Make Math Moments Academy › Forums › Full Workshop Reflections › Module 3: Teaching Through Problem Solving to Build Grit and Perseverance › Lesson 33: GoTo Tools to Build Grit & Fuel Sense Making › Lesson 33: Discussion Prompt
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Lesson 33: Discussion Prompt
Posted by Kyle Pearce on December 3, 2019 at 3:07 pmWhat was your big take away from this lesson?
How might you use the tool discussed?
What is something you are still wondering?
Noel McMillin replied 6 days, 10 hours ago 38 Members · 47 Replies 
47 Replies

Concrete manipulatives are the key. We use them to start the year in 2nd grade to learn place value, especially when we move to regrouping. Once students have the firm conceptual understanding, we can use pictures instead.

I agree, actual manipulatives are so important for learners, especially visual and tactile learners that need to see and feel for learning. I have recently purchased multiplication table Pop It’s and Hundreds board Pop It’s for some special education kiddos. Some of them really like them to use for learning or as a fidget. The main challenge in using manipulatives in how to incorporate them for online learning. I mostly teach online credit recovery. I will just need to provide them for the students somehow or use the online manipulative link you provided. I could also make a video showing manipulatives.

Manipulatives use are so important to make connections to abstract math. I really like to use algebra tiles. I think it helps make sense of combining like terms. Also counters that are colored red on one side and yellow on the help understand integers and how zeroes are made. I’d like to understand how to use more, especially for proportions.

Manipulatives are a great tool. It’s interesting trying to get middle schoolers to use them because they don’t want to look like “babies”. So I try to use them myself when I show my thinking or when a student explains I may ask “Is there a way you could show it those of us who are more visual?” And, i think someone mentioned in one of the 1st videos of the course that the manipulatives definitely have to be placed in the open because students won’t usually make the effort to seek them out them if they’re are in a drawer of closet.

I find that when students are reluctant to use the physical manipulatives, the use of these same manipulatives in an app called Pattern Shapes from the Math Learning Center is a great alternative.


Thinking more so about the use in my 8th grade classroom, even though we start weaning off manipulatives as we go higher in grades, I think it can incredibly valuable to bolster those visual representations. I like to do visuals with algebra and completing the square for quadratics. It blew my mind the first time I saw that completing the square actually “completes a square” physically (which I was not exposed to during my schooling). As we come back to inperson learning, I might want to do it with actual tiles and have students discover where that third term comes from through an exploration.

Completing the square is a fantastic one and giving students a perfect amount of tiles to make squares can be super helpful here… then start giving them tiles where one is missing etc and ask them what they might do from a “bank” of positive / negative tiles without changing the quantity (ie zero principle). Fun stuff!


I do feel that using manipulatives helps students to build conceptual understanding but I am having trouble figure out how to do that in my Trigonometry and Calculus classes. For those subjects, I am not sure how to do that and they are juniors and seniors so maybe I should just focus on my grade 9 Geometry students. For them, I can see us using the pattern blocks and physical representations of 3 dimensional shapes when we work with area and volume. I liked the “Trashketball” game for a lesson on Volumes.

I also have trouble imagining a place for manipulatives in my higher level high school classes. I teach geometry, too, and have found some areas where manipulatives can be helpful: talking about angle side relationships in triangles, it helps to have a few rulers or even different lengths of sticks around to test out relationships; actually moving shapes around to explore congruence and transformations; and like Kerri said 3D models for volume and surface area. It’s pretty tricky as the math gets more abstract, though, and I’ve found that most students who might gravitate towards using manipulatives will end up drawing a representation of those anyway, which is a pretty good problem solving strategy at the higher levels in itself.


We use concrete manipulatives quite a lot. Although we teach grade 10/11 (“Workplace Math”), working at an Alt Ed school, all of our students have had massive gaps in their learning due to consistent and prolonged lack of attendance throughout their school lives. Using manipulatives has become normalized. It’s pretty exciting to see students realize that the math truly means something when they see it visually and get to work with it physically. I would like to try using pattern blocks as I have not used them.

Fantastic to hear that you’re having success with concrete manipulatives. Concrete and visual models can be the conduit to help us reach more students who may not have a strong foundation coming into some higher grade levels.


I notice that concrete manipulatives are important and sometimes not used enough in classrooms. I wonder if it has an impact on sparking curiosity or keeping students engaged?

I like how concrete manipulatives force students to think about foundational concepts and also reinforce how they interact with various applications and topics within mathematics. It’s an opportunity for students to learn this without the teacher telling them. So much more valuable and enduring.

Our district uses Bridges Math as the K5 curriculum. This curriculum, by The Math Learning Center (the suggested digital manipulative site), encourages the use of manipulatives and workplaces every day. However, as I walk the classrooms, only some teachers are actively using these and providing exploration to students. I feel that the issue stems from “time”. There’s not enough time for students to explore, so teachers jump to the algorithm because, hey, “there’s state testing at the end of the year and they need to know how to do (insert skill) quickly; they won’t have manipulatives during the test and it’s a timed test.” This mentality really hinders good teaching and creates students who end up hating maths.

My big takeaway was the use of manipulatives in helping students to understand some basic concepts. I must admit that I never used these when I was in school (a long, long time ago), so I find them difficult to use. I have used some digital manipulatives with my students, but I even struggled with them to begin with, as I was not sure how they worked (for instance, factoring a trinomial). But I will continue to try to use them, and I do have some physical manipulatives in my classroom that I can try with, so that is what I shall endeavor to do.

As a middle school teachers, I work with some people who believe students should “grow out” of concrete manipulatives as they get into higher grades and more complex math, but I think this video really shows how the concrete manipulatives can help make complex math be more accessible to all of our students.

Absolutely! The stages are definitely iterative and we want to help students think abstractly with new concepts, but in due time. Keep up the great work and reflecting!


I am terrible at visualize fractions, I’m amazing at using the algorithms. I have two kids, 13 and 11. This summer I’m going to use a lot of these tools on them so WE all get better at visualizing/manipulating fractions/decimals. I’m going to use the book you suggested. I wonder why I never learned the background of fractions. Decimals are even worse than fractions.

I love concrete manipulatives. I have been using them in one form or another since I went to my first Marcy Cook presentation back in the early 90’s. She was on the forefront of using number tiles to solve problems. They seem like the DNA of the open middle problems floating around today.
Total transparency moment here, I couldn’t figure out the hex one on my own. Which I guess is good because I am sure there will be students who just cannot wrap their brains around how that might work.
I am for sure going to be using that web page where you can just use pattern blocks of whatever size you need. That is a really powerful tool.

I have been trying to give less away and thus spark more curiosity with one of my maths classes. I teach a set 2 with whom this works a treat, they get really into it and when it’s time to go they don’t want to. I teach a set 3 as well of the same grade 5 and I am a bit more reticent to try this as they are much needier, they ask for a lot of reassurance and they want things explained to them so many times… one could argue they are the kind of kids that most need to build resilience but I wonder if I give them less they will get more frustrated…

@colegiomarkham Your predictions may be correct, however, I’ve taught classes like you’ve mentioned here and the greatest benefit I’ve found over the years is that those classes become LESS needy and more resilient. It takes time to develop. Stick with it!


I have actually done this before reading Marian’s Book. However, my big take away is making sure to choose math problems based on readiness. I liked the comment that students need to feel confident with the manipulatives first before giving a task that is higher on the thinking scale.

I have manipulatives in my classroom, but on many lessons I wait to pull them out until students are struggling. I think I will put them in a more prominent place (with my other readytoaccess resources like multiplication charts) so that students know they can use them any time.
This year I would like to use algebra tiles to teach concepts like combining like terms and the distributive property. I have seen other teachers use them, and the students really seem to understand it better when they get to “play” with something in front of them.

I love teaching Geometry because of the manipulatives but I struggle using them in Calculus. But calculus has some great application problems that we can spark curiosity with.

I really like the quote, “Can you stay curious a little bit longer, and can you rush to action and advice giving just a little bit more slowly?” by Michael Bungay Stanier. I have trouble with this as I want students to get into action. I realize that my last submission was not that great and did not give students a lot to think about… I just changed the format of the text to make it a little more real. Staying quiet and not giving hints/solutions is a struggle for me.
I like the idea of manipulatives because it allows the students to work out ideas with their hands and does not require speaking (if they are math shy). It also allows for me to watch instead of wonder what is in their minds.

Definitely one of my favourite quotes as well. It is hard to actually do consistently, but with that in the back of your mind, it makes it so much easier.


I think the importance of not being too directive when it comes to manipulatives. We have lessons where we tell students the exact value of the manipulative and then script exactly how to use the manipulative instead of allowing students to explore.

My big take away is using the manipulatives and having them out in front of students from the beginning. I will often plan a lesson with manipulatives and find I am running out of time or rushing. I struggle with balancing time for exploring and playing with manipulatives. This is something I want to work on, rushing more slowly! I wonder how I can build the time in so I do not feel rushed.

I’m already on the train with concrete manipulatives! I am so blessed with many friends and people in community who just helped me to purchase ONE THOUSAND DOLLARS worth of manipulatives: algebra tiles, unifix cubes, pattern blocks, fillable 3D shapes, etc. I am ecstatic! I feel really comfortable using algebra tiles in my prealgebra and algebra 1 classroom, but would love more resources on how to use the pattern blocks and unifix cubes especially connected to my curriculum. I see the opportunity here for students to use manipulatives to work with fractions and sharpen their thinking skills, but struggle with helping them use the manipulatives for more “on topic” work. If anyone has any advice, here are the 10 broad topics I’ll cover in grade 8: solving linear equations (algebra tiles; I also plan to use the unifix cubes with a balancing scale I have. I’ll put a certain number of cubes on the tray and a certain number in a paper bag in such a way that they can’t see or feel how many cubes are in the bag), transformations (of geometric shapes on a coordinate plane, heavy focus on similar figures with the dilation), angles and triangles (angle relationship theorems and vocal words are heavy here), graphing and writing linear equations, data analysis and displays (scatterplots, line of best fit, twoway statistics tables and a VERY basic intro to probability), functions (what is a function, intro to function notation), real numbers and the Pythagorean theorem (intro to square/cube/nth roots, solving equations involving radicals/exponents), and unit 10 is similar solids and volume (esp comparing the volume formulae for 3D shapes). Has anyone here used manipulatives in these units, and how?

I think concrete manipulatives are a must. It makes me wonder if I would have learned math more deeply when I was growing up if I would have been able to use them when I was struggling to understand something. Instead I became a robot who memorized everything a teacher did and thought that I was “learning”. It wasn’t until I took a class called Math & the Mind’s Eye in the early 90’s did I finally understand how the manipulatives made my understanding concrete! All that memorization finally made sense to me and I started seeing connections I never knew existed.

I love manipulatives. I encourage parents to even play with the different colored sugar packets when out with their kids and just make patterns. For my middle schoolers, I find that I grab them to help demonstrate a concept and ask questions that they can show me their thinking from when they can’t find the words, or they don’t connect to yet from a written method. I do find that my starting and then letting them decide to use them anytime they want, breaks the ice. I also noticed that if the manipulatives are in a closet or on a shelf, they don’t get used often, whereas at desk stations, they are easy to grab and return so they get used more.
I like Marian Smalls’ ideas, and I’m thinking of incorporating them into the first week of school for a number sense “unit” for 7th grade. I want to work with positive rational numbers before jumping them in to integers.

Thanks for sharing Marion. I tend to put a collection of manipulatives on each pair of desks for students to easily grab. Saves getting up and moving across the room to get.


I am a high school teacher(I mainly have 10th graders) and I feel like we don’t use concrete manipulatives enough. I know I always say I am a visual learn but I still except my students to do thing without the help of the visual from a manipulative.
Next year I am teaching 9th graders for the first time in a cotaught setting and feel this is a good class to concentrate on using Concrete Manipulatives.

I will be working with students in K2 as a math teacher for the first time this year so I know that manipulatives are key and that I will be using them daily, but they are also so important in older grades as well. I previously taught 4th grade and they really make such a difference for students of all ages.

I’ve always wondered if I use manipulatives enough in my classroom. Now I see that I absolutely DO NOT! I am hoping to begin using them more this coming year.

I totally agree that manipulatives are a very useful tool in the classroom, but up until now I had thought of them as more of a resource to pull out when students were having trouble with the abstract concepts. In 7th grade I never considered the use to spark curiosity and absolutely LOVE how they were used in this activity. My struggle is twofold: 1 – how to get this kind of lesson in and still address ALL of the standards that I am required to get to before state testing which is sadly in early to midMay even though the year doesn’t end til midlate June and 2 – how to post the “learning objectives” which I am required to according to my teacher evaluation standards without giving away the anticipation. I have always believed in a more discovery way of learning for students and have been resistant to posting such specific objective and recently found a listing of generic ones that focus on the problem solving skills and such. I am hoping that this will satisfy the expectation as it frustrates me that they want me to straight up tell kids what they are learning each and every day. I don’t see where the mystery and fun is in that and I would much rather teach as you are sharing. I guess I will have to continue to be rebellious and NOT post them.

Great wonders here:
Here are a few places to learn the answers:
You can find more “answers” in our Q&A Calls Course and our Podcast Course.

Are these things I will be able to access after tomorrow? I missed the deadline to sign up for either of the yearly memberships. I was going to try the one with the lessons and such as I am not sure what Professional courses I’ll be needing for my next recertification. I am scrambling as it is to get this done in time before I lose access.

If you are stuck and want your membership to keep access, let us know via the blue box at bottom right of screen. Our team will help you out!



My big take away is using hands on manipulatives. I get frustrated with students that I know are struggling with a concept but decide to “play” with the manipulatives instead of using them to help them understand. I also need to educate students that manipulatives will help them get a deeper understanding…they are not babyish. Students in middle school are very selfconscious. I spend a lot of time in the beginning of a semester talking on growth mindset. Showing the videos from youcubed. Setting up the class as a safe place to try the unknown and explore different things they may not have understood. Many of the students embrace it but I always have a student that has their walls up so high I can’t get around them. I am hoping that the more students explore math using manipulatives the more open they will be to using different tools when they are offered.

That can certainly be challenging. One thought to consider is that often times, if students aren’t sure how the manipulatives can help them, they might resort to playing or fooling around. There might be a teacher move in there somewhere to help them understand what the manipulatives represent and how they might help them arrive at an answer.


I brought pattern blocks into my G10 class last month. While the idea was to support and review fractions, their focus was to play with the blocks… see how high they could be stacked. While I know that they could benefit from continued exposure to these manipulatives, since they have not had a history of using them, I’m facing a challenge to get the buy in needed to support their learning. Again… consistency vs intensity would be a good path to follow here. Building the expectations over time, rather than just singular intense interaction.

I have 2 big takeaways. One is to talk less! I actually try to do this and when I know I have been talking too much, I am thinking of what I can do to change the structure of the lesson. I have also been using this in my lesson planning which is more important to do before I start the lesson. The other takeaway is to use manipulatives more. When I can, I do use them but I’m sure there are some interesting ways to incorporate them into an 8th grade curriculum.

My big takeaway is using manipulatives. I am about to start an expressions and equations unit and I need to be better about pulling out either the algebra tiles OR using the polypad on the ipads that we have in our room. I would also like to explore some of the problems that are on the DESMOS site that involved the polypad that was just installed.

When I have a chance to share with preteachers, my advice is to be less helpful. Too often, we think we are doing a student a favor by mapping out the solution to a problem so they can regurgitate the process on the next problem. The productive struggle is necessary for any real understanding that then withstands the test of time.
I love pattern blocks. It is a manipulative that I put on the back burner years ago. I had a full set at my previous district and this just reminded me to find a set in my current building or buy a set!
On a side note, anytime I use manipulatives, I make sure to give the students some time to just play. I find that if I give them blocks, unifix cubes, or tangram pieces without the play time, a percentage of students are not engaged always. I use an online geoboard periodically and without rubber band design time, it just does not work.