Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 22: Consolidating The Sparking Curiosity Path › Lesson 22 Question
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Lesson 22 Question
Kyle Pearce updated 1 month, 4 weeks ago 54 Members · 97 Posts 
How will you spark curiosity this week in your lessons?
The Action step from Lesson 22 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?
 This discussion was modified 1 year, 10 months ago by Kyle Pearce.
 This discussion was modified 1 year, 10 months ago by Kyle Pearce.

Here is a lesson I will use this week. https://teacher.desmos.com/activitybuilder/custom/5fff0c0e6fd6150cedd0d28a?collections=5fe0e721a5c02c0d25081f7f
It uses a notice and wonder on a persepective picture, and we get to talking about why we cannot assume measurements in geometry. I have done this before, but now in COVID I am converting all my lessons into DESMOS so that kids at home can still be active in answering questions.

Awesome. How did this lesson from the workshop potentially impact how you’ll deliver this Desmos activity? Any new take aways?


I love the “cover the floor” lesson from the curious tasks list. We have been working on multiplication using arrays, and I love how this bridges the concrete array to the open array, setting up students for area and perimeter. We already use notice and wonder in our classroom, so I will start with act 1, then give students time to notice and wonder before moving on to act two. Students have already participated in a unit related to measurement, so I am hopeful that they will ask questions about dimensions. If they don’t this is a great place to reinforce the language from previous units. We’re in remote learning right now, but teachers are teaching from our school building. I am on the lookout for places in our school to film a similar video, which would be a great way to reconnect students to their school building while they are learning virtually.


Where can you find the Same perimeter, different area video (with the sticks) ?
I would like to use it with the next stage of exploring area.

Hi, here is the link:
If you highlight and click it offers “go to ……” Super cool, I am going to use this too along with Factris game.



I tried “shark bait” with my daughter who is in Kindergarten. She played with some cubes and guessed the worm was 20 cubes long before we even got to act 2. As I reflect, I realize how valuable it is to have a classroom community where different estimates and ideas can be shared. I usually like working with students individually so I can go at their pace, but with this problem based style of teaching that can engage all students I would like to have a group of students who can discuss and compare their predictions and methods.

I think balance is key. It is great to have opportunities to work with students in small groups, but it is also great to give them opportunities to productively struggle in a mathematics community.


I tried my own Kitkat videos. I had my daughter open a Kitkat and take a big bite, set it down and start opening a second. I didn’t get a lot of quantifiable questions so for act 2, I added a note hanging on my fridge at the beginning of the video that said, “No more than ONE chocolate bar a day.” They then viewed the act 1 portion leading into her eating portions of two more bars. They can’t really see total amounts left for each bar. For act 3, I showed the remaining portions of the three bars. This was how I introduced adding and subtracting fractions.

Awesome! Note that often it takes time to build that culture in your classroom so you might not get a ton of sharing initially. Keep at it and help along by sharing your own notices and wonders to help nudge them along. Soon enough, you’ll have to cut some off to keep moving it along 🙂


I looked through the tasks and noticed “Charge”. My 8th grade class has been looking at Scatter plots this unit but my students are struggling with the concept of slope and yintercept in context. I think I could have used this task at the beginning but doing it as a lesson/set of lessons at the end of the unit I think can work too. I am going to try “Charge” tomorrow. My plan is to give them the picture and let them notice and wonder then reveal more as suggested then use the Desmos. We may not get to the Desmos unti the next class, depending on how guys develop their understanding of slope and yinterecpt and ask questions and/or connect what they have already learned about slope and yintercept.
I think seeing another way to look at slope and yintercept once we eventually label some of the numbers they come up with as such could help solidify already presented content and then we can start to change numbers to see how they adjust their thinking.
Thanks!

@david.diehl You’re right, Charge is great to build a need to bring in and discuss slope as a rate and I’ve used it that way. I’ve also used it the way you’re thinking of using it this year — As a follow up to apply slope as a rate. This is a great use of the task as well! Desmos is a great tool to help make those connections easily. Let us know how it goes.


I went through the “Doritos Roulette” 3ActMath Task to reach the learning goal of experimental probability and proportional reasoning. I love this because the notice and wonder video does not give much information but has someone opening a Doritos Roulette bag. I know when I watched the video, I was asking questions like, “What are the Doritos Roulette? What is the ratio of hot to regular chips? Are these chips any good? (Of course, they are right, they are Doritos) But I am sure my 7thgrade students will have no problem wondering questions that will help lead to the learning goal of proportional reasoning and probability.
Then having an estimation of how many chips are in the bag (Low, High, prediction), then think of a fair probability of getting a hot Dorito in comparison to the regular Dorito. (Most Likely a 1:1 ratio prediction, but always fun to hear because I am sure students in the class may have tried these chips)
Having the students go through the anticipation by stating what information we need to know and how we will get that information to help us quantify the number of Doritos and the probability of eating a hot Dorito.
Then slowly release the information in act two of the task allows students to answer the focus question. Having students work in their collaborative groups to see if they can place the ratio of hot chips to total chips in the bag and how many hot chips in total they would expect to be in the bag total.

Sounds like lots of big take aways here! Curious to hear how it goes when you try that lesson in your class! Keep us posted!


I filled out the template for G. Fletchy’s Fish Tank task. It was helpful to think through how I would use it in the classroom. I attached my filled in curious lesson template, thinking through the elements. Planning for curiosity, I see now, is more than just showing the video, but creating anticipation and thinking of what information to withhold.

Great job on setting up your curiosity template! I agree saving the timer for after the initial notice and wonder would be helpful! Keep those ideas coming and open.


This week was the start back to inclass learning. I sparked curiosity but uprooting the norm that was our classroom before the break. I defronted my classroom and scattered the desks so that they were no longer in neat, organized rows. I had the desks facing a new direction (only for the times I need a projector). I have 2 whiteboards on opposite sides of the classroom so a pinned/taped Wipebook chartpaper (VNP surfaces) to add additional areas for groupwork. This was my start of a “Thinking Classroom – Peter Liljedahl.” I started yesterday with on noncurricular task and did Peter’s “How many 7’s?” activity with random groups of 3 on the VNP surfaces. I began by having students stand, not sit, at their desks while I explained the activity (nothing was written on any board). The activity started with How many 7’s are needed for the numbers 1 to 100 and then when each groups was ready I had them move on to how 7’s are needed for the numbers 1 to 1000. The collaboration I saw truly showed real thinking and having others students try to explain other groups students kept everyone interested in what was being said. This was just day one and it was a success. For today, I needed to try a curriculum task, one they been struggling with online, so I ran my lesson the same as yesterday in random groups working at the VNP surfaces with instructions given orally. I gave the groups the freedom to create their own theoretical probability within certain parameters using coloured tiles in a paper bag. I anticipated and planned for the progression of the lesson with further questions. I did not answer any questions a group other member could answer or I’d provide a hint. Students were encouraged to look at and ask about other groups’ work. Both days, the consolidation was so much more successful because I could use the strategies displayed in the student work. No plans for me stopping with the start of my “Thinking Classroom” and the strategies of the workshop.

This is fantastic to hear, @johngaspari! Awesome work! Glad to hear that you’re diving right in and seeing some positive results! This can be difficult at first as you shift the culture, but it sounds like you’re well on your way. Congrats!


Learners have been integrating the horizontal and vertical number lines into the coordinate grid…I am choosing a practice problem from the last lesson in the book to expand on this idea of context first.
The problem has a diagram on a coordinate grid with six points and gives the ordered pairs of each point. The learning objectives are to understand that distance is in absolute value and the relationships of horizontal and vertical points describe situations. I am nervous that I have misunderstood or am doing this wrong, that it is too “withholding” or I am not recognizing all that I am giving.
Modified version is
1) Providing a hexagon without ordered pairs or gridlines but with the Center of Town labeled as a point; include a compass rose on the side and give the context, “Sophia likes to go for runs. Her parents let her run by herself as long as doesn’t go farther than 1 and 1/2 miles away from the center of town.” Share by highlighting the path from one point to the next;
2) Ask for Notice & Wonders; anticipate, “why would she do that?”, How far did she travel? What is the distance between the places? How long did it take her? Focus on “how far did she travel?” and “How far is each place from the center of town?”
3) Give the context then model the distance from the Center of Town with my finger, east and north, to Home, then unveil coordinates of Home (a, 1/2) , Bank (1, b), Library (c, d) , unveil distance of Post Office is 1/2 mile from the Library and the Cafe and that School is 1 and 1/4 miles south of Home.
4) Look for students to identify the center of town as origin and that horizontal have same y value and vertical have same x value; find distance between points then perimeter.
Sadly, for my students, sparking curiosity is going to take me some time as I need to revamp my mindset…. This was hard for me: I was much too wordy and lost track of my objective. I think that eventually this will be able to be multileveled, with the information given/prompting question.

I have a lesson coming up on Scale Diagrams in Math 11. I was thinking of having students do a floor plan of our classroom, but work together (aka. only draw one piece of the classroom to scale). Once everyone took their measurements, I’d draw each piece on the SMART board (using their most likely different scales) and ask them why it doesn’t look like our classroom – or why can’t all of our tables fit?!
I will withhold what units to use (reallife and diagram), but am struggling with the rest of the curiosity path. Any tips?

I have a lesson coming up on correlation. I thought I heard it mentioned in one of the previous videos that there was a task on this subject but can not seem to find one. If there is one, could you point me in the right direction?

Try tapintoteenminds.com/3actmath/candleburning


My next lesson is an easy one to spark curiosity which will be in a few weeks. I am going to have to choose wisely. I have perimeter jumble or 36 fences from youcubed. I have R2D2 or girl scout cookie or Fish Tank. I know that there are more on perimeter, area and volume of rectangular prisms.
The topic after that I am not sure about. It was something I was going to ask you on the podcast tonight which was personal finance. I have to teach the difference between net and gross income along with different types of taxes like income tax. Not sure what to do about that.

Be sure to rebook that time slot. Would love to chat about that further!
Sometimes curiosity could be through simple placing objects like money on the table… then some is removed. What do you notice? What do you wonder? It could be the taxed being taken away.
If the sum of that money is say $10 and you removed $3, but your income is $50,000 how much will you expect to have taken?
You could even do a series showing different percentages taken as the quantity increases … just spitballing!


I join my firt day lesson about functions with students that have between 14 and 15 years old.
 This reply was modified 7 months, 2 weeks ago by Laura Las Heras Ruiz.

I have been doing an Activity on Similar Triangles and Proportions. I created a project for students to measure themselves and their shadows, and an objects shadow. Using Proportions and Similar triangles they will find the height of an object not easy to measure.
Note: Distance Learning
Notice and Wonder: There was a notice and Wonder, but it was just an image and we are in distance learning. I get some discussion for them, but not as much as I would in person.
If I redid my lesson, I would use this image instead to peak some interest.
https://petapixel.com/assets/uploads/2012/10/nova.jpg
Hopefully it would spark some curiosity into shadows and proportions. It is a funny picture and I could then add information but keep some out to make it more interesting.
Withhold Information/Anticipation:
I could give some information to get the students to start estimating some heights and get ideas of why I chose the picture. What does it have to do with math or the subject we are taking about in currently in class.
As an Assignment: I would then have them do the Activity at school with a partner.

Great activity idea!
When it comes to the anticipating / estimation piece, I am wondering whether you have any “reveal” details to give them? So for example, if I’ve noticed and wondered, anticipated and estimated, do I get any closure to that experience?
Loving the thinking here!


I used the voting video (Sonya and Eli) because we have been learning about percent. I wanted to try an entire lesson. The kids LOVED it. They noticed and wondered like crazy and they really got into justifying their estimates. The only problem I had with it was there was one student who wanted to just tell everyone the answer, once we got close enough to figuring out what the question was. It took a lot of moves on my part to make sure he didn’t just give out the algorithm. I ended up getting to the “do the math” part a little faster than I wanted to, because he was letting out too much information. I was still ultimately pleased with the great engagement and one student in particular actually wrote down some numbers, when she usually wants to copy off others or gives up at that point. The student who wanted to just give the answer was surprised when I did not immediately tell him he was correct – I asked him to show us how he got there.

Thanks for sharing @kathleen.bourne ! Looks like you handled the students who wanted to give the answers well! I think with time the “answer telling” will reduce! Keep it up!


This week, I had a go at creating my own MMMtMstyle lesson for my Year 7 class. The learning objective was using algebraic expressions to model scenarios, and tiptoed into our next concept, using substitution to evaluate expressions. I used a scenario called “pocket money day”. I felt pocket money would be an engaging topic, as it is relatable for kids and they enjoyed comparing their amount of pocket money with friends (some were appalled to find that their friends received pocket money “just for being alive!!” as one girl put it, ie without doing chores – I think there might have been some big dinner table talks that night!). I used my own child and children borrowed from my colleagues, and filmed them. The first part of the video showed them receiving play money in a formula of “age x $1.50” (only I didn’t reveal that, of course). Then I had a screen saying “what do you want to know now?”. The aim here was to build anticipation. We did our first N & W report back at this point. Then the 2nd part of the video showed the same kids holding whiteboards saying “I am ….. years old”. Then we added to our N & W and reported back again. I am always pleasantly surprised at how willing to lean in the students are during N & W – pretty much every kid is engaged and wondering some cool things! Then we started the task. I wanted to design it as “low floor, high ceiling”, I don’t feel I achieved that as well as I have with some other tasks as I felt this one was more directed and there weren’t as many opportunities for using different strategies but it did still allow kids to move at their own pace. The first questions were pretty directed, encouraging students to seek a relationship between the age of the child and the amount of pocket money (this had already come out during N & W so no spoilers), through to some “working forwards” and “working backwards” questions with either age of child or amount of pocket money being given, through to generalising their formula and then more complex formulae including adding in money for doing chores and money subtracted for misbehaviour. I didn’t anticipate the spread of the class – one student had finished all 9 tasks within 10 minutes which had me scrambling for more to keep him busy, while others spent almost their whole time trying to work out that it was $1.50 for each year of age. I was also keen to see who would think of organising the initial data from the video in a table (I deliberately filmed the kids out of order, and out of order again from Part 1 to Part 2) which then gave me a teachable moment on 2 value data tables. I was pretty happy with the task and the learning it encouraged.

@rachael.young Thanks for sharing your experience. It sounds like you planned this well so you could cover a number of learning outcomes. Nice work! Sounds like your next step is to think of ways to raise the ceiling! What are you thinking so far?


I am going to try the Trashketball lesson with my 8th graders, as it looks like a lot of fun. Volume of a cylinder and Sphere. I will begin the lesson by shooting some plastic balls (same size) into a 5 gallon bucket. I will then ask students how many balls will fit into the bucket. Next I will allow students time to complete a notice and wonder activity followed by a think, pair, share. If necessary I will pose the questions of what information is needed, and what shapes are familiar? Lastly, I will allow students to estimate the dimensions of the bucket, ball, and how many balls will fit in the bucket.
I will then reveal the diameter and height of the bucket, as well as the diameter of the ball. After providing students time to work on a solution, we will compare our answers to the estimates. Possible wrap up questions include: Is there any unused space in the bucket? Why? What happens if the width of the bucket were doubled? Would the number of balls that fit in the bucket double?

@jeremiah.barrett Love it! I really like your REFLECT/Next step questions! Let us know how this goes.


I was beginning a unit on area and perimeter so I used the Cover the Floor Task. Unfortunately I am still teaching mostly virtual so engagement has been a concern. The students made notices and wonders none of them talked numbers during their notice and wonder. I posed the question “how many blue tiles do you think it will take to cover the yellow shape?” I shared the photos with more information and one student was able to find the area and perimeter by using the floor tiles. When it came to figuring out how many blue tiles it would take that was a little more difficult. Once he covered the floor with the tiles some of the students saw the connection to area and multiplication.
I plan to try another task this week to show the connection between area and perimeter. I have created some slides with toothpicks to show different shapes with the same perimeter. We will try to figure out which shape has the largest area and why?
Then we will try a task with rectangles made of colored tiles with the same area and discuss the perimeter.
I definitely like this way of teaching better than using the workbook but I am concerned about the about of time it will take to create all of these tasks. Looking forward to learning more.

Hi there @gerilyn.stolberg Time can definitely be a concern if you’re designing your own tasks from scratch. We’d suggest using some of our tasks https://makemathmoments.com/tasks and spending your limited time on anticipating what strategies will use and how you can help them push further (more on that in future modules).


For this reflection, I spent some time going through the tasks from all the different grade levels trying to understand which tasks upon initial glance would create the biggest SPARK.
I think Sharkbait would be a winner for the young grades
I know Krispy Kreme works really well
R2D2 PostIt for sure
The Solar Panels seems approachable with lots of interesting connections
Area of Saskatchewan could use just 1 dimension North length (450 km) with the google Earth image. Also would be interesting to pit Saskatchewan against a country like France or Province like Nova Scotia, with minimal info on that image.
I think Corner to Corner would work well after they have explored simple Pythag problems first. Context could also be shoebox with a string.
<b style=”color: inherit; fontfamily: inherit; fontsize: inherit;”>New Idea 1: I’m brainstorming a 3 Act here where a right angle triangle is setup with the squares of the side lengths drawn. The hypotenuse square is filled with an array (5×5) of something say, stickies, cupcakes, quarters, stalks of brocolli an items start moving out into the other squares.
New Idea 2: I believe a very engaging 3Act could be made from The Carl Sagan Cosmos video search: <ytformattedstring forcedefaultstyle=””>Eratosthenes circumference of the Earth Where the distance between Alexandra and Syene, Egpyt was measured by cart and the angles of shadows were used to determine the circumference of the Earth! Hits a ton of concepts</ytformattedstring>
<ytformattedstring forcedefaultstyle=””>New Idea 3: Perimeter/length/elapsed time lesson with Strava running art???</ytformattedstring>

You’re pretty well versed in problem based lessons! Awesome!
Liking your ideas and would love to see them come to fruition!
We have a Pythagorean problem based unit almost ready for release here: learn.makemathmoments.com/tasks
Keep an eye!
Well I’m learning a ton from these modules. 🙂
Looking forward to seeing the Pythagorean problem based unit! I like the idea of having several rich tasks for teachers to choose from all linked to the big ideas of the unit. They would not have to use them all.
<font face=”inherit”>The key for success I </font>believe<font face=”inherit”> is having an appropriate observational tool so that teachers can get a general impression of where each student’s thinking is progression regarding those big ideas outlined in the unit when engaging in the tasks. Then the teachers adjust their next tasks in the unit based on the information they are gaining from the the students. All with the end of unit tasks being predetermined linked with the big ideas of the unit so that the teacher knows where they are heading. I’m only this far, maybe this is a similar idea to your units.</font>

I’d argue that your thinking is in line, however we have focused more on providing a path that could be used vs say options, however educators could add or replace different parts along that path.


After reading your post, I figured that using the relatable, nonthreatening, materials that you shared works well for any age group. Anyone can relate with Kristy Crème. Yum. Thanks for your post.


I’m struggling a bit here. I love, love, love the ideas presented, but get a little overwhelmed when looking at a textbook question and trying to figure out how to make it more engaging, more curious and more mysterious. I see Lesson 24 is about how to do this specifically, so I’m going to hang on until then. I am encouraged by seeing the success of others, however! That’s always good.

Hang in there my friend. Let us know how you’re feeling after 2.4!

I’m right there with you, @jennifer.kelley It is overwhelming but exciting. I might be overthinking things. We will get there! Andrea
 This reply was modified 3 months ago by Andrea Earle.


This has been transformational or a paradigm shift for me and my older brother who has retired from teaching. In our discussion, he lamented how it was challenging for him to teach trigonometric ratios. After hearing what he had to say, I immediately told him that he was not making math moments that matter. Clearly he was missing six elements of an effective pedagogy.
The educator as in the movie industry builds ANTICIPATION in the trailer, then while WITHHOLDING INFO allows the audience to NOTICE/WONDER, and allowing the audience to ADD THEIR VOICE, internally of course.
Placing a student at each angles of a right angle triangle, holding strings pegged midpoint from opposites sides will generate the ANTICIPATION for my next lesson.

The last week of school, I did an activity where we took information about the Oscar winners of the best actor and best actress going from 1990 to 2020. The information included the ages of the winners as well as the movie they were in and the domestic gross earnings of the movies. This gave us enough material do several types of statistical analysis and graphs. One of the interesting comparisons was the difference in ages of the winners. The two pages of data was pretty overwhelming for some of the students, so I think it would spark their interest to have a video that shows several of them receiving their awards and see if it will get them curious about their ages. It is too bad they didn’t do the awards live this year, because seeing 54 yearold Anthony Hopkins in 1991 and 84 yearold Anthony Hopkins in 2021 would have to be a great difference. Frances McDormand won at ages 39, 60 and 63, which would be another fun visual.

I tried to create curiosity from an existing lesson that I had planned for this week. Since there is only 2 weeks left of school, I decided that I did not want to invest a lot of time in teaching new routines, so I started with small changes. We were talking about investing in stocks. I displayed a graph of the price of 2 stocks (Dunkin & Starbucks). I withheld the key so Ss did not know which line represented which company. I asked them to notice and wonder about the graphs. Given last week’s graduation, the class size is 2 or 5. I didn’t use turn and talks.
In another part of the lesson, I incorporated estimation to determine whether a student’s answer was reasonable. Two different growth rates were used in the problem, I asked them to determine what percentage that they could calculate with mental math only. Common responses were 50% or 25%, all too high estimates but the answer was way lower than student’s original answer. I asked what is a really low percent that they could calculate with mental math. A few responses were 1% and 5%. It was a good start, but I am excited about the prospects for next week. I will keep using these as much as I can this week, so that I become a better facilitator.

Starting with small changes is so key. Don’t try too much, too soon. As you can imagine, not only does trying too much potentially cause you overwhelm, but it is also harder to determine what is working and what isn’t. Love that you’ve started – that is the key. Start somewhere and make more changes incrementally! Great work!


We are already out for 2 months (I don’t like to say summer because we go back with 11/2 months of summer remaining) so I redid a lesson from the 20192020 year (fall semester). I modified Robert Kaplinsky’s InNOut Burger problem to withhold information.
Begin by showing pictures of InNOut Burger’s single cheeseburger, double cheeseburger, 3×3 cheeseburger, 4×4 cheeseburger, and the menu with the prices covered. (The menu only has a cheeseburger and double cheeseburger).
Complete Notice & Wonder: I expect a wonder to be “What is InNOut Burger?”; “Why is there no 3×3 or 4×4 on the menu?”; and “What is the price?” (We do not have InNOut Burger in the eastern U.S. but we do have a restaurant where you order on one side of the building, drive around to the other side of the building to pick up your food much like an InNOut Burger.)
Reveal price of single cheeseburger and double cheeseburger. I would expect more questions: What about 3×3 or 4×4? That is the question to figure out. Then ask what would the cost of a 20×20 and a 100×100 cheeseburger.
This will go into multiple representations of linear functions.

Nice! Before revealing the information consider asking what information would help them determine the price of the 4×4. This will help them formulate a strategy before they even have numbers.


It is June for me so our students are writing end of term assessments right now.
But for the last 3 days of school I’m working on a Minecraft learning activity, it is just the beginning phase right now but I have a week to get ready to enter the world of Minecraft that my students love so much… I will add more details soon!

Love it. Is your district an office 365 district (meaning you have access to Minecraft Education Edition)?

Yes we are 365, really used teams a lot this past school year!



I teach at a school where the levels of student abilities vary widely. Many students have IEPs reflecting academic and life challenges that are often quite severe. It is difficult, sometimes, to engage and motivate.
So, this fall I’m teaching Calculus and Vectors (Grade 12, University Preparation). Using a video extract (28 seconds of a YouTube video by a Simon Sinek protégé), I intend to ask students to describe in words only to your friend (tablemate) what patterns they see.
Now, the unit is introductory and deals with the concept of rates of change but simultaneously deals with what Geert Hofstende describes in the sixth dimension of culture Indulgence vs. Restraint, immediate vs. deferred gratification, respectively. These often manifest themselves as not doing the homework (lacking consistency of effort and math engagement) engaging in “fun” activity then cramming the night before a test (engaging in an intense activity) or resorting to cheating (plagiarism) to get a (false) Agrade. The rewards (genuine understanding and ability to use math concepts learned) are far greater when students engage in consistent smallsteps than bigbang solution attempts.
I am hoping that both objectives might be met. Not bad for stripping away all the excess baggage; 28 seconds is more than enough to spark anticipation, wonder, etc. I won’t have to remind them of the importance of consistent homework completion and, as well, engage them in discussions regarding the rates of change that they see portrayed in the video. Let students discover both; for me less pontiff, more coach / guide.
 This reply was modified 4 months ago by Peter Gehbauer.


@mary.herbst7953 The anticipation is created almost automatically if you withhold the information or tell a story or create curiosity. If you’re looking for rates/ratios you might want to check out the Fast Clapper https://mrorrisageek.com/fastclapper/
or this one https://learn.makemathmoments.com/task/unclebensrice/


I noticed as I crafted a learning target there is some consolidation I can do. Here are two of my standards:
8.4(B) graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship.
8.4(C) use data from a table or graph to determine the rate of change or slope and y‐intercept in mathematical and real‐world problems.
During the consolidation, I know I want graphical responses so I would select students to share a table, then a graph since one would lead to the other. Then the following day I could extend the same task and then say what if I had light switches with motion sensors and I already saved 200 km of driving distance. How does this change your tables and graphs? What would usually be several days of repeated examples and instruction can be done more concisely.
Here is how I might teach Solar Panels in class:
 I would begin with the introduction video
 Then ask students to quick write what they notice and wonder about the problem for 3 minutes.
 After the 3 minutes, I would ask for students to start sharing as we fill out a group notice and wonder on the class whiteboard inviting everyone to participate.
 As we wonder add or tweak a student response to arrive at the focus question how much greenhouse gas emissions can the solar panels offset?
 Invite students in a thinkpairshare an estimate that is too low, too high, and a good guess before sharing out with the class.
 Next transition what do we need to narrow our estimation gap, is there any information you would like to know to help you do that? Think pair share/quick write before sharing with the rest of the class.
 Dare students to refine their estimate by revealing some information:
 5 panels offsets 4848 km
driven by passenger car  There are 582 panels (might
even allow students to look at the building plan to obtain this
information)
 This reply was modified 3 months, 3 weeks ago by Anthony Waslaske.

I am currently out of school for the summer, so I used the Pythagorean Theorem activity, “Corner to Corner,” since this was one of the last topics I taught.
As I went through the content of the lesson thinking about how this lesson would look in my classroom, I found myself adding notes indicating if the part of the lesson was for individuals, partners, or whole class. This is something I haven’t done in the past that I think will help lessons flow more smoothly.
Having students complete the notice and wonder is going to be a challenge in the beginning, but I hope that by this time of the year they will have grasped the idea that they need do their own thinking and that not everything is going to be handed to them and that all students are capable of analyzing a situation.
Withholding information from the students will also be a huge shift. I think with time, persistence on my part, and guidance from me, more students will be engaging in math and finding success.


@lisamarie.barnes Thank you for posting your example. It helped me better understand the “sparking curiosity pathway” for the primary level. I teach grade two and this would be a fantastic beginning of the year lesson to refresh their memory for estimating and counting. My purpose for using different coloured cubes would be to distinguish the counting benchmarks of 5 and 10. I’m looking forward to learning along with my students in the fall. Thanks again! Andrea
 This reply was modified 3 months ago by Andrea Earle.

@lisamarie.barnes YES! I had written down a very similar plan for my next year’s g2 class as a beginning of the year task. I especially am curious about the discussion we will have about the importance of colours or not, and I added to the question “why are the colours by 5?”


I’m teaching a summer bridge program that has no set curriculum other than a focus on social emotional learning. For math class, we are focusing on patience, perseverance, and a willingness to take risks.
Next week I plan on using one of James Tanton’s activities for his Exploding Dots – the Mind Reading Trick for #131.
Withholding Information: How does she guess our numbers every time?
Anticipation: Will it work again?
Notice and Wonder – I plan on giving them copies of the slides and letting them write directly on them with what they notice and what they wonder, but also guiding them to think about what is the same and what is different across the slides. Then once all that is done, I will then introduce the 2/1 Machine and let them play with that for a while to see if they can figure out the connection between the puzzle and the binary system of numbers.

The Knotty Rope Lesson (grade 3)
allows for withholding information as the first clip entails many notices and wonders about what is happening and will happen
vocab (what is a knot, some may call it a lump)
estimation for how many knots can be tied in the rope (individual, pair, class)
added pictures of lengths for when those questions are brought up and we move to the next stage
reestimate with the added information
allow them to explore how to solve this problem (see the different solutions)
discuss what if our estimations do not align with the actual length of rope, too many knots or too few
watch the end video
It is going to have me intentionally creating and planning lessons that will engage students in noticing, wondering, and using their knowledge and ideas to solve and understand math problems.

I used the solar panels task. After reading through it, my first thought was that getting kids engaged in this would be difficult because overall, they know very little about energy and don’t care much – and then it hit me! – UNLESS THEY ARE UNCOMFORTABLE! Every day, I continuously hear from the time the kids walk in the room that it is too hot or too cold. So, my thought was to turn off the A/C (it gets pretty hot where I live around the time I would do this lesson) and letting the kids walk into a hot room. They would nodoubt ask WHY it was so hot and I might allude to what we have here when it gets too hot – rolling blackouts. I would fib a bit, telling them that only our A/C is affected in the schools to explain why the lights and other tech still work. Then I would move into the lesson, showing the video, and following the majority of what is already laid out in the lesson plan. I am pretty sure the initial lack of A/C and tying that into using solar panels for energy will be the catalyst that gets them engaged and involved with the task. I will have to gather more information from our local utility to address more of the student questions that I am likely to hear about our school’s specific use of energy. Right now we are not in school, but this might be a lesson I start with very early in the year, so my task this summer will be to search out energy info for our school from the local company. I look forward to the kids being engaged and curious so I can see how far they take this activity.

Curious how this works out! Just make sure it isn’t “too” uncomfortable that you lose them! Ha!
Always remember, there are so many different ways to spark curiosity – even with ideas / things that they aren’t familiar with. The key is withholding information.


Launch Angle Pairs Unit:
Angle pairs created on floor from colored tape. (Seeing the tape on the floor creates anticipation.) Ask students to walk around and create Notice / Wonder tchart. TPS then share with class, I write on board. Someone will notice “pairs”.
How would you describe or name each pair? (My geometry variation of estimation) TPS, then share as a class, notice consistency, agreements…
Through class discussion, supply names, (partial list), for students to match and verify attributes…protractors used as needed.

Great idea. I’m liking how the approach doesn’t have to be hard or done with media/technology. Just getting students wondering!


After 22 years of teaching in my own classroom, I will be moving to the role of Interventionist for the whole school next year. It is currently summer, so I am thinking forward to the upcoming year. I viewed the tasks through the lens of someone who wants to spark curiosity throughout all grades, K5, in our building!
I selected the Fish Tank task because filling a vessel with water is likely to be familiar for everyone. My office will be centrally located, and most kids will pass by it on a daily basis. Knowing that this is my frame of reference for the task, I will explain how I would Spark Curiosity.
The Learning Goal is: Estimate the total number of cups it takes to fill the fish tank.
On the first day of the week, I would place a partiallyfilled fish tank outside my office with a large chart paper with two columns: What do you notice? What do you wonder? For their reference, I would place a lunchroom carton of milk that I have marked as ONE CUP. Practically all students are familiar with this amount of liquid because they are served it at both breakfast and lunch every day.
As I see students walking by, I would invite them to write their thoughts, or write it for them if they are too young. I would withhold the total volume of the tank, and how many cups of water I have already put in the tank. At the end of the day, I would circle the question that says “How many cups will it hold?” If no students put this down as a wonder, I would secretly write it in myself!
On the second day, students would see the tank with more water in it, a reference mark on the tank at 20 cups, and a new chart where students can put their responses with their names on sticky notes that they can add to the chart by grade… (Younger grades can do it with their teacher and post one answer as a class)
How many cups would definitely NOT be enough to fill the tank?
How many cups would definitely be TOO many?
What is your best guess?
What would you like to know to help you figure this out?
At this point, I will still withhold the total volume of the tank.
On the third day, the tank would be filled about half full, and the reference of how many cups were in the tank. (For example 40 cups filled up and the tank marked with this.) Students would be asked to adjust / zero in their guesses on their sticky notes from the day before.
Finally on the last day, I would reveal the correct answer – maybe on the morning announcements!
If applying one of the tasks schoolwide is an incorrect interpretation of this exercise, I can easily adjust it to use with one class into which I am invited. Through my role as Interventionist, I know one of my biggest responsibilities is going to be to get students to talk about math and build their own curiosity about it!
 This reply was modified 3 months, 2 weeks ago by Terri Bond.

Great job here! I especially like your questioning and in particular asking for how many cups will “not” fill the tank keeping the floor low so all can access!

I am also out for summer vacation but plan to use Donut Delight. LOVE this lesson to work on multiplication/division skills. Could also use with fractions which our 5th graders REALLY struggle with on a yearly basis. There are so many ways that students Wonder/Notice charts could take us as well (money, fractions, volume, weight, place value, etc.) Being from NC, where Krispy Kreme originated, is a huge thing. We take our donuts very seriously. 🙂
I really appreciate the idea of always being able to add more. Especially with this idea, there are so many areas to go to for future lessons! I enjoy providing students a curiosity trigger and then seeing where they go with it. That reveals so much to me as to where they each are in their mathematical learning. From their notices/wonders, I can create more specific learning opportunities.

Ha! Love that you’re all over Donut Delight and see it fitting into your long range plans! Can’t wait to hear how it goes!


I selected the solar panels lesson, as I, too, am on summer vacay. I could see using the lesson to spark some interest at the beginning of looking at the area of composite shapes. I would have them watch the video and do an estimation (too low, too high, best guess) of the total. Then because the total answer is revealed as the lesson continues, I would have them try to calculate how it would add up to that number so that they could see how overall the numbers add up. I found teaching area of the composite is either quick or some don’t get it. This might try the reverse approach and by giving them the total and have them lead the information that they need maybe it would spark interest.

I chose the “Krispy Kreme me”, although I do worry that kids could get distracted by the longing for or memories of eating donuts. In past years, I probably would have worried that kids would give up because the edge of the box hides parts of the donuts, but now I think it just adds to the mystery and anticipation. I’m pretty sure the wonderings will include “How many donuts?” without any prompting. I think the kids will enjoy the estimating, and what is new for me is the 3estimates approach, which I think is brilliant.
I’m actually expecting that kids will not think that there may be more than one layer – I can’t wait to see if i’m right! However, I will not prompt them if they don’t. This would be a perfect opportunity to let them think about why their answer might be wrong.
I think the biggest change in my practice will be to relax and see where their thinking takes them, instead of jumping in to “help.”

@miriam.reed This is a good recognition as I think it was one of the biggest realizations I’ve made over the years! Let’s do this!


I chose the airplane task because it has the potential of bringing together many parts of the classroom curriculum. I can see this problem as one that can help me build the climate of noticing and wondering in our classroom which will reach into many areas of learning. Since I teach from the belief that math is in everything, I tend to weave the subjects and make connections across the curriculum.
This task plays into the design process in science which can encourage the use of manipulatives for students who think they don’t “need” them anymore. I will probably use a story like Angela’s Airplane by Robert Munsch as part of the curiosity building for this activity. We can begin with their dreams for the future so that this problem builds from a child’s interests to the mathrelated. I can see revisiting this problem in different ways throughout the year as we study world communities in social studies, etc. For example, numbers can change as the student’s math grows and comparisons can be made between seats for more local flights and longdistance flights.
I, also, chose the Airplane problem because it goes back to subitizing and unitizing and yet also has potential for math equations. I am thinking of using it as an activity at the beginning of our grade 3 year to allow me to view the strategies the kids use and the different principles of counting the students understand to start the year. The potential numbers in this problem are big enough to engage stronger math thinkers with encouragement to use manipulatives while the limited information can also engage students who may have math anxiety or areas of thinking which will need to be strengthened.

I’m going to be modifying one of my early lessons for my 8th graders which has them doing rigid transformations. The original has squares and triangles “dancing.”
I will use a picture of me overtop of an above shot of the inside of our gym. I might make it less obvious it is me at first. I will simply translate the the figure over the gym then have them do a notice and wonder. I could have a video or slide show pre prepared. However, I’m considering adjusting what actually happens based on their questions that they come up with as they share. I will not have them use the actual math terms at first since this is an early lesson. However, the math terms will be shared as it becomes necessary at the end. We will likely include rotation. I’m not sure that reflection will happen. If I use a paper picture on my board I could simply flip it. I would want to make sure one hand is pointing so that it becomes more obvious that it has been flipped.

I like how you’ve been planning to hold back the math terminology a bit and let it emerge as deemed appropriate and/or necessary. This is a nice way to keep the experience non threatening and accessible for all.


How does this lesson impact how you might lead your math lessons?
I have chosen one of the tasks on the list: Free Throws For The Win (Binomial Distribution)https://tapintoteenminds.com/3actmath/dariuswashingtonfreethrowswin/
I actually watched numerous of the lessons on the list posted.
SPARK INTEREST: Introducing with a lead something related and interesting to teens (EG. Basketball Player who is Shooting Baskets)
ANTICIPATION: Think along the lines of “What question am I looking for from the students?” (EG. Do you think he will get in the next shoot) and where you can go with this – probability (Theoretical vs. Experimental), aspects that affect probability. May think along the lines of what other pivot the students may take regarding questions – EG. Quadratics.
NOTICE & WONDER: Prompt – “What is the chance of him being successful? Defend your point of view” Show the Video where information is withheld again.
*STUDENTS WONDER and want more info – Have Act2 video with some of that info revealed.
ESTIMATION: low value, high value, closer to comfort/real value accepted
*Then Act3 – where reasons, logic, and completion to the problem is brought forth.How would this impact my math lesson? Forward thinking for how to draw the information out – letting them lead the lesson, and make it look as if they were in control. Having to think of something they would be willing to wonder about that satisfied my goal for the lesson too.
**Am I getting the step of “ANTICIPATION” correct?
 This reply was modified 3 months, 1 week ago by Velia Kearns.
 This reply was modified 3 months, 1 week ago by Velia Kearns.
 This reply was modified 3 months, 1 week ago by Velia Kearns.

Nice work here.
While anticipation might involve students thinking about what question might be coming, we don’t want to funnel them too hard down a specific path. For example, I don’t want to say something like “what math question might I be thinking” otherwise that might shut down some students from participating / sharing their thinking.

I have a lesson that my students often enjoy about rates/ratios that is very similar to the R2D2 Postit note lesson. I would like to take the postit lesson and modify it for my rates/ratio lesson. Ratios can represent 3 different comparisons:
1. Part to Part
2. Part to Whole
3. Whole to part
We would discover the amount of postits total (whole), then we could make a list of the different colors used (parts). I would then introduce the new vocabulary for the unit and ask them to find the simplest way to write out the information without using complete sentences. I think I would need a bit more planning in how I would word this, but I think they would enjoy it.
I could even extend this by giving them a sheet of graph paper and have them create their own design and create an answer key for their classmates to do a gallery walk and work out their classmates’ art pieces. I would give them the option of cutting the graph paper to meet their needs so that no one has the exact same dimension.

I went back to review a lesson I created during the pandemic as an introduction to linear relationships. It starts with a notice and wonder video: scale is set to 0, then a cup about half full of M&Ms is placed on a scale, students see the weight. The next video shows the empty cup being placed on the scale, then the weight, then the weight of 15 M&Ms being added to the scale. Unfortunately, when my friend created these videos for my class she did not count the number of M&Ms so I do not have an exact number of M&Ms in the cup, but my students were able to use their data to find reasonable estimates.
Some changes I plan to make: In order to build anticipation and allow for estimation, I can cut the first video before you see the weight and have the students estimate the weight. I could then ask them what additional information they would need to make a better estimate and use the second video to provide some of that information. Once they make their estimates, I can show the first video again with the weight. Next I can have them use their information to determine how many M&Ms are in the cup. As I think more about this, maybe the estimation can be to guess the number of M&Ms that are in the cup. Maybe giving the students the dimensions of the cup and of 1 M&M could be helpful in making their estimates.
Here is a link to my original activity if anyone is interested, I plan on modifying it for next year.
https://teacher.desmos.com/activitybuilder/custom/5fa466505e661a2de5d91c39

We have 3Act tasks in our curriculum. I need to go back as a resource teacher and see exactly how they are structured. In addition, we will not be using the current resource we have after this year. So I need to become familiar with your tasks and figure out where to use them in our curriculum.

Love it. What curriculum were you using?
Definitely take a dive into ours and let us know how you are enjoying them.


When planning a problembased lesson, can you extend the struggle and consolidation over several days? My classes are 45 minutes. My thinking is I could extend a problem over 34 days because it is dependent and independent variables, function notation, and discrete vs continuous functions.

You definitely can. Sometimes coming back to it to let students finish off their thinking the next day prior to consolidation can be helpful as it gives them some time to think on it, generate new ideas and then potentially deepen their understanding of the concept. I never used to value doing things over a second day, but I see the potential now.


In my summer school class, I had them divide the numbers of the Fibonacci sequence. Most of the answers were around 1.618. They were curious why and when this happened and why it didn’t always occur.

I’m a math coach this year for grade k8. I have 11 years experience teaching upper grade math and am wondering how to approach Kindergarten content. The Shark Bait task looks really engaging and accessible. Using the sequence of: withholding info, anticipation, asking the students what they notice and wonder and then estimating seems like a really appropriate lesson.

Fantastic! Sounds like a great approach you can leverage with your colleagues you’ll be working with.


After looking through the tasks I will be using the video <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>Doritos Roulette Spicy Hot Chips! this upcoming year!
I will play the video and pause it to get some “notice and wonder” questions. Once we are done watching it I will ask them to estimate the amount of Doritos which are extra hot to normal and see if they can give me a ratio. They will then get into groups of 2/3 in which they will have to come up with the best estimate to put on a number line in the classroom. This will lead to a discussion and potentially a video/activity of the Doritos being eaten where they can get more information to tally up and verify their predictions.

I chose to use Soupdujour from the list of problembased lessons, in particular as a review for volume of prisms (Grade 8). Students had been exposed to this outcome in grade 6 but explore it in more detail in Grade 8.
To spark curiosity, students will watch the short video clip but only see a Campbell’s Soup box and a plastic storage container. They will be given no other information such as the container shape names and their dimensions. No question will be provided for students to answer. This will drive my students crazy! There will certainly be questions directed at me before we begin the next part. 😀
Notice and Wonder: Once students have viewed the video, they will have a short amount of time (12 minutes) to jot down what they notice in the video and what they wonder using the NoticeWonder template. Students will work independently then share with a partner before we move to sharing whole class. I will post many of the student responses on the board or chart paper. Most students will likely mention the obvious for what they Notice: a box of Campbell’s tomato soup, a plastic container. Some may notice the capacity measurement on the soup box. This may become a point of discussion (volume v. capacity). For Wonder, there may be students who will ask the purpose of this activity, others may wonder if there will be a recipe shown, and still others might wonder about the health conscious choice of eating boxed soup or the environmental choice of using plastic. However, I know there will be students who will wonder if the box of soup will be poured into the container.
Because the learning goal is finding volume for prisms, this will be the question chosen from the list to explore. Will the box of Campbell’s soup fit in the container?
Now we move to the next step – Anticipate. Students will predict if the box of soup will fit into the container. Will there be space left in the container after the soup is transferred or will it overflow the container or will it fit exactly? We can vote to see how many students fall in each group. This will be friendly competition (I hope).
Next, I will ask students if there is a way to make a prediction that is more accurate and if there is information that I can provide to make it possible. I hope that someone will suggest that knowing the dimensions would help. I will ask students to estimate the dimensions or provide them. They will work independently before sharing with a partner how they determined the volume, then we can share whole class.
This method for beginning our Math lesson should be very effective for roping in the majority of students. They will all have opportunity to express their voice…their ideas…their opinions. There is room for struggling students to stretch their learning and for strong students to consider other options for solving problems. I realize this process will take time to perfect, but in time, there will be a classroom of students who are eager to be in Math class.

I chose to use Soupdujour from the list of problembased lessons, in particular as a review for volume of prisms (Grade 8). Students had been exposed to this outcome in grade 6 but explore it in more detail in Grade 8.
To spark curiosity, students will watch the short video clip but only see a Campbell’s Soup box and a plastic storage container. They will be given no other information such as the container shape names and their dimensions. No question will be provided for students to answer. This will drive my students crazy! There will certainly be questions directed at me before we begin the next part. 😀
Notice and Wonder: Once students have viewed the video, they will have a short amount of time (12 minutes) to jot down what they notice in the video and what they wonder using the NoticeWonder template. Students will work independently then share with a partner before we move to sharing whole class. I will post many of the student responses on the board or chart paper. Most students will likely mention the obvious for what they Notice: a box of Campbell’s tomato soup, a plastic container. Some may notice the capacity measurement on the soup box. This may become a point of discussion (volume v. capacity). For Wonder, there may be students who will ask the purpose of this activity, others may wonder if there will be a recipe shown, and still others might wonder about the health conscious choice of eating boxed soup or the environmental choice of using plastic. However, I know there will be students who will wonder if the box of soup will be poured into the container.
Because the learning goal is finding volume for prisms, this will be the question chosen from the list to explore. Will the box of Campbell’s soup fit in the container?
Now we move to the next step – Anticipate. Students will predict if the box of soup will fit into the container. Will there be space left in the container after the soup is transferred or will it overflow the container or will it fit exactly? We can vote to see how many students fall in each group. This will be friendly competition (I hope).
Next, I will ask students if there is a way to make a prediction that is more accurate and if there is information that I can provide to make it possible. I hope that someone will suggest that knowing the dimensions would help. I will ask students to estimate the dimensions or provide them. They will work independently before sharing with a partner how they determined the volume, then we can share whole class.
This method for beginning our Math lesson should be very effective for roping in the majority of students. They will all have opportunity to express their voice…their ideas…their opinions. There is room for struggling students to stretch their learning and for strong students to consider other options for solving problems. I realize this process will take time to perfect, but in time, there will be a classroom of students who are eager to be in Math class.

Awesome job here. Love the detail you’ve provided for this task. You’re right it will take time, but as you build that routine, it will become easier and easier while requiring less time than when you initially begin.
