Patterning

BIG IDEAS

(taken from “Big Ideas by Dr. Small”)

Patterns represent identified regularities. There is always an element of repetition.
Patterns can be represented in a variety of ways (i.e. pictures, words, graphs, sequences, tables).
Some ways of displaying data highlight patterns.
By identifying the element of repetition, one can make predictions related to the pattern.

GOAL: I can classify, extended and describe patterns.

GOAL: I can represent a pattern in different ways (e.g. as a table, in pictures).

GOAL: I can make predictions related to a specific pattern.

create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets);
build a model to represent a number pattern presented in a table of values that shows the term number and the term;
make a table of values for a pattern that is generated by adding or subtracting a number (i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, …) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term);
make predictions related to growing and shrinking geometric and numeric patterns (Sample problem: Create growing L’s using tiles. The first L has 3 tiles, the second L has 5 tiles, the third L has 7 tiles, and so on. Predict the number of tiles you would need to build the 10th L in the pattern.);
extend and create repeating patterns that result from translations, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).

extend, describe, and create repeating, growing, and shrinking number patterns (e.g., “I created the pattern 1, 3, 4, 6, 7, 9, …. I started at 1, then added 2, then added 1, then added 2, then added 1, and I kept repeating this.”)
connect each term in a growing or shrinking pattern with its term number (e.g., in the sequence 1, 4, 7, 10, …, the first term is 1, the second term is 4, the third term is 7, and so on), and record the patterns in a table of values that shows the term number and the term
create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words (e.g., the pattern rule “start at 1 and multiply each term by 2 to get the next term” generates the sequence 1, 2, 4, 8, 16, 32, 64, …)
make predictions related to repeating geometric and numeric patterns (Sample problem: Create a pattern block train by alternating one green triangle with one red trapezoid. Predict which block will be in the 30th place.)
extend and create repeating patterns that result from reflections, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).