Daily math routines that spark student curiosity

It’s the educator’s eternal question: How do I keep students engaged?

When designing daily math practice, teachers are always working to make real-world math problems fresh and relevant, find new entrance points for concepts, or simply come up with surprises. All of these approaches can be very effective.

And though it may seem counter-intuitive, so can routines.

The power of instructional routine

The word routine can connote a sense of doing something mechanically, even without thinking. But teachers know that well-placed classroom routines can open opportunities for creative thought.

Routines provide a way for you and your students to build and maintain a sense of familiarity and structure throughout the school year. They also free up time teachers would otherwise spend giving directions. When students know exactly how a certain activity should run, and understand all instructions and expectations, everything goes more smoothly.

That’s why a core set of shared routines can be a powerful, practical force for establishing an effective classroom learning community..

Bringing math routine into the classroom

We know routines can be effective in any classroom. Now, we also have research offering direct evidence that certain routines are particularly effective in math classrooms.

Think-pair-share

Do you want your students to have more time to think before solving and sharing about a problem? 

GOAL: Provides opportunities to identify, compare, and contrast multiple strategies

TIP: During partnered discussion, consider displaying sentence frames such as, “ First they… Next they…” “Their strategy was to…” or “I see a/an… in both strategies.”.

How to do it:

  • Invite students to solve a problem that can be solved with multiple strategies. Then, display two or more different responses representing different strategies.
  • Give students time to analyze the strategies on their own and then invite them to discuss them with a partner.
  • Facilitate a class discussion to describe, compare, contrast, and connect the different strategies. Utilize open-ended questions like, “Why did different strategies lead to the same outcome?” or, “What was helpful about each strategy?”

Where to learn more

We worked with our curriculum team to develop routine cards for math teachers, so you can implement routines that are part of our math program in your classroom. Most of the routines you’ll find throughout Amplify Desmos Math have been specifically proven effective in math classrooms. All of them have been adapted from established teaching practices.

We invite you to access a sample set of some of our most popular routines and decide which ones to try out in your classroom!

Resources

Download free math instructional routine cards.

Explore Desmos Classroom.

Learn more about Amplify Desmos Math.

Desmos Math 6–8 earns perfect scores from EdReports

It’s great news when a student who has worked hard to do their best gets a perfect score on an exacting test.

We’d like to take a brief moment to share some similar news of our own: Desmos Math 6–8 has earned perfect scores and an all-green rating from EdReports!

This is a powerful affirmation not only of our program, but also of every Desmos Math 6–8 student who benefits from the high-quality instructional materials, student-centered instruction, and thoughtful technology in the math classroom.

The power of math technology

Here’s a bit about the program. Based on Illustrative Mathematics’ IM 6–8 Math™ and Open Up Resources, Desmos Math 6–8 features interactive, standards-aligned lessons that are easy to use and fully customizable.

The program empowers teachers with an engaging curriculum that helps them:

  • Celebrate student brilliance.
  • Put student ideas at the center of instruction.
  • Drive student achievement every day.

The technology in the program is purposeful: students are empowered to explore new ideas, and our teacher dashboard helps teachers bridge those ideas together. Whether teachers are observing student learning on our lesson summary page or guiding productive discussions with our conversation toolkit, our facilitation tools make teaching more effective and more fun.

The rigorous EdReports review process

EdReports.org is an independent nonprofit designed to improve K–12 education. Among other things, its expert reviews help equip teachers with the highest-quality instructional materials.

Their review process is necessarily individualized and rigorous. Educator teams develop rubrics and evidence guides; recruit expert reviewers with a collective thousands of years of experience; then conduct rigorous, evidence-based reviews.

The reviews collect evidence about important characteristics of high-quality instructional materials. These include the presence of standards, how well they are sequenced, and how deeply they are included.

Reviews take 4–6 months. Ultimately, multiple educators will analyze every page of the materials, calibrate their findings, and reach a unified conclusion.

And in our case, it was this: Desmos Math 6–8 received perfect scores from EdReports and met expectations for every one of their gateways.

See for yourself

Request a free 30-day trial today!

IM 6–8 Math™ and Illustrative Mathematics® are trademarks of Illustrative Mathematics, which is not affiliated with Amplify. Amplify is not an IM Certified Partner. EdReports and associated marks and logos are trademarks of EdReports.org, Inc.

EdReports.org is an independent nonprofit designed to improve K–12 education. Among other things, its expert reviews help equip teachers with the highest-quality instructional materials.

The power of technology in the math classroom

You might say math and tech go hand in hand. And these days, of course, kids and tech go literally hand in hand. So it makes sense that using digital tools in the math classroom can help teachers reach students, and teach the math content they need to learn. But truly integrating technology into math instruction is not just a matter of adding random gadgets and gizmos. We need to do more—especially if we want to leverage the power of math technology to engage all students.

Why integrate technology into the math classroom

Integrating technology into instruction delivers numerous benefits in the classroom–perhaps especially in the math classroom.

Numerous studies suggest that technology can support student learning in the math classroom. This tech might take the form of graphic calculators, digital manipulatives, or learning software. In general, such tools have been shown to help students improve both their understanding of math concepts and their performance on tests.

Thoughtful tech has these effects in part because it can make math more engaging. Students are generally more excited to dive into a visually appealing and interactive program than a black-and-white math textbook.

Integrating technology into a math classroom also means:

  • Personalized learning: Students can work at their own pace and get tailored guidance and feedback.
  • Collaboration: Students can work together regardless of their physical location.
  • Real-world applications: Technology can simulate real-world scenarios that require mathematical reasoning and critical thinking skills.
  • Saving teachers time: Technology helps teachers assess learning more effectively, providing real-time feedback and helping them identify where students need support.
  • Preparing students for the future: After all, most jobs require the use of technology!

How to integrate technology into the math classroom

The most effective technology approaches in the math classroom are active, not passive. They also invite deep thinking and productive struggle rather than speed and rote memorization.

The National Council of Teachers of Mathematics (NCTM) includes this guidance in its Principles to Action:

“An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.”

The NCTM recommends that teachers: “incorporate mathematical tools and technology as an everyday part of the mathematics classroom, recognizing that students should experience ‘mathematical action technologies’ and physical or virtual manipulatives to explore important mathematics.”

Here are just a few approaches that enhance engagement:

  1. Use interactive whiteboards or projectors: You can display math problems and solutions, diagrams, graphs, and simulations, allowing students to interact with and manipulate visual representations of math concepts.
  2. Use graphing calculators and virtual manipulatives: They can help students visualize and solve complex math problems, and prepare them for more advanced mathematical concepts.
  3. Use gamification techniques: Can make math more engaging and fun for students.
  4. Use online collaboration tools: These tools can help students work together on math problems and projects, even when they are not in the same physical location.
  5. Use select social media and other online platforms: To create math communities where students can collaborate, share resources, and ask questions.
  6. Use math software and apps: These programs can help students practice math, solve problems, and visualize math concepts in 3D or interactive models.

How Desmos Math 6–A1 delivers

Desmos Math 6–A1 is just that kind of program. It provides dynamic and interactive digital math learning experiences, alongside flexible and creative print activities. Its teacher dashboard is designed to encourage classroom discussion and collaboration. It invites students to explore a variety of approaches—and invites teachers to celebrate and develop interesting thinking in their classrooms.

The dashboard also shows teachers actionable formative assessment data for each student and the entire class, and allows them to leave written feedback for students in their lessons.

And we know it works. Teachers and students in our pilot program said that students learned more with Desmos Math 6–A1 than with their prior program. (See case studies in a large midwestern school district and in Naugatuck Public Schools.)

What’s more, Desmos Math 6–8 has earned perfect scores and an all-green rating from EdReports. This is a powerful affirmation not only of our program, but also of high-quality instructional materials, student-centered instruction, and thoughtful technology in the math classroom.

Learn more

Start your 30-day free trial of Desmos Math 6–A1.

Embracing artificial intelligence in the math classroom

Artificial intelligence seems to be everywhere these days. We use it when we ask Alexa or Siri for the morning weather report. We use it when GPS tells us how to best avoid traffic. We use it when we chill at the end of the day with a recommendation from Netflix. 

But what about during the day—and specifically, at school? Even more specifically, can AI be leveraged to enhance the math classroom? 

“While AI is an amazing tool, you’ve really got to make sure that you are focusing in on your expertise as well,” says veteran math educator and STEM instructional coach Kristen Moore, “And saying, ‘How can I use this to make something better?’ and not just, ‘How can I use this to make something?’” 

In this post, we’ll talk about the current state of AI in math education, and how it can support educators in making math better. (SPOILER: It’s not going to replace you!) 

First, some STEM learning for us: What is artificial intelligence? 

Artificial intelligence, or AI, refers to the development of computer systems able to perform tasks that typically require human intelligence. 

It involves creating algorithms and systems that enable computers to learn from data, adapt to new situations, and make decisions or predictions.

AI aims to mimic human cognitive functions such as understanding language, recognizing patterns, solving problems, and making decisions. It encompasses a range of techniques and technologies, including machine learning, neural networks, natural language processing, and robotics.

The term “artificial intelligence” was introduced in 1956.  The availability of vast amounts of data and advancements in computer power in the 2010s led to additional breakthroughs. And with the proliferation of smartphones, smart devices, and the internet, AI technologies began to work their way into our homes, cars, pockets, and everyday lives.

What’s the state of AI in education? 

AI is already commonplace in schools and classrooms. Here are just a few examples:

  • Adaptive learning: This software uses AI algorithms to adjust the difficulty and content of lessons based on a student’s performance, helping students remain engaged and challenged at their optimal level.
  • Assistive technologies: AI helps students with disabilities by providing assistive technologies like text-to-speech and speech-to-text tools, making educational content more accessible.
  • Plagiarism detection: These tools use AI algorithms to identify instances of copied or unoriginal content in students’ assignments, essays, and projects. 
  • Data analysis for teachers: AI analyzes data from student assessments to identify trends and insights, helping teachers make informed decisions about instructional strategies. It can also predict students’ performance trends, helping teachers identify at-risk students early and intervene to provide additional support.
  • Grammar, spelling, and style checkers: AI can provide real-time feedback to students (and teachers!) on their writing work.

Embracing AI technology in your math classroom

While AI is not here to replace teachers, it is here to stay. And experts say it’s only going to become more commonplace. But despite how common AI is already—both outside and inside school—not all teachers are familiar with its numerous applications and potential. Now is a great time for educators to start exploring its uses and get ahead of the curve.

Here are a few easy entry points for math teachers. 

ChatGPT: A common AI tool, ChatGPT is designed to understand and generate human-like text based on the input it receives. It’s trained on a wide range of internet text, which enables it to generate responses to a vast array of prompts and questions. 

Most students have likely experimented with ChatGPT, while teachers—though aware of it—are less likely to use it. ChatGPT has highly practical applications for both groups, though—including in the math (and science) classroom. 

It can, for example, help teachers plan interesting, relevant math lessons for their students. Kristen Moore, who discusses this topic on Math Teacher Lounge, suggests that math teachers use ChatGPT to:

  • Connect topics to student interests and vice-versa. (Teachers can ask ChatGPT for real-life applications of polynomials and select those that might pique student interest, or ask about math applications derived from students’ hobbies and pursuits.) 
  • Generate word problems (including step-by-step solutions), lessons, projects and rubrics, and more.

Toward the (near) future

As AI advances, it will continue to revolutionize education. Here are a few time-saving ways that educators can look forward to using it in their classrooms.

  • AI tutors: AI-powered virtual tutors will help math students with homework questions and provide explanations for various concepts. These tutors can be available at home 24/7, allowing students to seek an AI homework helper whenever they need it.
  • Automatic graders: Some AI tools can automatically grade math work, including multiple-choice and short-answer assignments. These tutors can be available at home 24/7 in any household with internet access, allowing students to seek more personalized instruction.
  • Personalized learning paths: These AI-powered platforms will work particularly well for math students by adapting to each student’s skill level and pace, offering tailored exercises and challenges that cater to their strengths and identify areas of improvement. They will analyze students’ performance and adjust the difficulty of content, ensuring that students get targeted support and opportunities to progress.

More to explore

To dive deeper into AI in math education—and get rolling with AI in your classroom—check out this two-episode mini-series on our Math Teacher Lounge podcast focused on just that: 

“I’m a believer that learning is inherently social,” says Carolan, who is quick to emphasize how technology can enhance that quality, not replace it. The same can be said for the role teachers play in the classroom—a role technology can support, but never take away. To learn more about this topic (and discuss it with your fellow educators!), head to our Math Teacher Lounge community! 

Problem-based learning in Amplify Desmos Math

This program brings problem-based learning into the math classroom, with an approach proven to help students develop math reasoning and problem-solving skills—not to mention deep understanding, fluency, and comfort with all things math. 

Let’s take a closer look at problem-based learning in math, and at the contours of this exciting curriculum. 

How problem-based learning helps math students—and math teachers

When you learned math, you likely started out learning arithmetic then moved on to solving word problems. You might have learned formulas, then practiced using them to determine the volume of a prism or which train will arrive at what time. 

But life works differently. Sometimes we tackle the problem first, not the formula. When you get a new piece of technology—a phone, a TV, a computer—you might read the user guide, or you might just turn it on and try some things. 

If that second style sounds like you, that’s common—and it’s an example of learning through problem-solving. 

“It’s something we naturally do,” says Kristin Gray, executive director of Amplify’s math suite.  “We’ve had a phone before, so we would pick up this new phone and try doing things that we know worked before, and then we would experiment. Does it work the same on this phone? This bouncing between experience and explanation is the foundation of how we learn through problem-solving.”

What does that look like in the math classroom? 

Students tackling interesting problems, raising questions about the math required, receiving an explanation, and applying it back to the problem—just as in the example of new technology. 

“When we show students how to get the answer, we send the message that math is solely about answer-getting and learning processes. Answers are important, but we want to use problems to teach the math, not just teach students to get the answer,” says Gray. 

Learning through problem-solving can also engage more learners in math, says Gray. By influencing the way students (and teachers) think about what it means to know and do math, problem-based learning has the potential to shift the way they think of themselves as mathematicians.

“Students are naturally curious and like solving challenges and trying things in new ways, so that’s a great start,” says Gray. 

And understanding is motivating. It inspires perseverance and confidence. It supports making connections, not learning concepts in isolation. 

When students are given a new problem and are able to use prior knowledge to help solve it, that “promotes the development of autonomous learners,” says Gray. 

Supporting the brilliance of student thinking 

Our program combines interactive problem-based lessons with explicit instruction, reinforcement, and practice. Lessons build a strong foundation in procedural and fact fluency, deepen understanding of concepts, and enable students to apply learning to real-world tasks.

To learn more about how and why it all came together, watch the following video featuring Amplify Director of Project Management Christina Lee, Amplify Math advisor and Desmos user Fawn Nguyen, and Desmos Director of Research Dan Meyer.

Christina: Hi, I’m Christina, the product manager at Amplify working on our K–12 math program. As you may have heard by now, Desmos Classroom is joining Amplify. This includes all of teacher.desmos.com, including all of the free activities, the free activity builder, and the Desmos math curriculum. I have Fawn Nguyen and Dan Meyer here to answer a few questions about what’s going on. Thank you both for joining! 

The first question is to you, Dan. One thing every Desmos user is going to want to know is, will the Desmos calculators and activities on teacher.desmos.com stay free to use forever?

Dan: Yes, period. It’s an important question and an easy one to answer. Our commitment to users, from day one, has been [to] whatever you can use for free. Now we’re not going to make you pay for that. We know how hard it is as a teacher to build your practice on top of software that could disappear, and Amplify shares that commitment in a rock-solid way.

Christina: That’s great to hear! Fawn, can you tell us a little bit about what you love about teacher.desmos.com? Why should a teacher who’s never used [it] check it out?

Fawn: How do I love teacher teacher.desmos.com? Let me count the ways! There’s nothing like it out there that allows teachers to build lessons from scratch. What makes it unique? Well, there are lots of things that are unique about Desmos, but the screen-by-screen build is a standout for me. It allows me to interact with students prior to moving to the next screen. More importantly, the interaction among the students and the teacher dashboard is just brilliant. It lets me see the students’ responses, especially the graphical ones, in real time. I feel like it’s a built-in formative assessment [in] the lesson. And not surprisingly, the structures from the five math practices by Peg Smith are built-in there with the selecting, sequencing, and connecting.

Christina: Dan, why does it make sense for Amplify and Desmos to build one core math program for grades 6–12?

Dan: We’ve been traveling on separate parallel paths for a really long time and it makes a lot of sense for us to go farther together. For instance, we’ve both been building a core curriculum based on the Illustrative Mathematics curriculum. We have both been doing that using core Desmos technology. We both share an understanding of the complexity of teaching, the brilliance of student thinking, and so it makes sense for us to merge together. Desmos brings to the table a deep understanding of how technology can support student learning, and Amplify brings to the table an understanding of how systems support students at scale. So we bring a lot of commonalities and a lot of elements that both of us need from the other.

Image showing an educational digital platform called Amplify Math in collaboration with Desmos Classroom. The interface includes various features such as textbooks, problem-based learning activities, interactive graphs, and practice exercises.

Christina: Fawn, you’ve been an advisor on the Amplify Math curriculum focused on problem-solving. In what ways do you think this knitting together of the two programs will help make teaching through problem-solving easier for teachers?

Fawn: I actually knit, Christina! So I really like your description of the partnership as knitting together the two programs. It’s like taking two luxurious fibers, if I may say––ironically, luxurious but free, which describes literally nothing except Desmos––and weaving them together to create a gorgeous and functional design. I’m thinking about a sweater vest for Dan, he would look great in it! Amplify truly understands what problem-solving is, that it’s non-routine. And Amplify’s math curriculum has many great activities. However, when this task can only live on a printed page it’s hard for it to stay as a problem-solving task. What I mean is that it’s hard for students to unsee things. So when it’s on paper, you have to show all the cards and that ruins everything to me, frankly. But with Desmos again, with that screen-by-screen build and the pause and pace functions, they are designed so that the timing of teacher moves can happen. I think the timing is really important. And then problem-solving is about tinkering with ideas and testing conjectures, and Desmos is built for such. It invites you to play, it invites you to take risks, and it doesn’t shame you when you make a mistake. So ultimately, Desmos brings school mathematics, which Amplify writes, closer to what doing mathematics looks like.

Christina: Dan, one final question for you. What’s going to happen to the Desmos calculators now?

Dan: The Desmos calculators, like all the other technology as part of this deal, will remain free into perpetuity. They’ll get spun over into a new corporation, a public benefit corporation called Desmos Studio, where they’ll have a lot more focus from the people who work on it and a lot more resources to expand and develop and do that work.

Christina: Thank you, Dan. Thank you, Fawn. Thank you both. I’m really excited about this opportunity we have to build something special for teachers and students! For more information about Amplify Math and Desmos Classroom, and everything else we’ve got going on, please visit amplify.com/futureofmath.

From math lesson planning to long-term success

Amplify Desmos Math makes it easy for both teachers and students to make the shift to a problem-based approach by providing captivating activities, powerful teacher-facilitation tools, and lots of support for differentiation and practice.

Lessons start with warm-ups that tap into prior knowledge and move into problems that require collaboration to solve. Teachers monitor, engage, and ultimately synthesize student work into the main idea. There are also ample opportunities for practice and reflection. 

Amplify Desmos Math will be available for 2025–26 school year implementation. Interested districts can pilot the beta release starting fall 2024.

Learn more about Amplify Desmos Math.

5 strategies to transform your math classroom

Want to shift your math teaching practices this year, but not sure where to start? That’s a good problem to have! 

You can boost your instruction this fall with problem-based learning, technology in the math classroom, and more—all in ways that put students at the center. 

“All students need the opportunity to feel like they can figure out mathematics,” says Jennifer Bay-Williams, Ph.D., an author and professor of mathematics education at University of Louisville. “That’s where they develop a math identity, [the idea] that they can do math. And they start feeling like, ‘I can figure this out.’” 

Bay-Williams spoke at our 2024 Math Symposium, along with other thought leaders and expert educators. Keep reading to see how their key takeaways can help you shift your math instruction this school year!

Center student ideas in a collaborative math classroom

Amplify Math Suite Executive Director Kristin Gray had great tips for teachers looking to center student ideas in the classroom. Simply put, it’s all about helping them make several types of connections. These can include any of the following: 

  • Connecting students’ classroom math experiences to real life
  • Connecting math ideas to one another
  • Connecting their ideas to the ideas of their classmates 

How do teachers foster these important connections? That’s where problem-based lessons come in. Rather than teaching a concept or formula in isolation, then having students practice it, try inviting students to collaborate on a real-life problem that will lead them to that math idea. (For example, you might ask them to work on designing a small traffic or subway system that requires developing ideas about distance, rate, and time.)

As a result, students build problem-solving skills collaboratively, feel their ideas are valued, develop their own ways to make math make sense, and learn from and with each other. Teachers also get to know and appreciate the different backgrounds and styles students bring to the classroom, opening up new opportunities for engagement—and connection. 

Reimagine student engagement

No matter how engaging you are as a teacher, it’s typically students who drive engagement—and that’s actually good news. You don’t have to reinvent the wheel or do somersaults to get their attention. In fact, a lot of engagement comes from creating routine and familiar opportunities for connection. And it can also come from allowing students to make mistakes. 

“We want all students to have an entry point into [math] tasks,” notes Amplify STEM Product Specialist James Oliver. “Those students that seem to always feel like they don’t fit or don’t have the identity in that math classroom, we want them to immediately have successes and have their curiosities tested.” Successes—and productive failures. “What we’ve learned is, you are not firing any synapses, nothing’s happening if you’re just getting it immediately correct.”

Nurture student curiosity

Which is better: letting students dive into a box of LEGO pieces to see what happens, or providing a step-by-step guide to building the airplane? 

It’s actually a tie. In both structured and loose approaches, the key is to spark curiosity and communication. “If we want them to be mathematicians, we should let them talk about math,” says Amplify Director of 6–12 Core Math Curriculum Kurt Salisbury, Ph.D. Here’s his 3D approach:

DISCOVER
Discovering the relationships among mathematical ideas is a key part of mathematical thinking. 

DESCRIBE
Students communicate their mathematical thinking by describing the processes, procedures, or relationships needed to work with a concept or pattern. 

DEVELOP
When students develop a strategy they can apply to a variety of contexts, their math thinking gets validation and purpose.  

So whether you lean into a more structured approach or prefer to let kids figure the LEGOS out themselves, small mindset changes like these can create more space for your students to discover, describe, and develop as mathematicians.

Make math fluency fun 

As with someone fluent in a language, someone fluent in math is able to think and calculate mathematically without struggle or effort—that is, with fluidity. 

In order to think and calculate fluently, students need to build a toolbox of strategies—and games are a great way to do that. 

While you’re making the learning fun, students are absorbing tools they’ll use throughout their lives. “When we ensure that every student has access to a range of strategies, and has regular opportunities to choose among those strategies, that’s what games do for us.” says Bay-Williams.

Elevate student voices 

When student thinking isn’t explicitly invited into the classroom, students may begin to narrow their focus, providing merely what they think their teacher wants to hear. But given genuine invitations to share, students are more likely to follow their thought process wherever it leads them, taking a more organic approach to problem-solving.

“Taking a step back as a teacher, and inviting students to take a step forward, [activates] students getting started with finding the answer,” says Stephanie Blair, vice president of Desmos Coaching. “And all of them might take a different step forward, which is okay.”

It’s time for math that does more for students

“All students need the opportunity to feel like they can figure out mathematics,” says Bay-Williams. We need to connect with our students, nurture their curiosity and comfort with math, and welcome their unique ways of thinking.

We hope the thought leaders and speakers from our Math Symposium have inspired you to do just that!