“Pick a digit. Pick your favorite digit–any one you want, from the pile on the table.” That’s how the “human digits” activity starts. It’s another social math activity, this one to teach place value, and to practice reading big numbers.
Make a Safer Space
I know I’m going to ask people to get themselves into groups, and some people will hang back and wait to be invited to join a group, which is stressful, and others will be nervous about being on their feet and not knowing what I have in store for them. So I put some energy into making the space more comfortable for everyone.
“I’m going to ask most of you to work in groups, but there are a couple of parts to today’s work that need to be done solo. So if you’d like to work on your own, come and see me while people are sorting themselves out.”
Form the Groups
“Take your digit with you, and sort yourselves into groups according to your shoes. The groups can be any size.” (If I know people may have trouble reading numbers larger than three digits, I ask them to make groups with a maximum of three students in each.)
Sampson says, “What do you mean, according to our shoes?”
And Bridget echoes, “Yeah, how do we do that?”
I say, “Find some other people whose shoes are somehow like yours.”
Sampson grins and points to his size 16’s. “You mean, BIG?”
“Whatever you like,” I reply.
In the meantime Lori and Samantha, who always want to work together, have figured out that they are both wearing sandals, and announce that they are starting a sandals group.
Four other students have got themselves in a ragged circle and I hear them saying to each other that they all have black shoes.
I see that Gayle is wearing black sandals, which gives her a choice–she can join the sandals group, or the group wearing black shoes, whichever she likes.
Don comes up and says he would like to work on his own. I thank him, make sure he has his digit with him, and fill him in on the job I have in mind for him.
The Groups Introduce Themselves
I ask each group to tell us how they came to be, and we are all introduced to the Sandals, the Black Shoes, the Boots, the Sneakers, and the Special Laces.
The Human Digits Form Numbers
“Make the largest number you can using all the digits in your group,” I say. “Line up with your digits so we can all see your number.” There is a little flurry as the Boots shift their position so their number can be read by the others. They had originally put themselves together looking down at their digits, then flipped them over so others could see; then Jamie realized that their number was no longer the largest possible, and got them all to move.
I ask for someone in the Sneakers group to read the number the Sandals have made, then ask the group in general if that is the largest possible number. People agree that it is. (That is another wonderful thing about Human Digits. Someone in the group always knows how to do it right. Or nobody knows, which is just as good, and the teacher is there to be asked.)
So it is time for Don to do his solo job. I ask him to stand to the left of the Sandals group with his digit, and ask someone to read the resulting number, now one digit longer.
Then someone from the Sandals group reads the number that the Boots have made, we check to see that it is indeed the largest possible number, and Don does his job again to make a number one digit longer.
And repeat around the room, without spending too much time on any one group.
A moment to look at all the numbers and discuss which is largest, which smallest, or anything else of interest, and the first round is over.
The Human Digits Make More Numbers
“Make the smallest number you can,” I say. And repeat the reading, checking and adding Don’s digit.
“Make a number with your largest digit in the ones’ place.” And repeat as before.
“Make a number with the smallest digit in the tens’ place.” And repeat.
Quit While It’s Still Interesting
That’s enough for today. Tomorrow, or later in the week, we’ll do it again. Depending on the class, I’ll ask for groups with a certain minimum number, or I’ll join two groups together to make a bigger number, or I’ll have a digit so that Don and I will both add our digits to each number.
And speaking of Don, there is another job I could offer him as well as being the “extra” digit: he could write all the numbers as they are made on the board, and at the end of the exercise, I would ask the students to write them in order from smallest to largest.
And if no Don requests the solo jobs, I could do them myself.
Why Human Digits?
I like Human Digits because it replaces that ugly exercise found at the beginning of many math programs–you know the one where students have to write the numbers in words, or match the words to the numerals, really, an attempt to give them practice in reading numbers. Human digits gets them reading many numbers in a few minutes, with immediate feedback. It also presents them with a model of the difference between a digit and a number.
The really big concept in early math is place value–all that adding, subtracting, multiplication and division of whole numbers and decimal numbers rests on an understanding of place value. So I want to focus on it for longer than the day it takes to do the ugly exercise. As well, people get a visceral sense of reversing the digits in the largest number to make the smallest possible number, what it means to stand “in the tens’ place” or “in the ones’ place,” and the physical separation of the groups of three digits inside a number with four or more digits.
Human digits, like any social math activity, has the advantages I wrote about last week. I like it because it’s always different–different groups, different digits, different numbers. And I can stack the digit deck, so that there are no zeros, or lots of zeros. I can adjust it for my students and my lessons.