What are binary shares 5th grade

Binary Number System. A Binary Number is made up of only 0 s and 1 s. There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary! A " bit " is a single b inary dig it . The number above has 6 bits. Binary numbers have many uses in mathematics and beyond. In fact the digital world uses binary digits. How do we Count using Binary? The same thing is done in binary . And that is what we do in binary . . but that number is already at 1 so it also goes back to 0 . . and 1 is added to the next position on the left. add 1 on the left. See how it is done in this little demonstration (press play button): Here are some equivalent values: Binary numbers also have a beautiful and elegant pattern: Here are some larger values: "Binary is as easy as 1, 10, 11." Now see how to use Binary to count past 1,000 on your fingers: In the Decimal System there are Ones, Tens, Hundreds, etc.

In Binary there are Ones, Twos, Fours, etc, like this: Numbers can be placed to the left or right of the point, to show values greater than one and less than one. gets 2 times bigger . gets 2 times smaller (half as big). The "10" means 2 in decimal, The ".1" means half, So "10.1" in binary is 2.5 in decimal. The word binary comes from "Bi-" meaning two. We see "bi-" in words such as "bicycle" (two wheels) or "binocular" (two eyes). A single binary digit (like "0" or "1") is called a "bit". For example 11010 is five bits long. The word bit is made up from the words " b inary dig it " How to Show that a Number is Binary. To show that a number is a binary number, follow it with a little 2 like this: 101 2. This way people won't think it is the decimal number "101" (one hundred and one). Example: What is 1111 2 in Decimal? The "1" on the left is in the "2×2×2" position, so that means 1×2×2×2 (=8) The next "1" is in the "2×2" position, so that means 1×2×2 (=4) The next "1" is in the "2" position, so that means 1×2 (=2) The last "1" is in the ones position, so that means 1 Answer: 1111 = 8+4+2+1 = 15 in Decimal. Example: What is 1001 2 in Decimal?

The "1" on the left is in the "2×2×2" position, so that means 1×2×2×2 (=8) The "0" is in the "2×2" position, so that means 0×2×2 (=0) The next "0" is in the "2" position, so that means 0×2 (=0) The last "1" is in the ones position, so that means 1 Answer: 1001 = 8+0+0+1 = 9 in Decimal. Example: What is 1.1 2 in Decimal? The "1" on the left side is in the ones position, so that means 1. The 1 on the right side is in the "halves" position, so that means 1×(12) So, 1.1 is "1 and 1 half" = 1.5 in Decimal. Example: What is 10.11 2 in Decimal? The "1" is in the "2" position, so that means 1×2 (=2) The "0" is in the ones position, so that means 0 The "1" on the right of the point is in the "halves" position, so that means 1×(12) The last "1" on the right side is in the "quarters" position, so that means 1×(14) So, 10.11 is 2+0+12+14 = 2.75 in Decimal. "There are 10 kinds of people in the world, those who understand binary numbers, and those who don't." Ari Paparo Dot Com. Teaching Binary to Fifth Graders. Last year I posted a fun review of how I tried to explain internet advertising to my son&rsquos kindergarden class. I got a ton of great feedback from other parents about using the techniques, and some folks in the ad industry even used it to explain what we do to other adults! So when my buddy Max (11) asked me to be the guest speaker in his class I jumped at the chance to continue my experiment in teaching.

Max had different motives &ndash he knew that I used to work at Google and wanted me to tell cool stories about self-driving cars, Google Glass, and GoogleX (Sergei&rsquos secret lab where he&rsquos turning himself into Bat Man ). I decided to split the time between the Google stuff and a lesson about how computers really work at the lowest level. Keep in mind that these kids know basic math pretty well at this point, so I was trying to keep it within their abilities for addition, multiplication, etc. Here&rsquos how the lesson went, I hope you find this interesting and helpful and leave comments with your thoughts. Starting with the Concepts. To get the kids talking and motivated I started with some simple questions: &ldquoHow many of you like computers?&rdquo &ndash All hands raised &ldquoHow many of you like math?&rdquo &ndash A couple of hands dropped &ldquoDid you know that math and computers are basically the same thing?&rdquo This got a couple of the kids intrigued and got some puzzled looks from others. I explained that when they&rsquore playing a game or a movie on an iPad, it&rsquos basically just an enormous number of math equations taking place that make that game run, and I was going to explain to them how it worked. Some kids said &ldquochips&rdquo, but pretty quickly they volunteered &ldquoelectricity&rdquo. With that I explained that a computer is just a machine that runs on electricity like a blender or anything else in your house.

But how do we translate electricity to math and then to games, words, videos, etc.? That&rsquos when I broke out the cheap, RadioShack flashlight ($3.99, in-store only). I turned on the flashlight and asked: &ldquoImagine if we wanted to count using electricity. If this flashlight was like an onoff switch that was used for counting, how would we count to 5?" One boy volunteered and came up to the front to turn on and off the flashlight five times. "Great, now what if wanted to count to a million or a billion?&rdquo The kids were flummoxed. Until I broke our my four-bit array of flashlights: How high do you think I can count using just four flashlights? I started counting from zero to 15 using the flashlights, stopping every once in a while to ask the kids how to get to the next number. For example, when I was up to 9, the 8 and the 1 were both on, and I asked &ldquohow would I get to ten?&rdquo and the kids were able to get it pretty easily. Once I got to 15 I made the point that with one flashlight I could only count to one, but with four I could count to 15. Going to the whiteboard (all kids classes seem to have them now) I wrote down &ldquo1 2 4 8&rdquo and noted that each new flashlight was double the value of the previous one. &ldquoHelp me continue the sequence. Who wants to tell me what&rsquos after 8?&rdquo With some help from me, we pretty quickly expanded two to the 15th power: With a fairly small number of flashlights we could reach very large numbers.

We could get to the millions with only a couple more doublings. Each flashlight is a &ldquobit&rdquo or &ldquobinary digit" Each group of 8 bits is a "byte&rdquo. To make this resonate I asked if anyone has heard the term &ldquomegabyte&rdquo (which everyone had, thanks to marketing of electronics) and explained that this was equal to &ldquoa million bits, or a million flashlights!&rdquo They were impressed. Next I wanted to transition from flashlights to the ones and zeros used in binary notation. I had prepared slidesprint-outs to use, starting with the familiar decimal notation: Then showing the binary notation: I was pressed for time, and the kids seemed a little freaked out, so instead, I used the whiteboard and wrote out much simpler decimal examples with only three digits like 156 = 1x100 + 5x10 + 6x1 vs simply binary numbers like 111 = 4x1 + 2x1 + 1x1 = 7. At this point, I&rsquod say there were one or two kids who&rsquos entire minds were blown wide open. The remaining kids were about 50-50 between those that were still with me and those that were a little confused. But How Do We Get from Flashlights to Games? Counting in binary is a building block, but I wanted to reinforce the lesson that binary math is the essence of all the higher level programs kids enjoy. I wanted them to use the binary math to create something visual, and an exercise was the best teaching technique. I printed out strips of paper that represented a 5-bit array and included greyed-out &ldquocheats&rdquo to let them know the decimal value of the places withiin the binary number: In advance, I had hand-written a set of specific numbers on each slip.

I asked the kids to put a big &ldquoX&rdquo within the cells of the paper slip that added up to the written number. For example, if I wrote &ldquo17&rdquo on the slip, the kid should have put the X in the 16 and the 1 boxes. (These instructions ended up being confusing, I&rsquom sure there&rsquos a better way to explain this and switching from ones and zeros to X&rsquos was probably a mistake). Most of the kids were able to complete the task pretty easily and I walked around the room to help those who were having difficulty. I then called out the following numbers in order and asked that if a kid had a slip with that number to bring it up to me: As I got the slips I taped them to the wall. When they were assembled, the &ldquoX&rdquo marks in the boxes created a bitmapped image of the letter &ldquoA&rdquo. This photo shows it, though its a little hard to make out since some kids put 0&rsquos in the empty spaces: Using just numbers, which were the equivalent of flashlight onoff switches, we had created the letter &ldquoA&rdquo, and the same techniques could be used to create an image, a video, a game, or anything else you might see on a computer screen. I think they got it, and if not it gave them a little inkling of what lies ahead as they learn some of these concepts in a more formal setting. I&rsquove put together my examples and exercise materials in a Powerpoint, let me know if you would like a copy. What are binary shares 5th grade All information in a computer is stored and transmitted as sequences of bits, or binary digits. A bit is a single piece of data which can be thought of as either zero or one.

This activity demonstrates how sequences of these two symbols can be used to represent any number. Script for your reference, for guiding children to discover binary numbers. Powers-of-2 flash cards and 01 cards. for each student. Have the students make these as described below. Large 01 flash cards (O on one side, 1 on the other). Copy of the Secret Numbers worksheet for each student. Help Cinda Get To School worksheet for each student. Binary Piano craft worksheets as desired. Binary magic trick handouts as desired. Counting to 1023 on Your Fingers worksheets as desired. The first part of this lesson is a discovery exercise which should stimulate students to learn to count in binary, as well as to reinforce their understanding of place value. You should review the questions in the script before leading the discussion with your students, but don't feel like you have to memorize the whole thing. Keep the script handy!

Also note that your discussion will probably not follow the script exactly. It is provided as a guide to help you keep your discussion on track. (The dialogue took place between Rick Garlikov and a class of 3rd graders.) Explain the motivation for the lesson, and tell the students that we're now going to play some games which will give us practice in writing binary numbers. Divide students into small groups (optional - this lesson can be done by individuals, pairs or small groups.). Distribute flash cards, one set to each student or group. The first time you do this lesson you'll have to have the students make their cards. The set should look something like this example: (The large cards are approximately 3in x 4in, and the small squares are 2.5in x 2.5in. Note that the small cards have a zero on one side and a one on the other.) Have students sort the cards in descending order so that the largest is on the left and the smallest is on the right. Discussion: "What do you notice about the numbers on the cards?

" For the younger kids it is enough for them to notice that 1+1=2, 2+2=4, etc. Middle kids should recognize 1 x 2 = 2, 2 x 2 = 4, etc. High school kids should say something like "powers of 2." They should also note that these are the place values discovered in the preliminary discussion. More discussion (optional): a. "If I had given you another card, what would it have been?" (32) b. "How many cards would I have given you if the maximum card were 128?" (8) More optional discussion: Another fun thing to point out is that each card is one more than the sum of all the cards lower than it. For example: 1 + 2 = 3 = 4 - 1, and 1 + 2 + 4 = 7 = 8 - 1. "Without taking the time to add up all the cards, can anyone tell me the sum of all the cards?" Game #1: Have the students turn over the cards so the numbers are hidden. To reinforce their memory of the different place values call out numbers for them to "find." When they seem to know where all the numbers are, with a playful grin call out a number which they don't have. For example, 3. Some students might point out that they don't have 3, but they do have 1 and 2. Do a couple other sums which involve 2 cards, then move to 3 cards, etc.

Now flip the cards back over so that the number is showing. Game #2: Call out a number, and have the students place 1s above the cards which sum to that number, and 0s above all other cards. For example, if you say 11, students place 1s above cards 8, 2, and 1, and 0s above 16 and 4. An easy one: 5 (answer 4, 1) harder: 22 (answer 16, 4, 2) last one: 15 (answer 8,4,2,1). If some students find the answers quickly, challenge them to find another solution (they won't be able to do so). Have older kids turn over the flash cards after the first example so they get to practice remembering the values. Ask if anyone in the class has a system for finding an answer. Upper grades should have done so. Request that a student demonstrate the system to the group quickly. (A good method for doing this is to subtract the largest power of two you can from the original number, then subtract the largest power of two you can from that number, then subtract the largest power of 2 you can from that number, etc. until you get down to zero. For example, 37 - 32 = 5, 5 - 4 = 1, and 1 - 1 = 0. Then, write 1s in the places of the powers of two you subtracted and 0s elsewhere: 37 = 100101.) Discussion a. "What's the largest number you can get?" (31) b. "What's the smallest number you can get?" (0) c. "Can you do your age?" (Sure, unless you're older than 31!) d. "Can you suggest an impossible number which is between the smallest and largest numbers?" Explain that since we know the system we're using is binary, the 0s and 1s represent the original number.

Older kids should see the binary expansion as a sum of products where the decimal value is equal to the sum of each binary digit multiplied by its corresponding power of 2. Spend a few minutes reemphasizing the connection between binary numbers to decimal numbers. For example, the decimal value 453 is equal to four 100s plus five 10s plus three 1s. Similarly, the binary value 111000101 is equal to one 256 plus one 128 plus one 64 plus one 4 plus one 1. You may want to point out that just as the place values in the decimal representation are powers of 10, the place values in the binary representation are powers of 2. Game #3: What number is (binary) 11001? 1011? Try to have the advanced students visualize the cards. Can we do all numbers up to the maximum discussed above? To answer this question we need 4 volunteers, each of which holds a large 01 card. (We won't go all the way to 31. That would take too long. Instead we'll go to 15.) Each of these 4 students represents one of the flash cards used in the earlier exercises. Have the remaining students direct the 4 students to show 0s or 1s, and sit or stand accordingly. Start with 0, all 4 students should show 0s, and be seated. Next do 1, students should show 0001, and the rightmost person should stand up. Then 2 should be 0010, etc. Try to elicit a system for incrementing the numbers.

Point out that this system is like adding 1 each time. Younger kids may not see a system. Discussion: Can all numbers be represented using only 0s and 1s if I gave you enough cards? What's a simple proof of this? (Answer: we can always add 1, so we can start at zero and get up to any number.) Closing discussion: briefly discuss with the students what number systems would be like for aliens with different numbers of fingers. The first part of this exercise gives the student the opportunity to demonstrate hisher understanding of the mechanics of changing a number to binary and back again. The second part asks for deeper understanding of the notion of place value. Advanced students may be able to prove that a binary representation is unique. Practice counting to 1023 using only your fingers (up = 1, down = 0). How high can you count if you use your toes as well? Allow students to discover certain pleasant characteristics of binary numbers. For example, to multiply a binary number by 2, simply add on another 0 in the least significant (rightmost) bit.

How can you divide by two? What number is represented by 1? by 11? by 111? by 1111? What is the pattern? What number is represented by 1111111111? Which of these characteristics have analogs in other bases? What base would an alien use to contact us initially? (Assuming the alien doesn't know that our numeric system is decimal, the alien would use unary (just 1s as a tally of the values).) Suppose the alien counts in base 13. If the it communicated to us in base 13, we wouldn't be able to recognize the values. Higher grade students should be asked to articulate the difference between numbers and their representations. Have children construct the Binary Piano, or make magic cards for the Binary Magic Card Trick. Have two students stand apart with 5 chairs between them.

Ask one to walk to the other, going left or right around each chair. (See the Help Cinda get to School handout associated with this activity.) How many ways to do this are there? The answer will become more clear if you place a tag on the floor reading "0" to the left of each chair, and reading "1" to the right of each chair, and then ask the children to write down the sequence that they spell out during their walk. How many ways to make a pizza are there, if there are 7 different toppings? (2 7 = 128, since there are two choices for each topping - either put it on, or leave it off). This extends nicely into a lesson on elementary combinatorics: How many ways are there to get dressed if you can choose between 3 pairs of pants, 5 shirts, and 4 pairs of shoes? (3 x 5 x 4). How I Taught Third Graders Binary Numbers. Last week I introduced my son’s third grade class to binary numbers. 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.

The Number Twenty-Seven in Tape Flags, Broken Into Powers of Two. Before my presentation, I put twenty-seven tape flags on the whiteboard, in an unorganized fashion like this: (I would have preferred to use magnets instead of tape flags, since they would have been easier to move and align but I didn’t have twenty-seven identical magnets.) I started my presentation by telling the class that I would teach them about something called binary numbers, but that first I would review the numbers they already know — decimal numbers (I took a moment to explain that this was not the same as &ldquodecimals&rdquo). The first thing we did was count the tape flags, and as we counted together I rearranged them into a line: Twenty-Seven Objects, Arranged In a Line. I asked them how they would write that number. One student came up and wrote &ldquo27,&rdquo which is the first answer I expected. Other suggestions were Roman numerals (&ldquoXXVII&rdquo) and &ldquotwenty-seven,&rdquo also as I anticipated. One student suggested writing it in Japanese (I was expecting a foreign language, but Spanish: &ldquoveintisiete&rdquo). Some students suggested arithmetic expressions, like 20 + 7. 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 singled-out the answer &ldquo27&rdquo and said it is written in place value. I reviewed how the places were powers of ten. Then, as the class counted along to twenty-seven, I rearranged the flags into base ten block powers of ten groups, under headings labeled &ldquotens&rdquo and &ldquoones&rdquo: Twenty-Seven Objects, Broken Into Powers of Ten.

We counted the powers of ten and wrote the totals in the blanks I drew below each grouping of blocks we came up with the numeral &ldquo27&rdquo: two tens and seven ones. 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 to 625, and 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: &ldquotwenty-fives,&rdquo &ldquofives,&rdquo and &ldquoones.&rdquo I asked &ldquoare there any twenty-fives in twenty-seven&rdquo and they said &ldquoyes.&rdquo We then counted out twenty-five flags, which I removed from the decimal grouping we’d just done. I built a block as we went, under the twenty-five label.

Next I asked if there were any more twenty-fives in the flags that remained, and they quickly said &ldquono.&rdquo They could also see there were no fives, and that there were only two ones left, which I moved under the ones label. Twenty-Seven Objects, Broken Into Powers of Five. We counted the powers of five and wrote them under each grouping of blocks, coming up with the numeral &ldquo102&rdquo: one twenty-five, zero fives, and two ones. Some kids wanted to pronounce this as &ldquoone-hundred and two&rdquo, but I told them you pronounce it as &ldquotwenty-seven,&rdquo or &ldquoone-zero-two base five.&rdquo Now I said let’s look at another example of place value: base two, or binary. 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 4096 before I could cut him off :)), which they remembered from my last visit. We proceeded as above, except we pulled out the powers of two (from the flags in the quinary grouping): first we looked for sixteens, then eights, then fours, then twos, and then ones. Twenty-Seven Objects, Broken Into Powers of Two.

We counted the powers of two and wrote them under each label, coming up with the numeral “11011”: one sixteen, one eight, zero fours, one two, and one one. 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 said any number could be the base, but you’d have to have enough symbols. I briefly explained why you wouldn’t want a multi-digit number in a place (it would make the numeral ambiguous). 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!) Students as Binary Numbers. At the front of the classroom, just below the whiteboard, I arranged five chairs, facing the class.

I wrote the names of the binary places above the chairs, left to right from the class’s point of view: sixteens, eights, fours, twos, ones. 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 pattern 11011, which 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. For example, when I said &ldquonine,&rdquo they called out instructions to make the volunteers stand and sit to make the pattern 1001. 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: All volunteers start out sitting, representing zero. Whenever I say &ldquocount&rdquo The ones place volunteer does the opposite of what she is currently doing: if she’s sitting, she stands if she’s standing, she sits. For everyone not in the ones place, if the kid to your left sits, you do the opposite of what you’re currently doing. I think this would have made the counting easier and more fun. ( Update 11712 : I gave this presentation again recently — to fifth graders — using the new counting scheme. It did not go over like I imagined. The kids were confused about when to stand and sit, and weren’t having fun. In the future, I’d omit binary counting in hindsight, it seems too &ldquocomputery&rdquo for this context.) I mentioned briefly that there is an equivalent of decimals in binary numbers. Instead of the tenths, hundredths, etc.

places there are the halves, quarters, eighths, etc. places. I think most of the kids understood the presentation certainly, they were all engaged. I’d like to think it gave them a better understanding of decimal, even if they didn’t understand the details of binary. I told them &ldquoyou may not understand this now, but when you see it again someday, you’ll remember back to this day in third grade and it will come to you.&rdquo Someone then asked what grade they teach this in. I said it’s not really part of any particular math class (as far as I know) but that they would be taught it in a high-school computer class if they took one. I used number words when I wanted to avoid writing decimal numerals for example, when describing a number or when labeling places. Unfortunately, number words have decimal place value built-in, but that’s the closest I know how to get to a base-independent description of a number. That said, I don’t think the class recognized this, so I don’t think it caused any confusion. I didn’t explain why we broke the numbers down by starting with the largest powers and working down. If I had more time, maybe I would have let them discover the algorithm themselves. I use the term &ldquonumber&rdquo when I really mean &ldquonumeral&rdquo, as in &ldquobinary number&rdquo or &ldquodecimal number.

&rdquo This terminology is unfortunate, but it is standard. I used a different approach, but a lot of the same concepts are involved. Rick’s method centered on binary counting, which lead to a discussion of powers and places. 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. I also liked the way I exhibited the concept of &ldquonumber vs. numeration.&rdquo This page contains videos on binary counting, which inspired my own binary counting demonstration. I taught my mother a little differently (at least in my second attempt), mainly because I think most adults don’t think explicitly about place value. I’d love to know if this method works for you if you try it, please let me know! 22 comments. What an awesome idea!

What is a way they could utilize what they learned right after you teach them? Is there something online? This is awesome. I teach 3rd grade math at an NGO in Brazil and will give this a try if I can! There is no applet online that I know of that presents you with a collection of objects and lets you rearrange them by base (sounds like a good project for one of my readers 🙂 ). As for general practice with binarydecimal conversion, check out the Cisco Binary Game. Thanks for the feedback. Good for you. Working with young people is really a treat. We have been teaching binary numbers and C programming to 7 & 8 year olds for a while.

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. Keep up the good work. I like it… and learned a couple of things! One thing that got me confused is that the “Ones” columnposition has more than one block per column, you have to count them vertically, on the other columns you can count horizontally. I dug up my son’s old “Growing with Mathematics” workbooks to see how they do it (maybe I should have done that in the first place instead of relying on memory?). They place the ones both vertically and horizontally, so I don’t think that’s the problem. (I don’t think strict adherence to either vertical or horizontal placement necessarily scales to higher places — and higher bases — anyhow.) 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. Here’s how I would redo the decimal diagram, for example, in Growing with Mathematics style: Do you think that works better? Thanks for the feedback! I’ve learned another activity for students to be active participants in there learning process. Thanks! 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. Kudos for thinking outside the box 🙂 That sounds like a good exercise. Did any of them figure out a systematic way to do it (wwww, wwwb, wwbw, wwbb, wbww, etc.) before you told them about the binary patterns? I thought about bringing in my binary clock too — but I’ll be sure to do it next time.

Thanks for the feedback. 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. It’s nice to see someone who’s been thinking of binary numbers almost as long as I have :). An interesting article. I tried to teach different base counting to a group of year 4’s to support their learning of 5 digit numbers and what the columns actually mean. 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’d love to take it the other way and look at hexadecimal. 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? (for example you put 4 bananas on a table and ask him how many there are… then you tell him there is 100 and then count with him: 1-10-11-100!) because if a five years old child could understand those basics, a few years later he could even be able to count, addsubstract, multiplydivide and even exponentiate mentally more than anyone! 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. Unfortunately, we don’t have words for binary numerals. We pronounce 101 as “one-zero-one”, not as something like “four and one” (or something totally new and not decimal number word based). 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. Then how about *inventing* systematic names for binary numerals, in the same way we invented the decimal ones? Here’s my proposition, from the top of my head: Let’s say, we can read 10110 as deedodeedeedot :)The pattern is simple: 1 is the “dee” sylable, 0 is the “do” syllable.

The ending “t” (unvoiced “d”) is just to mark the least significant digit, so that we can also express fractions this way: 101.001 is deedodeetododee. Or we could also stick with the unvoiced consonant for all the fractions to make deedodeetototee. Although this is quite easy to readpronounce, it is no longer easy to write, because the names get long. So I think a better option could be to something more compact, where we would not waste more letters than needed. The simplest conversion (a direct one) would be to replace every 𔄘” with one letter, and every 𔄙” with another, but there is a tiiiiny problem with it: consecutive 0s or 1s would then melt together in speech, making it difficult to distinguish how many of them is there 😛 Therefore we need to use syllables anyway, made of two letters: a consonant and a wovel. So we need at least *two* letters for each binary digit, which is not as compact as the binary numeral itself, but it is the best we can do, I guess. To make it less repetitive and easier to distinguish, we can use a different wovel for 𔄘” and different for 𔄙”, and the same goes with the consonants. In my native language, we pronounce the letter “i” as the English “ee”, so the notation is quite space-efficient and easy to pronounce & distinguish from hearing. 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., by changing the consonant that goes with it. One possible code could be: So now we can name numbers more efficiently 😉 almost like abbreviating them through tetral and octal 😉 Some examples: So we can see that the more digits repeat, the more space we can save through this “run-length encoding” scheme 🙂 Another possibility for the RLE is to double the number of repeating digits with each new code, which should make it even more space efficient in the long run (no pun intended, but appreciated 😉 ). I guess this could also facilitate mental calculations.

To facilitate learning this code, you can make diagrams like this one: 111 00 1 0000 1. and after a while your brain should pick up these syllables along with their corresponding bit sequences pretty quick 😉 For longer or more sparse numbers, like 0.000000000000000000001, it could become cumbersome to write down or pronounce them (sasasasati) 😛 so we can introduce something similar to the scientific (exponential IEEE) notation by stating the mantissa and the exponent separated by some unique letter, let’s say “r”. Then, for the long number above, we can simply write down pronounce the scale first (because it tells the most), then saywrite “r”, and then write down pronounce only the significant digits (𔄙” in this case), which gives: titatitatardi (1×2^-10100 in binary, or 1×2^-20 in decimal). 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). Have always been interested in teaching kids about ‘numbers to other bases’! I think introducing binary, then hex, up front is helpful..since it quickly sends. out the idea of number bases with other than 10 numerals? 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: 1111 1011 0111 1001. etc…this is solid computer lingo! I’m in the process of compiling computer science lessons for teachers, and your lesson really helped me clarify language and methodology that children will understand. Thank you so much for sharing! I’m glad it was helpful.

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. This looks amazing! I teach Engineering and Technology to 1-4th grades, and I definitely love the idea of this for my 3rd and 4th graders! Does anyone have any ideas for how to introduce this to 1st and 2nd (my biggest concern is that their multiplication skills aren’t the strongest, or nonexistent at that age). I read a book to first graders that was about the powers of two, although it was not stated in those terms. Maybe you could start there. Leave a Reply Cancel reply. (Cookies must be enabled to leave a comment.

it reduces spam.) Subscribe. Fathers, sons, daughters, brothers, sisters, aunts, and uncles should read this too. Middle-schoolers, high-schoolers, and college grads might learn something too. What are binary shares 5th grade Get via App Store Read this post in our app! How to teach binary numbers to 5th graders? I already tried the direct approach, starting with "this is how it works". That turned out ok but took too long and was boring for all of us. My second attempt was using the twofingered alien. This worked better but needs improvement. The problem was that most kids in 5th grade are not aware of how the 10 based number system works. They just use it. I ended up having to explain the 10 based system in the middle of my binary alien story. That kind of interrupted the flow. But explaining the 10 based system before starting binary takes away most of the "suprises" of the aliens counting with just two fingers.

edit: I should probably add that I'm a math teacher in Germany and that binary numbers are on the agenda at this grade. A sketch of one idea. I think it's probably better spread over a couple of days. Start them counting, from zero, out loud to you. Write the numbers on the board as they go. Zero (0), one (1), two (2), . , ten (10). Stop here. Prompt a discussion about what happened - how is the most recent number different than all of the previous numbers? I expect (admittedly I don't have a lot of experience with this age group) that they'll be able to come up with the fact that it's now a two digit number. Press them to explain why we weren't able to express ten as a single digit. With some guidance, I think it's possible for them to come up with something that approximates 'because we don't have any more numbers'. Go into that - explain that the digits 0-9 are symbolic in nature, and that we use them to represent quantities.

Since we have ten of them, we're able to express ten different values with single digits, and when we want to express other values we have to use the digits in combination. Start over now, except ask the class to imagine that there were only 5 numeric symbols in the alphabet (0, 1, 2, 3, 4) and that 5 through 9 never existed. Again, count up from zero to four on the board, but put it to the class how five might be represented. This may be a struggle since lots of them will want very badly to write '5' - potential for some humor here though as you can remind them that '5' doesn't exist. Hopefully you're able to get the suggestion of '10' (5) out of the class, and then you're able to proceed with '11' (6), '12' (7), on up to '14' (10). If you're able to get them to '20' for eleven, then you're set - they get it. Run through the base 5 counting exercise again. 1,2,3,4,10,11,12,13,14,20,21, etc. If things go well enough here then it's time to get into generalized discussion about how this sort of counting works in comparison with 'normal' counting. Ask if there's anything special about counting with 10 digits, or with 5 digits, or with any particular number of digits. I expect that they'll say no. Move to binary now - tell the kids that there are only two number symbols (0 and 1), and get them to count aloud and instruct you on how to represent the numbers. They'll probably get through 0, 1, 10, 11 without much trouble, but you can help them move from here to 100 if they're stuck by asking about the transitions from 9 to 10 and 99 to 100 in 'normal' numbers. If things are going OK at this point, it might be appropriate to talk about computers, yadda yadda. My original thought after reading this question was that binary for elementary students is an awful idea, and representative of the bad habit of 'back-porting' desired skills into inappropriate age groups. (We need computer technicians? Computers use binary!

Teaching binary to kids will help!). But done carefully, it can potentially speak to one of the great joys in math - the whole idea is that you can make suppositions and then wonder about their implications. Suppose 5-9 don't exist? Absurd, but OK. Now how does counting work again?? Uh, did I understand counting in the first place? It's confusing in the way that mathematicians (of any age) love to be confused. I think it's best to take the intermediary step here (base 5) because it's substantially less of a jump than going straight to binary. In base five, things proceed in the natural fashion most of the time - when incrementing the ones digit - and only the 'rollover' conditions are different. Binary rolls over with every other increment, and requires a carrying rollover very early on, which is really a difficult thing. By learning base 5 first, you make it easier for them to understand the fundamental validity of different numbering systems, which makes it easier to process the ultimate extreme of using binary. I've never done this, but maybe something like the following will work.

Since they don't really understand base $10$ (indeed, one can consider that being the end goal of doing the binary stuff), you don't want to get all tangled up in binary position notation and the like. Start by looking at the numbers you get when you begin with $1$ and successively double: Leave this list on the blackboard or in some other place where the students can see it in what follows. Then tell the students (in an age-appropriate manner) that even though this process removes relatively more and more numbers from a listing of all positive integers, the numbers that are left have a really neat property. Namely, every positive integer can be written as a sum of these numbers where each of these numbers is either used just once or not at all. Moreover, there is only one way to do this for each positive integer. For example, $13 = 8 + 4 + 1$ and $23 = 16 + 4 + 2 + 1.$ Then pick a number, say $53,$ and show students how they can find the powers of $2$ that work. First, find the largest power of $2$ that doesn't "overshoot" the integer. In this case it's $32.$ Now subtract $32$ from $53$ to see what's left: $53 - 32 = 21.$ Now find the largest power of $2$ that doesn't "overshoot" the part that's left. This will be $16.$ Next, subtract $16$ from $21$ to get $5,$ and so on in the manner we all know about. At the end, tell the students that we'll record the result using a shorthand code. In the case of $53,$ the shorthand code is $110101$ because (reading the $0$'s and $1$'s from right to left) we used $32,$ we used $16,$ we didn't use $8,$ we used $4,$ we didn't use $2,$ and we used $1.$ You can mention that the shorthand code always starts with a $1$ (because there will always be a largest power of $2$ we can use), but after that anything can happen.

Perhaps then give students two or three examples to try among themselves (small groups ought to be great for this). After most students seem to understand how to carry this out, you can then consider the reverse problem where someone gives you a code for the number and you figure out what the number is, such as $10010$ being $2 + 16 = 18$ and $110011$ being $1 + 2 + 16 + 32 = 51.$ Point out that when deciphering the code for a number, it's easiest to work through the digits from right to left (opposite the direction we used when finding the codes). So far there is nothing about positional notation or how this is base $2$ and we're used to working with base $10,$ but at least this will get across some aspects of binary notation without delving into abstract positional notation system stuff (which will likely fly right over their heads if you start there). You might also be able to work in the game of $20$ questions, explaining (carefully!) how the number of digits in the code tells you how many yesno questions are needed. When teaching binary to any age group I always start by taking a set of kitchen weights into the classroom. 2lb (32oz) 1lb (16oz) 8oz 4oz 2oz 1oz. Then make a table asking what weights yo1u would use to make up certain values. If a weight is used you show it with a "1" if it is not used you show it with a "0". What weights would you use for 1oz 1 2oz 1 0 3oz 1 1 4oz 1 0 0 5oz 1 0 1 6oz 1 1 0 7oz 1 1 1 8oz 1 0 0 0 9oz 1 0 0. A colleague of mine has pretty good success with a sitting and standing activity. The basic idea is this: Line up 3 to 5 chairs in front of the class with a person sitting in each chair. The rules are: You sit down or stand up (i. e. change position) if the person on your left sits down and the person all the way to the left can sit and stand freely.

The goal is to find the number of moves the person all the way to the left has to make to get the person all the way to the right to stand up. I often invent a land where the money comes in units of 1, 2, 4, 8, 16, . and then ask how to pay for certain amounts, using exact change, with the fewest possible coins. It's nice that the greedy algorithm of always using the largest possible coin always works! Then I make the analogy starting with $101 meaning one hundred-dollar bill, no tens, and one one to lead them toward using binary notation to represent the way that they're paying the amount of money that they need to pay. For completeness I'll add a reference to Rick Garlikov's use of the Socratic method to teach binary arithmetic to a third grade class. It took 75 questions in the instance he describes. A complete transcript and a summary of his thoughts on the process are at The Socratic Method: Teaching by Asking Instead of by Telling. Esmaya, I have done math circles around base 8 and base 3. I made a little story for base 8 called Eight Fingers. Your students might have fun illustrating it. (The 'code' at the end is actually binary. If you have time for that sitting and standing activity, they would go together well.) I have a suggestion for getting a feel for how the number system works, which might even convince them that it is a useful thing to know how to do. Step 1: A method of counting. Take a pile of small objects (beads, lollies, blocks, pieces of spirali pasta, Go counters -- whatever takes your fancy -- though anything that naturally joins together might have a slight advantage). Then say you are going to count how many there are by a new and creative method. First you'll group them into pairs.

There may or may not be one left over but that's ok. Next you'll group your pairs into pairs, making groups of four. There may or may not be a pair left over but that's ok. Now you'll group your groups of four into pairs, making groups of 8.Now group the groups of 8 into pairs, making groups of 16.Now group the groups of 16 into pairs, making groups of 32.If you haven't chosen too many things in your pile it means that now you'll have to stop because there are no pairs of groups. Of course if there are more you'll just keep going on pairing up the biggest groups. Now how many have we got? Well let's start with the biggest group. We have one group of 32, one group of 8, one group of 2 and a single object. So that's 43 things. As a way of counting it was quite efficient because we weren't actually counting at any point, only pairing things up. At this stage you can give everyone a pile of things and they can do the pairing up themselves and figure out how many objects they have. You can also imagine this being done with the students themselves -- get them to pair up, then pair up the pairs etc. Of course some of them might be a bit miffed at being the ones left out at the end. Step 2: A new way to represent numbers. You should be able to say at this point that in fact every number can be grouped like this because they can see that all their piles have been effectively split into pairs progressively. So that means it's a neat way of representing what number you have. But there's an even neater way to do it and here it is. List the sizes of the piles on the boarddocument camerascreen: 32, 16, 8, 4, 2, 1 Now underneath say you'll write how many of each pile you have.

In our example you have 1 0 1 0 1 1. Ask them to do this for their own piles and get some or all of them to write their numbers and their list of piles on the board. At this stage they should be able to see that every number has a representation as a string of 0's and 1's. Ask them if it's possible to get anything other than 0 or 1 (the answer is no, but you want them to be sure). Then you can say that this is the binary representation of a number. Each digit is how many groups of that size you get when you successively pair things up. It may be worth doing this process for other sized groupings, like grouping into 10's, which they may be familiar with from earlier years. Now you can give them various binary representations and ask them to tell you what number they represent. Step 3: Adding binary numbers. Now pair up your students and get them to add their numbers together and find out what the new binary representation is. See if they can do this without having to start from scratch. Hopefully they hit upon the idea that they can join any groups that are the same size into bigger groups, and continue this process until there are no more. They'll probably do this organically with no structure, and after discussion you can practice by always starting with the smallest piles. Then you can see how this works on paper with the binary representation. I think this method could work quite well to get them started on binary numbers, though including some other activities involving counting in binary with the fingers of your hand (as others have described) wouldn't go astray. Give them some motivation to learn it. Three years ago I was meeting 3 fifth-graders once a week for half an hour of math. Mostly we did puzzles and games. One time I gave them the rules of Nim we played it in various combinations, and (naturally) I could always win.

I even played all 3 of them simultaneously and won all the games. So by then they were asking how I did it. Some later week (reminding them about Nim) we discussed using bases other than 10, and converting back and forth. Then a third week I told them the method for Nim, based on writing the numbers in base 2. It may be helpful when introducing binary numbers to begin with showing the difference between counting and arithmetic in binary and binary codes: This may help clarify the complex issue of symbols and what these symbols are used for. By the 5th grade students have a fair amount of experience with the decimal system. Decimal codes are less common than binary codes and so when one moves to showing students how one can count and do arithmetic in other systems than decimal it may be useful that binary codes be part of what one does. Furthermore there are lots of lovely applications of binary codes (Huffman codes, for example). I'm posting this answer to complement @JoshuaZucker's one, whose idea is basically the same I'm introducing. Instead of using money, use weights and. the magic cards (they'll love them). Suppose we have a set of weights. One weight of 1kg, one of 2kg, one of 4kg, one of 8kg and one of 16 kg. Then, I propose the students to make a table specifying which weights are required to weigh 1kg, 2kg, 3kg, 4kg, 5kg, . 31kg.

For example, to weigh 7kg you need the weights of 4kg and 3kg. And so on. Actually, when they'll finish, they'll have a complete binary representation of numbers from 1 to 31. Just for amusement (motivation) and reinforce it, they can prepare the so called magic cards. You could even start the lesson showing the power of this cards. Show the cards with the PC and tell a student to think a number. Then tell himher what number it is. Magic cards are just tables in which you put all the weights you can weigh with each one of your original weight set. The first card includes all numbers that require the 1kg weight. The second, that require the 2kg weight. The third, that require the 4kg weight. And so on. Once the students are done with this activity, the best option is to continue as @DavidButlerUofA explains, just to make them realize how counting systems work. Then tell them how would they count when having eight fingers instead of ten!

I haven't tried this in a class but it worked in one-on-one conversation with kids at basically all ages (well, ability to count is needed but that's basically it). It also has the benefit, that you do not need to speak about positional notation or the 10 based system at all for the beginning. I can count to 1023 with my fingers. To show how, hold your closed fists, showing the backs of your hands. Show your right thumb and say "one". Fold the thumb in and the index out and say "two". Let the index out and also show the thumb and say "three", and so on. At some point some kids get where this is going and figure out how the 1023 comes into play. Some other kids need some more time but in my experience, basically anybody can figure out what the system is by doing it himself. Of course, many kids will find it funny to show the number 4 or (even better) 132. You can also ask how far two kids can count if they use all four hands… From that point on you can take different. You could go into the direction that the fingers really do not matter here and use another binary notation.

You could also investigate numbers that the single fingers represent. No matter how you do, you'll end up explaining the binary system. I am also in Germany and confirm that this is a topic in 5th grade and also that the books I've seen make no reference to "counting with your fingers to 1023" at all.