Investigation Four: Patterns and Rules

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Connected Mathematics Grade Seven
Variables and Patterns
Investigation Four: Patterns and Rules
Lesson  (...)
Lesson: Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.

Lesson: Introduces students to the idea of finding number patterns in the generation of several different types of fractals.

Lesson: Shows students that number patterns exist in the Pascal's Triangle, and reinforces student's ability to identify patterns.

Lesson: Students learn to identify a variety of patterns using sequences and tessellations.

Activity  (...)
Activity: Enter a set of data points, then derive a function to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.

Activity: Create your own fractals by drawing a "line deformation rule" and stepping through the generation of a geometric fractal. Parameters: Grid type, number of bending points on the line.

Activity: Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs. Function Machine is one of the Interactivate assessment explorers.

Activity: Students can create graphs of functions entered as algebraic expressions -- similar to a graphing calculator.

Activity: Create graphs of functions and sets of ordered pairs on the same coordinate plane. This is like a graphing calculator with advanced viewing options.

Activity: Plot ordered pairs on the graph, and they will be connected in the order that they are input. This enables you to decide how the pairs should be connected, rather than having the computer connect them from left to right.

Activity: Plot ordered pairs of numbers, either as a scatter plot or with the dots connected. Points are connected from right to left, rather than being connected in the order they are entered.

Activity: Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.

Discussion  (...)
Worksheet  (...)
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