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 Flash activity provides an opportunity for learners to develop their algebraic thinking skills. The activity uses objects in place of variables making this activity accessible to students in upper elementary grades. Learners are presented two or three weighing scales and must determine the weight of a specific object or group of objects. There are ten questions for each of the 3 levels of play and hints are provided for incorrect answers. | Activity, Interactive Media 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 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 second of three balance activities in which students develop intuitive strategies for writing and solving simple algebraic equations. In this follow-up activity, students create and solve balance puzzles in which the variable must first be isolated on one side of an algebraic equation in order to determine its value. 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 interactive Java learning tool allows a teacher to demonstrate and explore the distributive property with expressions in the factored form (a + b) (c + d) using a matrix multiplication method with students. Sliders determine the number values from 20 to -20 with increments of one-tenth. Check boxes show or hide the factored form, starting matrix values, matrix, products in the matrix, and solution. | Demonstration, Interactive Media 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 addition and subtraction of integers from -10 to 10 with a number line model with students. Users can change the values of the first and second term using sliders. Another option models subtraction of the first term, for example, - (-4) + (-5). Check boxes allow users to show each expression, model, and answer individually. | Activity, Interactive Media Grade Level: 5, 6+ | |

This activity promotes students to explore and analyze the number of different ways of achieving each of the specific outcomes when adding and subtracting positive and negative integers while playing the game, "Connect Three." By answering key questions, the players work out a strategy for improving their chances of winning the game. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for support, extension and answers to questions are provided. A pdf of the game board and a spreadsheet to simulate tossing the dice are linked. | Activity, Game, Interactive Media Grade Level: 5, 6+ | |

This problem helps children become familiar with the idea of a symbol (in this case a shape) representing a number. Students also have an opportunity to see the multiplication properties of one and zero in a challenging puzzle. By studying the twelve multiplication equations which use eleven different colored shapes, students are to determine each shape's unique number value from a list of 0 to 12. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, support with down loadable handouts and a link to an extension activity, What's It Worth? (cataloged separately). | Activity Grade Level: 4, 5, 6+ | |

This iOS app is a puzzle game that makes algebraic thinking both visual and interactive as equations are represented with balance scales, weights, and little creatures called Zogs. The goal at each of the 24 levels is to find the weight of each space creature and assemble a team for the next shuttle mission. Players must apply ideas such as equality, proportional reasoning, variables, and combining groups of objects. | Game, Interactive Media, Mobile App Grade Level: 5, 6+ | |

This problem offers a simple context to begin an exploration of the properties of numbers and to make conjectures about those properties. Learners explore the sums of consecutive numbers and whether all positive numbers from 1-30 can be written as the sum of two or more consecutive numbers. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support. | Activity Grade Level: 3, 4, 5, 6+ | |

This iOS app, designed as a companion tool for Shuttle Mission Math, an algebraic reasoning game (cataloged separately), allows players to build and solve their own balance scale puzzles. The player creates teams (from 1-4) using different zog type combinations and solves the puzzle created using the three basic strategies. | Activity, Interactive Media, Mobile App Grade Level: 4, 5, 6+ |