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Algebra

Extending to Symbols

6-8
In this investigation, students learn about the notion of equivalence in concrete and numerical settings. As students begin to use symbolic representations, they use variables as place holders or unknowns. This investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.  
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Measurement

My Pet

Pre-K-2
In this lesson, students develop and use spatial relationships and spatial memory by creating a map of a pet. The students use visual and spatial skills, measure with nonstandard units, and describe "trips" around their pet using directional and positional words.
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Measurement

Puzzling Relationships

Pre-K-2

Puzzles provide excellent opportunities for students to apply spatial relationships in an entertaining and meaningful way. In the first part of this lesson, the students use concrete materials to develop the skills needed to work with interactive tangram puzzles in the second part of the lesson. The students also further develop their understanding of spatial relationships and develop problem-solving skills.

Once students complete puzzles using concrete materials, introducing them to virtual puzzles enables them to experience turns, rotations, slides, and spatial relationships in a powerful way. These transformations are more apparent in a virtual environment than when using concrete tools.

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Measurement

Measuring Me

Pre-K-2
Students use yarn to measure lengths such as arm span and height. This gives the students practice measuring with nonstandard units. Pairs of students also compare their height and arm spans. They practice problem-solving and reasoning skills by discussing why there are similarities and differences between the lengths of yarn that represent arm spans and height.
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Algebra

Predicting Your Financial Future

9-12
Students often ask, “When are we ever going to use this?” Compound interest is a topic that provides an inherent answer to this question. In this activity, students use their knowledge of exponents to compute an investment’s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt.

 
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Measurement

Area Contractor

6-8
This lesson gives students the opportunity to explore surface area in the same way that a contractor might when providing an estimate to a potential customer. Once the customer accepts the estimate, a more detailed measurement is taken and a quote prepared. In this lesson, students use estimation to determine the surface area of the walls and floor of their classroom. They check the reasonableness of their estimates, and then measure the classroom for accuracy.
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Measurement

Planning a Playground

6-8
In this lesson, students will design a playground using manipulatives and multiple representations. Maximum area with a given perimeter will be explored using tickets. The playground will include equipment with given dimensions, which decreases the maximum area that can be created. This is an interesting demonstration of how a real-world context can change a purely mathematical result. Finally, scale models will be created on graph paper and a presentation will be made to a playground planning committee for approval.
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Data Analysis and Probability

Building Height

6-8
Students will use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class will compare measurements, talk about the variation in their results, and select the best measure of central tendency to report the most accurate height.
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Measurement

Adding It All Up

6-8
In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an interactive tool and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles.
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Algebra

There Has to Be a System for This Sweet Problem

9-12
We are confronted with problems on a regular basis. Some of these are easy to solve, while others leave us puzzled. In this lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.