Each day, I start class with a math routine. Whether it is a Number Talk string, If I Know Then I Know, Closest Estimate or Quick Image, those first 10-15 minutes are always my favorite math conversations of the day! Today I added Fawn’s (@fawnnguyen) Visual Patterns into the mix. I spend a lot of class time having students look for patterns and regularity in their math work, but this visual brought a wonderfully different “feel” to their work. As Fawn had previously blogged, the Visual Patterns have an entry level for everyone and every student in my classroom engaged immediately with the images.
I chose this one to kick off our work today:
I asked the students to work as a group to find the number of unit for Steps 1 – 6, 13, 43, and then n. Being their first time, we had to deal with what the “n” meant and after the initial “Is this algebra?” followed by numerous stories of siblings who are doing this math with letters, they were on their way. It was interesting to see some students go straight to drawing each image, others started looking for what was changing as the steps progressed, and then there were the students who love going straight for an expression for finding 13 and 43. After they all had the table completed, we came together to fill it in. I was so impressed with their work and their ability to find the expression for the nth shape, however the BEST part of the conversation was taking that expression and connecting it back to the images. Why was n doubling? Why is that 1 being subtracted?
I love how this student used a specific example to connect his expression (or almost an expression, we’ll get there:)
This student found the equation and decided to use “a” to stand for “answer.” I loved how she then tested it with other numbers.
These two students then put a different spin our our work. Every group in the room came to the expression n x 2 -1, and as one student was explaining how the 1 needed to be subtracted because it was being double counted, another student exclaimed that his group figured out that if you just split that block in half and made each said a mixed number you just had to multiply that by 2. For example on step 4, if you made each side 3 1/2 x 2, you would arrive at the same answer. How awesome!
I am excited to make this a part of my daily math routines, thanks Fawn for sharing, awesome stuff! I had students asking for another one before they left class that day, they loved it!
Love the way your students are able to put their thoughts on paper Kristin. Its been really cool to watch them grow through your blog?
What was the difference in students being able to articulate the pattern verbally and students who were able to create a written expression? I’m really interested to find out how quickly students are able to move from the verbal to the written form.
Thanks for sharing work samples…pictures are worth a thousand words.
Thanks Graham! They worked together, so at each table they arrived at the expression. However, as I walked around, I heard a lot of “It is just the same picture + 2 each time. It was a lot of teamwork! Some moved quickly to the expression, however I did have quite a few who got to the expression w/o thinking about what was happening in the pictures. I had to redirect them back to the pictures to find the connection, that was the hardest part for most I think. This could be because we do a lot of pattern work with number and that is where they are comfortable, which is why I am excited to add this to my classroom!
I feel a kindred spirit with your class! Several times, you’ve posted something we’ve done or are about to do!
What supports are in place or do you employ for students who “struggle” to communicate their thinking in these beautiful ways?
My self-contained class are mathematical thinkers, but they struggle (quite a but) with the communincation part!
Thanks for sharing Kristin!
Thanks Andrew! The students have done a great deal of listening and talking to each other all year. I am lucky they are a very comfortable bunch and ok with asking each other to explain further. They also know what they write in thier journal is an ungraded/unjudged picture of thier thinking. I also do a lot of sharing of all student work w/the class. I try to sequence the share from the verbal to the more sophisticated. I push those connections as a group. That, combined with some one on one convos, help move them. Dont get me wrong, some cases are tougher than others, but they get there!
Do you use a standard journal prompt, or is where they justify answers and record thinking about the class task or problem? I think I need to have them journal more, but the writing is so hard for them already, it needs to be heavily supported and prompted.
I use thier journals for everything, recording thinking, prompts, etc. The prompt will vary based on our work that day. I try to give prompts that allow access “What did you notice in your work today?” type questions. I also really encourage labeled drawings if words are not coming to them.
Maybe a future blog post about the varying journal prompts you use, when, and for what types of tasks 🙂
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Reblogged this on h App y Mothers and commented:
Great practice, Kristin