## Common Core State Standards for Mathematics

Grade(s) 6 resources related to the following standard:
Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

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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
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
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
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
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
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