. Immediate feedback is presented to students on the accuracy of their plotting. It is assumed that students already have learned how to plot points. When students are incorrect there are no hints or guidance provided. The appearance of grid values is optional, which allows user to prepare to graph on labeled axes and unlabeled axes.

Line Plotter



"Line Plotter" is an applet that requires users to graph a line when given one point on the line and the slope of the line. This practice applet provides slopes that are not always in reduced form, which allows students to see the connection between equivalent fractions. In the directions for the applet students receive a brief example of how to use rise/run to graph linear equations. Students click on the graph to create the two points and can manipulate the line by dragging. Once the line is created students are able to check their answers with immediate feedback. The feedback does not inform students if the original point was incorrect or if the second point (obtained from the slope) was incorrect. When incorrect students are able to try again and refer back to the directions for a bit of support.

<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Line of Best Fit



<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resource enables user to practice finding the line of best fit for a scatter plot. Students can plot points by entering a coordinate pair or by clicking on the coordinate plane itself. Data can also be copied and pasted from spreadsheets and then plotted. Once points are plotted they can be dragged around the plane. When all of the points are plotted the application allows user to determine their best guess of the line of best fit by manipulating a line which is presented. By clicking the "computer fit" feature students can compare their guess to the least squares regression line. Once the least squares regression line is visible students are able to experiment with the the line by adding and removing points. This enables users to gain a better understanding of how the line of best fit will be affected as the scatter plot changes. This resource also allows students to find the line of best fit with real world data from the NBA and analyze how the removal of data affect the line of best fit and the correlation coefficient.

Resource Evaluation

<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Block Patterns



<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">“Block Patterns” allows users to create sequences of figures with various shapes. Once a pattern is constructed students use the pattern to create a table comparing the number in the sequence with another attribute such as perimeter or area. This bridges the gap between graphs and real world phenomena. Once the table is completed the points can be plotted on the graph automatically. The final component of this resource is the ability for students to graph a function by inputting the rule. This enables students to determine the rule for a function though the use of the table and allows them to graph the function to ensure it is aligned with the points determined by the figures. Thus, this resource truly connects the multiple representations (tables, graphs, equations) of lines.

<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Sack Race



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This applet revolves around the concepts of slope, systems of equations, and piecewise linear functions. Two functions are provided, each representing a relationship between distance and time. Users are able to manipulate one of the two functions according to directions provided in a PDF. Teachers could also easily create their own direction for this applet. By manipulating the starting point of the function and the slope of different pieces of the function, the corresponding animation of the sack race is altered. This allows students to gain a better understanding of rate of change and how graphs correspond to real world phenomena. The line can also be manipulated so that the two linear equations intersect. This will enable the animation of the sack race to reinforce the idea that a solution to a system represents when two equations or positions are equal. There are many possibilities for this applet which furthers understanding of real world application through rate of change, piecewise functions, systems of equations and the connection between a graph and its corresponding animation.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: center;">Resource Evaluation

<span style="color: #000080; display: block; font-family: arial,helvetica,sans-serif; font-size: 180%; text-align: center;">**Ratios and Proportions**

Math Snacks: Overruled



This resource features a six minute video centered on two kingdoms (one ruled by a King and one ruled by a Queen) attempting to build a bridge. It is agreed upon that half of the bridge will be built by each kingdom. During the construction, the bridge does not meet in the middle of the water due to the fact that each kingdom measures a foot by the king's/queen's foot size. This causes a discrepancy in the height of the bridge. The video then provides the ratio of kings feet: queens feet and uses a table and a graph to demonstrate how each unit can be converted to one another so that both kingdoms will be able to use their unit of measure to build the bridge. After the video there is a supplemental resource for students. The worksheet provides students with a different ratio and encourages students to correct an error in a table which models the relationship between the two units of measure. Students are also required to graph the situation using the table. Finally, a third situation is presented and students are required to create two tables and graphs - one for each kingdom. This also requires labeling of the axis and identification of the dependent and independent variables.

Resource Evaluation

<span style="color: #000894; display: block; font-family: 'arial black',gadget,sans-serif; font-size: 180%; text-align: center;">**Writing Linear Equations**

<span style="color: #000894; display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Parallel and Perpendicular Lines



<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resource tests student understanding of equations of lines, x-intercepts, y-intercepts, parallel lines, and perpendicular lines. The applet requires users to determine the equation of a line when randomly provided with two pieces of information. For instance, students may be given a line parallel to the line in question, and may be given the x-intercept of the line in question. In this case students would need to have an understanding that the x-intercept comes in the form (x,0), would need to be aware that parallel lines have the same slope, and would need to be able to effective use substitution with the equation of a line (y=mx+b). Other combinations of information would require the students to utilize different concepts, yet the end result of finding the equation of the line remains the same. Students are quizzed on finding the equation of a line when given various pieces of information. Students are finding lines in the form y=mx+b, y=a, and x=b. The applet provides the students with immediate feedback on the accuracy of their equation. When the student is correct the applet with graph the line along with the provided information so that the student receives a visual of how the information provided relates to the equation of the line. Additionally, there is a link at the bottom of the page to a step by step tutorial on how to write the equation of a line under varying circumstances.

Resource Evaluation

<span style="color: #000894; display: block; font-family: 'arial black',gadget,sans-serif; font-size: 180%; text-align: center;">**Solving/Graphing Linear Inequalities**

<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">**Solving Inequalities**

<span style="color: #000000; display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resource quizzes students on two step inequalities with one variable. It is expected that students have already learned how to solve inequalities, as there is only one example provided before the quiz. The students are given an inequality and the inequality sign and are required to fill in the number that the variable is either less than or equal to. The applet provides immediate feedback on the accuracy of the answer. If the answer submitted is correct the resource states that. If the answer submitted is incorrect then the correct answer is given. The applet additionally keeps track of the percentage of questions correct and the amount of time spent on the quiz. Users can generate a report with these facts as well.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Linear Inequalities



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This applet enables users to graph systems of linear inequalities. Students are able to graph up to four linear inequalities in standards form by inputting the coefficients, the constant value, and the inequality sign. Once the linear inequalities are entered users are able to view the equation when y is solved for and when x is solved for. This enables students to determine if they correctly manipulated the equation to standard form. The resource graphs the linear inequalities and shades with multiple colors to demonstrate the solution points. Students are also able to enter coordinate pairs and the applet will graph the points. This enables users to visually test is a point is a solution to the system of linear inequalities.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: center;">Resource Evaluation

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Absolute Value Inequalities



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This applet allows users to manipulate an absolute value inequality and view how the corresponding graph is altered. Students are able to change a number subtracted from the variable in the absolute value, the absolute value sign, as well as the constant on the other side. Once the numbers are entered the graph will reflect the changes. This allows students to investigate how different factors affect change in an absolute value inequality. Below the applet there are guiding question to encourage critical thinking by the students, as well as links to another page with examples and an explanation of how to solve absolute value inequalities.

<span style="color: #000894; display: block; font-family: 'arial black',gadget,sans-serif; font-size: 180%; text-align: center;">**Solving and Graphing Systems**

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Systems of Equations



<span style="font-family: 'Calibri','sans-serif'; font-size: 15px;">This resource enables users to explore systems of equations through graphing. Students are able to manipulate the slope and y-intercept of two different linear equations. As the students alter the lines, the equations of the lines and the graphs change accordingly. Students can also enable the feature to “show solutions” so that as the lines are manipulated the solution to the system is shown to change as well. Users are not able to see a solution when it is outside of the window or when the solution has no solution or infinitely many solutions.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Systems of Linear Inequalities



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">The focus of this applet is graphing systems of linear inequalities. Users are able to create up to five different linear inequalities in either slope intercept form, standard form, or with x isolated. All of the linear inequalities can be altered by manipulating the constant and coefficients of the formulas (with the use of a slider) and by changing the inequality sign. As the inequalities are altered so are the corresponding graphs and the set of solutions to the system of inequalities. This enables users to explore how different aspects of equations affect graphs of lines and solutions to systems of linear inequalities. Once all of the linear inequalities are graphed, points can be checked as solutions by dragging the mouse over the graph. The applet informs the user if a given point is a solution to none of the inequalities, one of the inequalities, and so on. The “trace” feature actually provides users with all of the algebraic steps one would take to test if a point is a solution to a linear inequality. This feature provides much detail but can only be used for one linear inequality at a time.

<span style="color: #000894; display: block; font-family: 'arial black',gadget,sans-serif; font-size: 180%; text-align: center;">**Exponents**

<span style="color: #000894; display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Laws of Exponents



This resource provides users with definitions of a base and an exponent, and examples of the many laws of exponents. Bases to the first power, bases to the zero power, multiplication of powers with the same bases, and a power raised to an exponent are all discussed in detail. The laws are presented with variables, examples are given with numbers and there are written explanations as well. Negative exponents and fractional exponents are also explained in detail. Quiz questions are presented at the end of the lesson. The applet that accompanies this resource allows students to increase and decrease the base of a power to a positive or negative integer, as well as increasing the exponent of a power to either a positive or negative. The applet uses the base and exponent to produce the answer as well as the long version of all of the terms either being multiplied or divided. This enables students to better understand how increasing and decreasing exponents and bases affects the overall result of a power.

Resource Evaluation

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Practice With Exponents



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resources allows for differentiated practice with the laws of exponents. Students are able to choose the difficulty level of each question. The easy questions involve the power to product rules and the product to sum rule. The medium level questions add in more complex questions with the quotient to difference rule. Finally, the difficult questions require students to combine numerous rules to to a final answer. Students are presented with the bases and are required to input the exponents for each power. The applet then provides immediate feedback on the answer given. If all of the exponents are wrong the applet will suggest that you drop down to the lower level for practice. If only part of the answer is wrong the applet will provide the user with hints as to what went wrong and what rules should be applied to receive the correct answer. The personal feedback per question is excellent. Below the applet there is a link to the set of exponent rules. The rules are given, yet there is no rationale behind the rules provided.

<span style="color: #000894; display: block; font-family: 'arial black',gadget,sans-serif; font-size: 180%; text-align: center;">**Factoring**

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Algebra Tiles



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resource enables users to work with algebra tiles to model factoring, the distributive property, evaluating expressions, and solving equations. When factoring and distributing there is a row and a column for students with which enter the two monomials/binomials. Once these are represented with tiles a box is formed where the factors need to be placed. Students then use the tiles to represent the answer and type the answer in the solution box. Immediate feedback is given based on if the factor or distribution is correct. The substitution feature of the applet allows students to represent an expression with tiles, substitute numbered tiles for the variable and then simplify the expression. Again, immediate feedback is given on the accuracy of the evaluation. Solving equations revolves around a similar process. Students represent the equation with variables and number tiles. Students are then expected to solve by adding or removing the same tiles from each side of the workspace. The process of adding tiles, removing tiles, and changing from positive to negative tiles is a bit complex. There are detailed directions provided above the applet.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: center;">Resource Evaluation

<span style="color: #000894; display: block; font-family: 'arial black',gadget,sans-serif; font-size: 180%; text-align: center;">**Quadratics**

** Grapher **

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This applet allows students to graph three different functions simultaneously and color coordinate the functions for easy viewing. Students have the options of graphing several families of functions. There are options that enable the graphing of linear functions, quadratic functions, exponential functions, square root functions, rational functions, and absolute value functions. For all of the aforementioned functions, the graphing window can be altered, graphs can be zoomed on, and the domain can be specified. Additionally, the constants a, b, and c can be inserted as part of functions. Parameters can be placed on these variables. Their incorporation into a function allows the user to drag the slider and manipulate their value as the graph simultaneous is manipulated. There is also the option to use a slider to trace points on the graph as the x-value varies. This allows for users to find intersection points of two functions that are graphed concurrently.

Lesson Plan

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Quadratic Equation Solver



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resource allows users to manipulate the a, b, and c values of a quadratic equation in standard form. As this is done the corresponding graph of the quadratic function and its characteristics are also altered. The applet provides students with the roots, the discriminate, the vertex, the factored form, the sum of the roots, and the product of the roots. Complex roots are also given and students are able to view the graph and its lack of zeros. This resource additionally explains to students the various forms of quadratic, how solutions are derived through the use of the quadratic formula, the relevance of the discriminate, and what complex solutions mean. This resource could be used as an explorative tool with the applet, or as a teaching tool with the examples and explanations of quadratics.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 20px; text-align: center;">Completing the Square



<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: left;">This resource takes students through the process of completing the square. Problems are presented with varying difficulty from when a=1 to when a>1. Written directions are presented and students are required to fill in the missing numbers. First students are required to “move the constant term to the right”. Immediate feedback is provided on the accuracy of the step. If the user inputs the correct answer the next step is presented. If the answer is not correct there is specific feedback to the error and students are given another attempt to correct the mistake. As the students progress they will perform the following steps with directions from the applet: “add the magic number to both sides”, “factor the left hand side and simplify the right hand side”, “take the root of both sides”, and “finally solve for x”. On all of the steps there is immediate feedback which is specific to the step. When finding the magic number the applet will inform students if they forgot to square the number or to divide by two. The feedback is very detailed. For students to better understand the process there is a link after the applet to another page, which describes the rationale for each step.

<span style="display: block; font-family: 'times new roman',times,serif; font-size: 14px; text-align: center;">Resource Evaluation