SBAC Practice Activities: Patterns and Formulas

This activity will provide students with a chance to review recursive and explicit formulas for arithmetic and geometric sequences.  Students will build formulas to model both patterns and real world situations.  They will check their formulas by using Desmos, and answer questions relating to each situation.  The Google Doc is available at this link.

Problem 1 is below, and asks students to use a recursive formula to identify a pattern from this page.

All patterns are from Fawn Nguyen's Visual Patterns website.  A few of the patterns that students will be looking at are below.  You can see that pattern 7 fits our recursive description for problem 1.

Once students have identified the correct pattern, we send them over to Desmos to add their data to a table.  When we are talking about patterns in math, we describe them as starting with stage 1, and then progressing to stages 2, 3, etc.  In the table below, we are saying that stage 1 has 5 blocks, stage 2 has 7 blocks, and so on.  You can see the each stage has two more blocks than the previous stage.

Students love using Desmos to see their pattern data plotted in real time.  Once students have the points plotted, we discuss how a recursive formula is limited in its usefulness because it doesn't have predictive power.  For example, I can't use a recursive formula to predict how many blocks will be in stage 100.  To do this we need an explicit formula.  Students can input an explicit formula into line 2, and immediately see whether or not they have the correct formula based on whether the line goes through the data points.

After practicing a few more problems with patterns, we move on to real world scenarios.  The scenario below was adapted from a worksheet found on betterlessons.com by Colleen Werner.

As with other SBAC practice activities, teachers coach students on how to answer the questions in order to receive full credit. We never know what the rubric will look like on standardized tests, so we've created three areas of focus:

-1 point for showing work
-1 point for explaining your thinking
-1 point for giving the answer with units

Part III of the lesson is a mini-performance task, modified from the SBAC Practice Test performance task. This is great if you have an extended period of time for the lesson (90 minute block).  Otherwise we found parts I and II to be great practice activities to help students get ready for SBAC.