'15-'16 Number Systems - Circle, Triangle, Square

I have been teaching number systems for several years, but this is an interesting way to approach it. I definitely plan on trying it to see how it goes!

An additional resource for explaining number systems is KhanAcademy. He goes more in depth with Base 10, Base 2, and Base 16.

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This lesson was not particularly apparent to me during the PD. I have to revisit and figure it out again. It makes sense, but the concept of using shapes threw me off. I fully understand the concepts but looking at it in a different light. I do see how it all ties together though. and it will build up the base for future lessons. I will use the lesson as written and utilize the concepts that I learned during the PD in my class.

Did not teach this lesson during the PD, but enjoyed the lesson as a student. Canā€™t wait to teach it in the next few weeks

This is also a great math lesson to build number sense, especially in terms of place value.

Great question to ask! After watching the Teaching Tips video available, one key to this activity is to have students think about the next logical pattern change. Forcing a certain order and pattern will allow them to more easily understand how to transition to creating a rule for the changes.

We did this lesson in PD and I didnā€™t like it because of the way the group structure worked. In my own class I am going to probably only go with pairs because our groups were too big to get any consensus on a plan. I will work really hard to not have students shutting down like my group did during PD.

I like the idea of using shapes; this is very visual and so as I think about the idea of differentiation this supports that focus in the lesson.

Developing a pattern for laying out all the permutation was initially daunting but absolutely necessary to discovering the answer. I "solved " my dilemma by switching from shapes to numbers (0,1,2). The abstract imaging was difficult.

As I recall from PD-this lesson was a bit awkward at first using manipulatives and having enough blocks to create ongoing pattern. I think Iā€™ll need to further review and decide if I should go with standard approach or modify in a more manageable way with students. Talking to math teacher for input doesnā€™t seem like a bad ideaā€“I would like to supplement with a historic/cultural overall view of numbering systems around the world.

I taught this lesson and after passing out the student activity sheets, some groups were immediately trying to create a number system with squares, triangles, and circles after only a few permutations. I enjoyed their thought processes however, I kept leading them back to ā€™ how many permutations? whats the patter? How will we know what is next? And I am thinking the next time I teach this lesson, I will give all groups an extra day to complete their number system 0-26 and present either through a gallery walk or something. Yesterday, worked with the binary number system and now that we are finished, I will pose the reflection question from Lesson 6 at the beginning of class as a journal writing prompt.

We did this in the PD and I got frustrated with the activity. I donā€™t know if we were rushed or I just was not at my peak that day. I did however like the fact that we had a hands on activity to learn the lesson. Itā€™s not how perfect the answer is, itā€™s about how you solved it (the process). I am anxious to see the outcome of this lesson, I plan on doing it next week.

I plan to use the lesson as written. I am very interested in observing how students discover the connection between symbols and their values.

Most of my students have been taught binary number systems last year, I am curious how these lessons will go, but plan on giving them as intended.

I anticipate lots of confusion and frustration with this lesson even though I think at the heart of this lesson is organization. If students can determine a way to organize their work they should be able to see a pattern. I might start with just two objects and then move on to 3.
Initially I was wondering if color mattered but then I read that all you need is 3 distinct objects.
I donā€™t anticipate most students will grasp the concept and wonder how necessary it is for us to move on to the next lessons.

I love this lesson. I will make sure student groups post their number systems and use as talking piece for the following lessons. This is a great talking wall piece for visitors in the classroom - students can share their critical thinking.

I like the practice of having students struggle through the creations of their own systems first, before studying the other number systems that they will be learning about. This personalizes the experience of learning how other created their systems ad gives students insights into the decisions others made when they devised their systems.

What I like about this lesson is that you start creating a number system without using numbers. I Like how these lessons stay true to not intimidating a student who is not as confident in math.
I also appreciate that all the lessons have student activity guides. I find them useful in having a guide for students, evidence of participation, and vocabulary.

Iā€™m looking forward to teaching this lesson!

My students struggled so much with this lesson. How important is mastery at this point? They were able to come up with the 27 combinations and they realized that each of those could potentialy represent a quantity and thus have rules. But that was very few students. I wonder if I should move on or spend another day on this lesson,