Expressions and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

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Resource | Resource Type Grade Level | Rating |
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This virtual manipulative allows a teacher or student to represent a linear equation and solve it through the use of a balance beam. Unit blocks (representing 1s) and x-boxes (representing the unknown), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, the learner can choose to perform any arithmetic operation to both sides of the equation keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance thus giving the value of x. There is also the option of creating your own equations to solve. | Activity, Interactive Media Grade Level: 5, 6+ | |

This Sketchpad activity, which opens on Geometer's Sketchpad as well as on iOS with Sketchbook Explorer (cataloged separately), is the first of three balance activities in which students develop intuitive strategies for writing and solving simple algebraic equations. Students drag a shape whose numerical value is known onto one side of a scale and then drag copies of a shape with an unknown numerical value to the other side of the scale until both sides are level. Students then solve the equation to determine the value of the unknown shape. A five-minute movie provides detailed instructions and downloadable PDF of teacher notes and student worksheets are also included. | Activity, Lesson Plans, Video Grade Level: 4, 5, 6+ | |

This Sketchpad activity, which opens on Geometer's Sketchpad as well as on iOS with Sketchbook Explorer (cataloged separately), is the third of three balance activities in which students develop intuitive strategies for writing and solving algebraic equations. In this final activity, users must simplify algebraic equations by removing identical shapes from both sides of a scale. A five-minute movie provides detailed instructions and downloadable PDF of teacher notes and student worksheets are also included. | Activity, Lesson Plans, Video Grade Level: 5, 6+ | |

This lesson plan introduces the game Deep Sea Duel, which develops students' operation skills and strategic thinking, and can be played online or with cards. After playing several variations of the game, students attempt to identify a winning strategy and compare the game to other familiar games. Variations include whole numbers, decimals, fractions, exponents, and words. The lesson includes printable cards and a student worksheet, questions for student discussion and teacher reflection, assessment options, and extensions. The online game and the cited article are cataloged separately. | Activity, Game, Lesson Plans Grade Level: 3, 4, 5, 6+ | |

This interactive Java learning tool, which was constructed using the cross-platform open educational resource GeoGebra, allows a teacher to demonstrate and explore the distributive property of multiplication over addition with students. The student also sees the relationship between two different formulas, a(b+c) and a(b) + c. The expression a(b+c) is shown in both expanded and factored form. Sliders change the values of each of the three variables with the whole numbers from 0 to 5. Check boxes also allow the user to hide or show expressions. | Demonstration, Instructional Strategy, Interactive Media Grade Level: 5, 6+ |