V. Numerical and Algebraic Operations & Analytical Thinking

  1. Operations and Their Properties
  2. Algebratic and Analytical Thinking

 

Additional Links to General Mathematics Sites

 

2. Algebraic and Analytical Thinking

Middle School

  1. Benchmark 1. "Read and write algebraic expressions; develop original examples expressed verbally and algebraically; simplify expressions and translate between verbal and algebraic expressions; and solve linear equations and inequalities."
    1. I want a credit card - or do I? - Algebraic and Analytical Thinking (V.2.MS.1)
      Students will pretend to borrow $1000.00 on a credit card. They will pretend to make minimum payments for a year. When they're done, they will make a pie chart showing how much of their payments reduced their debt, and how much was interest. A student worksheet, resources, and lesson extensions are included. Students will be writing and solving one-step linear equations in one variable. This includes a teacher lesson plan and is a student activity.
    2. Math Files - Equation Match - Algebraic and Analytical Thinking (V.2.MS.1)
      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.)
    3. Mrs Glossers Math Goodies - Algebraic and Analytical Thinking (V.2.MS.1)
      Interactive Site that reviews Writing Algebraic Equations. Students can read questions and pick Equations that will answer the question.
    4. Multimedia Math Glossary - Algebraic and Analytical Thinking (V.2.MS.1)
      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
    5. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - Algebraic and Analytical Thinking (V.2.MS.1,2,3&4)
      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.
    6. Waldo's Interactive Math - Algebraic and Analytical Thinkings (V.2.MS.1&2)
      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.
  2. Benchmark 2. "Represent algebraic concepts with geometric models (e.g., algebra tiles), physical models (e.g., balance beam), tables and graphs; and write algebraic expressions to correspond to the multiple representations."
    1. Algebra Balance Scales - Algebraic and Analytical Thinking (V.2.MS.2)
      This interactive site allows student to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam.
    2. E-Lab Grade 8 Activity 5- Modeling Like Terms - Algebraic and Analytical Thinking (V.2.MS.2)
      This site allows students to use pictorial representations of algebraic tiles to mode algebraic expressions by combining like terms. They may generate their own problems or use computer generated problems. A work page is also available for students to review and practice algebraic concepts using positive and negative terms.
    3. It's Your Life - Algebraic and Analytical Thinking (V.2.MS.2&3)
      This is a 3-part lesson utilizing census data of the mean income of workers 18 years or older by education attainment levels. Students will analyze census data to create graphs and take part in a simulation using this same data as a starting point to make financial decisions and budgets. Internet census links, student worksheets, and a log/journal are available to use with this site. Part of student problem solving process will include solving problems by using the correct order of operations. This includes a teacher lesson plan and is a student activity.
    4. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - Algebraic and Analytical Thinking (V.2.MS.1,2,3&4)
      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.
    5. Waldo's Interactive Math - Algebraic and Analytical Thinkings (V.2.MS.1&2)
      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.
    6. Virtual Manipulatives Algebra Tiles - Algebraic and Analytical Thinking (V.2.MS.2)
      Virtual Manipulatives Algebra Tiles - interactive.
  3. Benchmark 3. "Solve linear equalities and inequalities using algebraic and geometric methods, and use the context of the problem to interpret and explain their solutions."
    1. Algebra - Fun with Calendars - Algebraic and Analytical Thinking (V.2.MS.3)
      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.
    2. California Here We Come! - Algebraic and Analytical Thinking (V.2.MS.3,4&5)
      This site allows teams of students to choose any state capital on the east coast as their starting point. They travel west stopping at each state capital along the way and record miles traveled. Each student group will create a chart or table showing the number of miles traveled from state capital to state capital and then total numbers of miles driven. Lesson plan, evaluation, extensions, and student activity sheets are included. Skills used will involve solving linear equations and inequalities over the rational numbers, as well as solving multistep problems involving rate, average speed, distance and time, or direct variation. This includes a teacher lesson plan and is a student activity.
    3. Grap Mole Game - Algebraic and Analytical Thinking (V.2.MS.3)
      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.
    4. Linear Inequalities - Algebraic and Analytical Thinking (V.2.MS.3)
      Manipulate and visualize the solution sets of linear inequalities in slope-intercept form.
    5. Slope Intercept Form - Algebraic and Analytical Thinking (V.2.MS.3)
      Interactive tool to experiment with the slope and intercept of a line. See how the slope of a line is calculated.
    6. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - Algebraic and Analytical Thinking (V.2.MS.1,2,3&4)
      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.
  4. Benchmark 4. "Analyze problems modeled by linear functions, determine strategies for solving the problems and evaluate the adequacy of the solutions in the context of the problems."
    1. Ask Dr. Math - Algebraic and Analytical Thinking (V.2.MS.4)
      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.
    2. Escape from Knab - Algebraic and Analytical Thinking (V.2.MS.4&5)
      This site is a wonderful interactive game/simulation that allows the student to learn basic finance.  Students land on the planet Knab and have to earn their ticket back to Earth.  Students learn financial vocabulary, such as budget, capital gains, income tax, using a highly accessible glossary.  Students will choose a job, calculate income, calculate tax withholdings, estimate long and short term expenses.  Students have to analyze real life financial situations and make decisions based on their findings.  This game could be played as teams or individuals.  There is a spot for teachers to find lesson plans, tips and curriculum alignment information.
    3. Math for Morons Like Us - Algebra - Word Problems - Algebraic and Analytical Thinking (V.2.MS.4)
      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.
    4. Solving Functions - Algebraic and Analytical Thinking  (V.2.MS.4)
      An interactive site to develop strategies to solve functions.
    5. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - Algebraic and Analytical Thinking (V.2.MS.1,2,3&4)
      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.
  5. Benchmark 5. "Explore problems that reflect the contemporary uses of mathematics in significant contexts and use the power of technology and algebraic and analytic reasoning to experience the ways mathematics is used in society."
    1. Escape from Knab - Algebraic and Analytical Thinking (V.2.MS.4&5)
      This site is a wonderful interactive game/simulation that allows the student to learn basic finance.  Students land on the planet Knab and have to earn their ticket back to Earth.  Students learn financial vocabulary, such as budget, capital gains, income tax, using a highly accessible glossary.  Students will choose a job, calculate income, calculate tax withholdings, estimate long and short term expenses.  Students have to analyze real life financial situations and make decisions based on their findings.  This game could be played as teams or individuals.  There is a spot for teachers to find lesson plans, tips and curriculum alignment information.
    2. Figure This! Math Challenges for Families - Algebraic and Analytical Thinking (V.2.MS.5)
      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, "Try This" section, additional related problems with answers, questions to think about, fun facts related to the math, and resources for further explorations. Math Challenge #21 is an example of a problem that would help teach this particular benchmark.
    3. Lemonade Stand -- Algebraic and Analytical Thinking (V.2.MS.5)
      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.
    4. Webmath - Algebraic and Analytical Thinking (V.2.MS.5)
      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.
    5. Word Problems for Kids - Algebraic and Analytical Thinking (V.2.MS.5)
      Has numerous story problems that students read and answer the questions. If they need help they can click on the hint link and receive hints to solving the problems.

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