7.19 The student will represent, analyze, and generalize a variety of patterns, including arithmetic sequences and geometric sequences, with tables, graphs, rules, and words in order to investigate and describe functional relationships.

Lesson: Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.

Activity: Decode encrypted messages to determine the form for an affine cipher, and practice your reasoning and arithmetic skills. Input your guesses for the multiplier and constant. Caesar Cipher III is one of the Interactivate assessment explorers.

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: 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: This applet allows the user to make observations about the relationship between speed and position and how both of these are affected by initial velocity and the incline on which the biker is traveling.

Activity: Recognize patterns in a series of shapes, numbers, or letters. After determining the pattern, the student fills in the missing pieces. Three levels of difficulty are available.

Activity: Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs. Positive Linear Function Machine is one of the Interactivate assessment explorers.

Activity: Step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

Activity: Step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

Activity: Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers.