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Algebra

Pick’s Theorem as a System of Equations

9-12
Students will gather three examples from a geoboard or other representation to generate a system of equations. The solution will provide the coefficients for Pick’s Theorem.
Algebra

Rates of Change in Pick’s Theorem

9-12
Students will use a spreadsheet to investigate rates of change among various figures created on a geoboard. The coefficients of Pick’s Theorem are easily determined from these rates of change.
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Algebra

Chairs Around The Table

3-5
Students investigate the number of chairs that can be placed around an arrangement of square tables. Three related problems in this lesson yield different linear relationships for students to discover.
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Algebra

Hanging Chains

9-12
Both ends of a small chain will be attached to a board with a grid on it to (roughly) form a parabola. Students will choose three points along the curve and use them to identify an equation. Repeating the process, students will discover how the equation changes when the chain is shifted.
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Algebra

Movie Lines

9-12
This lesson allows students to apply their knowledge of linear equations and graphs in an authentic situation. Students plot data points corresponding to the cost of DVD rentals and interpret the results.
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Algebra

Supreme Court Handshake

6-8
During this lesson, students will explore the handshake problem, a classic problem in mathematics that asks, "How many handshakes occur when n people shake hands with each other?" Groups work to determine how many handshakes take place among the nine Supreme Court justices, and then generalize to the number of handshakes in any size group. Students explore the problem using a verbal description, a table, a graph, a picture, and an algebraic formula.
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Algebra

Beyond Handshakes

6-8
Using spreadsheets, students will explore another pattern, that of the triangular numbers. This exploration will enhance students’ ability to generalize a pattern with variables.
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Measurement

How Long? How Wide? How Tall? How Deep?

3-5

In this lesson, students use historical nonstandard units (digits, hand, cubit, yard, foot, pace, fathom) to estimate the lengths of common objects and then measure using modern standard units. They will discover the usefulness of standardized measurement units and tools.

Many students have not had enough experiences with nonstandard units and therefore have an incomplete understanding of measurement. This lesson provides more of these experiences as well as a bridge into familiar standard units of measuring length. Interested teachers could also connect this lesson to information about measurement in many ancient cultures.

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Geometry

Tetrahedral Kites

6-8, 9-12
Each student constructs a tetrahedron and describes the linear, area and volume measurements using non‑traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed.
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Algebra

Mix It Up

9-12
In this lesson, students will use two colors of beads to form two different percent mixes, and then form a final mix using scoops from the two mixes. From this tactile start, students will develop and use a formula to determine the final percent mix from two source mixtures.