Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 2-2: Consolidating The Sparking Curiosity Path › Lesson 2-2 Question
Lesson 2-2 QuestionPosted by Jon on May 1, 2019 at 11:44 am
How will you spark curiosity this week in your lessons?
The Action step from Lesson 2-2 requested that you do one of the following:
- Option 1: Modify one of your lessons this week.
- Option 2: Choose a new lesson.
How does this lesson impact how you might lead your math lessons?
MemberJanuary 29, 2022 at 7:42 pm
I used the shotput lesson to emphasize what the different parts of an equation represented. This was a great lesson. Students were all curious, some suspicious of my motives? ( How is our teacher going to bring math into this problem.) I had students that typically don’t participate notice and wonder and participate in estimation. In fact my student that never participates was closest to the actual shotput throw length. Towards the end of the lesson I could tell I was losing interest. I did do the extend, but I was worried about continuing on with similar problems on the following days and how I was going to keep their interest.
MemberFebruary 23, 2022 at 10:43 pm
This week I got to co-teach with a 6th grade teacher who was beginning a unit on Expressions and Equations. We used the Shot Put lesson to introduce this concept. I decided to try the Shot Put because it matched very well with the unit and it really helped watching Kyle’s video teaching it virtually.
During the lesson, students were actively talking math the whole time! I had one student who kept trying the “silly” answers and I kept writing those down and pretty quickly he began noticing things he thought as silly and I was able to spin them as something important for the lesson! (Priceless!). One student even noticed the yellow markers with the 22 or 23 on them and was trying to do their estimation based on that notice! The low-mid-high estimation was tricky for students, they were estimating as 42, 42.5, and 43 – so that was a harder and new concept to wrap their brains around.
The lesson itself took about 80 minutes, so the consolidation piece ended up being all me, rather than students coming up with an equation to explain the concept mathematically. (That rush you get of “OMG I have to finish this lesson!”) However, I believe the students achieved a much better understanding of where the numbers in the equation were coming from and the teacher now has a lesson to “look back to” and make connections with during the rest of the unit.
My wondering is, what now? Now that they have the algorithm, do we continue with the “normal” textbook practices and do another MMMTM task for the next unit? Are there other interesting problem based lessons that we can incorporate for students to work through, independently or in groups, so that they’re not working with “naked problems”? How do I guide my teachers to trust the process and continue with this?
AdministratorFebruary 24, 2022 at 6:24 am
Hi there Lizzie,
This is awesome to hear about your success on this lesson. Did you happen to check out Day 2 of this unit to see the purposeful practice and math talk?
MemberFebruary 24, 2022 at 7:29 pm
Thank you for pointing that out. Yes, I did see the other days there, but I didn’t have the opportunity to teach those, since I’m not the current teacher. I will reach out and suggest she continues with the other days. I’m afraid she will be hesitant to continue because of the need to cover the curriculum. I’ll let you know how it goes. Thanks!
MemberFebruary 25, 2022 at 5:29 am
This past week I’ve been working on probability with a class of 11th grade IB year 1 class. I started with a textbook 3-circle Venn diagram problem about speaking additional languages, with a list of information, and then parts a-e asking about number of elements in certain sets and probabilities.
Anticipation: Before showing the problem, I asked my students whether they thought a person speaking, for example, French in addition to English might be independent or not from a person speaking Spanish in addition to English. This was a good opportunity to discuss and address the common misconceptions about independence, and really work on our understanding of the concept as it relates to probability.
I did not find a good tie in for estimation, but I was just now thinking that I could have changed the languages to make it more relevant to my situation (an international school in the Persian Gulf region), and then asked them to estimate how many people in a random group of 60 students they think might speak these languages. Maybe next time this would be a good opportunity for engaging them in the problem. I also forgot to do a notice and wonder, but could have easily added that in when they were first presented with the clues.
I removed some of the clues about the number of students in intersections, and removed the instructions to draw a Venn diagram, and gave them an abbreviated set of clues. Their job was to figure out what information to ask for so that they could find out how many total students were in the survey. This is my favorite part of all of this, because you get to really see students thinking through things and working together to figure things out. They eventually got to Venns, and asked the necessary questions, and were able to move on to figuring out whether speaking these languages were independent of each other.
I need to like tattoo on the back of my hand that this makes math class more fun for everyone so that I remember to do it more often. It’s usually pretty easy to modify problems if I can remember to think about it!
AdministratorFebruary 25, 2022 at 6:29 am
Sounds like a great attempt here! Note that sometimes predicting can be used in place of estimation. For example, you asked them to predict about the numbers of people who speak different languages – so I think you hit that piece.
As for doing it more often, it definitely is a habit to form. Consider thinking about the path each lesson… that should be your filter and it’ll remind you to make small tweaks!
MemberFebruary 28, 2022 at 8:12 pm
I was teaching my Calculus students about Optimization which is always really difficult for them. We started with just a picture and I had them jot down what they noticed and wondered and they came up with really great insights and observations. It was a great way for them to recall prior knowledge. I did this using the attached Google slides (in PDF form here) by withholding information and really giving a lot of time for them to anticipate, notice and wonder. I am happy to say that the students who don’t often speak up had great things to say and that they class as a whole did much better with this topic than my classes in the past have.
- This reply was modified 4 months ago by Kerri Brodie.
MemberFebruary 28, 2022 at 11:36 pm
This week I tried a 3 act lesson. We are at the end of our unit on systems of linear equations. The lesson is already created and it’s one created by “Tap Into Teen Minds.” I think it’s designed byJon & Kyle https://tapintoteenminds.com/3act-math/piling-up-systems/
The lesson definitely sparked curiosity. I had students use a Jamboard to record their noticings and wonderings. We shared and discussed things out-loud too. At this point, I had the students coming up with questions individually.
Once we moved to the estimation phase, I kept the students working individually. I wanted each student to have a stake in the the activity. I had them publish their individual predictions on the Jamboard with their initials. I promised prizes for the top 3 closest estimates.
The 2nd Act was fun. I grouped the kids into 5 groups of 4. I made sure to put the strongest 4 students together. I did this to avoid having one student dominating the work in each group. I had an extension prepared and anticipated that the strong group would need it. Again, they published their work on team Jamboards.
I announced that the group to get closest to the actual weight of the glue stick and glue bottle would win a prize. 4/5 groups got reasonable solutions and surprisingly enough, the winning group was not the advanced group.
When I played the 3rd act video, it was crazy. Kids were cheering and carrying on. Such a blast. I really love these types of lessons.
As an exit ticket, I had the students complete a reflection and to post their work in their virtual notebooks. I also had the top 3 groups explain their thinking before accepting their prizes. I had the best initial estimate explain their strategy for estimating. It was interesting and I opened the conversation to others who were eager to explain their initial strategies. Such a rich task.
Upon reflection, this was a lesson that could have easily been skipped, avoided or replaced with practice etc… However, it was a rich task that involved and engaged every single student. It also might go a long way towards future engagement in math class for some students. On the downside, there were a few students who didn’t ever fully understand the solution. I did offer to have a follow-up from the lesson in tutorial time, though I only had one student take up my offer.
AdministratorMarch 27, 2022 at 9:12 am
@david.mcknight We’ve come to realize that the consolidation of the lesson is very important to the success of all students (coming in module 5). We find that doing a formal take up and some sort of note to help with making sure the students understand the big idea/learning goal of the day is very helpful.
MemberMarch 14, 2022 at 11:18 am
I have not yet decided which way I want to attempt to go with this.
MemberMarch 26, 2022 at 4:09 pm
I am currently working on a rhythm, feeling out where and when it works to get the most impact from the 3-act math tasks. This unit, I decided to implement the strategy suggested where we started with the hardest idea of the topic. (I believe this was a suggestion on one if the podcasts) In this case we started with Pizza Party and finished our unit with Salting the Driveway, where I actually used Salting the Driveway as a final assessment. The curiosity of what I would do for a task based final assessment developed lots of interesting questions and comments. While I have tried to work hard for the past couple of years to get away from a grade focused mentality, where my student don’t actually receive a grade until their report cards, instead using a combination of just feedback and then some descriptive attainments (aka meeting expectations). However, some of them still have the mentality of doing well. I also think though this comes from a mentality of wanting to find success with something that they have worked hard at. At the beginning of the year many students shared with me that they struggled with fractions. We therefore took lots of time to revisit and I actually taught them all a new visual strategy with fractions (fraction ladder method). This may then all contributed to the excitement with this fraction task. I did still get the famous question “what does this have to do with math”…even though we have done these 3-act math tasks before. I have realized though as well that it takes time for kids to make the mindset transition of seeing math as an everyday thing. With them experiencing years and years of math being understood through algorithm of numbers, it takes time to get them to see math and much more than numbers and step patterns. Overall, though I will say as a collective whole, I saw a lot more positive faces turning in their assessment this time round using a 3-act math task rather than a traditional pencil and paper test. I still have lots of questions on assessment but I will save that for another reflection. : ) I have added photos of some responses.
AdministratorMarch 27, 2022 at 9:16 am
@kami-fevery Thanks for sharing! We’ll touch on assessment in module 6 but as you know there is so much to discuss and learn around this important topic. We’ve built a full course on assessment that many workshop participants choose to complete as a follow up to this course. You can peek at that course here: https://makemathmoments.com/afg
MemberApril 1, 2022 at 1:35 am
I did “the clapper” activity from Graham Fletcher to introduce our new unit of ratios. It was great to see the various ways students used ratio reasoning before it had been introduced in class.
MemberApril 12, 2022 at 2:30 am
Using estimation is a great way to deal with a question to to help students understand the. tasks and the range of answers that could be considered correct. I like the wonderings sections where students are allowed creativity by answering really diverse questions, some of them meaningful and good to explore: My own wonders are:
I wonder if some of the student’s wondering could be explored further so the teacher would re-adjust as-you-go
AdministratorApril 12, 2022 at 6:45 am
We try to readjust or at least acknowledge their noticing and wondering. Answering wonders they have if possible can show you care about their thinking as long as it doesn’t give too much away for the intentionality of the lesson. You could adjust the problems etc too as long as it keeps you on the path to your intended learning goal for the day 🙂
MemberApril 18, 2022 at 2:23 am
I will try to spark curiosity by using the Boat on the River 3 Act Math problem. I love that this video just shows a short clip and withholds all the information from students that a typical math problem may have and that it’s presented in video form. I also love that there’s so many things that my lower level learners will be able to “notice and wonder” like why is this boat tilted in the first place, will the boat make it, etc. and more importantly gives me a chance to value students’ voice and contributions to the lesson. I also love that this activity builds estimation, as we tell them the scaling in Act 2 and before doing any math it builds number sense in students where students try to estimate how tall the bridge/boat is.
AdministratorApril 18, 2022 at 7:04 am
Definitely a great problem that almost naturally presents the Curiosity Path for you. Love it.
MemberMay 28, 2022 at 10:08 am
I have created a lesson similar to this one where the students have to calculate whether the entry for the “largest uncooked spaghetti noodle” competition will fit inside certain boxes. after processing the “Corner to Corner” problem I think my problem needs some revision.
-I realized I didn’t include any of the Curiosity Path, all I really did was take a text problem and re-write it in a different context. There was no establishing of a reason to solve the problem. I even went as far as writing out the steps to solve the problem. Didn’t really even give them a chance to do any thinking on their own.
So, I am going to come up with a different way to set the problem.
-I don’t know why I couldn’t re-enact the first part of the lesson (the hook) with the students in the room? Maybe even get a student or two involved holding string.
-It might even spark a little more curiosity to run out of string on the way there…which would ask the question without me having to ask.
– I was also thinking about filming the video starting with me stretching some string from the corner out into the room (along the diagonal) and then once I have some stretched, then picking it up and heading for the opposite corner
-after the video I would have the students complete a notice and wonder table on the groups NPVS. Once they have had some time and I have noticed the ones we need. I will compile a list on one of the boards.
-once we have collected that list then we will be ready to make our estimations. All the while we can be looking for the step of how will we measure this…what tools will we need to solve this problem. Can we find the distance without actually measuring the distance.
-Once we have the method and have made some attempts I will give them the measurements of the room. I think it would be interesting to not use traditional measurements…if we used only string and made them base the measurements on something else…like the length of the desk.
-I’d love to ask an extension problem…if I did this from both corners, where would the strings meet?
MemberJune 11, 2022 at 6:35 pm
I have been incorporating some curiosity path elements into my teaching for a few years after completing long-term professional development on task-based learning in 2019 and reading Peter Liljedahl’s book Building Thinking Classrooms last year. However, some of my lessons have remained direct instruction, in part because we are often taught that’s the best way to do it with special education students (I’m not sure that’s true).
I chose one of my most teacher-led lessons to transform using the curiosity path. I’m not 100% sure I’m there, but it’s definitely better than it was before. I’m using the suggestion that the “spark” doesn’t have to be a real-world application: it can be math-based from the get-go.
The lesson: converting fractions into decimals. I usually just teach them to turn the fraction bar into a division sign, and then we practice it.
The lesson, reworked using the curiosity path:
(Important background information: I teach 7th grade special education math. Many of my students have very low number sense. I hope to change that with lessons like this that help them think about the number line conceptually.)
- Withholding information: I show an empty number line. Only the ends are marked, but not with numbers, just tick marks. I put down one 1/4 fraction tile starting at “0” (the first tick mark).
- Anticipation: I think this will build some anticipation because students won’t have enough information to know what we’re going to do today. However, they might have some ideas about what information they might need. They might even be able to anticipate the question.
- Notice & Wonder: I would expect the following types of comments: The tile is yellow. The tile says 1/4. The tile takes up about 1/4 of the length of the line (a stretch, but maybe someone will say it!). And the following types of questions: Why did you put that tile on the line? Are there supposed to be numbers on the line? What are the numbers? How many of those tiles could you fit on the line? And the question I hope they ask, in some way: What decimal number does the 1/4 reach to?
- Estimate: Based on students’ questions during Notice & Wonder, I could begin to reveal some information. The first things I would reveal would be the 0 and the 1. I’d ask them to make estimates that are too low, too high, and their best guess. Then, I would reveal the 0.5. I’d ask them to revise their estimates. I think I would begin to get students guessing 0.2 and 0.3 at this point.
From this point, I might consider “guiding” students to the right answer. But more than likely, I’ll leave their best guesses on the board or on chart paper for us to revisit later. I’d then repeat the process with several more fractions, starting with 3/4, but maybe building up some confidence with 2/5 or 4/5 first. I could keep track of all their “best guesses” on the board.
I’m not sure how to wrap up this lesson. It would be easy to say “Okay now, let me tell you a trick: all you do is divide the numbers,” but I think I’d like them to try discovering it in some way. Does anyone have suggestions? The best I can come up with is to give them a calculator and an equivalent fraction–decimal pairing, asking them to figure out what they could type into their calculator to turn 1/4 into 0.25. I may also do some sort of matching activity where students have to match fractions (with pictures on the number line) to decimals. I could even do a separate notice and wonder there.
I’d love any feedback you can give, since this lesson doesn’t have a clear conclusion. Thanks!
MemberJune 15, 2022 at 9:50 am
I used the Squares to Triangles lesson from the list, as I had just completed a unit on Pythagorean theorem with students in 9th grade. I am not confident with my submission.
MemberJune 15, 2022 at 8:14 pm
I used the Trashketball Lesson
AdministratorJune 16, 2022 at 6:55 am
How comfortable do you feel as you prepare to deliver this lesson?
MemberJune 16, 2022 at 8:49 pm
This was more a practice on sparking curiosity then planning an entire lesson, as I am on summer break right now and don’t currently have a class. However, I am starting to feel a lot more comfortable at developing ways to spark curiosity. Realizing just how much more information I can withhold without confusing the students has been very helpful. Also using multiple strategies to engage my students was working at the end of this school year and I hope that with practice over the summer (I am testing out strategies on my cousin as I tutor him) they will become even more effective as I use them
AdministratorJune 17, 2022 at 6:53 am
Gotcha! Well you’re doing a great job thinking this through and getting yourself ready to spark curiosity straight out of the gate next year! Bravo!
MemberJune 20, 2022 at 12:55 pm
I did the Boat on River lesson. I would do this in Chapter 8 of Geometry and as an introduction in PreCalculus to our trig unit. One question I have is would I do this before the students know about sine, cosine, and tangent? If so, when do I introduce that concept to help them solve the problem?
- This reply was modified 2 weeks ago by Renee Holmquist.
AdministratorJune 22, 2022 at 6:30 am
You can use this task as a way to introduce a “need” to use/learn the ratios.
You might want to start this lesson with notice and wonder, and possibly taking a poll to see if students think the boat will hit the bridge.
Ask students what strategies / resources they would need to determine if the boat will hit the bridge.
Then you could pivot away from this lesson to introduce the trigonometry ratios (https://mrorr-isageek.com/introducing-trig-through-slope/) then pivot back to allow your students to use the ratios to solve the problem.
MemberJune 22, 2022 at 3:00 pm
That completely makes sense!
MemberJune 26, 2022 at 3:08 pm
I am hoping to use the 3-act task with with basketball shot video to amp up my unit on quadratics.
MemberJune 27, 2022 at 10:41 am
I want to use the shot put lesson as an introduction to two-step equations. It hits all the key elements of notice and wonder, withholding information, anticipation and some estimation. It will be interesting to see how students solve some of the extension questions and whether or not they create a two-step equation, or work backwards, or try something different. Looking forward to trying this one.
MemberJune 28, 2022 at 6:51 pm
As a K-12 math specialist/coach, I am thinking about using the R2D2 video at the beginning of the next school year (for our opening professional development days) to introduce a different way for teachers to do Notice and Wonder activities in their classrooms. Our current curriculums (both elementary and secondary) have these type of activities every two to three weeks but I think it might be worth teachers time to incorporate them every week.
I can see myself setting up the activity very similar to how it was done for us with the exception of allowing teachers to pair share how “my” version is different than what they did last year in their classes. Then as a group, talk about the benefits of their own experience with Notice and Wonder. Using that saying “you can lead a horse to water but you cannot make him drink” is where my headspace is at right now. Teachers have to experience things to see if it is worth their effort in their own classrooms. And one way I can challenge their thinking about what they do in class is to make them experience Notice and Wonder as a student. We shall see!
AdministratorJune 29, 2022 at 6:28 am
Great points here. Something to also consider is that this approach is more of a state of mind vs a method that you bring in once a week or once a unit. Developing a culture of curiosity and thinkers is what we are after which means we should be thinking of ways to draw both out daily.
MemberJune 29, 2022 at 7:16 pm
My worry is that teachers always feel as if they don’t have enough time to cover everything and if I am asking they try to do this every day, then I may lose some of them who “don’t have the time” to turn questions into a notice and wonder. Unfortunately those teachers who are not confident in their own math abilities make the time excuse more times than I can count 🙁
MemberJune 28, 2022 at 9:40 pm
As an upcoming 2nd-year teacher I don’t really have lessons to modify yet, so I went with the corner-to-corner task on Pythagorean Thm. Students’ curiosity was spared because information was withheld (the length of the string and the length, width, and height of the classroom; the Pythagorean Thm formula, area formulae of squares and triangles), they were asked to notice and wonder (keeping track of their thoughts in a 60 second quick jot then think-pair-share), to estimate the length of the string sensibly. Since I teach PT in my grade 8 class in Alabama, I’m excited to try this lesson this year!
AdministratorJune 29, 2022 at 6:25 am
Awesome to hear you’re coming out of the gate hard with some curious tasks already thought out!
MemberJuly 2, 2022 at 11:45 am
The problem I am working with is How much water is wasted from a dripping faucet? Is it enough to fill a glass, sink, or tub?
I use this problem with my College Algebra class to introduce the 5 steps of math modeling that are used in the class. This problem would be completed in the first or second week of school.
– how fast is the drip happening
-the dimension of a glass, sink, or tub
– size of the drip
This is the part that I am struggling with because I feel this will come from the notice and wonder discussion. I would ask the students what information we would need to know to answer this questions and talk about how we could get this information. In this part I might also that about what assumptions we are making to help us solve this problem
Notice and Wonder:
Show a video of a dripping faucet.
Estimation the amount of water that is wasted. Estimate which container this amount of water fill: glass, sink, or tub.