Graphing Patterns

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Objective

SWBAT represent a pattern on a line graph by graphing ordered pairs.

Big Idea

A picture is worth a thousand words. A graph communicates a great deal of information about a pattern.

Warm-Up

5 minutes

Students determine the rule of a simple pattern that has more than one operation.

Step

Total

3

153

4

203

5

253

n

 

They share strategies used to determine the rule and the 100th step.  

Guided Practice

10 minutes

A pattern, a table, and a graph are posted on the board.  

The purpose of this launch is to show students how these three are connected.  Ask students to make the pattern using tiles.  As they are working, prompt them to consider a real life connection. "What could this pattern represent?"

A student suggests that these tiles represent a stage for the Super Bowl.  

I ask, "If you were asked to determine the 1000th figure in this arrangement, how could you figure that out?"

Students turn and talk with a friend briefly and then share out.  I ask them to share in a progressive model, so I call on groups based on their responses.  In order to start from the least effective model, I first say,  "I would keep adding one more tile until I did that 1000 times".  Then I ask students to critique my strategy.  We agree that is neither effective nor efficient.  

Students suggest we use math to determine an expression that applies.

Together, we complete the table, checking back to the pattern each time.  This helps the students make a connection between concrete and abstract representation. Then, we determine the rule. I remind students of the focus questions from yesterday's lesson.  

  • Where did the pattern start?  
  • What did it change by? 

 

Next, connect the pattern and model (tiles) to a graph to demonstrate that a line graph can comprehensively depict the rate of change in the pattern.*

During the guided practice, I plot each point and think-aloud as I do.  This demonstrates to the students that I am using the labels to help make sure I plot the points correctly. 

*It is assumed at this point that students are to recognize steady increase, steady decrease, and accelerated growth on a graph.  If this is not the case, prior learning must take place before making these connections.  

Now You Try

25 minutes

Students are given time to create a pattern and record it using a table.

I ask the groups to share their patterns and record them on the board.  Then, I combine them into one table.  I fill the table with the 4 different patterns that the groups generate.

I do this to help the students see that there are many ways to represent multiple patterns. Sometimes each separate pattern is recorded on its own table, other times these tables can be combined.

After 4 patterns are shared on the board, I ask the students to determine the rule and 10th step for each.

Next, they graph the patterns using a different color for each pattern. To make this more clear, I was sure to use different colors when I wrote each pattern.  Then, the colors could match the patterns on the board.

Group Share and Ticket out

10 minutes

Students share a personal favorite pattern, table, and graph.

I take pictures of these as I circulate the room so they are able to share their work on the board. To accompany their display, students describe how they determined the pattern and why information is communicated through the graph.  I prompt them through this process.

As a ticket out, students take a few minutes to polish up the pattern they are most proud of and pass in their work.