# Binary addition lesson plan

I wanted to build on my prior visit, where I introduced them to the powers of two. By teaching them binary, I showed them that place value is not limited to base ten, and that there is a difference between numbers and numerals.

My presentation was based on base-ten-block-like imagery, since I knew the students were comfortable expressing numbers with base ten blocks. I thought extending the block model to other bases would work well. I think it did. Before my presentation, I put twenty-seven tape flags on the whiteboard, in an unorganized fashion like this:. The first thing we did was count the tape flags, and as we counted together I rearranged them into a line:. I asked them how they would write that number.

One student suggested writing it in Japanese I was expecting a foreign language, but Spanish: One unexpected answer was from a girl who wrote it on the board in base ten blocks, which is how I was planning to rearrange the tape flags next! I suggested tally marks as another alternative, and wrote twenty-seven in tally marks on the board.

I reviewed how the places were powers of ten. I told the class that place value is not limited to base ten. I said, for example, you could write any number in base five, or quinary. I wanted to take an intermediate step to binary, which is the simplest base, having only a maximum of one instance of each power. I had them compute the powers of five from one toand I explained that these are the places in quinary. I told them we would group the flags into powers of five.

I wrote three headings on the board: I built a block as we went, under the twenty-five label. I said it is based on powers of two. We computed the powers of two from one to thirty-two my son was rattling them off to before I could cut him off: We proceeded as above, except we pulled out the powers of two from the flags in the quinary grouping: When I was done with the tape flag examples, I took a moment to explain that base ten has ten digits, base five has five digits, and base two has two digits.

As an example, I said that in base ten you could never have a 10 in any place, because that would be the same as a 1 in the next higher place. Similarly for base two, a 2 in a place would equal the next higher power of two, which also would be the same as a 1 in the next higher place.

I told the class that you could write any whole number in any base. One kid asked if I could do it in a base that was greater than ten I forget which base he used as an example. I mentioned base sixteen, and said it uses the letters A through F for the values ten through fifteen. I did not intend to get into hexadecimal, but hey, I wanted to answer the question! At the front of the classroom, just below the whiteboard, I arranged five chairs, facing the class.

I got five volunteers to come up, and said that I would turn them into a binary number. I said if I told them to sit in their chair, they would count as a 0; if I told them to stand in front of their chair, they would count as a 1. For my first example, I put the students in the patternwhich the class correctly read as twenty-seven they added the place values above the chairs of the standing students — that or they read the numerals I had left on the board under the tape flags: I did a few other examples like this, which amounted to binary to decimal conversion.

They got them all right. Next I did what amounted to decimal to binary conversion, asking the class how to arrange the volunteers to represent a given number. They got all of these examples correct as well.

The above discussion took about twenty-five minutes, so with the extra five minutes I squeezed in a demonstration of a binary counter.

I took a new set of five volunteers and had the class direct them through the sequence zero to thirty-one. We got through the count, but I think a few students got lost as some of the faster adders called out instructions. In any case, there were definitely some who understood the process, enough to know that when I asked them to display thirty-two, they said we would need another volunteer.

If I had more time, I would have done the count a second time, with the volunteers driving the counting; I came up with this scheme after I left the class:. I gave this presentation again recently — to fifth graders — using the new counting scheme. It did not go over like I imagined. I mentioned briefly that there is an equivalent of decimals in binary numbers.

Instead of the tenths, hundredths, etc. I think most of the kids understood the presentation; certainly, they were all engaged. I used number words when I wanted to avoid writing decimal numerals; for example, when describing a number or when labeling places. If I had more time, maybe I would have let them discover the algorithm themselves. I used a different approach, but a lot of the same concepts are involved. My method started with powers and places, and lead to binary numerals and then binary counting.

Rick discussed other bases after discussing binary, whereas I discussed them before. Also, he discussed binary arithmetic, but I did not. One thing I liked about my approach is that I built in the concept of base conversion, showing the equivalence of whole numbers written in any base. This page contains videos on binary counting, which inspired my own binary counting demonstration. What an awesome idea!

What is a way they could utilize what they learned right after you teach them? Is there something online? Working with young people is really a treat. They are really easy to work with when the good teacher is at ease with the topic. In reading what you have done I get that you are at ease. All the math I learned in school was due to the comfortable teachers I had.

The two that I got not from were definitely out of their league. They key thing I think they do though is put more space between the ones blocks. As is, mine looks like an incomplete rod; I can see why that is confusing. I also taught Binary to third graders.

I had them sort blue and white mancala beads into as many patterns as they could using exactly 4 beads blue blue white white, blue white blue white, etc. Used the smartboard to further examine patterns in binary numbers. Brought in the binary clock — big hit. This was an enrichment lesson during my time unit. That sounds like a good exercise. Did any of them figure out a systematic way to do it wwww, wwwb, wwbw, wwbb, wbww, etc. I hope some of you who are interested in teaching children about binary will have a look at funforms, a place order, binary, tally mark system.

A narrated power point presentation is available at. Funforms reminds me of that. I ran out of time to get to binary. I had played with 21 as a number and had groups using connectable cubes so they could easily group. I wonder if it would be possible to then look at how drawing software adjusts mixes, averages, subtracts colours depending on brush options.

Do you know if it would facilitate the comprehension of numbers to a children by teaching them first binary around 4 years old and then teaching them decimal around 5 years old. I mean… do you think a young child could process and understand the basics of it? My point is that math is a language in the same way that English is one and if children could be mathematically bilingual the same way he could be directly, his mathematical development could be insanely boosted!

I agree that it is like a second language, but only to a point. That said, I think there is great value in introducing another base, though probably after base ten. Like learning a second language makes you understand language better, learning another base will make you understand numbers better. The pattern is simple: Or we could also stick with the unvoiced consonant for all the fractions to make deedodeetototee.

So I think a better option could be to something more compact, where we would not waste more letters than needed. If we wanted something more compact, we could also try to join consecutive digits of the same kind somehow into one syllable, in groups of two, three etc. One possible code could be: I guess this could also facilitate mental calculations. For longer or more sparse numbers, like 0. The system is so simple that I think it could be easily taught to a kid even before the decimal system except the exponential notation, which could come later.

I think introducing binary, then hex, up front is helpful. Then you can get right into it by showing how each 4 bit binary segment of a 16 bit binary word equates to each single hex digit of a 4 digit hex word: Thank you so much for sharing! This is some much more interesting and simpler than the lesson we use on our computer class with our 5th graders.

They glaze over after 10 minutes. I was looking for more interesting material for them. I will definitely try this this year.