What math do you see in this necklace?
Their responses allowed me to know what they thought when looking at the necklace, and also gave me a deeper view into what they considered to be be math.
D. A. suggested we can count all the beads.
H. S. said we could look for patterns in the necklace.
A few students suggested we could measure how big the necklace was. I asked them what they meant by big? They agreed they wanted to know how tall it was. I should mention that the necklace cannot be opened. It is made of wire and has been welded together therefore it cannot be detached. I placed the necklace vertical and asked them if they wanted to measure it this way? I then placed the necklace flat and asked them if they wanted to measure it this way? One student made a circular motion with her hand. I told them if they wanted to measure how big it was around, it was called circumference.
J. S. said "I think there is 100 beads!"
S. C. "I think there's 120 beads!"
I told them that this was called estimation. We could guess how many beads are on the necklace.
This little discussion amazed me. They came up with so many math concepts all stemming from looking closely at a necklace. I decided to use this opportunity to set up a little estimation provocation. I placed post it notes and told students that they could come anytime and guess how many beads were on the necklace. To make it more fun, I told them that whoever guessed the closest would win a prize!
D. C. and J. S. were interested in counting the beads so I told them to keep their answer a secret so we could figure out who was the closest to the actual number of beads.
"I looked at the beads and I thinked my number and wrote it down on a sticky." P. I.
"I looked at the last bead and the first bead. It helped me to estimate." O. M.
"I looked at the whole circle of beads and I guessed my number and then I got a sticky and wrote my number." K. W.
"I looked at the beads to see the first bead and the last bead and then I guessed." O. S.
"What strategy I used is I heard the people that know the number saying another number and it wasn't the real number but it was close." Z. G.
"I pointed at the beads and thought about the number." C. D.
We counted together and there were one hundred beads on the necklace! Three students guessed the number exactly. I was very pleased that many students were close. Some students guessed very low numbers. So we used this opportunity to demonstrate what that number of beads looked like in comparison to one hundred. The three winners were gifted three plastic little flies which they adored!
The following day, students asked if I could give them another challenge using the necklace. I asked them if they wanted to explore ways to measure how big around the necklace was? I set up another provocation and let them investigate it freely.
Once again we came together to discuss and demonstrate our findings. I enjoyed watching the many different techniques students used to try and determine the circumference of the necklace. It was interesting to listen to the conversation that emerged from the demonstrations.
"I used the measuring tape to measure." C. C.
"I measured using the purple measuring tape." K. W.
"So K. W. did it the same as C. C. I used rulers around the circle of beads. I got four feet. I know that one feet is one ruler." S. C.
"I don't know if it's a good way because it is a square and we are supposed to measure a circle?" P. I.
"I agree that it's not because some is not touching the circle." K. W.
"It doesn't all fit in, it's not a square, it doesn't go around." O. S.
"I agree with S. C. because it's a good way to do it." J. S.
"Some of it is touching and some of it is not." E. E.
"There is a triangle there and two triangles makes a square!" B. P.
"We used string to go around the necklace and then we measured the string and cut it, then we took the measuring stick and started at 0 and went to 98!" E. E. & O. S.
"I think this was a good idea because they measured the string around it and then they checked on the measuring stick." K. W.
"Yea it's a good idea, first they put it around and then put it on a ruler and made it straight on the thing to measure it." A. T.
All the students who took on the challenge of measuring how big around the necklace was also received a plastic fly.
I thought this was the end of it but the next day more students asked if there was another challenge that I could give them to do with the necklace. This time I told them to figure one out themselves. I was blown away by the concepts they discovered.
B. K. counted the different coloured beads.
W. E. created a survey asking his peers what their favourite math technique was for the necklace?
M. O. counted the different coloured beads.
S. C. and K. W. created a survey asking their peers what was their favourite bead colour?
P. I. Decided to measure the necklace diagonally.
So much learning from just a simple necklace. The students also got creative with the flies they were given by making habitats and stories!