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  • Posted by Jon on May 1, 2019 at 11:46 am

    Select one textbook problem you plan to use with your students in an upcoming unit. Use the blank 2.4 Curiosity Path Template to plan how you will use the Curiosity Path to transform your problem into a curious challenge kids will want to solve.

    Share your result here.

    What problem did you choose?

    How did you change it?

    How did your students respond?

    Anna Clark replied 3 days, 5 hours ago 24 Members · 33 Replies
  • 33 Replies
  • Katrien Vance

    Member
    June 25, 2019 at 7:30 pm

    I have a question about the “growing blocks” problem Kyle uses as his example.  What if your students themselves “rush to the algorithm”?  When I did this problem, the kids did not come up with the creative patterns Kyle mentions; they ALL saw it the same way — times 2 plus 1.  At that point, do you just move on, or do you push kids to come up with multiple ways to think about a problem, when the way they have thought about it is already effective?  When I do that, they look at me as if to say, why are you wasting my time asking me to do something less efficient?

    • Jon

      Administrator
      June 25, 2019 at 7:58 pm

      I tend to think of the big picture in this case — representing linear relations in multiple ways. So, yes, I would push for other ways to represent the pattern. I have found the phrase helpful: “I saw another student in another class represent this relation in a different way. How might they have represented it?” Or rephrase it as a challenge “how many ways can you represent this linear relation pattern?” The big picture is to have they recognize the connections among representations. 

    • Daniel Whittaker

      Member
      July 3, 2019 at 9:01 pm

      I think you could also just give a more complicated pattern next that more easily lends itself to multiple representations.  Either way, the key is to make them understand that there are different ways to do the same problem.  I find so many students that think there is only 1 correct method to solve the problem, I love any time I can highlight a different approach.

  • Daniel Whittaker

    Member
    July 3, 2019 at 9:17 pm

    I’m thinking about my Linear Programming unit. A typical problem would be something like:

    “Sally makes gingersnaps and snickerdoodles to sell. She has 20 eggs and 15 cups of sugar. A dozen gingersnaps requires 3 eggs and 2 cups of sugar. A dozen snickerdoodles requires 2 eggs and 3 cups of sugar. She can sell 1 dozen cookies for $5 each. How can she maximize her sales?”

    Students really tend to struggle with the many steps in these problems. I always work hard to break down the steps and have them really understand, but they struggle. So, I’m trying to think through the process in this way.

    “Sally is making cookies to sell at the fair.” – What do you wonder? (What kind? How much do they cost? How much will she earn?)

    “How can she maximize her sales?” – (Advertise! Make more cookies!)

    “She makes snickerdoodles and gingersnaps and sells them for $5 per dozen.” – What do you notice/wonder? (What is keeping her from making as much as she wants? If she sells 100 dozen, that is $500!)

    “She has plenty of most ingredients, but only has 20 eggs and 15 cups of sugar.” – (I wonder how many eggs and how much sugar it takes to make those cookies.)

    “It takes 3 eggs and 2 cups of sugar for a dozen gingersnaps. It takes 2 eggs and 3 cups of sugar for a dozen snickerdoodles.”

    Now they have all the information, but will they be able to work out an answer? They could do it via some trial and error, but I’m not convinced this will get them to the correct answer.

    This is really thinking about next year. I always introduce the unit by having them create some lego furniture and working through the process that way, but they always get hung up on the constraints and the graphing part of the solution.

    https://teacher.desmos.com/activitybuilder/custom/563870954871f4bb4c18ac45

    • This reply was modified 2 years, 4 months ago by  Kyle Pearce.
  • Patricia Scheler

    Member
    January 4, 2022 at 12:39 pm

    Original Problem: Shari had 24 charms on her bracelet. The bracelet broke and the charms fell off. Shari found 17 of the charms. How many were lost?

    Changed Problem: Show a picture of the bracelet and don’t say anything. After some time, show a picture of the broken
    bracelet with some of the charms missing? Ask students what they notice and wonder.

    Estimation: I could show a close up of the charms on the floor. Students could how
    many charms are on the floor. I could also show the bracelet after the charms are put back on. I could ask whether or not the charms are
    identical. Did Shari find them or did she purchase some more?

    I think this is a little harder to do with younger age groups, but I can see the point in expanding the imagination of our learners.

    • Kyle Pearce

      Administrator
      January 5, 2022 at 7:22 am

      The younger students are, the more willing they will be to share. This also means huge tangents that will need to be managed without discounting any of the voices in the room.

      One thing I think is so key is listening to their estimates. We quickly realize that student perception and their understanding of magnitude is much more underdeveloped than we may realize. This process can be huge to help them develop their number sense.

  • Stephanie Pritchett

    Member
    February 18, 2022 at 12:46 pm

    The original problem is looking at a positive exponential function and having students make observations in regards to the negative x values. It also asks students to complete a related table that matches the graph. Students are asked to look for patterns in the graph and to use fractions so they can see those patterns.

    I decided to remove the prompt about looking at x when it became negative. I just asked students to notice and wonder. Removing a specific focus, opened it up for all students to engage in any way that was possible for them.

    My goal was to add in small small pieces of information that would engage my students further into the problem. I asked them to look at the points on the graph and determine inputs and outputs and to gather that information into a table and to notice and wonder about patterns that emerged.

    My special ed students needed a lot of guidance on completing the table. I did want them to use fractions, so they could compare positive and negative exponents.

    After the initial notice and wonder my students really struggled connecting the relationships and completing the table.

    I’m wondering if I needed to back off and go over reciprocals and fractions to strengthen their overall concept of fractions.

    After the lesson, my gut response was “good attempt.” My students who struggle with math were engaged initially. I struggled with keeping their curiosity through the process of the lesson.

  • Tarini Arte

    Member
    February 20, 2022 at 1:41 am

    The screenshot attached is a textbook problem I worked on to transform into a more explorative and curious investigation for students after listening to this lesson 🙂

    • Jon

      Administrator
      February 25, 2022 at 6:24 am

      Great job here Tarini! Love the slow reveal you’ve created here.

      Is this your introduction to systems of equations? Our next step would be to anticipate how students will solve this problem!

      • Tarini Arte

        Member
        March 9, 2022 at 6:29 pm

        Hey Jon, thanks! Yes I thought it could be a nice way to ease into systems with having them use their strategies first and then get into how we can represent it with equations.

  • Lizann “Lizzie” Herrera

    Member
    February 24, 2022 at 12:17 am

    The original text book problem is attached below. I would modify this problem to be delivered in the following order:

    1. Han is planning to ride his bike 24 miles.

    2. WDYN/WDYW

    3. How long will it take? (hopefully comes up in the wonder)

    4. Ask, what do we need to know to answer this question? Make an assumption (how fast Han goes) and an estimate (how long it will take)

    5. Give info: If Han goes 3 mph?

    6. 4mph?

    7. 6mph?

    8. Can we make a graph that represents this? (use Desmos)

    9. Generalize an equation that Han can use to find the time it takes to ride 24 miles at r (any) mph

    10. consolidate – t=24/r where t is the time it will take, r is the rate Han rides the bike, and 24 is the miles (how far) Han rides.

  • Jonathan Lind

    Member
    February 26, 2022 at 12:13 am

    My before and after of a typical goat on a rope problem is below; first round I left the general question in, but then realized that it wasn’t really necessary and not having the question would really open up the exploration and questioning phase.

    When an 11th grade IB class was presented with this problem and asked to notice and wonder, they (having probably seen similar questions before) came up with the classic questions that could be asked here, but also came up with much more interesting questions, and we decided to answer one of those instead:

    How long would the rope have to be so that the goat could reach the entire field if it was tied to the opposite corner.

    This also gave students an opportunity to estimate the length of the rope after they asked for and were given the dimensions of the field.

    IB questions are often very scaffolded, which is great if you’re taking a test, but pretty lame for classroom explorations. This exercise helped the class have a much richer discussion than we would have solving the original problem.

    • Jon

      Administrator
      February 28, 2022 at 6:21 am

      Love this @jonathan.lind Great withholding information here. The question the students posed is very clever! I might be borrowing this for my classes.

  • Kerri Brodie

    Member
    February 28, 2022 at 9:17 pm

    This is my textbook problem:

    A school
    gymnasium is being remodeled. The basketball court
    will be similar to an NCAA basketball court, which
    has a length of 94 feet and a width of 50 feet. The
    school plans to make the width of the new court
    45 feet. Find the perimeters of an NCAA court and of
    the new court in the school.

    I changed it as shown in the PDF (Google Slide) shown.

    I am planning to use this problem on Friday in my class so I don’t know how the students will respond yet but I will post after I use it in class.

  • David McKnight

    Member
    March 1, 2022 at 1:35 am

    I have a question related to quadratic modelling. I happen to be near the end of the unit, though this might work anywhere in the unit. This is for my Honors Mathematics Class and generally look for the most “mathematical” approach. I sort of wish I could turn back the clock and do this earlier in the unit.

  • Gwyneth McIntosh

    Member
    March 8, 2022 at 12:50 pm

    In the modified question, we withheld most info and gradually released it. We noticed/wondered as well as did high/low/best estimates. It wasn’t the most interesting prompt to begin with (we actually modified this lesson on the fly – right before class), but the lesson went really well. Even though the prompt wasn’t that interesting, following the curiosity path helped our students buy in and get engaged in the question. It was pretty cool to see that we were able to transform the question quickly, easily and effectively. And…the prompt didn’t actually have to be amazing. Withholding, notice/wonder, as well as estimating were really enough to get them into the question.

    • Kyle Pearce

      Administrator
      March 9, 2022 at 6:43 am

      So happy you shared this and also articulated the importance of the curiosity path itself (not the visual itself). The visual is a support for a great prompt – not the other way around. Glad it worked out well and didn’t take you a ton of time to get started with it.

  • Terry Hill

    Member
    March 19, 2022 at 10:30 pm

    I have attached a PDF that shows the original problem and the PowerPoint that I used to do the problem following the Curiosity Path. I started them out with Notice and Wonder, and wrote down everything everyone said. This seemed to really start off very well. I made sure to get at least one notice or one wonder from every student, and while a couple simply said theirs was the same as another student’s answer, most of them gave some very good answers. As we worked through the problem, gradually releasing information, it seemed to go pretty good as well. (The blank page in the PowerPoint was so we could draw the three fields and then try to first guess, and then second, figure out their dimensions.) Overall I thought the lesson went very well and I did see more participation than usual. However, it did seem like it took a very, very long time to cover one problem, and there still seemed to be some confusion about what the problem was really all about.

    I did show the students the original problem after we had completed it using the gradual release of information, and most agreed they liked the way we did it better than just being given the problem. Some even stated that it helped them to understand what the question was actually asking them, which was great.

    • Kyle Pearce

      Administrator
      March 22, 2022 at 6:52 am

      Fantastic to hear!

      Note that at first, this process can be a bit confusing to students as they are not used to the process. However, remember that we do need to be explicit in the consolidation to ensure students understand why we did what we did… some students will have made connections on their own, but others will not.

      Glad that your first go was a success!

  • Fernando Perez

    Member
    April 12, 2022 at 2:41 am

    An original question asked whether a plane could fit underneath an arch, the information given was the plane dimensions and the arch dimensions as well as the high at which the plane needed to fly. This question didn’t open much room to imagination so this is what I did:

    The question title slightly changed to “Can the Qatar Airways Airbus 380 fit underneath Al-Wakra bridge?” This way, the question was about a local company and a local bridge in the city (Doha, Qatar). Students were lost a the beginning and realized they needed to find information about the plane, and also about the bridge, indeed, they were required to find that information online and no more info was given to them, they even have to think about the height at which the plane should fly and whether it was realistic or not. There was a great deal of noticing and wondering, anticipation, estimation and, of course, withholding information.

  • Kami Fevery

    Member
    May 7, 2022 at 12:35 pm

    So I found this problem that to me with a quick glance would seem (on the spectrum of curiosity creating) maybe a bit more on the full curiosity side as anything with a picture seems to do so. However, I realized how limiting this question became when the words were added. I can see now what you mean how most text book questions function in a way to tell the student how to think. I decided to get rid of all the words and keep just the picture.

    Here I came up with a list of notices my student would perhaps come up with. While I don’t think the highlighted ones would come up first, I have found doing more curiosity creating tasks, that each student’s response rolls off the previous, gradually thinking deeper and more mathematically.

    • Kyle Pearce

      Administrator
      May 10, 2022 at 6:51 am

      Great realization!

      I’m also a fan of not “titling” the activity. No need to reference curiosity or what your intent is… they figure that out eventually vs sort of trying to encourage them (or give away) what you’re trying to do (spark their curiosity).

  • Colegio Markham

    Member
    June 4, 2022 at 2:31 pm

    1- video of penguinarium feeding time. Notice and wonder – Withhold info/anticipation- discuss data needed to solve some of the wonders

    2- How much fish is needed to feed all the penguins?

    Eliciting data needed, estimation of these: how many penguins there are in the video, how much does one penguin eat (can google that). Share with neighbours and class.

    Reveal 1

    In this aquarium, penguins are fed 3 times a day. Breakfast is 5/12 kg of fish, mid afternoon 1 ¼ kg and supper is ⅚ kg. See how students solve for how many does one penguin eat. They know equivalent fractions by now, but may use braining camp fraction tools

    Reveal 2 – there are 20 penguins. <i style=”background-color: var(–bb-content-background-color); font-family: inherit; font-size: inherit; color: inherit;”>Again see how they solve, may multiply by ten first and the double, may double first and then multiply by ten, may add 2 and ½ in in groups etc.

  • Karl Hirschmann

    Member
    June 10, 2022 at 12:37 pm

    This is the original problem from the first unit of my 9th grade algebra curriculum. I used this problem in August of 2021 and it didn’t work very well. The question [as written] did not encourage spark curiosity, nor did it ask my students to think about the math.

    ORIGINAL PROBLEM

    Who got the better deal?

    Both Larry and Linda bought the same value meal deal.

    The menu price for the meal deal was $4.99.

    Larry had a $1 off coupon he used first and then got a 10% student discount.

    Linda used her 10% student discount first, and then used the $1 off coupon.

    Who got the better deal?

    REVISED PROBLEM

    [1] Both Larry and Linda used discounts to buy the same value meal deal … [I deleted the title and set the scene. I also added “used discounts” to the wording of the original problem for clarification].

    [2] Who got the better deal? … [I ask the question].

    [3] Estimations … [I encourage students to make estimations based on what they know].

    [4] Release of more information … [In response to student questions, I release more information].

    [a] The menu price for the meal deal was $4.99.

    [b] Larry used a $1 off coupon he used first and then got a 10% student discount.

    [c] Linda used her 10% student discount first, and then used the $1 off coupon.

    While I haven’t used the revised problem in class [yet], I believe that my students will find it more interesting in its revised form.

  • Christine Pomatto

    Member
    June 12, 2022 at 4:07 pm

    Many of the word problems we use for area & circumference of a circle have room for some GREAT math, but they are so boring the way they’re provided. Here is how I reworked one of them (attached).

  • Renee Holmquist

    Member
    June 20, 2022 at 1:40 pm

    I selected a problem from the introduction part of AP Calculus. It is meant to get students thinking about tables and graphs and assumptions you can make and not make from tables to graphs.

  • Deanna Semyon

    Member
    June 22, 2022 at 1:57 pm

    What problem did you choose?

    A 30 foot tree casts a shadow of 12 feet. What is the length from tip of tree to the shadow tip?

    How did you change it?

    Show pictures of 3 or 4 trees casting shadows. Ask students what they notice and wonder. Have students partner share notice and wonder and then share to class. (why are all the tree shadows going left? why do I care about tree shadows? What do you need the shade for? What are you going to do under the trees? There are only 2 trees… we need more trees to have shade. Are all the trees the same height? How far does that shadow go now? Does it change. I wonder if we can make a zip line?)

    Ask students what they need in order to make a zip line. (the supplies: wire, stake, ladder to get to top, etc)

    Ask students to estimate the length of zip line. (students may state that they do not have enough information and then students may discuss what is needed.)

    Inform students that the height of the one tree is 30 feet. (students may then discuss what else is needed to make a zip line to the shadow tree tip). Allow discussion and guide students to ask for additional measurement. (If I am lucky a student may recall something learned about a triangle.) Provide the shadow length and for practical purposes allow students to work with the right triangle concepts.

    Ask for updated estimations. Allow students to work in pairs to come up with answers. (hopefully closer estimations).

    • Kyle Pearce

      Administrator
      June 23, 2022 at 6:44 am

      Nice work here!

  • Reney McAtee

    Member
    June 26, 2022 at 3:48 pm

    I hope to revise this problem for the upcoming school year.

    • Kyle Pearce

      Administrator
      June 27, 2022 at 6:38 am

      Nice. What specifically are you feeling needs adjusting?

  • Stefania Lambusta

    Member
    June 27, 2022 at 11:18 am

    In our first unit we introduce GCF and LCM. A textbook problem says find the LCM of 3 numbers, for example 2,3,and 5. I found this activity that I want to try with my students. It starts with a video of 3 different hour glasses. Students can notice and wonder and I can guide the thinking to when will the timers all be empty together again.

    https://mrorr-isageek.com/hour-glass-multiples/

  • Julie Gonzales

    Member
    June 29, 2022 at 6:56 pm

    As a math specialist/coach for the district I am really excited to have teachers experience a way to turn a textbook problem into a notice and wonder. I will try this at the beginning of next school year during our professional development in-service days. I will have to be deliberate in how I set up groups of teachers because I will have K – 12 teachers during in-service and I want all teachers to be able to access the question. Once I go through this activity, I will actually show the problem from the book and ask teachers to discuss their experience with a partner and then discuss as a whole group. It is my hopes that teachers will bring out their level of engagement/curiosity compared to what it would have been with just giving the original problem. I have found in my job that I have to challenge teachers’ thinking about their own routines in the classroom before they will consider changing what they do. The best way is through their own experience.

    Original problem from Geometry: The tallest building in the world is Burj Khalifa in Dubai (as of April 2019). If you are standing on a bridge 250 m from the bottom of the building, you have to look up at a 73 degree angle to see the top of the building. How tall is the building.

    First I would just show a picture of this building and ask teachers what they notice and wonder. There are many different notices and wonderings the teachers will come up with! After sharing with a partner and then with the group, I would then ask them “how tall is the building” (I believe this will be a natural wondering teachers will have). I would ask them to talk with a partner what they might need to know in order to answer this question. Once the group brainstorms some ideas, I would show the picture again but with a person standing 250 m from the base of the building and the 73 degree angle looking up to the top and ask them to solve. (I am considering changing the base length and angle to make it even more accessible for elementary teachers!)

  • Anna Clark

    Member
    July 1, 2022 at 5:10 pm

    Original Problem taken from 8th grade math (pre-algebra) unit on solving systems of equations: A taxi ride costs $3 plus $2 for each mile driven. You spend $39 on a taxi. This can be modeled by the equations 2m+3=39, where m represents the number of miles driven. How long was your taxi ride?

    Curious problem:

    Step 1: My mom is taking a taxi ride.

    Step 2: WDYN&W? Maybe they wonder where she’s going. She must not have her own car OR she’s in an unfamiliar place (my Alabamian students will immediately go to NYC!). How long is the ride? How much money is she going to spend?

    Step 3: Pick the wonder about how far she traveled and make an estimation. Allow students to google the average cost of a taxi and come up with a reasonable distance for a taxi to be taken. Ask students, what questions do you have that would help you make your estimate better?

    Step 4: Slowly introduce information. The equation that models the cost of the ride is 2m+3=39. What does this tell us? WDYN&W now? Can you update your estimate?

    ALTERNATIVELY for Step 4: First say that the taxi driver charges $3 up front. Update estimate. Then say the taxi driver also charges $2 per mile. Update estimate. Then say the total cost of the drive. Update estimate.

    Would love for someone to weigh in here and critique this! I’m wondering which information is best to give them since the goal of the word problem is to give them an equation in hopes they solve it with inverse operations…but is that really necessary here? I feel like as an extension (if using my alternative step 4) I could ask the students to write a linear equation that shows the relationship between miles and cost, but then I’m not really asking the same thing this question is asking. To be fair, I really don’t think this question is asking something practically applicable to the real world!