8th Grade Task: Growth Patterns

Essential and guiding questions:

Why are the figures in Sets A and B called “Growth Patterns?” How do the figures in Sets A and B demonstrate growth?
Which representation was more helpful in illustrating the nature of the pattern for the figures in Set A? (Set B?)
Was the same representation more helpful when creating the expression for the nth figure in the pattern?

Blooms taxonomy level:

Understanding

Differentiation suggestions:

If students can’t get started….
Assessing Questions

What kind of pattern is illustrated by the numbers 1, 2, 3, 4, 5?
If the top and bottom rows of the figures in Set A that each contain two square tiles were removed, describe the shapes that remain. What kind of pattern do these figures form?
If the two tiles that stick out were removed from the first three figures of Set B, describe the shapes that remain. What kind of pattern do these figures form?

Advancing Questions

Write a predictable pattern you are familiar with that contains numbers. Draw a graphical pattern to illustrate the numerical pattern you chose.
Draw a set of rectangles that illustrate a pattern. Create a numerical sequence that illustrates the same pattern.

Extension suggestions:

If students finish early….
Assessing Questions

Create a set of growth figures that illustrate a pattern. What characterizes the pattern you chose? Can you write an expression for number of tiles it will take to create the nth figure in your pattern?

Advancing Questions

Given the expression n2 – 2n + 3 as representing the number of
square tiles necessary to build the nth figure. Create the first four figures in a growth pattern that satisfies the given information.

Originator: