Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 21: Three Techniques to Engage your Students and Hook them into Learning › Lesson 21 Discussion
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Lesson 21 Discussion
Breanna Greer updated 1 month ago 78 Members · 138 Posts 
Please post your thoughts and questions on the 4 techniques you learned about in lesson 21: “How you see these fitting into your lessons this week.”

As you guys know, this was one of the biggest takeaways from your workshop for me, and doing one small thing–withholding information–made a huge difference in the way I taught this past year. I didn’t always have cool tasks for the kids, but even when we were learning how to multiply polynomials, I let them play with the blocks and notice and wonder until they started seeing patterns for themselves. Not preteaching them everything but instead withholding some information was a fabulous beginning to a major shift in my teaching.

Couldn’t agree more! So glad this was a takeaway for you. Really does put the thinking into the hands of the learner.


I have also tried to use the withholding information technique. As your quote from Dan Meyer says “you can always add but you can’t subtract”.
In a more typical lesson on “finding angles in polygons” we discussed our findings from a prior lesson (sum of angles in polygons), students were told there was two steps needed to solve each question and given a worksheet with boxes to fill in each step to find the missing angle. Rather than a demonstration students were left to try the questions on their own, discuss why they were doing each step and we’re only prompted if they had gone off course.

Awesome. Thanks for sharing!
Wondering if there might be a way we could withhold even more information from that activity? Any thoughts or ideas here?


I use notice/wonder a lot in my classroom, and I do agree that kids get much better at it with practice. As a teacher in a sheltered (second language) classroom, It not only helps to spark curiosity, but it’s also a really great way to build and assess the class comprehension of relevant vocabulary. I would really like to try to use the “withholding information” technique a bit more, but it’s not something that comes naturally to me and will take a lot of conscious effort on my behalf to do it well.
Something that jumped out at me was that once you give kids the algorithm, they will always want it. In my educational context, students are trained to use the algorithm from a very early age (I teach grade 2 and grade 3). I have noticed that I can ask students to do problems, for example involving twodigit by twodigit multiplication. They know that the problem is asking them to multiply, and they rush to set up the algorithm, but they don’t know how to deal with the tens place in the second factor. so they just stop. They have said to me “we haven’t learned that yet”, and refuse to draw a picture, or break the numbers down, or think about another way that they could represent the problem. Do you have any strategies for getting kids to BACK UP from the algorithm?? Looking forward to more.

Backing up is so hard when they’ve been trained that they can’t do math without being explicitly shown exactly how to do each type of problem. This is extremely problematic.
An approach we use often is asking students to convince us… the answer doesn’t matter but what we really want is for you to prove to me why something works. This is incredibly difficult for students to do when they haven’t been asked to do this in the past and will likely require backing up to earlier concepts. For example, if they can’t represent an array of 3 groups of 4, then 2 digit multiplication is out of the question.
Students who are only procedural are not proficient in mathematics as there are 5 strands. Give this a shot and let us know how it goes!


I use notice and wonders alot already, but this conversation brings in some finer details that I need to attend to, especally the withholding of information. For example, for a recent notice and wonder, I showed a graphed system of inequalities, just 2 linear inequalities shaded on desmos and did a notice and wonder, to hope get kids to see the double shaded area. They had never seen a system before, but they have graphed single linear inequalities. I am wondering if that is to specific for a notice and wonder.

Is say that there are no set rules to a notice and wonder, however withholding information is the beginning.
So MY wonder for you is… what are some things you think students might wonder when you show them that? Is there much meat on the bone or is it pretty obvious as to what you’re “fishing” for? If it is too obvious, then it might not feel “worth it” to the students. Just a thought.


When I think about the 4 techniques shared in this lesson the big takeaway for me was the addition of the estimation or prediction of the answer. It really gets students thinking about what might be realistic. All too often I find students answer questions and have no idea if the answer seems right. They respond when pushed with “I guessed.” This estimation strategy gives them some parameters to work with.
I also appreciated the whole class’ voice in the notice and wonder and estimate and predict. When all answers are solicited and that culture is created that all ideas are valid. You target those reluctant students and give them a voice which is often overlooked in a math class.

Awesome to hear. Apply that to an upcoming lesson and let us know how it goes!


Estimating is something I want to use more. It gives everyone an entry point for the task and helps them get some “skin in the game.” Once they share their best guess, they will want to see if they are right and maybe even try some different strategies to improve that guess. And really, this is what math is for – making more accurate predictions.

I am thinking a lot about the ideo of starting the math dial at 0. I sometimes think about how math is weird to be a “seperate subject” and in an ideal world the class is “life” and we explore all the parts of it – including the mathemaical part. That would allow us to less likely define ourselves as”nonmath people” and more by our strengths because we all come into this class with the “math dial” at 0 and look at the situation from whatever context we are coming in with as people. It is a lot like the Ignatian Pedogogical Paradigm (https://www.google.com/search?rlz=1C1GCEA_enUS910US910&source=univ&tbm=isch&q=ignatian+pedagogical+paradigm&sa=X&ved=2ahUKEwj9mPSD99XuAhVqB50JHeU_CTAQjJkEegQIARAB&biw=1280&bih=578&dpr=1.5). We can start to get involved in the problem (even Johnny the humor guy with his strength).
It also reminds me of slow reveal graphs that Dan Meyer introduced me too (https://slowrevealgraphs.com/). We used this as an anticipatory set last week when we started with a SEL check in on what animal they were feeling like. Then did a slow reveal graph with those same animals eventually leading to a scatter plot analysis of brain weight vs. body weight (using Amplify’s new curriculum field trial). I see a lot more areas for more quesitoning and valuing student voice and estimation than I did last week as I look forward to this week.
Thanks!
This week I will be less afraid to let guys look at data/pictures/graphs without my voice jumping in but instead obselving for the opentings into the math that they will create.

Loving that you have some learning you can put right into practice out the gate!


This was a very interesting lesson to reflect on. Having done various 3 part and 3 Act lessons and trying to create engagement, it was great to learn why with certain lessons engagement intensified and then waned. I could never pinpoint why. I also reflected on when I created my own 3 Act Math lesson with a video, I withheld information which created a great deal of engagement. My problem was that I did not think through all the steps. I still had an engaging math lesson that I did not plan for because students gathered the missing information through a physical model but the different physical models were not what I intended or expected. The math went on a tangent that lead to different concepts being explored which was great and my revealing of withheld information was no longer that important. What these last few lessons have me thinking is how I can reuse my 3 Act math lesson to teach multiple concepts and not just what I originally intended. Next time I use my 3 Act math lesson, I will be much more intentional with the goal in mind and also anticipate how my students my engage with the math.

Great reflection! I feel like you’ve uncovered a game changer for yourself when you can extend a context to explore more than one concept. This will not only save time, but it will also keep students in a state of flow longer.


The bringing the dial down struck me. The belief is that we can apply math to everything we do but is separated from all other school content. (well, except for science, when the science teacher wants to complain that the students do not know how to graph.) But the idea of dialing it down and allowing kids to make those generalizations into other content and real world problems will hook them and enable us to turn the dialup.
The one technique I should work on is the “Withholding Information.” I have used notice and wonder with various success. Still, when there is missing information, students take it as a mystery of what information they will need to solve the problem. Like what was used in the chocolate problem where it was asked, “What information would you need to better solve the problem?” (I do not know what the exact direct quote is for that question) But if the students ask for the information, they would be more invested than if I just gave the information to them.

As I look back at my math learning experiences, I remember feeling annoyed at any mention of estimation. I thought of it as a waste of time, and it was never demonstrated that it could be a means of engaging in a math problem or be a useful skill,. Like Kyle, I didn’t see the point.
These four aspects of sparking curiosity are such a great starting point, and I appreciate seeing the design principle of planning 3, 2, 1, then 4. As a preservice elementary teacher, I am excited to try out these new skills in teaching, and I’m thinking of how these principles apply in other subjects.

My take away is that I need to be better about withholding information from kids. I know how important productive struggle is, but I have such a hard time not hinting and prompting. My new goal is to allow more wait time, withhold more information, and let the productive struggle commence.

So to be honest being new to my standards and not having a curriculum to follow creating tasks seems overwhelming at the moment. I don’t know what is coming in terms of building understanding or how students are going to react to it because it is my first time teaching these topics. I know that I want an engaging classroom and I know I can teach that way due to my science background, but I don’t know which tasks to select or which problems are the standard problems. I like that you broke down the steps based on your experience and can see the importance of building my own experiences, but I am still lost to where to start. I wrote on my notes when you talked about backwards planning my first step is finding the concept or word problem to create the withholding of information from.

This is so common and you aren’t alone especially when new to a curriculum or grade. I’d start with taking a task you’d typically use anyway and how can you hold back some of the information? It could simply be words to start or show an image from Google to get them talking. Of course, it is great to get a really elaborate curiosity sparking task, but in the beginning you need to keep your head above water and simply apply the curiosity path in a meaningful way for you.
Have you checked out our problem based units?
learn.makemathmoments.com/tasks


I have received in service training on these 4 aspects but I don’t think they were presented in any sequence. I see the value in the order, and am excited to try it. I am teaching isolating the variable and balancing equations next week so I will look at the videos you have made to see what fits. If you have any suggestions, I would appreciate it. We will also be writing 1 and 2 variable equations and independent and dependent variables. I teach 6th grade in the US. I am enjoying this course so far. You both speak from real experiences, sharing successes and mistakes.

Hi Teresa!
Glad that you see the value in these ideas and feel like you can put them together in a logical way!
For solving equations, the Shot Put unit is a great one: https://learn.makemathmoments.com/task/shotput


The need to build a classroom culture that encourages questions and curiosity was my biggest take away from this video. It makes so much sense the way you explain it. I’m hoping to learn more about how to promote the “math fights” which lead to this type of classroom culture.

Awesome to hear! Any particular round of math fight you’re hoping to explore first?

I guess I’m wondering if they all follow the same pedagogical approach, and if that is the case then I’m wondering what are the key steps in facilitating these fights. If they are different, then do certain types lend themselves easier to middle schoolers or to high schoolers?

I’d argue those we shared in this lesson apply across the grades. We will be exploring math fights in more depth later in the workshop so hang tight for that 🙂



Withholding information stood out to me most. I’ve noticed that when I withhold information, students are more engaged in trying to understand the problem or story rather than being the first one to solve it. Offering context right at the beginning with images and videos that are relevant to their lives has also helped spark curiosity and more interest in math. I’m hoping to become better at coming up with context through images and videos that will continue to spark their curiousity.

I have been using notice and wonder activities in some of my other subjects I teach and it is great to see how I could use these in my math classes. I agree that reallife problems don’t necessarily spark curiosity (and in some cases are actually quite boring), so I really enjoyed seeing ways to change these problems to be more engaging. Currently, all of my classes are remote, and I am aware I need to work on withholding information more in this environment. I struggle with the feeling that I need to give students all the information since we aren’t in class together and I can’t physically see many of them working through the problems.

I am eager to change as many of the textbook problems to NoticeWonder type problems as I can. I am certainly someone who has changed the name so the problem is about me, or me and a student with 2 different answers – and it helps a bit, at times, with some kids – but definitely not the ultimate fix.
The ones that really come to mind are Sequences and Series problems – pretty easy to withhold information and let them analyze it one piece of information at a time.
I do really like the area/rectangle and the moving dots for systems of linear equations. I can wait to use them in my grade 10 and 11 math classes!

@holly.blahun You’re right! Sequences and series is a great topic to easily withhold information. Show the first two numbers and let them predict the third before showing them the third.
I’m also reminded of this sequence video from Veritasium: https://www.youtube.com/watch?v=vKA4w2O61Xo

I love this! We cover conjectures and counterexamples in Math 202 and this fits perfectly <3



Some really great strategies were shared in this lesson. I have definitely tried to spark curiosity in my math lessons before and have used Notice and Wonder, but now I’m thinking that I probably didn’t spend enough time building the culture of noticing and wondering early on. Some students would always share while others were more reluctant to engage.
I have also encouraged estimation, both with ‘regular’ math problems, and also through using tasks such as Steve Wyborney’s Estimation Clipboard and Estimysteries, which my 5th grade students have loved. However, I do see students skipping that step when it’s expected as part of their problem set.
So far, I’ve used Notice and Wonder and Estimation type tasks as more of a warmup, before moving on to the Eureka lesson of the day and trying to plough through all the requirements that go along with that. I’m excited to see how I can take these techniques and weave them into the content, so that the engagement lasts throughout the math lesson and not just for the beginning. That task feels very daunting right now, but very worthwhile.

At first, it definitely feels daunting! However in time, it’ll flow naturally. Something to consider is potentially skipping some of the warm ups that are disconnected from your lessons and build using these ideas around the lesson to have a built in warm up. Ie: sparking curiosity could be the warm up.


Last wednesday I introduced my functions lesson doing a kind of performance. I told them that we will infect us with coronavirus. We settle the velocity of infection at 1 and then I give a piece of paper to the first infected that he had to give an infection paper to one student, this new infected did the same, and so one. One student secretary was counting and writing on the board the number of the new infections and the accumulation of them.
Then we did the same with velociti 1,5 so the first infected gave one paper to one student and a half of paper to another one. The students who had one paper or half and half could infect the others. And finally we did the same with a velocity of 0,5. We take the data and we make the plots.
Now I think that to make this activity more interesting, and with more curiosity I could make them stand up and take datas without saying that we are making an experiment about coronavirus infections. And after that use the notice and wonder strategy. I think they could have more curiosity.

I think that would certainly leave them with a memory of the learning that they could lean on when experiencing this idea in the future.
One thing worth considering is that the challenge we have when we use context is that certain contexts can affect students in different ways. So while I’m sure you approached this particular context with care and concern, it is possible that covid has affected students in different ways. Just something to be cognizant as @jon and I are only now realizing that some of the things we’ve done in the past may not have been ideal for all students.
Keep up the great work!


The biggest takeaway for me in this lesson is “withholding information.” As a resource specialist, I am always prompting, using scaffolds, preteaching, using mnemonic devices. This is something I need to work on. Currently, in my parallel math class, my students don’t know what do when left to think on their own. I get silence most of the time. This is one reason, I don’t advocate for classes that are are leveled. My students need to work with their general education peers and see how others think and then begin to feel confident in themselves and their ideas.

Great reflection and inspection here @helen.calaway We find that students generally would rather think less. We need to put them in situations where they think regularly. This will build their confidence as long as we’re there to support that thinking.


I use some Notice and Wonders, but I have been doing them in online learning, so I haven’t been able to really see the benefits. I have been using pictures, but will try to incorporate videos in the future. I like starting with a notice and wonder because it ignites some thinking and gets the students brains working. I really liked the candle burning example. I am curious about the 3act math tasks. I am not familiar with them.

Hi Dawn!
Yes, online learning introduces even larger barriers to engagement including determining how engaged an entire group is. It is clear that this learning environment is not anywhere near as interactive or engaging as being face to face (and even that was hard enough!)
Despite the challenges, problem based lessons are still the way to go rather than straight direct instruction. Here’s some problem based units you might want to check out to help you along;
learn.makemathmoments.com/tasks


I have a few students who just “want to get on with it” and a few who check out as soon as they walk in the door. When I tried with holding some info and having them notice/ wonder the kids who don’t normally say anything were suddenly participating, and those who are impatient to “just do the math” had to wait, but they did not seem upset about it. I tried it with some work we are doing with financial literacy, using pictures of homes and asking them to notice/wonder about them.

I have had a go at designing a few lessons of my own based on your model and some kids are now finding Exploration day (Mondays) their favourite lesson. They like Notice and Wonder – they like the “success for all” aspect of that part of the task, but also some definitely compete to come up with what they see as the most sophisticated mathematical questions. I am also enjoying trialling “withholding info” and seeing good results of higher engagement and more leaning in.

This is fantastic to hear! If you utilize a problem based approach (like we do in our units learn.makemathmoments.com/tasks) then every new problem based lesson day will be an exploration! Glad to hear it is impacting your practice! Give it a go!


PS what software did you use to make the “Maya flower bed” video?

We use Apple Keynote for animations, but PowerPoint is really powerful, too!


Love all this so far and need to be more intentional about withholding information and taking more time when needed!
My biggest question is…how do you start the school year off? Do you start day 1 with some random notice and wonder task to get kids excited? I know in high school common first days are here is the syllabus…
I’ve done Jo Boaler’s week of inspirational math, but curious how you all would start?

Great question! We have a whole mini course in the Academy about how to start the school year off right which you should definitely check out.
The key upfront is building a community of math learners which can happen in a number of different ways. I tend to start with getting to know you type activities and then dive into some mathematics – I try not to hold off on math too long because I want students to quickly see / experience what math class is going to be like vs maybe what they might know / have been exposed to.


After watching this video I used a Notice and Wonder in my lesson on Volume of a cylinder. I really liked it as a questioning strategy and was suprised about how much prior knowledge it activated and student interest it sparked. I also made it a point to have students estimate answers and again was very pleased with how effective this was. Students were regularly able to identify if a solution was reasonable/unreasonable based on their estimates.
Witholding information seems like a great way to build conceptualization, but it is new to me and I will need more practice before implementing. I am looking forward to learning more about it.
Lastly, I loved the idea of “cranking up the math dial”. What a great way to keep students engaged and also develop their math stamina!

I have used notice and wonder in my classroom in my ELA and Science and Social Studies lessons usually with pictures and vocabulary. I have used it occasionally in math with geometry and patterns. I try to encourage and accept all comments when children share.
I really like the idea of withholding information I am interested in learning more about this. When teaching problem solving at the beginning of the year I will share a problem 1 sentence at a time and encourage students to draw the problem as I read each sentence. This has helped to get students to think about what the problem is asking. Sometimes after sharing each part of the problem and encouraging them to draw I will ask them what they think the question might be or what we might be solving for based on their picture.

@gerilynstolberg We agree! Unfolding the problem in stages allows students to think about strategies and adjust those strategies as they get more information. Great for their problem solving skills.


I laughed through the section where you talked about the inappropriate and unrelated comments. One key to building relationships with my students is to value their voice, even when it’s not related to the content. They just want to be heard. There are so many times that students (especially high school students) just want to be noticed and get attention. Let them have their moment, don’t give it any power, and move on.
Regarding the transformation of textbook questions into notice and wonder style questions… My brain is really starting to work thinking of ways I can change these boring textbook questions, omit information, and create anticipation by changing it to bare bones style. I’m also very thankful that you two have done a lot of the video creation for us. My video skills, while getting better, aren’t quite as good as yours!!

I used the “put your arms around it” task from Mindset Mathematics book in several Gr 24 Elementary Math classes. Students explore perimeter by going around the room with a string (students get all different sizes) and they have a chart – objects that are too small and objects that are too large and they write them down on their clipboard. They draw the object in the room that the string wraps around perfectly on the back of their page. What I am realizing about this task is that it works because there is alot of estimation going on as Ss try to predict which objects in the room it could fit around. There is not much information given to them and there is lots of noticing and wondering going on. They get to explore objects that are of interest to them. Will my string wrap around my waist? Around this globe? Around this recycle bin, water bottle… etc. It’s also a nice visual and physical model / manipulative to refer to later. How the teacher presents the students with their string and starts the questioning would be important to “withhold info, create anticipation, get noticing and wondering and then estimation…” Knowing what I know now, I think I’d do a better job with this lesson next time I try it.

Discuss prior findings from a prior lesson, discuss why they were doing the steps they needed to in order to solve the problem, withhold information because it leads to the students wondering what if questions and activate their own discovery for finding how they need to solve various problems, have the students notice and wonder different patterns on their own rather than immediately sharing what the patterns are for various problems.