Grade 7 - Patterning and Algebra
Standard 7.PA.1 - Find the constant of variation using the data in a word problem.
Included Skills: Algebra, Division
Patterns and Relationships • represent linear growing patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets) and strategies (e.g., make a table of values using the term number and the term; plot the coordinates on a graph; write a pattern rule using words); • make predictions about linear growing patterns, through investigation with concrete materials (Sample problem: Investigate the surface area of towers made from a single column of connecting cubes, and predict the surface area of a tower that is 50 cubes high. Explain your reasoning.); • develop and represent the general term of a linear growing pattern, using algebraic expressions involving one operation (e.g., the general term for the sequence 4, 5, 6, 7, ... can be written algebraically as n + 3, where n represents the term number; the general term for the sequence 5, 10, 15, 20, ... can be written algebraically as 5n, where n represents the term number); • compare pattern rules that generate a pattern by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term (e.g., for 1, 3, 5, 7, 9, ..., the pattern rule is "start at 1 and add 2 to each term to get the next term") with pattern rules that use the term number to describe the general term (e.g., for 1, 3, 5, 7, 9, ..., the pattern rule is "double the term number and subtract 1", which can be written algebraically as 2 x n - 1) (Sample problem: For the pattern 1, 3, 5, 7, 9,..., investigate and compare different ways of finding the 50th term.).