Youโve made it through the summer PDs, untangled your first set of math manipulatives, and maybe even remembered all your login passwords. Now what?
Whether youโre new to Illustrative Mathยฎ or looking to sharpen your setup, here are four tools that will make your year smoother,
Secret Weapon #1: IM Assessment Tracker- More Insight, Less Guesswork ๐
This free Google Sheet tracks every checkpoint and end-of-unit assessment from Grades 1โ5. You can tag mastery by standard, see class trends at a glance, and even link student work samples. Itโs simple, shareable, and way more organized than that โAssessment Dataโ folder collecting digital dust in your drive. Grab the free tracker here.
ย Secret Weapon #2: IM-Aligned Spiral Reviews-Retrieval Practice To Start Each Day ๐
These no-prep warm-ups are built to match your IM unit pacing. Each week includes new content + a handful of throwback questions from earlier units to keep concepts fresh.
๐ง Why it works: Retrieval practice and spaced review are two of the most research-backed ways to boost retention. When combined, theyโre like the peanut butter and jelly of long-term learning. Read more about spaced retrieval practice in the IM curriculum here. Find the IM-aligned Spiral Review packs here.
Secret Weapon #3: Zearn โ Your Digital Co-Teacher ๐ฅ๏ธ
Zearn isnโt officially aligned with IM, but it pairs surprisingly well in a flipped model. Students preview a concept at home (or independently), so your small groups can jump straight into discussion, problem-solving, or reteaching. Alternatively, use Zearn for intervention students.
Just be sure to set clear expectations. Keeping students on the right lesson can be tricky. I gave them freedom to work ahead (less work later = big win), and tied progress to our Classroom Economy. That combo kept things running smooth(ish).
๐ Check out Zearn.organd this correlation chart to help it fit your IM pacing. Note: I’m not endorsed by Zearn. I just think it’s outstanding!
Secret Weapon #4: Math Mysteries- Unit Assessment Review With Maximum Engagement ๐ต๏ธโโ๏ธ
Each unit-aligned math mystery blends rigorous problem-solving with a story-driven twist: a circus thief, a missing wand, a rogue robot. Students solve clues to narrow down suspects and crack the caseโno re-teaching required.
Each mystery takes about three hours total, making it ideal for test prep, end-of-unit review, or adding some math-themed drama to your Friday plans.
Honorable Mention: Prodigy- Your Secret Weapon for State Test Prep ๐ฎ
Yes, itโs fun. Yes, itโs gamified. But when used to target state standards and review old concepts- not just for free play, itโs a powerful way to reinforce learning and boost state testing scores.
Set clear goals, assign targeted practice, and use the reporting to guide real instruction. Students love it, and it’s easy to implement. Don’t walk up the down escalator when it comes to math review. Let the kids play and learn at the same time.Check out Prodigy here.
Final Thoughts: Stack Your Toolbox Early ๐ ๏ธ
No one tool does it all, but this lineup can seriously lighten your load. โ Data? Tracked. โ Content? Reviewed. โ Unit Assessments? Crushed. โ Kids? Engaged. โ You? Still sane by October.
Need More Support? Get in Touch ๐
If youโre in a leadership role and want to pilot the above resources in your school/district, fill out this quick form. Weโll follow up with a Google Drive link with the products. ๐ Note: The above form is just for instructional leaders (principals, coaches, curriculum directors, etc.).
If youโre a classroom teacher, scroll to the bottom of each product category page to grab free samples and try them out right away.
Youโve just wrapped up the unit on area. Your students seemed to get it, they measured rectangles, calculated square units, and explained their reasoning beautifully. But now itโs Unit 5. You ask a multiplication-based area question, and get crickets. Sound familiar?
The Illustrative Mathematicsยฎ curriculum is conceptually rich and thoughtfully sequenced. But it moves fast. Without an intentional review structure in place, earlier learning fades fast. This can be an issue when state testing rolls around.
๐น Forget-Me-Not: What Research Says About Helping Students Retain Learning
Forgetting is normal. In fact, our brains are built to forget unused information so they can focus on what feels most relevant.
Thatโs where spacedretrieval practice comes in.
Spaced retrieval practice means recalling information from memory, not re-reading or re-hearing it. In IM, this looks like students answering questions from past and current units.
Research backs up spaced retrieval practice:
John Hattie (2009) ranks both retrieval practice and spaced practice well above the 0.4 threshold that marks a strategy as worth implementing. When combined, they offer a powerful effect on long-term learning.
Dunlosky et al. (2013) identified retrieval practice as one of the most effective learning strategies across a wide range of age groups, subjects, and learning environments. Their research highlights its exceptional value for promoting long-term retention,
When state testing rolls around, students whoโve practiced retrieving content all year long are far more prepared to access what theyโve learned, without the panic.
๐นThe Easiest Way to Build in Spaced Retrieval Practice Without Added Workload
OurIM-Aligned Spiral Reviews are perfect for implementing this practice without adding teacher workload.
Each week includes:
15-20 questions to promote explicit practice of the current and most recent IM Unit Topics.
4โ5 questions that spiral back to content from earlier Units
Low-stakes review to reduce pressure and increase participation
A Teacher Tip of the Week to explain new concepts simply for families
No extra prep. No reinventing the wheel.
๐น Conclusion: One Routine, Big Payoff
Spaced retrieval practice helps students hold onto what theyโve learned and what they’re learning at that time
Spiral Reviews deliver both, plus a calmer classroom, an easy homework solution, and better preparation for state-testing.
๐น What Next? Try It Out
If youโre a school or district leader interested in piloting this and other IM-aligned resources (available for Grades 2โ5), take 5 minutes to fill out this form. Weโll be in touch shortly with next steps.
If you’re a homeroom teacher, scroll down on this page to access the first three weeks free and discover how consistent review can make a big difference in your classroom.
๐น Bonus Read: Better Scores, Calmer Starts, and Happier Homework
โ Calming Start to the Day
Teachers tell us it creates smoother mornings, less downtime, and a focused start to the math block. Check out what this user said.
โญ๏ธโญ๏ธโญ๏ธโญ๏ธโญ๏ธ โWhile using this resource, my students stayed engaged and excited to learn. It was challenging yet fun for them to work on these sheets.โ
โ A Homework Option that Actually Helps
IM doesnโt come with built-in homework. These Spiral Reviews can fill that gap with work thatโs both purposeful and printable.
โญ๏ธโญ๏ธโญ๏ธโญ๏ธโญ๏ธ โMy students are enjoying this resource as homeworkโฆ they feel homework is faster and less stressful. As a teacher, I don’t have to spend time looking for resources to download and print.โ
Whether youโre brand new to Eureka or have a few years under your belt, this post will give you a fresh set of tools to make the program work even better for you and your students.
After using the tools and approaches in this post, I noticed real gains in student understanding and assessment scores. You can see our class MAP data below. More importantly, students felt proud of what they accomplished, and thatโs what stuck with me most.
By combining Eurekaโs structured lessons with a few creative and student-friendly tools, I saw big shifts in understanding and engagement. Iโve written about some of these before, but today Iโm putting the full list in one place.
Secret Weapon #1: Zearn (Flipped Classroom Model)
Zearn is totally free, works perfectly with Eureka, and honestly feels like something youโd usually have to pay for. Itโs full of engaging visuals and step-by-step lessons that help students understand concepts more clearly. Best of all, kids love it. Trust me… theyโd choose Zearn over listening to my boring voice any day!
This year, I used Zearn in a flipped classroom setup. Students completed the next dayโs lesson for homework, which meant they came in ready to go. I explained the system clearly at the start of the year, talked it through with parents, and tied it into our classroom economy. Every completed Zearn lesson earned students $50 in class money. That little incentive kept motivation sky-high.
Want to change things up this year? Try flipping your routine with Zearn.
Secret Weapon #2: Math Mystery Assessment Reviews
You know that collective groan students let out when they hear the word assessment? That’s the sound that inspired me to create the fictional world of Mathville, home to quirky characters like Sir Mathsalot, Kitty Purry, and Sheriff Subtraction. Each Math Mystery review features one of these characters facing a curious problem. Something has gone missing, and itโs up to your students to solve math problems, uncover clues, and crack the case.
In the Grade 3 Module 2 review, for example, theyโll help Stinky Pete figure out which pirate stole his ship by solving multiplication problems. In Grade 4 Module 3, theyโll work alongside Dr. Quantumblunder to stop a computer virus from spreading through Mathville. The stories are lighthearted, but the math is rigorous and students stay motivated from start to finish.
Hereโs a look at how other teachers have used these mysteries in their own classrooms.
Secret Weapon #3: Spiral Reviews To Cover Earlier Content
Spiral Reviews became a quiet hero in our classroom. By the time end-of-year testing rolled around in May, it had been 8 months since students had worked on rounding in Module 1, 6 months since measurement conversions in Module 2, and 3 months since multiplication in Module 3. Still, they handled the โNumber and Operationsโ section with confidence, and 60 percent of them scored in the 80th percentile or above.
Breakdown of Achievement Percentile: Blue = 80th and above, Green = 61-80, Yellow = 41-60, Orange = <20
That kind of long-term retention does not happen by luck. Each morning, students warmed up with short, skill-packed problems that pulled from both current and earlier modules. These were not the usual worksheet yawners either. We incorporated our usual wacky characters into problems, keeping things playful and unexpected. When students are having fun and enjoying their work, learning is so much deeper. Take a look below to see how we mix humor with rigor across concepts.
Whether you use them to start the day, send home for practice, or revisit tricky concepts, Spiral Reviews offer a flexible way to keep learning on track. With so much content to retain, itโs been helpful to have something that touches on earlier modules in a fun and meaningful way.
Take a look at what other teachers have said about them:
If youโve heard of Prodigy, you might be thinking, โIsnโt that the game where kids just run around and avoid doing math?โ That can happen, but only if expectations arenโt made clear. In our classroom, Prodigy is a privilege. When used well, itโs a powerful tool for math practice. The platform offers strong tracking features and lets you align questions to your state assessments like CAASPP, STAAR, MAP, or MSA. With a little teacher input, it becomes a smart way to keep students engaged in targeted practice.
If this were a blog post about boosting ELA scores, I would go into further detail about the amazing Prodigy English game. However, since weโre focused on math, Iโll let you discover the benefits of Prodigy English on your own!
Secret Weapon #5: Building Thinking Classrooms
Iโll be honest, Iโm the kind of teacher who side-eyes anything that isnโt backed by solid research. After watching schools jump into trendy programs (and then scramble when they donโt work), I try not to fall for the next big thing. That said, Building Thinking Classrooms really got me thinking.
While itโs still light on large-scale research, what I saw in my own classroom was hard to ignore. BTC got my students talking, thinking, and solving problems in new ways. If you want to read about how I brought BTC to life in my classroom, take a look at Part 1 of my blog series on the topic here.
Honorable Mention #1: Module Brochures
Developing conceptual understanding is at the heart of the Eureka program. Parents might grumble that Eureka spends too much time exploring the same concepts in different ways. โWhy canโt we just teach multiplication the way I learned it? Whatโs the deal with the area model?โ
Explaining the โwhyโ behind Eureka to parents can be tough. Thatโs why we created the parent-module brochures. These were a hit at orientation night and served as a handy reference for parents throughout the year. The brochures helped outline the program for both teachers and parents. While I canโt directly link high MAP scores to these brochures, I know parents appreciated being kept in the loop. We have two formats (Common Core and TEKS), both available in English and Spanish. Digital versions are also included to send home via Seesaw, email, etc.
Ever found yourself wondering what to do with those speedy students who finish their Problem Sets 20 minutes before everyone else? The Module-Aligned Choice Boards are the perfect solution. Fast finishers wonโt disrupt your small-group instruction once you introduce these choice boards.
The activities are module-aligned and reinforce skills in an engaging, creative way. With a variety of activity types (artistic design, puzzles, research reporting, team games, etc.), thereโs something fun for every student.
Data and organization come together for our final honorable mention. This simple tool made report writing so much easier and gave admin a clear snapshot of our Grade 4 progress. It tracks mid- and end-of-module assessments, with color-coded cells to show where students are performing: above, at, approaching, or below grade level. You can also mark whether each standard has been met. Combine this with your targeted practice, and youโve got a powerful system to support student growth.
The best part? These gradebooks are free to download. Just grab the one you need from the links below.
Eureka is a stellar program. Just following the lesson script usually yields great outcomes. But the โsecret weaponsโ Iโve shared are how Iโve built on Eurekaโs solid framework by adding a touch of excitement and fun. If you’d like to keep updated on all of our future tips and resources, follow our TpT store.
Iโd love to know how youโve implemented any of these ideas or how youโre planning to use them this year! Let me know in the comments box!
As elementary teachers, we guide our students through the Eureka program, a journey filled with new concepts and deep learning. Each module opens up a new area to explore. While the program is beautifully sequenced, it can also feel overwhelming due to the sheer amount of content. This can be tough not just for students, but for parents too.
In his book Building Thinking Classrooms in Mathematics, Peter Liljedahl reminds us that, much like navigating land or sea, learners need two things to move forward: a sense of where they are and a clear idea of where they are going. Without both pieces, itโs easy to feel lost.
For someone to be able to navigate, by land or by sea, they need two pieces of informationโwhere they are and where they are going. Both pieces of information are vital and of equal value. If they donโt know where they are going, they are destined to get lost. And if they donโt know where they are, well, then they are already lost. The same is true of students trying to navigate their own learningโthey need to know where they are and where they are going.
(Peter Liljedahl, 2020)
To help with this, we created the Eureka Module Parent Brochures. These brochures act as a compass and map, showing where students are in the program and what lies ahead. They are helpful for families, but they also give teachers a clear, quick reference without needing to dig through pages of the teacher manual. Brochure bundles are currently available for:
Think of these brochures as your compact guides through the Eureka program. Theyโre not just informative & stunning; theyโre a breath of fresh air in the often-overwhelming world of the Eureka program.
For the Busy Teacher: We know your time is as precious as the first cup of coffee in the morning. Thatโs why these brochures are quick to prepare and easy to use. Simply print, fold, and distribute!
For Supportive Parents: Parents often feel like they need a translator for their childโs math homework. The Eureka program often uses unfamiliar language and methods, leaving many parents unsure of how to help. These brochures break down key concepts using simple explanations and clear visuals. They give parents a straightforward understanding of each Topicโs goals, making it easier to support learning at home.
Key Concepts highlighted & explained with illustrated examples
When Paper Fails, PDFs Prevail
Ever feel like half the papers you send home with students enter the Backpack Bermuda Triangle, never to be seen by parents? Worry no more! Each Module Brochure comes with its own Digital Guide, a lifesaver in the age of ‘my dog ate my homework.’
The Digital Guide is a more simplified, easy-to-read PDF version of the brochures. Whether it’s through Classroom Dojo, Seesaw, or email, parents stay informed about what their child is learning. With the digital version sent home, students wonโt be able to blame the backpack Bermuda Triangle.
Digital Guides that can be shared on any digital platform
Aligned and Ready: CCSS and TEKS Versions Available
Note: These TEKS guides align with the older TEKS version of Eureka. They do not align with the 2025 version of the Eureka for Texas curriculum. Are you a TEKS teacher tired of coming up short when looking for Eureka-aligned resources? Youโre not alone. That’s why our guides come in both flavors- TEKS for the Texas trailblazers and CCSS for the Common Core crew. Even though the TEKS and CCSS programs are as different as pi and pie, our tailored TEKS version ensures you won’t get lost in the math maze, no matter which curriculum map you’re following. At the top of each brochure, we clearly outline the specific standards (CCSS or TEKS) for each Topic. This feature helps parents quickly see that their child’s learning is comprehensive and on track! Whether youโre teaching in Texas or anywhere else, youโll have a roadmap thatโs built to match your path. Cue the cowboy hat tip.
Standards tagged for each Topic in both CCSS & TEKS versions
Bilingual Brochures for Bilingual Homes
Understanding Eureka can be tough for parents, especially when English isnโt their first language. Thatโs why each brochure includes a Spanish version. Whether itโs multiplicaciรณn or multiplication, these translated guides make it easier for families to follow along and support their childโs learning at home.
Spanish versions available for both CCSS & TEKS brochures
Earning Applause in the Hallway and Home: Brochure Brilliance!
These brochures donโt just help students and families, they also make you look like a rockstar to admin. When parents understand the math and feel supported, it shows. And when principals and math leads see your communication tools in action, you just might earn yourself a few extra gold stars. PTA applause, anyone?
Give a visual pop to your brochures by printing on colored card stock.
Teacher-Tested, Parent-Approved
Sure, we think these brochures are pretty great, but donโt just take our word for it. Hear from teachers whoโve actually used them and seen the difference at school and at home.
Closing Credits:
Thatโs the magic of the Eureka Parent Brochures- clarity, connection, and a whole lot less chaos. These handy guides help your students stay on track, your parents stay informed, and your admin stay impressed.
No more confusion, no more guessing, no more โI had no idea we were learning fractions this week.โ With these brochures in your corner, youโve got everything covered.
So take a bow, teach. Youโve made the Eureka journey feel like smooth sailing.
Brochures for all Modules available for Grades 3, 4, 5
Grab your grade level bundle using the below links:
Picture it: Youโre in the middle of a peaceful teaching moment, guiding a group through their Problem Set. Pencils are quietly scratching away when, out of nowhere, a student pops up and proudly announces, โFinished!โ You check the clock. Itโs only been ten minutes. Now youโve got one eager speedster and a whole lot of time left on the clock.
Thatโs where Fair and Squared Choice Boards come in. Theyโre the perfect answer for your early finishers.
Meet the Eureka-Aligned Choice Boards
These Choice Board Activities are fun, interactive games and puzzles designed for 3rd, 4th, and 5th graders. They align with the Eureka and EngageNY curriculum and cover important math concepts from multiple modules. Each activity is built to make learning both enjoyable and approachable, whether youโre in the classroom or at home. With clear instructions, teacher examples, and a variety of tasks to choose from, every student can find success with a choice board. Letโs explore what makes these boards such a favorite among teachers and students alike.
9 activities per choice board
Stress-Free for Teachers, Fun for Students
Our Choice Board Activities pair with the Eureka/EngageNY modules as naturally as peanut butter and jelly. Each activity lines up with the content students are learning. Covering perimeter in Grade 4? Kids will be up and measuring real-world objects with string. Exploring fractions in Grade 3? Theyโll tackle a crossword using terms like โnumeratorโ and โhalves.โ Itโs a smooth mix of learning and fun that keeps students engaged and buys teachers the rarest classroom commodity: time.
Print, Distribute, and Go!
How many teachers does it take to change a light bulb? Just one, but she’ll have to do it during lunch break, while eating a sandwich and grading quizzes! Your time matters. Thatโs why these choice boards are truly print-and-go. Theyโre simple to prep, easy to distribute, and perfect for keeping things running smoothly. Print a stack, pop them in a folder, and youโre always ready for the student who finishes before you even finish your coffee.
Activities for everybody!Teacher examples of each activity to support
Math Fun the Whole Family Can Join
These choice boards are not just for the classroom. Teachers can send them home, giving families a chance to take part in the learning journey. Instead of more screen time, kids can work with parents on challenges like building sundials or finding fractions in the fridge. These choice boards are perfect to send home before a holiday or summer break, giving families creative, low-prep ways to keep math minds sharp while school is out.
Content-related word searches to complete with mom & dad
Developing Conceptual Understanding, the Fun Way!
Learning should feel exciting, not repetitive. These Choice Boards offer a variety of fun activities that help students build real understanding of math concepts. With creative tasks and engaging challenges, students make stronger connections and enjoy the process.
Hear It from the Experts: Teachers Whoโve Tried Them
And On That Note…
Wave goodbye to the โIโm done, now what?โ moments and say hello to a classroom that hums with purpose. The Fair and Squared Choice Boards keep fast finishers engaged, families involved, and your sanity intact. Ready to dive in? Each grade level bundle is linked below. Grade 3 can be found here. Grade 4 can be found here. Grade 5 can be found here.
You can find all of our choice boards, along with all of our free & paid products at our store here!
We’ve all been there! You’re approaching the end of another module and start to think about how your learners will do on the upcoming assessment. Suddenly, that nasty thought creeps into your mind; how your students do on this test may reflect on you as a teacher. Low scores can be deflating to our confidence as teachers. Of course, strong growth on tests leads to happy teachers, students, parents, and admin. That’s what we’re often aiming for, right?
So, what’s the best solution? You started this module over a month ago and students have surely forgotten concepts from 5 weeks ago. You could give them a practice test where the questions are similar but the numbers are changed. However, that simply encourages mimicking and doesn’t give us accurate data on student understanding of the module’s content. So, we propose an alternative.
Enter, Mathville Code Breakers Math Mystery activities!
Engagement is key to effective learning, and nothing captures students’ attention like the hilarious tales in these Math Mystery activities, transporting learners to the lively realm of Mathville.
Hilarious Stories & Characters
Who wouldn’t love to read about Stinky Pete & his runaway pirateship? Or Kitty Purry and her missing ukelele? Or even the brave knight, Sir Mathsalot and his fearless companion teddy bear, Lord Huggsy ? The wacky stories told in theis Math Mystery series are a huge hit with learners.
Students love these wacky stories from the world of Mathville
Alignment With Topics From Each Module
The beauty of having students work on these activities is that they are practicing math skills that are aligned to the various Topics of each Module in the Eureka/EngageNY Grades 3, 4, 5 program. Do your students need to review the Grade 4 module on fractions? Give them “The Mystery of the Lying King.“ Do they need to revise the Grade 3 module on perimeter & area? Give them “The Mystery of the Jurassic Fart.” Need a review of data & graphs from Grade 3, Module 6? Have them complete “The Mystery of the Missing Toilet.” Regardless of the content that needs review, there’s a Math Mystery activity for whatever your learners need.
Perfect for revision of concepts found on the EoM assessment
A Wide Range of Benefits
They’re extremely fun! Don’t be surprised to hear “Can we stay here and keep working on this during recess?”
The Math Mysteries promote revision of concepts for assessments without encouraging mimicking from practice tests.
They’re low prep! Print out a bunch of them and keep them in a folder for easy access. Never worry about those fast-finishers again.
These activities come with all the tools a teacher needs (answer keys, black & white version, certificate of completion)
They foster a love for math in students, leading to pleased parents and admin.
After each approach is outlined, we will highlight why that practice is important and beneficial to teachers who use the Eureka curriculum.
When you see (Liljedahl, 2019), know that Iโm referencing information directly from the Building Thinking Classrooms text.
Those who have implemented the approach, please comment with your thoughts, ideas, and resources.
The post will take approximately 10 minutes to read. Grab a coffee and enjoy!
– We recommend watching this video to get a snapshot of a Thinking Classroom in real life:
On that note, let’s dive into the fourth practice to develop a thinking classroom within the Eureka framework.
Practice #4: Defront the Classroom โ The Board Isnโt the Boss Anymore
To encourage deep thinking, we need to move away from the traditional front-of-classroom setup. This means that we should try to not have a “front” from where we teach in our classroom.
“Every time we worked in classrooms that were super organized we had more difficulty generating thinking. Classrooms need to have just-right amount of disorder for thinking to flourish.” (Liljedahl, 2021). Arrange furniture so that students face each other in groups, rather than facing the front. Ideally, group tables should be positioned away from the vertical whiteboards to allow space for movement and clear sightlines.
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? As we discussed in blog post #1, the ultimate goal of the BTC approach is getting students to think through problems. The Eureka program doesn’t always promote this concept. Altering the layout of classroom furniture & de-fronting the classroom signals to students that thinking and collaboration are valued more than quiet compliance. The flexibility of movement in the classroom will promote the idea that yours is a thinking classroom and those that work within it are active constructors of knowledge, not passive receivers of it. This is the practice I struggle with most, and thatโs okay! Thinking still happens in my classroom, so I remind myself that progress matters more than perfection. You should, too. (Insert Kumbaya song here) ๐
Practice #5: How We Answer Questions โ With Questions, of Course
Pop quiz: how many questions will a typical teacher answer every day? Answer: 200-600!! Share that one with your learners ๐ While it may seem that answering student questions always helps our students learn, Liljedahl found that this is not always the case.
Liljedahl identified 3 different types of questions that teachers get asked. They are… ๐) ๐๐ซ๐จ๐ฑ๐ข๐ฆ๐ข๐ญ๐ฒ ๐๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง๐ฌ: These are questions that students will only ask their teacher when the teacher is close by. They do this to conform to the role of a student, even if they know or can find the answer themselves. (Example: “What class do we have after recess?” “How many questions do we need to answer?”
๐) ๐๐ญ๐จ๐ฉ-๐๐ก๐ข๐ง๐ค๐ข๐ง๐ ๐๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง๐ฌ: Thinking takes effort, and students often prefer to avoid it if they can. Therefore, they will often ask their teacher stop-thinking questions. (Example: “Do we have to learn this?” “Is this answer correct?”
Liljedahl found that out of the hundreds of questions teachers receive each week, around 90% fall into the proximity or stop-thinking categories. It’s important that we encourage as much thinking as possible from our students and therefore, it’s important that we avoid answering these questions. So, what about the other 10% of questions that we get asked? They are known as…
๐) ๐๐๐๐ฉ-๐๐ก๐ข๐ง๐ค๐ข๐ง๐ ๐๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง๐ฌ: These are asked by students so that they can further engage with the task at-hand. They are usually about clarification or extensions. (Example: “Can we get the next set of questions?” “Can we solve this problem using a tape diagram as well as the standard algorithm?” These questions drive further thinking and should be encouraged in our classrooms.
I informed my students about these 3 types of questions. They know that they have to think to learn and they very quickly stopped asking proximity & stop-thinking questions. Students will even correct their classmates when they hear proximity questions being asked. Liljedahl recommends acknowledging to students that you heard their question and redirecting it with another question or statement. “What do you think?” “What makes you ask that?” “I think it would be better if you explained your answer to me rather than me telling you the correct one.” Yes, even walking away is an option when students ask a non-thinking question. It may feel abrupt at first, but it reinforces the shift toward a student-led thinking environment.
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? When Eureka lessons focus on modeling Problem Sets, students learn that the teacher holds all the answers. This teaches them to rely on the teacher anytime theyโre unsure, rather than working through the problem independently. Encouraging only keep-thinking questions shifts the responsibility to students, prompting them to seek answers through their own reasoning, classroom resources, or peer support. This shift places students at the center of learning and further defines the teacherโs role as a facilitator, not a deliverer of information.
Practice #6: When, Where, and How to Give Thinking Tasks โ The Fast & Curiou
When To Give Thinking Tasks– To get the most out of a thinking task, it should be assigned within the first five minutes of the lesson. If a new concept needs to be introduced, aim to keep that explanation short and focused. Research shows that student attention drops off quickly after the five-minute mark.
As Liljedahl puts it, โThe further into the lesson the teacher waited before giving the task, the less effective it became.โ (Liljedahl, 2021) Sticking to this five-minute window helps maintain focus and builds positive energy in the classroom. It signals to students that thinking is expected right from the start.
Where To Give Thinking Tasks– Liljedahl recommends giving the task while students are standing. Personally, I deliver thinking tasks to my fourth graders while theyโre seated on the carpet. Standing might be more effective for middle or high school students, but in my experience, sitting doesnโt seem to interfere with engagement, so long as the task is given within the first five minutes.
When assigning a curricular task, I usually use the final Problem Set question from the Eureka lesson. If you prefer, feel free to use any question that will help students understand the lesson’s learning goal.
How To Give Thinking Tasks– Liljedahl suggests giving the task orally first, while writing only the key information on the board. This โtextual residueโ helps reduce cognitive load and encourages students to build their skill in interpreting word problems. Itโs important not to write the full question, just the essential points.
Hereโs an example from Grade 4, Module 2, Lesson 2: Original word problem: “Javierโs dog weighs 3,902 grams more than Bradleyโs dog. Bradleyโs dog weighs 24 kilograms 175 grams. How much does Javierโs dog weigh?”
Textual residue on the board: “Javier dog: 3902g > Bradley’s dog. Bradley’s dog: 24kg 175g. Javier’s dog?”
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? Eureka mini-lessons can sometimes lead to passive learning, with students simply watching the teacher solve problems. But students are far more engaged when theyโre given the chance to jump in and tackle challenges themselves. By presenting the task within the first five minutes of the lesson, you maintain focus and create a sense of flow that keeps students invested.
Because Eurekaโs Problem Set questions are often word-heavy, itโs essential for students to develop the skill of figuring out what theyโre being asked. Giving tasks orally while writing only the key information, or โtextual residue,โ helps them build this skill over time. Youโll likely find that students become more confident at interpreting problems on their own. Liljedahl explains, “giving tasks verbally produced more thinking-sooner & deeper- and generated fewer questions at every grade level.” (Liljedahl, 2021)
That wraps up our look at Practices 4, 5, and 6 from Building Thinking Classrooms in Mathematics by Peter Liljedahl. While the first three practices focus on how to introduce BTC routines to your students, these next steps are all about shifting your teaching behavior. Each one nudges you further into the role of facilitator and helps center your classroom around student thinking.
Try the Following This Week โ Homework for the Teacher ๐
Rearrange your classroom furniture to eliminate the โfrontโ of the room and encourage student-facing groupings.
Give your thinking task within the first five minutes of the lesson, keeping any concept intro under five minutes.
Present a word problem orally and only write the key โtextual residueโ on the board โ leave the full question off.
After each approach is outlined, we will highlight why that practice is important and beneficial to teachers who use the Eureka curriculum.
Those who have implemented the approach, please comment with your thoughts, ideas, and resources.
When you see (Liljedahl, 2019), know that Iโm referencing information directly from the Building Thinking Classrooms text.
The post will take approximately 10 minutes to read. Grab a coffee and enjoy!
We recommend watching this video to get a snapshot of a Thinking Classroom in real life.
Liljedahl ends the book with a reminder thatโs worth starting with. The main goal of the book is to get your students thinking. It’s important to “๐ด๐ฆ๐ฆ ๐ต๐ฉ๐ฆ ๐ง๐ฐ๐ณ๐ฆ๐ด๐ต ๐ง๐ฐ๐ณ ๐ต๐ฉ๐ฆ ๐ต๐ณ๐ฆ๐ฆ๐ด” (Liljedahl, 2021). The โforestโ is a classroom full of students who are thinking. The โtreesโ are the 14 practices that help you get there. If your students are thinking while engaging in math, youโve already succeeded. Donโt get too caught up in doing everything perfectly. The goal is thought, not perfection.
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? In many classrooms, Eureka lessons can lead students to mimic the teacherโs steps without truly thinking. “Thinking is a necessary precursor to learning.” (Liljedahl, 2021). To benefit from programs like Eureka, we need to foster a thinking environment that also encourages students to deepen their understanding of the concepts explored without simply mimicking procedures.
On that note, let’s dive into the first practice to develop a thinking classroom.
Practice #1:Ditch the Mini-Lesson: How Thinking Tasks Elevate Your Eureka Classroom
I ditched my mini-lessons and introduced “thinking tasks” to my students instead.
Liljedahl breaks the tasks that we should give to our students into these 2 categories. โ Non-curricular thinking tasks โ Curricular thinking tasks
๐๐จ๐ง-๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐๐ซ ๐ญ๐๐ฌ๐ค๐ฌ are simply tasks that promote problem-solving & thinking among your students. These are often known as Low-Floor, High-Ceiling tasks. They are not tied to the content that youโre studying, and their main goal is to get your students into the mindset that theirs is a thinking classroom, where ideas are valued more than right answers.
Non-curricular tasks have many access points and can be explained in a variety of ways. Here is an example of a non-curricular thinking task: โIf I were to write the numbers from 1 to 100, how many times would I use the digit 7? What if I wrote 1 to 1000? How many zeros?โ (Liljedahl, 2021). Liljedahl says that using 3-5 of these non-curricular tasks is enough to shift your studentsโ mindset from “mimickers” to problem-solvers.
After completing 3-5 of these tasks with your students, substitute the non-curricular tasks for ๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐๐ซ ๐ญ๐๐ฌ๐ค๐ฌ.
๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐๐ซ ๐ญ๐๐ฌ๐ค๐ฌ are tasks that are aligned with the Eureka program. I give my students the last question from their Problem Sets. This way, they have answered the most difficult question that they will encounter later as they work independently.
A key point that we will cover in the next post is the importance of giving the task within the first 5 minutes of the lesson. That means if you have to pre-teach a new concept, you should aim to do it in under 5 minutes. In a nutshell, student attention drops off rapidly after 5 minutes. Always reinforce the idea to students that they are thinkers in a thinking classroom.
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? Starting with curricular thinking tasks, even before modeling, helps students become self-reliant problem-solvers in mathematics. Itโs far more engaging than simply showing them how to do it. Students donโt want everything handed to them. They want a chance to figure it out! That doesnโt mean we skip modeling; it just comes after theyโve had a go. The result? Deeper understanding and way more buy-in. (More on this in next weekโs post!)
Practice #2: Mixing It Up – How Random Groups Fuel Eureka Math Moments
This step is profound and has had a huge impact on collaboration & social interaction in my classroom, leading to happier learners!
Peter Liljedahl recommends pairing students in Grades K-2 and forming groups of 3 for Grades 3 and up. Trust him on this. Three is the magic number. In groups of four, someoneโs always on the edge, doodling a dragon or distracting other group members.
Make sure that you randomly select these groups and that the random selection is visible to students. I use lollipop sticks- they’re fast and build suspense. Each group only gets one marker to work with. This is important as it forces collaboration- no marker hoggers!
Students may be resistant in the first week to work with their group, but โthat resistance is usually completely gone at the three-week point.โ (Liljedahl, 2021). My students love getting assigned random groups & their ability to collaborate in randomized groups has been astounding. This increased socialization with peers they wouldnโt normally converse with is a big part of why students grow to love math under this framework. Remind your students to collaborate well (more on how we can measure this in a future post), and encourage them to pass the marker frequently.
In this chapter, Liljedahl also introduces another concept that I love. Itโs called โknowledge mobility.โ Itโs the idea that knowledge and ideas for task completion will move around the classroom from group to group. Itโs not cheating or copying.
Students often walk over to other groups to get hints or ideas that help them move forward. They might compare answers or strategies. When a group gets stuck, I usually encourage them to check out another groupโs work to help them get back on track.
This kind of knowledge mobility shifts your role in the classroom. Instead of being the one with all the answers, you become a facilitator who supports students as they work through the task themselves. It also gives you the chance to step back and really observe the learning as it happens. More on knowledge mobility in blog post #3.
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? Eureka Math is a highly explicit program where students often work independently and the teacher provides most of the instruction. By introducing randomized grouping, along with Practice #3, youโll increase student engagement and bring more social interaction into your classroom. It also helps create a more positive learning environment and frees up your time to focus on intervention. I even apply this approach to Problem Sets by having students check each otherโs answers once theyโve finished! This shifts the responsibility for learning to the students, giving you space to check in with those who need support, or to sneak in that last heroic sip of lukewarm coffee. ๐
Practice #3: Use Vertical Non-Permanent Surfaces to Bring Group Thinking to Life
This one is a big shift, and it makes a huge impact. Liljedahl promotes the use of vertical whiteboards when completing thinking tasks. I said whiteboards, but any board where you can easily erase the writing works well. I use the 2 whiteboards & windows in my class. Iโve even used the doors when we were short on space. Imagine the excitement that this generates for students.
Liljedahl encourages using VNPSs for the following reasons:
They get students to task faster
Student work can more easily be erased, making learners feel safer to take risks & make mistakes
They improve collaboration
They heighten knowledge mobility between groups
Standing improves mood & gives a larger canvas for non-verbal communication between group members
When sitting, students can make themselves anonymous more easily
Teachers and learners can see student thinking.
When time is up on the task, the teacher can choose work from the students and annotate it using a different colored marker to consolidate what was learned. This is my new mini-lesson. It is during this time that I highlight what the students did well and share what the learning goal of the day was. More on this in blog post #3!
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? When students stand to work, it brings back the energy thatโs often missing in traditional math lessons. Youโll feel the buzz as students communicate and work through problems together. Itโs a complete shift from passive learning to active engagement. As I said, I give the last Problem Set question as my curricular thinking task and students LOVE IT! Before, students were sitting on the carpet while I talked them through the solution. BORING!! Get them on their feet and talking. Itโs a simple shift with big results.
That wraps up our post on practices 1, 2, and 3 from โBuilding Thinking Classrooms in Mathematicsโ by Peter Liljedahl. Thank you for reading and we hope that this post has inspired some ideas for you!
Try the Following This Week- Homework for the Teacher ๐ 1. Begin one lesson with a non-curricular thinking task instead of a mini-lesson to kickstart problem-solving. 2. Randomly assign students to visible groups of two or three and give each group one marker to promote collaboration. 3. Have students complete their thinking task on a vertical surface like a whiteboard, window, or door. 4. Send us an email and tell us how it went! info@fair-and-squared.com
See you soon for Part 2 of Building Thinking Classrooms In The Eureka/EngageNY Program, The Fair and Squared Team ๐
Hi everybody. Here is the fourth and final post on this topic. We’ve loved reading your comments about integrating BTC into your classroom. Please keep telling us about your journey with BTC. Have you heard it being discussed in your school? How has your admin reacted to it?
Some points to note:
After each approach is outlined, we will highlight why that practice is important and beneficial to teachers who use the Eureka curriculum.
When you see (Liljedahl, 2019), know that Iโm referencing information directly from the Building Thinking Classrooms text.
Those who have implemented the approach, please comment with your thoughts, ideas, and resources.
The post will take approximately 10 minutes to read. Grab a coffee and enjoy!
– We recommend watching this video to get a snapshot of a Thinking Classroom in real life:
On that note, let’s jump into our final exploration of “Building Thinking Classrooms” by Peter Liljedahl within the Eureka program.
Practice #11: How Students Take Notes In A Thinking Classroom
Reading this chapter reminded me of my own days preparing for the Leaving Certificate, Irelandโs version of the SATs. Every afternoon, I would spend three hours copying โnotesโ from textbooks. By the end of the year, I had filled 15 A4 notebooks with paraphrased sentences. Did those notes help me? Not at all. What I really needed was someone to teach me how to take useful notes. Even better, I wish someone had handed me a note-taking template like the one Iโm about to share. Taking notes effectively is a skill. Liljedahl points out the problems with the traditional method of having students write while the teacher talks. Students either cannot keep up, never look at the notes again, or avoid note-taking altogether. So how do we help students consolidate their learning? In my classroom, students typically complete their learning during the problem set or concept check, and thatโs often enough. However, that’s not to say that my students never take notes or consolidate their misconceptions. I’m a firm believer in the idea of deliberate practice. I know that 80% of my students will understand the concept from that day’s lesson. Therefore, why would I have them spend up to 15 minutes writing notes on the day’s learning? Instead, I use note-taking, a response technique for when misconceptions are shown in the End of Module assessment. After reviewing the assessment together, I ask students to identify the questions they missed. They then spend around 30 minutes writing notes on those concepts. To make this more effective, students need guidance. A blank notebook page will not cut it. They need structure to break down the concept clearly. Liljedahl offers a great framework for this, and it closely mirrors the note-taking template weโve created. Our template gives students specific sections to work through so they can fully process the idea. You can see an example in the image below, along with a breakdown of partial products. Download our amazing note-taking template for free using this link.
This focused, purposeful note-taking has been a hit with students. They take pride in the notes they create and see them as a meaningful way to fix their misconceptions. They also understand this process as part of being in a Thinking Classroom. It keeps them engaged and helps them take ownership of their growth.
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? Eureka is a spiraled program. Mastery is not expected on the first attempt, and students will revisit concepts throughout the module. Rather than forcing students to take notes after every lesson, give them the space to review and reflect over time. Wait until the End-of-Module assessment reveals which concepts still need work, and then use structured note-taking to help students build lasting understanding. When paired with the review approach in Practice #13, this empowers students to take further responsibility for their learning.
Practice #12: What We Choose To Evaluate In A Thinking Classroom
Peter Liljedahl reminds us to โassess what we valueโ (Liljedahl, 2021) in our thinking classrooms. But first, we need to ask ourselves: what exactly do we value? Take a moment and think of the three skills or competencies you most want your students to develop. Got them? Great. Scroll on.
In his research, Liljedahl found that teachers almost always landed on the same three core competencies: 1. Perseverance 2. Willingness To Take Risks 3. Ability to Collaborate
Do those resonate with you? Whatever your top three may be, the key is to name them clearly and build your evaluation practices around them.
Traditionally, rubrics have been used to assess learning, but most rubrics are written from the teacherโs perspective and packed with confusing language. Students often struggle to self-assess using them. Deciding between a 2 or 3 out of 4 can feel more like a guessing game than a learning tool. Liljedahl suggests a better option: use a co-constructed, non-numeric rubric focused on a specific competency.
Okay, let’s break down what that means. Targeted competency: Pick one skill you want students to build, such as collaboration, perseverance, risk-taking, or problem-solving. Co-Constructed: Spend 3โ4 minutes discussing the competency as a class. Together, decide what behaviors show strong use of that skill and what behaviors show a lack of it. Use a Continuum, Not Numbers: Instead of giving students a score, the rubric works like a sliding scale. On the left are the actions that donโt support the competency. On the right are the ones that do. This format is simpler, more transparent, and easier for students to engage with.
I co-created a rubric for collaboration with my students last week. Check out how we co-constructed the parameters together below.
This thinking came from a 5 minute discussion.
Using the parameters we developed together, I created the rubric below in Canva. Notice how the desired behaviors are listed on the right. Students can point to where they fall on the continuum, based on how closely their actions match those expectations.
Co-Constructed rubric with desired learning behaviors on the right and unwanted ones on the left
For example, my class co-created a rubric for collaboration last week. Since weโre working on a unit about energy transfers that requires a lot of teamwork, I keep the rubric handy. If a group drifts off-task, I quietly place it on their table. That gentle nudge is often all it takes to get them back on track. You can get the above template for co-constructing rubrics, along with a guide & sample rubrics here.
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? This approach wonโt help when marking end-of-module assessments, but itโs incredibly valuable during daily instruction. The Eureka program does not prioritize group work, which limits opportunities for students to build collaboration and problem-solving skills. Adding BTC-style tasks gives students the chance to work together meaningfully. Co-constructed rubrics then help you guide and support that collaboration with clarity and intention.
Practice #13: How We Use Formative Assessment In A Thinking Classroom
If someone took away your phone, your map, and every road sign, could you still find your way to the nearest grocery store? What about the next town? The next city? Chances are, youโd struggle without some kind of guide.
The same goes for students learning math. Eureka expects learners to make connections between concepts across a module, but it rarely gives them a clear roadmap to do so. Peter Liljedahl emphasizes the importance of giving students those guides. His research shows a striking difference in performance between students who can break a unit into subtopics and those who see it as one giant block of content. Students who recognized the unitโs structure scored around 90%. Those who didnโt typically scored below 75%.
So, we need to give our learners these guides! The good news for Eureka teachers is that the program is perfectly structured for this! Read on to find out how.
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? Each module is divided into topics that explore different parts of a broader concept. That makes it easy to create visual โmapsโ of the unit. At the start of each module, I walk students through this map, quickly highlighting what each topic will cover. Throughout the unit, we revisit the map to show how current content links back to previous ideas or leads forward into whatโs next. You can see this in action on pages 235-240 in the BTC text. However, where Liljedahl has input numbers, I input questions that grow in difficulty as the rubric moves from Basic to Intermediate.
Creating this map helps in the following ways: 1)It helps students see the structure of their learning. They can better understand how each lesson fits into the big picture.
2)Itโs an excellent revision tool. Instead of using Embarcโs review sheets, which often mimic the assessment, I give each student a copy of the module map. They spend 40 minutes answering the most advanced questions they can. If they can do so without help, they know theyโre ready. If not, they write notes for that question and revisit it.
Couple that with our “Fair and Squared Math Mystery Assessment Reviews” for classwork or homework the week before, and youโll have a group of learners who are confident, prepared, and truly understand the content, not just the test format.
Our Math Mystery activites are perfect forEnd-of-Module Review
Practice #14: How We Grade In A Thinking Classroom
Okay, I have a riddle for you: Always on the prowl, with a critical eye, For numbers and stats, they often pry. They’re not a student, teacher, or in the band, But in the school’s corridors, their demands often stand. Who is this person, with data they’re smitten, Always asking for more, as if you’ve been bitten?
If you answered, “The school’s data-focused administrator,” you are absolutely correct! ๐
Data plays an important role in education. It helps us tailor instruction and support student needs. At the same time, it is often collected to satisfy leadership teams who need numbers for reports and evaluations.
So how do we balance the student-centered ideas from Building Thinking Classrooms with the number-focused systems many schools still use?
Peter Liljedahl recommends moving away from โevent-based grading,โ where a single test determines performance, and instead using โevidence-based assessment,โ where we gather insights over time. It is a strong approach, but most schools still require module assessments and expect those scores to be submitted.
Here’s how I please admin while upholding the concepts of BTC. Thank you to my colleague, Sam for recommending this one! I now track two kinds of data: 1) Module assessment scores, which meet school requirements. 2) Thinking classroom competencies, which reflect the learning behaviors we value.
After students complete their Problem Sets or Concept-Checking Questions, they upload their work to Toddle (a platform similar to Seesaw). I attach a simple rubric that highlights the behaviors we want to encourage, such as:
Did the student show all their work?
Was their thinking clearly explained?
Did they understand the concept?
Was their work neat?
Did they collaborate with their group?
These rubrics can be adjusted to match any skill you want students to build.
Over time, students begin to recognize that learning behaviors matter. They start to focus more on clarity, teamwork, and persistenceโnot just getting the right answer.
When it is time for report cards or parent meetings, I can speak to both their academic progress and their growth as learners. It gives a fuller picture of their development. Check out our two examples below.
Rubrics that we use with submitted to encourage desired outcomes.
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? In the traditional Eureka approach, Problem Sets are used to practice the dayโs skill and often focus only on accuracy. By using rubrics that highlight important learning behaviors, we help students see that how they learn is just as important as what they learn. It reinforces the idea that they are part of a classroom where thinking, collaboration, and perseverance are valued every day.
โค๏ธ That wraps up our final post in the Building Thinking Classrooms in Mathematics series by Peter Liljedahl. Thank you so much for following along. We hope these posts sparked fresh ideas and gave you practical ways to bring more thinking, collaboration, and joy into your math classroom.
Homework for the Teacher (Thatโs You!)
1. Choose one BTC practice you havenโt tried yet and give it a go this week. 2. Co-create a simple competency rubric with your students. 3. Swap a traditional mini-lesson for a consolidation session using student work. 4. Create a โlearning mapโ for your next unit to guide student revision and reflection.
๐ Weโd love to hear from you! Send your feedback, suggestions, or takeaways to info@fair-and-squared.com or drop a comment below. What stuck with you? What are you excited to try?
To find all of our resources, including items that will support you in setting up a BTC framework in your classroom, check out our TpT page here: https://edu.fair-and-squared.com/TpTstore
We’ll wrap up this series next week with the final 4 practices from Building Thinking Classrooms by Peter Liljedahl. Some points to note:
After each approach is outlined, we will highlight why that practice is important and beneficial to teachers who use the Eureka curriculum.
When you see (Liljedahl, 2019), know that Iโm referencing information directly from the Building Thinking Classrooms text.
Those who have implemented the approach, please comment with your thoughts, ideas, and resources.
The post will take approximately 10 minutes to read. Grab a coffee and enjoy!
– We recommend watching this video to get a snapshot of a Thinking Classroom in real life:
On that note, let’s dive into the next 4 practices to develop a thinking classroom within the Eureka/EngageNY program.
Practice #7: Homework in The Thinking Classroom- From Groans to Growth
Why did the parent bring a helmet to the parent-teacher conference? Because they knew discussing homework would be a real head-banger! Homework is a source of stress for everyone: teachers, parents, and students. Peter Liljedahl presents compelling evidence that homework has little impact on actual learning.
According to him, students need to see homework as something that benefits them, not their teacher. Once that mindset shifts, students are more likely to complete it willingly.
To support this, Liljedahl recommends not checking homework or even asking about it. Save yourself the energy, and save your students and their families the stress. Homework completion should not be your hill to die on.
At this point, I’d like to highlight how I assign homework in my class. I attribute strong MAP score growth in my class to this approach. Here it is: Implement a flipped classroom and assign Zearn for homework. Students complete the next day’s Zearn lesson for homework the night before. This leaves them ready for the thinking task right from the get-go.
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? Eureka includes homework sheets with each lesson, but letโs be honest โ theyโre dry and rarely inspiring. In my experience, students often find the answer key online and copy it. Thatโs a clear sign they view homework as something to please the teacher, not to help themselves.
Zearn, on the other hand, gives students a platform they actually enjoy. Itโs trackable, aligned to the lesson, and it prepares them for deeper thinking in class. I tie Zearn completion into my Classroom Economy system: students earn classroom dollars if they choose to complete it.
If youโre aiming to build a love of math in your classroom, skip the worksheet slog. Assign Zearn instead. Itโll save you class time, cut down on homework battles, and set your students up for success.
Quick tip: If your district requires written homework or youโd like to offer extra practice, try using the Eureka-aligned Spiral Review Pack. I typically use it for morning work, but it works just as well as at-home practice.
Practice #8: Mobilize Knowledge In Your Classroom- Harness The Power of Peers
Liljedahl encourages teachers to foster student autonomy by โletting goโ of overly controlled instruction. We should not position ourselves as the sole source of knowledge, and we should avoid micromanaging how students engage with content.
He points out that “the amount of thinking students were required to do, and did, was sharply reduced in situations where their actions were managed- even micromanaged.” (Liljedahl, 2021). One of the best ways to avoid micromanaging is by promoting knowledge mobilization. We introduced this concept in Part 1: students move among peer groups to see how others are approaching the thinking task. They return to their own group with new insights, and continue working collaboratively.
While this might sound like it encourages copying, Iโve found the opposite to be true. It leads to some of the most thoughtful, energized group work Iโve ever seen. Although knowledge mobilization will often occur on its own, it helps when teachers actively direct groups to check in with others. Ask questions like, โWho else is making progress?โ or โWhose board has a different strategy?โ This light touch can trigger movement, fresh ideas, and deeper thinking.
* Knowledge mobilization is possibly my favorite takeaway from the BTC textbook. The best part of knowledge mobilization is that it will relieve so much of the responsibility on you as the teacher and it will energize your classroom!
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? The Eureka program promotes a highly structured, explicit form of learning. While explicit learning has its merit, it’s “the chili in the dish” where deep learning is the desired outcome. It’s vital to strike a balance between explicit learning and fostering implicit learning experiences in math education. Great math classrooms need both explicit teaching and opportunities for implicit learning. Implicit learning experiences, like those created through knowledge mobility, allow students to explore, discuss, and construct deeper understanding through collaboration.
The introduction of knowledge mobility to your classroom will allow for that implicit learning & deeper conceptual understanding to take place. When we mix the structure of Eureka’s explicit learning with the impliciteness (that’s probably not a real word?!) of the BTC framework, we end up with learners who not only understand mathematical processes, but also build a more meaningful understanding of why those processes work.
Practice #9: Using Hints & Extensions To Maintain “Flow”- The Goldilocks Zone
Liljedahl opens this chapter by emphasizing the importance of asynchronous learning in the classroom. At the same time, he acknowledges the challenge of providing differentiated learning experiences for large groups of students.
To support his point, he references the work of psychologist Mihaly Csikszentmihalyi, who introduced the concept of cognitive flow. (Check out this video for a great explanation of what โflowโ means.)
Cognitive flow is the state where a person is completely absorbed in a task. The nervous system is fully engaged, and the mind is focused without distraction. This state occurs when the level of challenge is just right- not too easy and not too overwhelming.
Because learning is at its strongest during moments of flow, itโs clear that we want our students to enter this state during math tasks. The question is: how do we help them stay there?
According to Liljedahl, we achieve this by using hints and extensions to adjust the level of challenge as needed. This keeps students engaged, appropriately stretched, and deeply involved in their thinking.
In my classroom, hereโs how this plays out in real time:
Hints: When I notice a group struggling, I offer just enough support to help them regain momentum. For example, if a group forgets to carry the one during an addition problem, I might do a quick think-aloud and walk through their process with them. The goal is for them to discover the mistake on their own. Other times, Iโll encourage knowledge mobility by directing them to check out how another group approached the problem correctly.
Extensions: This is where things get exciting. When a group finishes their thinking task ahead of others, I give them an extension that pushes their thinking further. Sometimes the extension connects to a skill weโve already covered. Other times, it introduces a concept theyโll encounter in an upcoming lesson. Using extensions in this way has allowed us to review past learning in a more meaningful way and to preview future content with surprising success. Iโm consistently amazed at what my students can do when challenged just beyond the lesson objective
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? As we discussed in the first post, the heart of the BTC approach is getting students to think. But when tasks are too easy, too difficult, or too dry, students check out. Eurekaโs mini-lessons donโt always support that ideal state of engagement known as flow. Hints and extensions help bridge that gap. When used well, they ensure: โข Students stay engaged throughout the entire thinking task. โข Earlier concepts are revisited through active problem-solving. โข Students get a sneak peek at future learning, which builds confidence and curiosity.
One of the most powerful shifts Iโve seen is in students who come in with high math anxiety and little belief in themselves. Through consistent success with thinking tasks and extension challenges, that fear is gradually replaced by confidence. I still remember telling one student, โGuess what? You just mastered tomorrowโs lesson,โ and watching their whole face light up. These moments do more than teach content, they reshape identity.
Practice #10: Consolidating Learning (The New Concept Development)- Tie it Together Explicitly
This practice is a game-changer. Say goodbye to your traditional mini-lessons and instead use a โconsolidation of learningโ approach. Once students complete their thinking tasks, the class gathers to review the work together. Itโs during this time that you introduce the learning goal for the day.
Show, don’t tell: Start by using student work to introduce the learning objective. Choose one groupโs board and annotate directly on it using a different colored marker than what students used. Before offering any explanation, have the class discuss the groupโs thinking. Ask questions like: โWhat do you notice?โ โDid your group get the same answer? Why or why not?โ โWhat model did they use?โ
Consolidate from the bottom: Begin with a group that made an error. This approach keeps higher-achieving students engaged by deepening their thinking, while also giving developing learners a place to start consolidating at their own level.
Get moving: From there, guide the class through the work of one or two other groups, moving from less accurate to more accurate solutions. Ask students to compare, discuss, and reflect on each groupโs approach. As Liljedahl notes, โthe more steps, the better.โ (Liljedahl, 2021)
Keep in mind the following:
While students work, keep an eye out for the groups you want to highlight during consolidation.
Let those groups know in advance and remind them not to erase anything. Even if the work contains mistakes, students feel valued when their thinking contributes to class learning.
Never erase student work without permission. As Liljedahl says, โErasing devalues their work.โ
Students may still be buzzing from their thinking task. Establish clear expectations to help them stay focused and engaged during this part of the lesson.
๐ด ๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? “If all students could learn by having us just tell them how to do it, we would not have any of the problems that we have in mathematics education today.” (Liljedahl, 2021) Students donโt want a one-way, 35-minute lecture disguised as a mini-lesson. They want to engage. Inviting them to analyze another groupโs work creates far deeper understanding of the concept. As Liljedahl puts it, โRather than explaining oneโs own work, trying to decode someone elseโs work changes consolidation from telling to thinking.โ (Liljedahl, 2021).
The best part? Once students have attempted the task, you can often explain the Eureka learning objective in under five minutes, right on top of their own thinking. Youโll likely even have time to consolidate an extension or two.
That brings us to the end of our post on Practices 7, 8, 9, and 10 from Building Thinking Classrooms in Mathematics by Peter Liljedahl. We hope this has sparked some fresh ideas for your classroom!
Try the Following This Week โ Homework for the Teacher ๐
๐๐ก๐ฒ ๐ข๐ฌ ๐ญ๐ก๐ข๐ฌ ๐ข๐ฆ๐ฉ๐จ๐ซ๐ญ๐๐ง๐ญ ๐๐จ๐ซ ๐๐ฎ๐ซ๐๐ค๐ ๐ญ๐๐๐๐ก๐๐ซ๐ฌ? As we discussed in blog post #1, the ultimate goal of the BTC approach is getting students to think through problems. The Eureka program doesn’t always promote this concept. Altering the layout of classroom furniture & de-fronting the classroom signals to students that thinking and collaboration are valued more than quiet compliance.
That wraps up our look at Practices 4, 5, and 6 from Building Thinking Classrooms in Mathematics by Peter Liljedahl. While the first three practices focus on how to introduce BTC routines to your students, these next steps are all about shifting your teaching behavior. Each one nudges you further into the role of facilitator and helps center your classroom around student thinking.
Liljedahl ends the book with a reminder thatโs worth starting with.
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