V. Numerical and Algebraic Operations & Analytical Thinking

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

Additional Links to General Mathematics Sites

• Mathematics Games and Student Activities
• Mathematics Lessons Plans
• Interactive Learning and Problem Solving Activities
• Word Searches and Puzzles in Mathematics
• Miscellaneous Sites

Middle School

1. Benchmark 1. "Use manipulatives and diagrams to model operations and their inverses with integers and rational numbers and relate the models to their symbolic expressions."
   1. Cynthia Lanius Lessons - Fractions - Operations and their Properties (V.1.MS.1)
      This site allows students to manipulate or color in boxes to represent various fraction problems.  Students receive immediate feedback, so they can correct any wrong answers.  Students can choose from a variety of fraction problems to practice.
   2. Geometric Factoring - Operations and their Properties (V.1.MS.1)
      This lesson plan uses manipulatives (tiles and graph paper) to teach students the connection between multiplication and geometry. This concept is extended to explain that the area of a rectangle can be used to find the factors of a number. Reproducible materials can be printed, good questions and follow-up assignment are included. Hyperlinks to other lesson plans available.
   3. Line Jumper - Operations and their Properties (V.1.MS.1)
      Students use a number line to answer addition or subtraction integer problems. An immediate response of correct or incorrect are given for each jump. Students have the opportunity to choose between various levels.
   4. National Library of Virtual Manipulatives - Operations and their Properties (V.1.MS.1)
      Outstanding - This is an outstanding site for any manipulatives for  numbers and operations.  Once you have pulled it up, then click on the icon you wish to practice.  This is a very interactive site for students.
   5. National Library of Virtual Manipulatives for Interactive Math - Operations and their Properties (V.1.MS.1)
      This is a student interactive virtual site that has interlocking circles. Students use positive and negative numbers so that the sum in each circle equals zero.
   6. Visual Fractions - Operations and their Properties (V.1.MS.1)
      This site allows students to look at fractions on a number line or in circles and answer questions about them.  The graphics change with students answers.  This site would be helpful in fifth and sixth grades, especially.
2. Benchmark 2. "Compute with integers, rational numbers and simple algebraic expressions using mental computation, estimation, calculators and paper-and-pencil; explain what they are doing and how they know which operations to perform in a given situation."
   1. Equation Basics - Operations and their Properties (V.1.MS.2&4)
      This interactive site allows students to work through a tutorial followed by practice problems they can complete on-line. Correct answers are given as well as help in solving equations if students have difficulty.
   2. Introduction to Algebra -Operations and their Properties IV.1.MS.2)
      Introduction to Algebra Variables, Expressions, Equations, Solution of an equation, Simplifying equations, Combining like terms, Simplifying with addition and subtraction, Simplifying by multiplication, Simplifying by division, Word problems as equations, and Sequences.
   3. Late Delivery - Operations and their Properties (V.1.MS.2)
      This is an interactive game for students to solve algebraic expression problems. Tips are given and students can learn about evaluating expressions and powers under the "key ideas" section.
   4. Math Forum - K-12 Math Problems, Puzzles, Tips and Tricks - Operations and their Properties (V.1.MS.2)
      General information for mental calculation including tips to beat a calculator, divisibility rules, and multiplication tips.
   5. Math Goodies: Lesson on Order of Operations - Operations and their Properties (V.1.MS.1)
      Students learn how to compute using order of operations.  Practice problems for students to work on are provided.  There are several variations included in this site such as exponents, integers, and equations.
   6. Multiplication With Integers - Operations and their Properties  (V.1.MS.2)
      This is an interactive site for students to learn the rules for multiplying positive and negative integers and then a game with different variations to practice their skills.
   7. Operation Order - Operations and their Properties   (V.1.MS.2)
      This site is an interactive game where students have to place integers in the blanks of an equation using order of operations to get the given answer. Immediate feedback for students.
   8. Teacher's Lab - Operations and their Properties (V.1.MS.2&4)
      This is a student interactive site. Students are asked to find the number of cards needed if a class exchanges cards. Seven different methods for solving the problem is demonstrated.
3. Benchmark 3. "Describe the properties of operations with rationals and integers (e.g., closure; associative, commutative and distributive properties) and give examples of how they use those properties."
   1. Addition Properties - Operations and their Properties (V.1.MS.3)
      Students play an interactive game consisting of commutative, associative, additive identity, and distributive properties. Students are given a problem with one of the properties demonstrated and the student must choose the correct property. The game immediately says if the student is correct or not and gives a running total of their score.
   2. Algebra Help - Operations and their Properties (V.1.MS.3)
      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 problemns 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.
4. Benchmark 4. "Efficiently and accurately apply operations with integers, rational numbers and simple algebraic expressions in solving problems."
   1. Absurd Math Pre-algebra From Another Dimension -- Operations and their Properties (V.1.MS.4)
      This site presents an interactive mathematical problem solving series. This site has four different locations. Each location has two objectives, a mathematical objective and a game objective. Both of these objectives must be accomplished in order to progress further into the game. The student writes simple algebraic expression and then substitutes in integers to solve the problems. The students have access to the use of a calculator on the screen. The student receives immediate feedback on correctness of the problem. The student has access to helpful hints and can redo the problem until they have it correct.
   2. Equation Basics - Operations and their Properties (V.1.MS.2&4)
      This interactive site allows students to work through a tutorial followed by practice problems they can complete on-line. Correct answers are given as well as help in solving equations if students have difficulty.
   3. Factor Game - Operations and their Properties  (V.1.MS.4)
      Interactive game to sharpen multiplication of integer skills.
   4. Product Game - Operations and their Properties   (V.1.MS.4)
      Interactive game for factors and multiples.
   5. Teacher's Lab - Operations and their Properties (V.1.MS.2&4)
      This is a student interactive site. Students are asked to find the number of cards needed if a class exchanges cards. Seven different methods for solving the problem is demonstrated.
   6. Word Problems for Kids - Operations and their Properties (V.1.MS.4)
      This site contains word problems for students and teachers, classified into grade levels 5 -12. Hints for solving problems and answers are available to students.