Association of Teachers of Mathematics in Maine

Week 7: Call to Action (Option 2)

04 Jan 2018 3:40 PM | Anonymous member (Administrator)

Choose a rich problem from an upcoming lesson and plan how you might give students the opportunity to springboard off their first solution. The questions "What new questions do you have?" or "What are you wondering about now?" might help. What new questions did students generate or what new questions do you think they may generate?

Comments

  • 04 Jan 2018 7:23 PM | Anonymous member
    I want to use an image from 101questions.com. It is a picture of geometric shapes filled with skittles. I want to allow students to spend time asking questions about the image. following this I want to put 3/11 on the board and ask "If this is the answer, what could the problem be?" I anticipate this will be very difficult for my students at first because I have not done enough of this. I be intentional about the productive struggle. If scaffolding is needed I will change the "answer" to 1,326 skittles and see if they are able to generate possible questions, then we could use a different fraction 36/132 and see if they could generate questions.
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    • 14 Jan 2018 6:26 PM | Anonymous member
      I read your question and was immediately engaged! It was interesting to see how excited I was. I was picturing Skittles myself without having seen the picture. I think having Skittles (brightly colored candy) helped even more so to engage! I wish I had used 101qs.com for my problems of the day when I taught 6th grade math. They would have been more fun and memorable.
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  • 07 Jan 2018 10:07 AM | Anonymous member
    We are studying proofs. We are continually woking on how to reason through a two column proof, which are really difficult for students. I am going to use the wonder and notice to introduce the next set of proofs. I am going to put a picture of 3 parallel lines cut by a transversal (we have done two lines cut by a transversal) and ask what do you notice or wonder. Instead of giving the students a "given" statement and leading them to what I want them to prove, they will decide what they want to prove through the wonders that they have. Hopefully this will springboard students thinking of "If I can prove this about the pictures, could I also prove this?"
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    • 10 Jan 2018 11:21 PM | Anonymous member
      Hi Kaitlyn,

      I am starting the parallel lines & transversals part of the Angles unit with my Geometry A class tomorrow. Thanks for the idea, as proofs are always a source of struggle (since they have little exposure to them).

      Pam
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  • 07 Jan 2018 5:58 PM | Anonymous member
    I displayed the Ticket Roll Image from 101qs.com by Dan Meyer to my 7th and 8th grade students and asked what questions come to mind? Students listed questions that ranged from Why are the tickets green? to How much does each ticket cost?
    Next I asked them to place a check mark next to their questions that were mathematical. They had also asked questions such as.: How many tickets on a roll?, What is the circumference of the roll? What is the area? What is the volume?
    Finally, I asked, if we were to find the answer to. “How many tickets are on a roll,” what information do we need? They came up with: What is the diameter of the outer roll and inner roll?, What is the volume of the roll? What is the actual size of the ticket? This week we will follow-up using Dan Meyers Three Acts to find the answer to this problem.
    There was a high level of engagement in this activity. We began this at the end of class and are ready to tackle the problem. We just completed a geometry unit on volume and surface area, so they are feeling confident the they have the ability to solve the problem.


    The website: Which One Doesn’t Belong http://wodb.ca , inspired by Chris Danielson’s book mentioned in Chapter 7, is another great place to find shapes, numbers, and graphs to inspire student mathematical thinking. There are four parts to each image, and you need to find out why each one doesn’t belong. It’s easier for you to go check it out than for me to explain it. It’s a great way to start class and wake up adolescent brains as they look for similarities, differences and patterns.
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  • 10 Jan 2018 9:54 AM | Anonymous member
    I used a large print of the Empire State Building in which the building and surrounding cityscape is created from thousands of individual photos. This exercise was done with my alternative math class - a small group of 6th graders. I had them look at the print from a distance of about 5 feet for their first "I notice" and "I wonder" comments then I gave them the opportunity to look at the print up close for another round of "I notice" and "I wonder". The second round, as I expected, produced richer and less general responses. Some of the "I notice..." responses in the first round were - "The picture is very cool; It's a skyscraper; There are lots of colors; It's the Empire State Building; It looks like a grid; The building has office spaces in it." Some of the first round "I wonder.." responses were - "Who made it?; Is it all little pictures?; What is the building used for?; How tall is it?; Was the picture hand drawn?" Some responses to "I notice..." in the second round were - "It is made out of photos of NYC; The sky is made from different photos than the buildings; It is a grid of photos; It is little photos of buildings in NYC; There are pictures of people making up the skyscraper." Some responses to "I wonder..." in the second round were - "How many pictures are in the print?; If the people in the pictures that make up the skyscraper work in the building on the floor their picture is part of?; How tall is the building?; If we can use multiplication to find out how many photos are in the print?; If the grid would make it easier to find out how many photos?" The students were not prompted to think mathematically. This lesson provides a springboard for many rich mathematical paths of discovery. Thank you Max Ray-Riek.
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  • 10 Jan 2018 11:16 PM | Anonymous member
    One common theme among many of my students is the avoidance of attempting word problems, whether on a standardized assessment or just part of a classwork set of problems. Our current unit in Geometry is similar triangles. To see what students might be willing to try, I gave them a page of relatively simple word problems that represented similar triangles in context and scale factor distance problems. I asked them to read through the first 8 problems and pick one to try to make a diagram for. I gave them large sheets of paper so they had plenty of room to draw.

    My first class, amazingly, went right to work with their drawings. Some started asking if they were “doing the problem correctly”. I explained several times that all I wanted was for them to try to make a diagram to show what they thought the problem was asking. I told them that they could then solve it, but that I was more interested in their process than an “answer”. I also explained that it was not “graded” (which definitely made them more relaxed). Some students even went ahead and did a second drawing for another example. I gave them about 10 - 15 mins. to work and they could get help from a friend if they were struggling.

    My positive take-aways where the following:
    a. The students did not hesitate to try, which wasn’t what I expected.
    b. Some students worked together on strategies (instead of comparing answers).
    c. Other students helped their classmates after completing their own drawing and the help was willingly accepted.
    d. The dynamic of the class changed from “drudgery” (complete the first 8 word problems) to “creative drawing” (with an attitude that word problems might not all be hard to do).
    e. Students asked "mathematical" questions and some utilized proportions and applied ratios without my prompting or model examples.

    I would like to have more follow-up discussion about why “they” felt more willing try and how “they” could approach word problems in the future. I will give them this opportunity again in the upcoming Trigonometry unit, to see if the students can have a more positive attitude toward word problems (and maybe take on the challenge of writing their own problems). I would like them to “inquire” about ways to apply right triangle trigonometry to everyday situations and why one trig function is would be more appropriate to use than another, instead of me “feeding” them information by the spoonful.

    Pam
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  • 12 Jan 2018 9:55 AM | Deleted user
    I posted a picture of an owl that was made using pattern blocks. I asked my kindergarten students what the picture looked liked to them? A lot of my students believed it was a bird, some said a penguin, turkey, and an owl. I asked them what they noticed about the pattern blocks? The students responded they saw, triangles, hexagons, diamonds, (one student learned it was a parallelagram from her grandmother and shared that with her classmates). They noticed how many of each pattern block was used to form this image. They noticed which blocks had more or less, they asked what would happen if you replaced blocks with other blocks like (2 trapizods for a hexagon, or 6 triangles for the two trapezoids). I allowed them to talk about what they noticed and how they thought they could exchange blocks within the picture but still keep it the same. After our conversations, the students took the picture and pattern blocks and built their own owl in teams. They all copied the picture the first time through with groups of 4. I noticed the kids that are always quick to answer or always want to be right, struggled a bit more than the other students who typically have to work through their math problems. The students plugged away at it with trial and error and had a lot of conversation on what was working and what was not. I then asked if they could actually exchange some of their shapes to see if they would work. As I walked around the classroom, I noticed each student thinking through on what they could make different as we made it a challenge to keep the same picture but exchange as many of the cubes as you can. A student finally asked, "Can we make a differenct picture using our pattern blocks?" I put the question back on them and asked them if they thought they could do that. They all agreed they could do something different. Some of my students dove right in and started to create their own picture while others slowly watched and started putting their pattern blocks in some sort of order. We did a gallery walk when all projects were complete and then came back together as a group. I asked the kids what they noticed as they walked around the pictures. Some of the answers were, "I noticed Group A used more hexagons than Group B.", "I noticed Group A and Group B made the same picture but used different pattern blocks.", "I was not sure what to make so I just started using my pattern blocks until I could see I made something." I found that by putting one simple picture out to start a conversation, we learned a lot about shapes and the different ways we can configure them to make the same as well as different pictures. The students came up with their own questions and then worked to find their answers.
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    • 13 Jan 2018 12:36 PM | Anonymous member
      Dawn,
      I always enjoy hearing what's going on in kindergarten classrooms. Your students are thinking deeply and engaging in mathematical discourse. It continues to amaze me how capable five year olds are. Keep up the great work!
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  • 14 Jan 2018 6:38 PM | Anonymous member
    Our number this month is 5. We have learned to write the number 5. After reading this chapter and responses, I am excited to ask the students to show me 5. They will be able to use anything in the room or on themselves to show me that they understand what 5 means. I will ask them if they have questions about 5. I will ask them to wondering anything else about 5. I can already tell that their responses will teach me more about their knowledge depth of numbers.
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  • 14 Jan 2018 6:56 PM | Anonymous member
    http://mysterydoug.com I was just invited to this site and viewed the question. It goes perfectly with asking questions (real video of student asking question) and wondering!!
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  • 17 Jan 2018 9:35 PM | Anonymous member
    I used a few videos that were designed for a "notice and wonder" activity. One showed someone folding paper into polygons and stacking books until the paper crumbled, the second was a person timing a second person coming down an escalator.
    The activity went well, students noticed the obvious and some of the not so obvious. They also had a few good questions that they wondered about. I did this activity "cold" with no real introduction other than we are going to do this activity for this purpose. When I incorporate this in the future I will need to put more exact parameters on what I mean by notice and wonder within the context of the video/problem. As with any time you first introduce an activity kids got stuck on the ..."I wonder why someone would walk down an escalator" type questions and did not hit on the more relevant math content.
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