Use this as a space to record your feedback and questions about this lesson.

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

**david_ellich**#3

Will use the lesson chunk pretty much as is although I may have students write out the different figure permutations rather than have them create them with manipulatives. I think writing them out will give a better visual and â€śforceâ€ť them to come up with a pattern to obtain all 27 variations.

The lessons are fitting together because they are building the concept from each other, adding more complex variations so the student can understand how to encode/decode numbers in binary and in other numeric systems. The Internet simulator is perfect for these lessons.

I think I will talk to the math teacher at school before I teach this lesson. I had a hard time with this lesson during In-Person PD. I understand the concepts but I worry that my students will struggle with the mathematical systems and creating them. By using the math teacher as a resource, I can provide continuity by using the same terms they use in math class and draw connections between the two classes

**clair_schenk**#6

This did this in-person PD and I loved this lesson. Itâ€™s great simple way to teach binary numbers. I am looking forward to try this with my school.

I like this lesson in particular since it brings out an appreciation for the various number systems that are present around this world. The activity of using circles, triangles and squares helps to understand how pattern and placement of the shapes equate to a numbering system. Like David said, I would have the students write out the combinations even before they use the shapes, so it helps them to come up with their unique patterning system. The other lessons in this chunk, specially the one using the simulator are going to bring out a lot of questions for discussions about choosing the best method to send and receive information.

**jdozal**#9

I recall we did this lesson in PD in FL. I think students will enjoy finding their own structure and patterns to the shapes.

**rrwilliams1**#10

I plan to use this lesson as written; this lesson is a strong foundation for other lessons because students must solve problems using a set of rules so they will be able to consistently solve similar problems that become increasingly rigorous but familiar

**dawnguest**#11

We presented this lesson and I remember reminding students about order. How do we know what is next? is a question I kept using to focus thinking on pattern and rules.

**plohara**#12

I like this lesson, it gives the artists/creative thinkers a chance to explain something to the math people, even though many would categorize this as a math lesson.

**sligator**#13

I think it is an interesting way to teach binary, and other number systems. I would definitely use the shapes when teaching this.

**terryy**#14

I look forward to this lesson. I have learned a great deal and I canâ€™t wait for my students to have the understanding as well.

**acrowe**#15

Iâ€™m in an interesting spot with this lesson most likely coming right after I return from 2 weeks of paternity leave. I have a pretty competent sub lined up, and will have my students doing some research and writing to deepen their understanding of the previous chunk of lessons, and then do some preview work on number systems. I am actually thinking of having them jigsaw parts of the Computation article that is listed as an extension for this lesson before I return, and then jump right in to this when Iâ€™m back.

I will definitely have them start with the manipulatives, but then push them to start diagramming things out on paper, abstracting to make things quicker and easier. I like Dawnâ€™s reminder about making sure to ask about order and how they know what symbols come next, and what they represent. I feel like itâ€™s OK for kids to not totally master the concepts in this lesson, but to refer back to it as we get in to binary in subsequent lessons. I think things will click then.

**david_j_baker**#16

I really think this lesson will go well! I especially like the warmup activity of how many different ways can we represent the number 7! I am a little worries that this may be too easy of a lesson for some though! I plan on doing it as isâ€¦but may have to adjust!

**dlewin**#17

I just did this lesson with mostly juniors and seniors. They had a hard time seeing the patterns and many had to be prompted as to their options. The majority figured out how to recreate the pattern vertically but not horizontally. I was ok with this as it will fit nicely with the next lesson. I gave the students the option of manipulative or not. most decided to write the permutations out.

**mmcneil**#18

Again I have to say I really like the flow of these lessons they seem to fit well together.

**nplotnick**#19

I will likely introduce the Roman Numeral system as a way to activate prior knowledge of the existence of alternatives to base-10. The use of an Abacus would be another device that can be used to show how numbers can be represented with a physical device.

I have included a tutorial on Chisenbop, an ancient counting system with probable roots in Korea. Other cultural links can be useful. For example, in both Arabic and Hebrew letters are also used for numbers.

One of my co-workers is from India and related how his father counted using â€śhandsâ€ť. Since each hand as 14 joints, he would use multiples of 14 to determine an amount. There are several methods outlined in the second link.

**colleen_m_adams**#20

I love this prompt at the end of the lesson:

â€śReflection: In 50 words or less, describe the concept of a number system. Why are rules required for a number system to be useful?â€ť

I think that this starts the students thinking about concisely answering questions instead of what many do which is try to write as much as possible thinking that the more they write something should eventually be correct or get them some credit.

I plan on delivering the lesson similar to how it is planned but I am going to give each group different items, they will all get 3 different types of items and at least 7 of them, but different shapes or colors or symbols to see if they think that makes an impact on their results.