Patterning

 

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One of my all time favorite activities to teach kids is patterning.  It connects so well to algebraic thinking, graphing, visualizing math, and it requires kids to think outside of the box.  I love having discussions about patterns to launch the activity. 

I always ask my students:

• "What do you notice and wonder about the pattern?"  
• "How do you see the pattern growing?" 
• "What do you think the next figure will look like? and Why?"

My favorite way to launch is to ask a low floor- high ceiling question, like what do you notice and wonder.  There is very little risk with this question because every student will notice and wonder about something.  It engages all students and learning styles.  It also doesn't put an advantage to some students who have been lucky enough to get extra tutoring or support.  This question levels the playing field. 

Then we go into the more in depth questions.  In general, my students love sharing how they see the patterning growing. They want to get up and "be teacher" and explain to the group ways that it is growing.

After I have oriented my students with the Math Talk on patterning, I generally break them up into partners (randomly) and then we start the problem solving on whiteboards. 

With patterns, we start easy and then level up.

Usually, the questions are layered as such: 

1. What would the next figure in the pattern look like?  How many cubes would it have?
2. How about figure #34?
3. Would there ever be 187 cubes in the pattern? Why or why not?
4. Can you make a rule or algebraic sentence for how many cubes would be in any given figure number?
5. What would a graph of this pattern look like?

I give the questions one at a time, as they finish one, they get the next.

As a debrief, we walk over to a board and I ask questions like:

• How is this board similar and different to that board?
• Jimmy (from board A) can you explain what you think this group B was thinking based on the work on their whiteboard?
• What strategy did this group use?
• How is their thinking made visual?/
• (If a group made a mistake) What did this group understand?  What thinking were they trying?

Then, we sometimes take a picture of the work on the whiteboard and I have the kids caption it with what they learned that day.  

If you are interested in this, you can find some lessons on my new website here.