Algebra Tiles

Use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor.

Balancing Shapes

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.

Road Rage

In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into each other.

Number Representations

Students learn about the repeated subtraction and repeated division methods for converting a decimal number N to a numeral in base b, provided b is an integer other than ‑1, 0, or 1. Students also learn about the Fibonacci representation, which is a method for representing a numeral as a sum of Fibonacci numbers. The Fibonacci representation will be useful in later lessons in this unit when exploring Nim games.

Balancing Algebraic Understanding

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.

Beyond Handshakes

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

Patterns and Functions

Students investigate properties of perimeter, area, and volume related to various geometric two- and three-dimensions shapes. They conjecture, test, discuss, verbalize, and generalize patterns. Through this process they discover the salient features of the pattern, construct understandings of concepts and relationships, develop a language to talk about the pattern, integrate, and discriminate between the pattern and other patterns. When relationships between quantities in a pattern are studied, knowledge about important mathematical relationships and functions emerges.