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### Are They Possible?

6-8

Students examine some isometric drawings that seem to be impossible and
investigate one way Escher used to create these "impossible" figures.### Cubes Everywhere

6-8

In this lesson, students use cubes to develop spatial thinking and review basic geometric principles through real-life applications. Students are given the opportunity to build and take apart structures based on cubes.### Line 'Em Up

6-8

A self discovery approach in understand the process of plotting points on a coordinate plane, using a program for TI Graphing Calculator.### Factor Game

3-5, 6-8

The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers. ### 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.

### 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.### 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.### Algebra in Balance

6-8

Students use the Balance Pans Applet- Expressions Tool to explore algebraic expressions. They determine if algebraic expressions are equal. They balance pans to solve a system of equations and use graphing to find the solutions to a system of equations.### Balancing Shapes

6-8

Students will balance shapes on the pan balance applet to study equality, essential to understanding algebra. Equivalent relationships will be recognized when the pans balance, demonstrating the properties of equality.### Balancing Algebraic Understanding

6-8

Using a balance in the classroom is a first step to algebraic understanding. Use this pan balance (numbers) applet to practice the order of operations in simplifying numerical expressions and to demonstrate the conventions of using algebraic logic in simplifying expressions.