What Makes Something a Pattern?

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Objective

SWBAT find patterns that fit a given sequence and then to use these patterns to predict the next few terms of the sequence.

Big Idea

Can you figure out the pattern? If you can, what can you do with it? Students learn how to write rules for patterns and explore how these rules can help us predict future events.

Opening

20 minutes

I use a PowerPoint Presentation in today's opening. I begin class with a mind map where students can call out whatever comes to mind when they think of the word "algebra".  Next, I show students the pattern on Slide #2.  I ask them the questions below the slide and be enthusiastic about the beauty of patterns! I finish by letting students know that today, they will be examining some patterns that occur in sequences.

 

Instructional Note: This activity can be as long or as short as you want, the intent is to get students to think about what they already know about algebra and to give them some ideas of the concepts you will be studying.  You can follow What Makes Something a Pattern PowerPoint from the Resources.  

Investigation

20 minutes

Next, students will work in small groups or individually on What's Next.  What's Next is an activity that can be found in the IMP Year 1 book on page 4.  Be sure that students are clear that they will write the next three terms of each sequence and also DESCRIBE the pattern they see.  Let groups work together and try not to help too much!

Another example of a pattern you might start with is growing dots.  Remember to focus on having students describe the pattern and how they can convince you of the next three terms in the sequence.

DIFFERENTIATION:  If some groups are ready for an extension activity, you can have them trade the picture sequences and number sequences they created with a different group.  You can encourage them to make their sequences challenging to solve!

Discussion

10 minutes

I leave a lot of time to discuss today's activity. I ask different groups to report out about the patterns they found. I ask students to describe the patterns in their own words.  

For Questions 5 and 6, different groups may find different patterns that fit the sequences. I make sure to emphasize to students that there is no one right answer. This is also a good opportunity to highlight and applaud different approaches to the same problem. I make this a theme throughout my course. It is important to maintain the presence of this theme by continually supporting it in the classroom.

Closing

10 minutes

For an Exit Ticket, I give my students the following prompt:

Write your own definition for the word "pattern."  Describe a pattern that involves numbers that occurs in your life.

I will ask my students should work on "Keep It Going," page 49 in the IMP Year 1.  This exercise will give them a chance to play around with more patterns. It also challenges them to break out of relying on a recursive method to find the 100th term of a sequence. This assignment is well aligned to the Common Core Standard: 

  • CCSS.Math.Content.HSF-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

In particular, students will practice writing Question 1c both recursively and with an explicit formula.

 

Citations

Some of this material is adapted from the IMP Teacher’s Guide, © 2010 Interactive Mathematics Program. Some rights reserved.

Growing Dots is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

http://www.mathematicsvisionproject.org/secondary-1-mathematics.html