Warm Up

 

A. Patterns in Relations

To describe a pattern in words, state what is being represented (numbers, letters, shapes, etc.), where it starts, and how it changes (increases or decreases by a certain number, etc.).

Example 1

Describe the pattern in words.

10, 4, −2,...

Integers that start at 10 and decrease by 6 each time.

 

To describe a pattern using a table of values, organize the values in a table.

Example 2

Describe the pattern using a table of values and in words.

Figure 1 2 3
Number of Triangles 4 8 12

Figures that start with four triangles and increase by four triangles each time.

 

To describe a pattern using an algebraic expression, define the variable(s) and determine which operation(s) generate the next element in the pattern.

Example 3

Logan has many game disks. He purchases 5 more game disks. State the expression that describes this situation.

Let d be the number of game disks Logan originally has.

The expression for the number of game disks Logan will have after purchasing five more is d + 5.

 

To describe a pattern using plotted points on the Cartesian coordinate plane, note the ordered pairs. Then determine any consistent pattern.

Example 4

A graph of a relation is provided.

Complete the table of values. Describe some observable patterns, in words.

x −3 0 3 6
y −1 1 3 5

  • The points (-3,-1), (0,1), (3,3), and (6,5) form a straight line.

  • From the starting point of (-3,-1), movement 2 units up and 3 units to the right leads to the next point on the graph. This pattern is consistent for all points on the graph.

  • y-values are consistently increasing by 2 units.

  • x-values are consistently increasing by 3 units.