2. Algebra (A)
Seventh Grade
Understand and Apply Directly Proportional Relationships and Relate to Linear Relationships
- A.PA.07.01 Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship.*
- Determining Ratios - This is an interactive site where students can reduce the given ration into lowest form. The student receives immediate feedback to their answer. If the solution is correct you move on to a different problem. If the solution is incorrect the students are told why there answer is wrong.
- Dot Patterns and Sierpinski Gasket - This site allows you to generate the Sierpanski Triangle. You can enlarge the triangle one row at a time allowing you to see the changes at each stage of the triangle.
- Doubling Pennies - This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
- Lesson Plans: How Big is That Star? - This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
- Paper Pool Games - Number and Operations - Number Sense and Numeration - This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
- Play Pool on Different Sized Pool Tables - In this interactive activity students will predict which pocket the pool ball will go into as well as the number of hits needed to sink the ball. By changing variables they will see patterns and generalizations to aide them in their predictions. Data will be represented by a model as well as a spreadsheet and a graph.
- Proportion Basics - This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
- Ratios - This is an interactive math site where students solve for ratios. The students are given a ratio and one part (either the numerator or denominator) of another ratio. The students then have to solve for the missing expression. They are given immediate feedback to their answers.
- Rectangle Pattern Challenges - This site explores patterns in rectangles and then has students organizing the data they find into a table. Also has discussion questions at the end. Use as whole class instruction or print off for individual use.
- Waldo's Interactive Math - This interactive site allows students to manipulate triangles on a coordinate graph in order to explore their relationship. The site relies on Java applets.
- A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.
- Bouncing Tennis Balls - This is a lesson plan that has the students graph information found by bouncing a tennis ball. They will use this information to determine the dependent and independent variables.
- Determining Ratios - This is an interactive site where students can reduce the given ration into lowest form. The student receives immediate feedback to their answer. If the solution is correct you move on to a different problem. If the solution is incorrect the students are told why there answer is wrong.
- Dot Patterns and Sierpinski Gasket - This site allows you to generate the Sierpanski Triangle. You can enlarge the triangle one row at a time allowing you to see the changes at each stage of the triangle.
- Doubling Pennies - This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
- Lesson Plans: How Big is That Star? - This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
- Online Graphing - Outstanding - Will graph functions like a graphing calculator would do, only easier. Great for those without access to graphing calculators.
- Paper Pool Games - Number and Operations - Number Sense and Numeration - This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
- Play Pool on Different Sized Pool Tables - In this interactive activity students will predict which pocket the pool ball will go into as well as the number of hits needed to sink the ball. By changing variables they will see patterns and generalizations to aide them in their predictions. Data will be represented by a model as well as a spreadsheet and a graph.
- Proportion Basics - This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
- Principles and Standards for School Mathematics: Learning about rate of change - Students interact with 2 line graphs, one with a constant variable, the other with 2 changing variables. They answer questions to learn about change and linear graphs.
- Ratios - This is an interactive math site where students solve for ratios. The students are given a ratio and one part (either the numerator or denominator) of another ratio. The students then have to solve for the missing expression. They are given immediate feedback to their answers.
- Rectangle Pattern Challenges - This site explores patterns in rectangles and then has students organizing the data they find into a table. Also has discussion questions at the end. Use as whole class instruction or print off for individual use.
- Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
- The Hand Shake - A data collection and analysis class experiment. Use a table to show the number of handshakes when every person in the room shakes hands with everyone else.
- The Rich Get Rich - Students complete a chart which explains whether it would be better to take $1,000,000 or take $0.01 the first day and have it doubled every day after that. There is a story that the students follow to get to the answer.
- Waldo's Interactive Math - This interactive site allows students to manipulate triangles on a coordinate graph in order to explore their relationship. The site relies on Java applets.
- A.PA.07.03 Given a directly proportional or other linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit.*
- Bouncing Tennis Balls - This is a lesson plan that has the students graph information found by bouncing a tennis ball. They will use this information to determine the dependent and independent variables.
- Determining Ratios - This is an interactive site where students can reduce the given ration into lowest form. The student receives immediate feedback to their answer. If the solution is correct you move on to a different problem. If the solution is incorrect the students are told why there answer is wrong.
- Lesson Plans: How Big is That Star? - This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
- Paper Pool Games - Number and Operations - Number Sense and Numeration - This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
- Principles and Standards for School Mathematics: Learning about rate of change - Students interact with 2 line graphs, one with a constant variable, the other with 2 changing variables. They answer questions to learn about change and linear graphs.
- Proportion Basics - This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
- Ratios - This is an interactive math site where students solve for ratios. The students are given a ratio and one part (either the numerator or denominator) of another ratio. The students then have to solve for the missing expression. They are given immediate feedback to their answers.
- Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
- A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed.
- Ask Dr. Math - This site gives students a number of algebraic word problems to work. Ask Dr. Math is a great site for students to receive feedback to enhance their understanding of the problems.
- Figure This! Math Challenges for Families - Figure This! Mathematics challenges for families provides interesting math challenges that middle-school students can do at home with their families. Each challenge features a description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a "Try This" section, additional relational related problems with answers, questions to thinks about, fun facts related to the math, and resources for further exploration. Math challenges #3 and 4 are examples of problems that would help teach this particular objective.
- Illuminations Fraction - Percent, Decimal Model - This tool explores several representations for fractions using adjustable numerators and denominators. You can see decimal and percent equivalents, as well as a model that represents the fraction.
- Lemonade Stand - Students run a virtual lemonade stand. The goal of the student is to make as much money as they can in 30 days. Students have control over every part of the business, including pricing, quality control, inventory control, and purchasing supplies. The game also mentions outside factors such as weather and how that would affect business.
- Math.Com (Geometry) - An informational site for teachers and students. There is some interaction for students in the lessons. Students can participate in quizzes at the end of each section. This is the general site for geometry. You will need to choose the area of interest. Great site for middle school geometry.
- Math for Morons Like Us - Algebra - Word Problems - This site provides explanations, examples, and vocabulary definitions that can be used in solving word problems using algebraic equations. As follow-up the student can take a short quiz that includes an explanation of what problems were missed and what was done wrong. This site contains general information and is a student activity.
- Problem Solving - Interactive game. Great fun with problem solving skills required. Also, pattern and grid coordinates are tested to escape from the dungeon.
- Shape Explorer - Students can interact with area and perimeter on various shapes. Students will enjoy interacting with various shapes and observing how perimeter and area are both calculated and relate.
- Solving Word Problems - Interactive word problem site. Helps with students translation of word problems into a numeric equation. Students get instant feedback with the exercises on this site.
- Webmath - This site allows the students to see how math is used in everyday life. The student has access to calculators that figure out restaurant tips, sale prices, windchill, electric bills, simple interest, compound interest, retirement, loans and stocks. The student is active in figuring these things out.
- Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
- A.PA.07.05 Recognize and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity.*
- Determining Ratios - This is an interactive site where students can reduce the given ration into lowest form. The student receives immediate feedback to their answer. If the solution is correct you move on to a different problem. If the solution is incorrect the students are told why there answer is wrong.
- Figure This! Math Challenges for Families - Figure This! Mathematics challenges for families provides interesting math challenges that middle-school students can do at home with their families. Each challenge features a description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a "Try This" section, additional relational related problems with answers, questions to thinks about, fun facts related to the math, and resources for further exploration. Math challenges #3 and 4 are examples of problems that would help teach this particular objective.
- Lesson Plans: How Big is That Star? - This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
- Math.Com (Geometry) - An informational site for teachers and students. There is some interaction for students in the lessons. Students can participate in quizzes at the end of each section. This is the general site for geometry. You will need to choose the area of interest. Great site for middle school geometry.
- Paper Pool Games - Number and Operations - Number Sense and Numeration - This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
- Proportion Basics - This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
- Ratios - This is an interactive math site where students solve for ratios. The students are given a ratio and one part (either the numerator or denominator) of another ratio. The students then have to solve for the missing expression. They are given immediate feedback to their answers.
- Shape Explorer - Students can interact with area and perimeter on various shapes. Students will enjoy interacting with various shapes and observing how perimeter and area are both calculated and relate.
- Soda Constructor - This is a very interactive site in which the students will have the opportunity to actually construct shapes. The teacher must give directions of what shape the students are to construct and the teacher can also request the shape to be something that represents something in our physical world.
Understand and Represent Linear Functions
- A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and express the answer as a fraction and a decimal; under- stand that linear functions have slope that is a constant rate of change.
- Determining Ratios - This is an interactive site where students can reduce the given ration into lowest form. The student receives immediate feedback to their answer. If the solution is correct you move on to a different problem. If the solution is incorrect the students are told why there answer is wrong.
- Lesson Plans: How Big is That Star? - This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
- Paper Pool Games - Number and Operations - Number Sense and Numeration - This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
- Proportion Basics - This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
- Ratios - This is an interactive math site where students solve for ratios. The students are given a ratio and one part (either the numerator or denominator) of another ratio. The students then have to solve for the missing expression. They are given immediate feedback to their answers.
- A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.
- Ask Dr. Math - This site gives students a number of algebraic word problems to work. Ask Dr. Math is a great site for students to receive feedback to enhance their understanding of the problems.
- Determining Ratios - This is an interactive site where students can reduce the given ration into lowest form. The student receives immediate feedback to their answer. If the solution is correct you move on to a different problem. If the solution is incorrect the students are told why there answer is wrong.
- Lesson Plans: How Big is That Star? - This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
- Math for Morons Like Us - Algebra - Word Problems - This site provides explanations, examples, and vocabulary definitions that can be used in solving word problems using algebraic equations. As follow-up the student can take a short quiz that includes an explanation of what problems were missed and what was done wrong. This site contains general information and is a student activity.
- Paper Pool Games - Number and Operations - Number Sense and Numeration - This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
- Proportion Basics - This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
- Ratios - This is an interactive math site where students solve for ratios. The students are given a ratio and one part (either the numerator or denominator) of another ratio. The students then have to solve for the missing expression. They are given immediate feedback to their answers.
- Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
- A.FO.07.08 Find and interpret the x and/or y intercepts of a linear equation or function. Know that the solution to a linear equation of the form ax+b=0 corresponds to the point at which the graph of y=ax+b crosses the x axis.*
- Algebra - Fun with Calendars - A fun mathematical puzzle that shows students a use for algebra. By using a simple linear equation students can determine what four days on a calendar someone has chosen.
- Grap Mole Game - Introduction to Coordinate plane. Learn about the X and Y axis and how to plot points on the graph. Game comes in different levels of difficulty. The game is a good review, students will have fun while learning coordinate plane.
- Linear Inequalities - Manipulate and visualize the solution sets of linear inequalities in slope-intercept form.
- Slope Intercept Form - Interactive tool to experiment with the slope and intercept of a line. See how the slope of a line is calculated.
- Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
- A.PA.07.09 Recognize inversely proportional relationships in contextual situations; know that quantities are inversely proportional if their product is constant, e.g., the length and width of a rectangle with fixed area, and that an inversely proportional relationship is of the form y = k/x where k is some non-zero number.
- Bouncing Tennis Balls - This is a lesson plan that has the students graph information found by bouncing a tennis ball. They will use this information to determine the dependent and independent variables.
- Function Machine - Students are able to enter a number to represent the variables and then determine what function is taking place. The activity explains linear functions and allows the students to ask how, what, and why for solving the problem.
- Graphing and the Coordinate Plane - This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane. Students will be able to give the rise over run for slope.
- Linking Length, Perimeter, Area, and Volume - This is a lesson plan where students will work with 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters or area of similar figures. Graphs are drawn for students to visualize the linear and non-linear relationships of perimeter, area, and scale factor.
- Mathline: The Yo-Yo Problem - Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator.
- A.RP.07.10 Know that the graph of y = k/x is not a line, know its shape, and know that it crosses neither the x nor the y-axis.
- Bouncing Tennis Balls - This is a lesson plan that has the students graph information found by bouncing a tennis ball. They will use this information to determine the dependent and independent variables.
- Function Machine - Students are able to enter a number to represent the variables and then determine what function is taking place. The activity explains linear functions and allows the students to ask how, what, and why for solving the problem.
- Graphing and the Coordinate Plane - This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane. Students will be able to give the rise over run for slope.
- Linking Length, Perimeter, Area, and Volume - This is a lesson plan where students will work with 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters or area of similar figures. Graphs are drawn for students to visualize the linear and non-linear relationships of perimeter, area, and scale factor.
- Mathline: The Yo-Yo Problem - Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator.
- A.PA.07.11 Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition.
- Algebra Help - This site gives students a step by step description of description of distributive property, order of operations solving equations, combining like terms, F.O.I.L method, simplifying exponents, and substitution method of solving equations. Students have an opportunity to work on problems after the short lessons. This site has many different calculators available that will show all work on a problem typed in by the student just like a student would do the work.
- E-Lab: Two Step Equations - Students will apply the additive inverse and multiplicative inverse properties to solve two-step equations.
- Molecular Expressions, Science, Optics, and You - This site takes you through a step by step lesson to teach powers of 10 and has an interactive applet that allows you to view several things under a microscope!
- The National Science Center - Concepts and Properties of Numbers (IV.1.MS.3) - This site gives a lesson plan for an activity to discover the value of pi. Students will use measuring and averaging, and hopefully discover the value of pi.
- A.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) – 5x + y, or x(x+2) and justify using properties of real numbers.*
- E-Lab: Two Step Equations - Students will apply the additive inverse and multiplicative inverse properties to solve two-step equations.
- Math Files - Equation Match - This is an interactive game for students. They must find two equations that have the same solution. It is similar to a game of "Concentration". (Warning to teachers: Students may need a few minutes to play with the long arm.)
- Molecular Expressions, Science, Optics, and You - This site takes you through a step by step lesson to teach powers of 10 and has an interactive applet that allows you to view several things under a microscope!
- Mrs Glossers Math Goodies - Interactive site that reviews writing algebraic equations. Students can read questions and pick equations that will answer the question.
- Multimedia Math Glossary - Outstanding - Gives students a visual along with the definition. Some examples are animated, but all examples have the word and the definition is read to them. Grades K-8.
- The National Science Center - This site gives a lesson plan for an activity to discover the value of pi. Students will use measuring and averaging, and hopefully discover the value of pi.
- Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
- Waldo's Interactive Math - This interactive sites includes an activity allowing students to manipulate a number line in order to solve equations. Students may choose the difficulty of the equations they wish to solve. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
- A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. * revised expectations in italics
- Algebra - Fun with Calendars - A fun mathematical puzzle that shows students a use for algebra. By using a simple linear equation students can determine what four days on a calendar someone has chosen.
- Grap Mole Game - Introduction to Coordinate plane. Learn about the X and Y axis and how to plot points on the graph. Game comes in different levels of difficulty. The game is a good review, students will have fun while learning coordinate plane.
- Linear Inequalities - Manipulate and visualize the solution sets of linear inequalities in slope intercept form.
- Slope Intercept Form - Interactive tool to experiment with the slope and intercept of a line. See how the slope of a line is calculated.
- Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.