I challenged my advanced math students to not blurt out the solution, but to stop and think about the process that led them to their conclusion - the general solution for N. I reminded them that even though the candy bar problem is simple, it is good to remember the problem-solving process because sooner or later a more difficult problem will likely require them to use the problem-solving process.
I get my kids up and moving around for as many activities as possible. I had them up in groups for this activity. I used the candy bars which unfortunately led to too many requests of, “Can we eat the candy now?”
I challenge students with different learning levels by mixing them with groups of various learning abilities and personalities. I assign activities that force all students in the group to participate in some way. There must be collaboration from everyone.This way the shy students will begin to open up and the aggressive students will allow others to take lead.
I have a strong class of learners and there are only a couple of students that will need to assistance. I will pair these students up with higher level learners. After they try the activity I will also demonstrate the answer for the visual learner to see.
I pretty much followed the lesson plan for this activity. I do have a worksheet for students to complete about the problem though.
It is that whole growth mindset. As long as you can get them thinking, they are being challenged. Some will make the connection quickly and you want to push them farther. Some will struggle with making the connection so you push them too.
I have a classroom full of computers so when I did this activity we used paper and talked about how many folds it takes to get 12 equal pieces. It was the same concept but made so much more sense when they actually “tore” the paper so it was more similar to the break of the candybar. Otherwise it created some confusion because they counted the folds incorrectly.
When I see students with a more advanced level of problem solving experience, I ask them to generalize the pattern.
I try to get all the students involved. If you have a strong student in the group a lot of times the others will set back and let the strong one do the thinking for them. So I try to mingle and make sure everyone is giving input. Changing the teams up helps with this problem also.
I challenged my students to think outside the box. Are there other ways to break the candy than a straight line? Are there other methods that have different results (like dropping the candy to break it).
I like the idea of hand picking the students in groups for this activity. The stronger problem solvers might be able to help the others in the group “see the light”. Some students will struggle with this type of activity because they are not used to solving problems by themselves.
I find it best to start with an easy to solve issue, then increase the difficulty. It is also good to use problems with more than one way to solve it.
I have found that students with more problem solving experience are more than willing to help others by encouraging and questioning them. Also, there are no wrong answers. Students have to defend their solutions.
My students got wrapped up in how many breaks if the pieces were same sized v. different sizes, if they broke into halves each time v. thirds, etc. Several are in higher level math classes and had done similar activities. They also got into how many times a piece of paper could be folded before it was impossible to fold anymore.
Finally, they started looking at the “infinite candy bar” video online about the candy bar that never diminishes as you break off a piece at an angle. (It is an optical illusion but quite interesting.)
carefully organized groups matching students of varying abilities…stronger students help the weaker ones…weaker ones ask questions that prompt more thinking about the problem
I typically challenge students with different levels of problem solving experience by grouping them based on their prior knowledge (learning ability). I make sure there is a strong student within each group that can provided additional assistance or modified explanation. I have found students sometime pick up on another student’s explanation faster than the explanation that I provide (they understand the jargon more readily).
This problem seems pretty simple based on where my students are so so I plan on added some additional problems. We have iPads at school and I plan on using the app CargoBot with different levels of problems coming from the different levels in the game, all of which you can have the students go through the problem solving process.
I first had them complete this by only thinking the problem through and discussing it with a problem and then into small groups. Then they completed this by actually dividing the candy bar - physically touching it to check their original answer. Some students were surprised how their answers changed. Then I asked them to look at the problem again (using a piece of copy paper to represent a pan of brownies) and asked if there was more than one way to cut up the brownies to divide among the students in the class. When I put them into groups I tried to have a girl in each group since I have so few in my class. I also matched my OCS students with a strong AIG student.
I use the mixed-level method for forming groups and am making an effort to mix the mixed groups so there is a minimum or repetition and maximum of diversity within the groups. I have used random sorting (playing cards for instance) to assign leadership roles but also take advantage of organic events that cause some students to self-select for leadership and other roles (being careful not to have the “smart kids” or the " frequent contributors" always taking the roles)
I like the pairing up idea, but I do this using different learning styles. Each student completes a learning style survey at the beginning of the year, and I will place them with people who have different styles. They are able to share a lot of information rather quickly due to this huge difference.