The first week of school is packed with emotions—for students and teachers. There’s excitement, nervous energy, fresh notebooks, and sharpened pencils… but also a mountain of expectations and routines to set. It’s tempting to dive straight into the curriculum, especially with pressure to stay “on pace,” but I want to encourage you to pause and ask:

What if the best way to teach more math… is to teach less in the first week?

Hear me out.

After 30+ years in the classroom, one of the most important things I’ve learned is this: the first week of math sets the tone for the rest of the year. If we take the time to build solid routines, model expectations, and create a classroom where math feels safe and purposeful, everything that comes after flows more smoothly.

Will you worry about getting behind?  Probably.  Will other teachers be complaining all year about how their students don’t work together well or attend to lessons? Most likely.

I promise you–invest time in the first weeks for massive payoff.  I’ve done it.  It works.

What Should That First Week of Math Look Like?

The truth? It’s not about jumping into Chapter 1.

The beginning of the school year should be about setting the stage for a year of learning, talking about math, making mistakes, and GROWING.  Here’s what I’m talking about.

Establishing classroom norms and expectations

The first few days of school are when students learn how your classroom works—and math time is no exception. Take time to clearly model and practice the expectations you want to see during your math block. How should students transition to math? What does “being prepared” look like? What are your expectations for noise level, participation, or working with partners?  How will YOU be helping and coaching?  Students need to feel that trust factor right away.

Instead of jumping into instruction right away, let students see and practice these expectations in action. Use short, accessible math activities, create anchor charts, and use positive reinforcement to make them stick. When students know what to expect, they feel more confident—and that confidence leads to more productive learning down the road.

Getting students comfortable with materials and tools

It’s easy to assume students know how to use the math tools we provide—but that’s not always the case. Spend time in that first week introducing your classroom materials: math manipulatives, whiteboards, number lines, journals, or technology tools you’ll be using throughout the year.

Give students time to explore and experiment with them in a low-pressure way. You might even create a “math tool scavenger hunt” or mini-stations to rotate through. As you go, be explicit about how to store, access, and care for materials. A few minutes of modeling now can save hours of chaos later! I actually believe that the number one reason many teachers don’t want to use manipulatives or games is that they are worried about the management of them.  This is “fixable”!

Beginning to build a culture of math thinking and discourse

The first week is also your chance to shape how students see math—and how they see themselves as math thinkers. If we want students to be risk-takers and problem-solvers, we have to start laying that groundwork immediately.

Talk about what it means to have a “math mindset.” Read a math-themed picture book. Ask students to reflect on what makes math feel exciting or scary. Use open-ended prompts like, “What do you notice?” or “What do you wonder?” to get them talking—and then actively model and celebrate different kinds of thinking.

By creating space for discussion and collaboration early on, you’re telling students: This is a place where your thinking matters.

Practicing routines they’ll need all year long

Math block routines shouldn’t be saved for later—they should be front and center from day one. Whether you plan to use centers, small groups, math journals, or independent practice, now is the time to introduce those structures slowly and intentionally.

Start small. Model what a math rotation looks like. Practice moving between activities. Set expectations for getting help or turning in work. Use simple, low-stakes tasks so students can focus on learning the structure rather than the content.

These first few days aren’t about testing how much math your students know—they’re about preparing them to thrive in your math classroom all year long.

Try these first week of math ideas!

Math Warm-Ups: Start every day with a short, low-stakes math prompt to get students thinking. These can be open-ended, discussion-based, or visual. The goal is to build confidence and curiosity—not get “right” answers. I have a post about how I use math warm ups, if you are interested.

Materials Exploration: Give students time to explore and get comfortable with math manipulatives, journals, and tools. Set expectations for how to use and store them—this prevents so many issues down the road!

Talk About What It Means to Be a Math Thinker: Start building that growth mindset early. Use anchor charts, class discussions, or math-themed read-alouds to help students see themselves as capable and creative problem-solvers.

Teach Your Math Block Structure: If you use rotations, small groups, or whole-class instruction, don’t wait—model it from the beginning. Practicing transitions and routines early helps everything run smoother later.

Want Your First Week’s Plans Done for You?

If you’re nodding along and thinking, “Yes! But how do I pull all that together in time?”—I get it. That’s exactly why I created my new mini course, Launching a Week of Math. Having been a classroom teacher in the trenches–I know how CRAZY stressful the beginning of the school year is, and I thought about what I could do to help out my fellow teachers–and after tons of work, this is what I built!

This short, low-cost, on-demand minicourse is packed with the exact lessons, routines, and materials I used in my own classroom to start the year with confidence. It includes:

✅ Video guidance and real examples (it’s like PD on demand–but in short, meaningful bits)
✅ A full week of flexible, printable plans
✅ Downloadable tools and templates  (like everything you need–from games to printables and more!)
✅ Routines you’ll use all year long

I designed it to be practical, realistic, and classroom-tested—something you can implement right away without stress. So if you want your first week of math literally DONE FOR YOU, check it out!

You can learn more about this “launching your year” minicourse and see if it might help you out.  Feel free to share with other teacher friends who might enjoy the stress relief too!

Final Thoughts

Starting your math year with intention doesn’t have to mean doing more—it just means doing the right things at the right time. By slowing down in those first few days, you’ll save yourself so much time and stress in the weeks to come.

Whether you build your own plan or want to borrow mine, I hope this reminds you that your math block deserves a strong start. And so do YOU!

Want to get even more ready for back to school?  This blog post is all about growth mindset ideas for back-to-school.  Or you can check out my Growth Mindset Toolkit for easy-to-use activities. This post is full of other great BTS ideas to inspire you!

The post Your First Week of Math Unpacked appeared first on The Teacher Studio.

What is project based learning?

Project-based learning (PBL) is a teaching method where students learn by working on real-world projects that are meaningful to them. Instead of just listening to the teacher, doing worksheets, or reading textbooks, students dive into interesting questions or problems, using what they learn from different subjects to find solutions.

As a part of this, they collaborate with classmates, think critically, and get creative.  All this happens while their teacher (that’s us!) guides and supports them. PBL makes learning fun and practical, helping students understand how their education applies to real life and preparing them for future challenges.

Why use project based learning in math?

So often, we teachers are struggling to fit in our content.  We have crazy pacing guides that steer our planning as we push students from unit to unit and standard to standard.

Where PBL activities come into play is that we can take all those important standards (and they ALL seem important, right?) and ask students to combine them in meaningful ways.  Here’s what I mean.  When we teach addition with regrouping–that’s what we practice.  Students develop fluency and can master it.  The same goes with fractions.  With measurement.  You get the picture.

What we REALLY want is for students to be able to take all the math we have taught them and know WHEN and HOW to use it.  We want them to think about the problem facing them and draw upon their math experiences to get a plan, try the plan, and modify the plan if needed.

If we don’t ever ask students to APPLY the math they are taught, we take away the thinking. If they only multiply when we tell them to multiply, they don’t learn how to USE math. Project-based learning activities can help give them those opportunities with fun topics that relate to their real world!

Benefits of PBL in Math

PBL can be a very effective way to teach math. Here are some of the benefits of using PBL in math:

• Engages students and keeps them motivated. PBL projects are typically more engaging than traditional math lessons. This is because they allow students to work on real-world problems that they are interested in. When students are engaged, they are more likely to be motivated to learn. My students LOVE doing real-world, meaningful math.

• Helps students develop critical thinking and problem solving skills. As mentioned earlier, PBL projects require students to use their critical thinking and problem solving skills to solve problems. This type of learning can help students develop these skills in a meaningful way.
• Promotes collaboration and teamwork. PBL projects are ideal for cooperative work!  The math talk and dialogue about strategies make the math even more powerful.

• Encourages creativity and innovation. PBL projects often require students to be creative and innovative in their solutions and strategies.  Because so many of them have multiple entrance points and lots of ways to tackle the problem–there is no “one way”!
• Helps students see the relevance of math in the real world. PBL projects often involve real-world problems that students can relate to. This type of learning can help students see the relevance of math in the real world. (From sleepovers to bake sales to planning parties to amusement parks?  Engagement soars!)

How to implement project based learning in math

• Start with a clear goal or objective. What do you want students to learn?  This could be specific skills (such as subtraction with regrouping) or could relate to math practice standards such as perseverance, using models, and so on.
• Break the project down into smaller tasks. This will make it easier for students to manage. This is a GREAT way to differentiate.  Different students will need differing levels of support and structure.  I love that I can use the same task with my class and just scaffold more when needed!
• Provide students with resources and support. They may need help finding information, solving problems, and working with others. You may even want to make sure tools such as calculators, grid paper, or manipulatives are easily accessible so students can grab them when needed.
• Be flexible. Things don’t always go according to plan, so be prepared to adjust the project as needed. I’ve had to stop the class when I see things going poorly, bring them back together to give some clarifying information or instruction, then send them back to work.
• Celebrate students’ successes. This will help them stay motivated and engaged. I love to share great work!  We do gallery walks, showcase work under the document camera, and give compliments to classmates who have found great strategies.  It’s so empowering for students to be recognized for more than just getting correct answers!

Are you convinced yet?

PBL is a valuable teaching method that can be used to teach math. If you are looking for a way to engage students, develop their critical thinking and problem solving skills, and help them see the relevance of math in the real world, then PBL is a great option.

Want to read another great post about problem solving?

Interested in some of the tasks I use?  Click the images below to learn more about them.

The post How Project Based Learning Can Help Students Love Math appeared first on The Teacher Studio.

I know many teachers stress out about the noise, the supply management, the storage, and so on.  There is no doubt that you need to teach students HOW and WHY we play math games explicitly.  Once you establish the culture and climate, you can reap the rewards!

5 Benefits of Math Games

1. Increased motivation.

Games can be a fun and engaging way to learn math, which can help to increase student motivation. Studies have shown that students who play math games are more likely to be engaged in the learning process and persist in facing challenges.  If you set the stage, game time is certainly motivating for students!

2. Improved understanding.

Games can help students to develop a deeper understanding of mathematical concepts by providing them with opportunities to practice and apply what they are learning in a fun and interactive way. Games can also help students to develop problem-solving skills and to learn to think strategically.  We push students to do SO much with pencil and paper.  Games are a completely different way to get fluency work and practice.

3. Enhanced collaboration.

Games can help to promote collaboration among students by requiring them to work together to achieve a common goal. This can help students to develop communication and teamwork skills, as well as to learn to appreciate the perspectives of others. Sportsmanship and fair play are super valuable life skills as well. I know in my classroom, some students struggle with this more unstructured time and need coaching, but it is SO important for them to learn to work together.

4. Differentiated instruction.

Games can be a great way to differentiate instruction for students of all levels. For example, you can provide students with different levels of challenge or allow them to choose the games that they want to play. This can help to ensure that all students are engaged and learning at their own level. Games are also amazing to use during math intervention time.

5. Fun!

Games are simply fun! When students are having fun, they are more likely to be engaged in the learning process and to retain what they are learning. So, don’t be afraid to incorporate games into your math lessons!

Math Games for Back to School

Block Out Addition Game

This game is PERFECT for refining basic addition facts (two versions are included, facts through 10 and facts through 20).  Students need to make different combinations and it gets them thinking in so many ways.  Even my top students love this game! I introduce it for back-to-school, but my students revisit it all year.

Back to School “Times” (It’s even a FREEBIE!)

Perfect for building multiplication fact fluency–and great back-to-school theme!  Super easy to teach and just needs dice and counters.  Did I mention that it’s free?

Double Trouble Game

Do you have students who still need work on doubling and halving? This is SUCH a critical skill, so the beginning of the school year is a great time to tackle it!

Fall Into Factors Game

More work with multiplication facts in a way that encourages students to look for patterns and common factors.  It comes in two versions for differentiation!

All of these games can be found in my math game bundle at a huge discount!

Thanks for stopping by!  Check out even more math game posts here and here.

Want Your First Week of Math Plans Done for You?

If you’re getting ready for back to school and want to make some changes in your math teaching but think, “Yes! But how do I pull all that together in time?”—I get it. That’s exactly why I created my new mini course, Launching a Week of Math. Having been a classroom teacher in the trenches–I know how CRAZY stressful the beginning of the school year is, and I thought about what I could do to help out my fellow teachers–and after tons of work, this is what I built!

This short, low-cost, on-demand minicourse is packed with the exact lessons, routines, and materials I used in my own classroom to start the year with confidence. It includes:

✅ Video guidance and real examples (it’s like PD on demand–but in short, meaningful bits)
✅ A full week of flexible, printable plans
✅ Downloadable tools and templates  (like everything you need–from games to printables and more!)
✅ Routines you’ll use all year long

I designed it to be practical, realistic, and classroom-tested—something you can implement right away without stress. So if you want your first week of math literally DONE FOR YOU, check it out!

The post 5 Effective Math Games for Back to School appeared first on The Teacher Studio.

Over the years, I’ve figured out that students get most engaged in a few different situations:

• When the topics are “cool” and interesting
• Get this–when they know that it’s ok to NOT get the right answer
• When they can work collaboratively
• If the math ties to something current (holiday, current topic of study)
• When there are logical stopping points along the way where they feel accomplished

Understanding Low Floor, High Ceiling Tasks

So what am I talking about with these big, open-ended tasks?

Low floor, high ceiling tasks are math activities that are easy for all students to tackle but can be extended to challenge even the most advanced learners. In other words, the task allows all students to get started, but then has more challenge that unfolds. These tasks allow for differentiation within the same classroom, making math both inclusive and challenging. They are particularly effective in developing flexible problem-solving skills and let all students feel successful.

As students get to the early intermediate grades, finding “real world” open-ended tasks can keep students super engaged as they explore different problem solving strategies. That’s what I want to talk about more today!

The Importance of Scaffolded Learning with Math Tasks

Scaffolding is a teaching strategy that involves providing support to students as they learn new concepts. Teachers can gradually remove this support as students become more proficient. In the context of low floor, high ceiling tasks, scaffolding can help ensure that all students can engage with the task at their own level. Techniques such as guided questioning, step-by-step instructions, “chunking” problems into sections, and visual aids are great ways to make these amazing problems more accessible to all students.

Other ways to scaffold involve providing “tools” such as manipulatives and calculators to help free students’ brains to tackle the problem solving while getting a quick “assist” on the math.  Similarly, breaking larger tasks into smaller, manageable chunks is another great way to scaffold challenging math tasks.  Once students have a grasp on the first part of the task, you can gradually unfold the task part by part as students are ready.

So often, teachers reserve this kind of rigorous, high quality task for more advanced students.  ALL students deserve access to quality math problems!  We just need to use these techniques to make the problems accessible. Sometimes it’s a matter of changing numbers to make a “Level A” and “Level B” option.  Sometimes we can get our more struggling students started as a small group and then send them off to work.  At other times, strategic pairing makes all the difference.  No matter how we differentiate, we must make sure to give great problem solving tasks to ALL our students.

Productive Challenge

I love to use these more complex, open-ended tasks.  That being said, many of my students begin the year as very beginning-level problem solvers.  Giving them a task that is TOO challenging simply pushes them to shut down completely.  I’m a huge fan of productive struggle, but shutting down completely is NOT productive.  For me, finding the “sweet spot” is part of the art of teaching.

I learned that for some students (and for all at the beginning of the year), I need to break these great tasks up into smaller, manageable pieces.  Later in the year I can give more open-ended tasks, but I start with that scaffold.  Notice that the “scenario” is presented at the top with all that students need to know.  What I do next is divide the problem into three tasks.  I then split the math into those three sections so students do one part at a time.

Check the photo below to see what I mean!

When Do I Use These Math Tasks?

Like I mentioned above, I use these more “scaffolded” tasks earlier in the year to explicitly teach open-ended problem solving.  As the year unfolds, I mix these scaffolded problems in with other that are more sophisticated. Gradual release isn’t just appropriate for a single lesson–but for how our year unfolds as well!  Along that line, as my students develop their problem solving skills, I back off on how much I introduce the tasks, how much I read to them, how much coaching I do, and so on.

I love to use these tasks:

• Between units
• When I have subs
• When the topic matches the season or our curriculum (before our zoo trip this year, my students were SO into the zoo task pictured below!)
• For cooperative work practice
• In centers
• For fast finishers

Powerful Math Lessons

Low floor, high ceiling tasks, combined with scaffolded learning, offer a powerful approach to teaching math. These tasks not only make math accessible to all students but also provide the challenge needed to develop strong problem-solving skills. As teachers, experimenting with different tasks and strategies will help find what works best for your students.

By fostering an environment where every student can succeed and be challenged, teachers can help develop a love for math and a growth mindset in their students. This approach not only supports the development of essential math skills but also encourages lifelong learning and curiosity.

Check out some of these great tasks below!

This first collection is my most scaffolded set–the math needed to solve these is very “third grade”, but the tasks are really broken into manageable chunks. I love that they have a seasonal “flair” but all can certainly be done at any point in the year.

This set is a little more complex.  The math is a little more advanced (better for fourth and up), and the tasks are more “open”.  Students are presented with a situation and they need to figure out how to break it into steps.  There are multiple entry points, but students need to be a bit more independent.  These tasks are perfect for single class periods and can be great supplements to your curriculum.

This final set of tasks is perfect for a little more extended problem solving.  They are differentiated so students can work at different levels, and there are tons of extensions so you can have them extend over several days if you want!

I hope this post has motivated you to incorporate some of these tasks into YOUR math plans!  Want to try one for free?  GRAB THE MATH TASK HERE!

Do you follow me on social media yet?  I’d love to connect there!

The post Scaffolded Low Floor, High Ceiling Math Tasks appeared first on The Teacher Studio.

Instructional routines are specific, repeatable activities or tasks that support both the teacher and students in the classroom. They give all students the opportunity to engage more fully in learning opportunities while building crucial mathematical thinking habits. (Kelemanik, Lucenta, & Creighton, 2016).

A well-designed instructional routine in math opens up math dialogue and deep thinking about mathematics that might not happen without these structures in place. (McCallum & Nowak, 2018). Math warm up activities are a great way to accomplish this!

The benefits of spiral math review tasks

When we think about “traditional” math instruction that simply moves chapter by chapter, topic by topic. The challenges of this more traditional math instruction include:

• • Students often struggle to understand new concepts if they aren’t linked to previous learning.
  • They may forget what they have learned in previous units.
  • They may become discouraged and frustrated as the material gets more and more challenging.

Instead, giving students a math routine at the beginning of each class that is familiar in format and has a spiral math review component can be so powerful.  When planning MY warm up tasks, I want to make sure I don’t have to waste time explaining the procedures, so I stick to a few tried-and-true tasks.  The students know what to do and can focus on the content and the math talk!  I’ll give you just a few examples.

Spiral Math Review Ideas

First, check out the perks of THIS type of problem. Students learn to focus on the directions.  In this case–HOW MANY.  One solution is just the beginning!  You can also see that there are no WRONG answers, just tons of practice multiplying.  The power comes in the discussion of strategies and how students made their decision.  I love these tasks because all students have access to the math.  Some students may only find a few solutions while other find many and can even work to organize their thinking.

This is a similar task.  My students learn to look for the words “write a list” and know what that means.  Again, the discussion of strategies is key.

One of my students’ FAVORITE math routines is “Which one doesn’t belong?”.  I use one of these every few weeks and we have the BEST discussions.  These are great for working on academic vocabulary which can easily fade over time if you don’t spiral your review.  From geometry to decimals–we use this format all the time, and as soon as my students see that rainbow circle, they know what to expect. Again, one answer won’t do it–and the explanation is key.

I’ll show you one more–although we do a number of other problem types as well.  Look at the math thinking.  Look at the math vocabulary.

Why use daily math warm-ups?

Daily math warm-ups can help students develop fluency and automaticity.

Fluency is the ability to perform a task quickly and accurately without much thought. Automaticity is the ability to do something without having to consciously think about it. Both fluency and automaticity are important for math success, as they allow students to focus on the more challenging aspects of a problem.

Daily math warm-ups can help students build conceptual understanding.

Conceptual understanding is the ability to understand the underlying principles behind a mathematical concept. This is important for math success, as it allows students to generalize their knowledge to new situations.

Daily math warm-ups can help students develop problem-solving skills.

Problem-solving skills are essential for success in math and in life. Daily math warm-ups can help students develop these skills by providing them with opportunities to practice solving problems in a variety of contexts. Remember, problem solving does not necessarily mean word problems (although it might!).  Problem solving simply means that students need to think, choose strategies, and make sense of a math situation, not merely compute.

Daily math warm-ups can help students develop positive attitudes toward math.

When students are successful in math, they are more likely to develop positive attitudes toward it. Daily math warm-ups can help students be successful by providing them with opportunities to practice and improve their skills. When you “spiral” your math review, it provides multiple teaching opportunities AND multiple opportunities to notice when students struggle.  This is a window into their understanding and a chance for you to coach.

What else?

• These tasks get students’ brains ready for learning. Just like athletes warm up their bodies before a workout, students can warm up their brains before a math lesson. This can help them focus and be more attentive.
• They review previously learned material. Daily math warm-ups can be a great way to review previously learned material. This can help students solidify their understanding of concepts and skills.
• Daily tasks help teachers identify areas of weakness. If students struggle with a particular math concept or skill, daily math warm-ups can help them identify this early on. This allows teachers to provide targeted instruction and support.

A few more tips!

• Make math warm ups short and engaging. Students should be able to complete the warm-up in 5-10 minutes.
• Vary the types of activities. Use a variety of activities to keep students engaged, such as problems, puzzles, games, and challenges.
• Make them relevant to your standards. The warm-up should be related to the concepts that students are currently learning or provide key practice opportunities for previously taught topics.
• Use a variety of levels of difficulty. This is a great opportunity for students to work collaboratively and to share ideas and thinking.
• Provide feedback. Give students feedback on their work so they can learn from their mistakes and improve their skills.

Overall, there is a lot of research to support the use of daily math warm-ups. They can be a valuable tool for helping students develop fluency, automaticity, conceptual understanding, problem-solving skills, and positive attitudes toward math.

Give it a try!

So dig through your curriculum and get creative!  See how you can help your students build these daily routines.  Of course, if you are busy and want some help, I’ve got you covered!

See below for yearly bundles (individual sets available too!) of warm ups for grades 3, 4, and 5–totally standards-based and ready to use.  They can be printed or used digitally…whatever works.  The work is done and you can just get started!  See what you think.

SHOP FOR READY-TO-USE WARM UPS BELOW!

3rd GRADE WARM UPS

4th GRADE WARM UPS

5th GRADE WARM UPS

Do you follow me on social media yet?  I’d love to connect there!

Facebook

TikTok

Instagram

Youtube

Or sign up for my email list RIGHT HERE for freebies, teaching tips, and more!

The post Daily Math Warm-Ups: A Powerful Way to Start Math Class appeared first on The Teacher Studio.

Over time, it has evolved and grown and gotten more components to help teachers teach fractions.  It’s truly my “baby” and has helped LITERALLY thousands of teachers improve their instruction.  It’s like lessons and professional development all in one.  From “in the trenches” photos to teaching tips to helpful hints, it’s a great tool to use either on its own or as a supplement to a textbook or other resource.

How is this different from fraction lessons in a textbook?

I’m so glad you asked! I am on a quest to help teachers really learn WHY fractions are challenging to teach–and to help them develop strategies.  I have a TON of blog posts, but I want to draw your attention to one short series in case you are interested.  You can click the links below to learn more.  Again, teaching fractions is a HUGE part of what we do in grades 3-5, but many of us haven’t been given the professional development needed to do so effectively.  Let me help!

1.  What makes fractions so difficult?
2. Teaching fractions with a gradual release model
3.  A balanced approach to teaching fractions

The goal of my fraction unit is to build deep understanding by having students USE and explore fractions, not merely learn how to compute with fractions. I want students to:

• Play and model with fractions
• Talk about fractions in increasingly sophisticated ways
• Use deep reasoning to talk and write about fraction concepts
• Explain their thinking using clear math language
• Critique the thinking of others and defend their reasoning
• Look for patterns and connections
• Find and explore real-world examples of fractions
• And so much more!

Fraction Unit Updates

Although the content hasn’t really changed over the years, I’ve continued to add features, explanations, and tools to help teachers.  The latest?  A more detailed table of contents complete with learning targets to help your planning.

In the unit, I include a NUMBER of different tools to help you get students talking about fractions and using quality math discourse.  The unit weaves this into individual lessons with modeling and ideas. I also included additional tools to help you really get them talking!

This includes help making sure you tackle the Standards for Mathematical Practice which are completely woven into the lessons in this unit.

Fraction Lessons:  The Progression

One thing I wanted to do is to help teachers see how these lessons unfold.  Again, many teachers use this unit as a supplement to the fraction work they already do because they don’t feel it’s rigorous enough.  This table of contents can help you tie these lessons to the other resources you have.

You can even print this document out, take notes on it, and use it as a great planning tool!  You will notice a great deal of repetition as the lessons work to build on previous work to deepen understanding.

Want to learn more?

I’d love for you to check it out!  Just click the image below or RIGHT HERE.  Check out the preview I’ve included–it really gives a good feeling for exactly what you get!  Want even more fraction resources?  Make sure to check out my fraction BUNDLE which includes the unit plus a ton of other powerful fraction resources and tools!

Want some great fraction freebies?  I’d love to send you some! Just CLICK HERE or the image below to get signed up!

The post Fraction Unit Update appeared first on The Teacher Studio.

If you come to my class on Tuesday, it will definitely look very different than it did on Monday. I love that–and my students do too. They never know what to expect in terms of how lessons will be delivered–and it keeps everyone on their toes. Of course, certain things are set in stone–and expectations are crystal clear. Work quality, math talk, behavior–all are extremely clear to students.

Another thing that DOES remain constant is starting off each day with a powerful, daily math warm-up.

What varies is how I approach that powerful math warm-up!  Check out some ideas before on how I keep things fresh and keep my students engaged in this worthwhile math task.  Remember, the first chunk of math class is valuable real estate!  Don’t waste your students’ best thinking time with mundane tasks, correcting homework, or procedures.  Get them thinking right away!

We know that elementary students have a limited attention span; let’s use that information to switch activities several times during a math class–and starting with a great warm-up is a good way to get the ball rolling!

Remember, these warm-ups are meant to last 5-10 minutes, so the process is quick–but powerful.

Daily Math Warm-Ups: Project and discuss

One way to incorporate math warm-ups with VERY little prep time is to pull up the slide and project one.  In fact, some weeks I go in, make a copy of each slide I want to use, and paste it into my weekly slide show.  That way I get all 5 warm-ups ready at once and there is no thinking or materials.

This is a great way to dig into math talk right away.  What I typically do is present the problem for a minute or two where I allow NO talking.  I want the students to have “think time”.  Then, I may read the problem aloud and give a little more think time.

After that, I invite the students to partner up, use notebooks or white boards if the problem requires it, do some work together, and then be ready to share out with the group.

I love having these large group discussions–but after they have had time to dig in.  Depending on the warm-up problem type, I might ask questions like:

• What was challenging?
• How did you get started?
• Did you make any mistakes?  How did you fix them?
• Does this problem have one answer or more than one?  How do you know?
• What math skills did you need to be successful?
• Did you and your partner have similar or different strategies?

Or send them digitally!

In addition to projecting these warm-ups, remember that you can always send them to students digitally!  They can either work independently or in partners, can either write on the slides or just discuss and solve and prepare to come back as a large group to discuss.  By varying your “delivery” method, you keep the ROUTINE, but keep things fresh!

Print them off and put them in a spiral

Another way I use math warm-ups is to physically print them off and have students glue them into their math spirals.  This allows students to interact more with the problems, write directly on the task, and then work to solve.  This is especially helpful for geometry problems and number lines.

Otherwise, the process is the same!  I give them some alone work time.  After that, I ask them to share in partners or small groups.  Finally, we have a quick class discussion about the problem, the solutions, and the strategies.

Extend the Math

A third way I sometimes build up deeper understanding with these warm-ups is to take a problem from one day, revisit it the next, and have my students try to write similar problems.

This is a great way to have them apply the math in new ways!  After they write their new problem, they can work in partners to solve each other’s tasks, and compare answers.  We then come back together as a group to talk about how it went!  Sometimes we’ll share a few sample problems under the document camera to showcase how some students tackled the challenge.

Modeling Math Organization

As the year unfolds, I continue to stress math talk and math organization with my students.  Taking time some days to share student work samples that show different ways to organize work can be so powerful!

At the beginning of the year, we make an anchor chart with suggestions about how to keep our math work organized and neat.  Being able to see “real” examples of this being done is super motivating for students and helps them see the target you are reaching for.  What makes this so powerful is that many students who might struggle with actual math can work to make gains in this area and can become known for that–super motivating and helps build confidence!

Using Your Daily Math Warm-Ups for Assessment

When a math warm-up or any problem is challenging, coming back to revisit it at a later time can be so powerful.  In fact, using problem types that you have previously explored can be a great assessment tool!  You can grab a previously used problem or, because I have a number of similar problems, use a novel one.

For example, if you spend some time exploring number lines as warm-ups, it certainly seems reasonable to use one of the number line warm-ups a few weeks later as an assessment to see how that exploration went.  It can help guide you as to how much more explicit teaching needs to be done.

The same is true for many of the different problem “types”.  Use a few here and there to take the temperature of the class and assess how everyone is doing with some of the different concepts.

I hope some of these tips help you find ways to use math warm-ups in new and powerful ways!

Want to check out the daily math warm-ups I use?  I have them for grades 3, 4, and 5!  Just click the images below to see more!

[one-third-first][/one-third-first]
[one-third][/one-third]
[one-third][/one-third]

The post Daily Math Warm-Ups: Tips to Keep Them Fresh! appeared first on The Teacher Studio.

Many teachers start the year working on place value concepts, but it’s truly a topic that we cycle through all year long in increasing sophistication!  Remember, place value is a complex topic that develops as a progression from the very first days in school (or earlier!) to much more advanced mathematics.  Check out this list and see how critical this concept is! If there is a break down at any stage, we run the risk of creating gaps for future learning.

Place Value Progression

1. In the early grades, a huge focus is on the idea that we can build numbers up to 10, and then “add more” to make bigger numbers.
2. Students then begin to see how addition and subtraction work together to make (compose) and break (decompose) these numbers into parts.
3. We see students using objects to “show” these stories.  Gradually, we want them to represent them with numbers and symbols.
4. As students develop a better understanding of our place value system, we want them to be flexible enough to add or subtract 10 from a number.  This shows a critical understanding of the ones and tens places.
5. Once students have developed this understanding, we introduce the hundreds place and go through these steps again with these larger numbers.
6. We also want students to learn about estimating and rounding so they can check work for reasonableness.
7. We want students to be able to represent numbers in different ways. This could involve manipulatives, number lines, or other models.
8. As students develop their place value understanding through the hundreds place, we continue to push the addition and subtraction concepts with these numbers.  Again, we stress the idea of composing and decomposing using these different places.
9. Eventually, we hope the solid place value understanding leads to addition and subtraction fluency.
10. As students get older, we expect understanding of “place value” for even larger numbers, and then “parts” of numbers with decimals and fractions.

Some Math Lesson Ideas and Motivation for You!

Want some inspiration for your own place value instruction?  Check out the following posts for more!

How about a post about looking for and coaching through place value misconceptions?  CLICK HERE or the image below!  

Estimation is a critical component of place value instruction.  Check out this post for details and strategies!  CLICK HERE or the image that follows.

Looking for some information about “structuring”–looking at composing and decomposing smaller numbers.  This is perfect for lower grades or for intervention work for intermediate students.  Click the image below or RIGHT HERE.

How about number lines?  This post is all about using number lines to help students model their thinking.  CLICK HERE or the image below!

Wait!  Want to read ANOTHER blog post about number lines?  This one might really get you thinking–and hopefully realize that we can be pushing our students so much more than we do.  Developing “number sense” with large numbers is so important!  CLICK HERE or the image below!

My blog has a ton of other posts for you as well–just search for what you need!  Thanks for stopping by…

Don’t forget that you can always search my Teachers Pay Teachers store for place value resources as well.  Click RIGHT HERE to get started! Click the image below to see my HUGE place value bundle!

Also, remember to follow me on INSTAGRAM and FACEBOOK for more ideas, deals and so on!  Click below to get started with my newsletter as well…teaching tips, freebies, and more.

The post Place Value: Everything You Need to Know! appeared first on The Teacher Studio.

Back five or six years ago, I was searching for an activity that I could have available in my classroom for students to do at a variety of times:

• If they finished work early.
• Or if I needed a math station.
• If I wanted students to work on a challenge so I could pull small groups

The problem I ran into was that my students just weren’t independent enough early on to read a lot of directions or do complicated problem-solving.  (Mind boggling, right?) I kept thinking, “What if I could create a challenge where the only math “skill” they needed was addition (most of my students come in with a decent foundation in this) but they had to APPLY it in more challenging ways.  I figured there would be bonus points if students could work together, have to persevere, use estimation, and so on.

And this is how “Mind Boggling Math” was born!  I like to keep it displayed in my room all year and change the numbers depending on the level of challenge (check out the bottom of the post for details).  Here is how my board looks currently–though I am considering reprinting the numbers in a new color to shake things up!

NEW!  Digital Components!  My original “Mind Boggling” resource now has all 10 challenges available digitally as well, ready for use with Google Classroom or other online sources!

The post Mind Boggling Math: Infusing the Standards for Mathematical Practice appeared first on The Teacher Studio.

Gradual Release of Responsibility Model for Word Problems

For those of you who are unfamiliar with the work of Fisher and Frey, I strongly encourage you to dig in.  The research is sound, and the methods are practical.  In a nutshell, the GRR involves a shifting of “cognitive work” from the teacher to the student.  It is not a linear process (a common misconception), but a cyclical, ongoing practice where the teacher provides explicit teaching first. After this, opportunities for questioning and prompting of students as they work in small groups help guide students toward deeper understanding.  Teachers can intervene as needed, return to the targeting lesson content, and then back away.  Finally, we want students to be able to do the work independently and apply their understanding to novel situations.  This is where problem solving and the standard “Makes sense of problems” comes into play.  It’s also where things often break down.

The Importance of Modeling our Think Alouds

When we hear “modeling” in math, we often think of modeling with objects. This, of course, is exceptionally valuable.  It may be super relevant with word problems as well if students need concrete objects to model the actions of the problem.  Where I think we sometimes drop the ball is with respect to modeling our thinking.  I think we DO this…but I think we sometimes don’t model the right thoughts.  Check out the difference between these two think alouds.  They aren’t dramatically different–but the second one does much more coaching about the “WHY”, not just the HOW.  See if you can tell what I mean.

“So first I added the $4.55 to $2.95 twice to get the total amount she spent on candy.”  (Tells HOW the teacher solved the problem.)

“I knew that there were three bags of candy that she wanted to buy.  One cost $4.55.  The other two bags cost $2.95 each.  I know I need to add that $2.95 two times to make sure I get all three bags of candy included in my total.” (Tells WHY the teacher solved the problem and HOW his/her thoughts were organized.)

The Importance of Students Sharing Their Thinking

So, in addition to us being truly mindful of how we share our thinking–which is, in essence, a form of coaching, we must also provide ways for students to share their thinking.  This is important for so many reasons.

• Students deepen their understanding when they talk about their work.
• Students can help others by explaining strategies in a new way.
• Misconceptions can be uncovered and redirected.
• The classroom is full of teachers.  The more people talking, the more learning is occurring.
• Research suggests that math class should be at least 60% discourse among students.
• It is far more efficient for students to be a part of a learning community where they work collaboratively than to have to wait for a teacher’s guidance.
• Students are more likely to be engaged when they are active participants.

Because of this, it is absolutely essential that we get students talking about math.  We need to model how to do it–then provide opportunities for practice.

Large group sharing

There are tons of ways for students to share in a large group setting.  Students can put work samples under a document camera and explain their thinking.  Students can simply raise their hands and share strategies.  When we do number talks, we can get all sorts of student thinking exposed to the entire class.  We can even do things like gallery walks where students can see work samples from lots of students.  There are pros and cons to any large group work, but this is certainly an important part of giving students practice sharing their ideas and listening to and learning from others.

Small group sharing

Sometimes we can get more students sharing–and more students listening–by using small groups.  Whether you help coach students on how to work in their desk groups or if you have students do a lot of work in partners, we can give explicit coaching on how to take turns, share ideas, ask for clarification, agree and disagree, and much more.  Providing displayed sentence starters for this “accountable talk” is super helpful.  By making this a part of every day’s math instruction, students learn to expect it and get better and better.

We, as teachers, can circulate as spies.  We listen for things to reinforce (“I love how Becca told WHY she multiplied because that makes sense to me.”) as well as intervening when misconceptions occur (“So is it possible to take 46 doughnuts and put them into 4 equal groups?  Can you prove that?”).  So often teachers forget how important our presence is during these small group sharing times.

One-on-one sharing

Sometimes it’s important to work one on one with a student to see exactly what they know and where understanding might be breaking down. Listening to students “think aloud” is a great way to intervene right at the point where meaning breaks down and to better see what tools students actually DO have in their toolbox.  Sometimes we wait too long to diagnosis when a quick one-on-one conference can shed some light into student thinking.

How I Teach Problem Solving with Word Problems

There are tons of problem solving acronyms out there that are supposed to make it easier for students to solve problems.  I have some concerns about acronyms (ex “CUBES”) that turn into cute anchor charts but aren’t explicitly taught.  I’ve often felt like many of these problem solving “strategies” don’t really do much in terms of really helping students make sense of problems.  They are short and to the point–and that has its merits, of course.  That being said, I want a tool that actually helps me teach students to be better problem solvers.  I don’t want my students to say, “Oh, I used CUBES to solve the problem.” I want them to be able to do SO MUCH problem solving that these steps because automatic.  Until that point, I need to teach and model and coach them through the steps.

It takes YEARS for students to become masterful problem solvers–and as they move up in years at school, the math content of the problems becomes more complex and these steps become all the more important.  So here’s what I do.  Like with the gradual release model, students need to understand that these steps aren’t necessarily linear; they are “recursive”.  This means they may need to revisit previous steps at different points–and that’s what good problem solvers do.

1. Read and reread
2. Visualize the situation
3. Find the question
4. Estimate a reasonable solution
5. Select a strategy to try first
6. Check your results 
7. Finish it off

It doesn’t make a very good acronym, does it?  It also isn’t super helpful for students–unless each of these steps is taught and retaught and modeled over and over. So I like to turn these steps into student-friendly language as a part of the process.  See what you think about this version–and my explanations to you about the steps and why they are so important.

Read and reread

becomes “What is this problem telling me?”  We want students to know that reading a math problem requires them to slow down and read carefully–and perhaps multiple times.  They need to be on a quest to discover what information the problem is telling them–and possibly find information that isn’t even relevant.

Visualize the situation

becomes “I can see the problem like a movie in my mind.”  Visualizing is a strategy frequently taught and practiced during reading instruction but is often overlooked in math.  When a problem says, “Michael put three pans of cookies in the oven.  Each pan has 12 cookies.”, students need to be able to “see” that so they know that we are talking about multiple groups of 12.  If the problem stated, “Michael had 12 cookies.  He put them into three boxes.”, we want students to “see” him sharing the cookies out into groups as a division problem.

So many math errors happen because students fail to choose the correct operation.  We teach students incorrectly to look for signal words like “total” instead of showing them how to visualize what is happening and to choose an operation to match. This is also essential for helping students to know if their answer is reasonable.  Sometimes I close my eyes after reading a problem and say things like, “I see a bowl of 100 jelly beans.  Try to imagine me taking out three handfuls of 20.  I know the amount in the bowl is getting smaller so my answer needs to be less than 100.”  You get my point.

Find the question

becomes “What is the problem asking me to find out?”  So often students fail to understand that many problems COULD have lots of questions asked about them.  Consider the following situation:

Marcus bikes to school and home again every day.  The trip is exactly 1.5 miles.  It takes him 10 minutes to bike each way. 

By presenting a problem such as this WITHOUT a question, we can ask students to generate a list of questions that COULD be asked with the information presented.  For example, this problem could generate questions such as…

• How many miles does Marcus bike each week?
• How many minutes does he spend biking each week?
• If school starts at 8:00, what time should he leave his house?
• How many miles does he bike each day?
• If his friend lives 0.4 miles closer to school, how much farther does Marcus bike than his friend each day?

You get my point.  The more we expose students to problems like this, they start to get creative with thinking about questions–and as a result, they become far more “clued in” to the actual questions being asked in problems they encounter.  I love hearing students say things like, “I was thinking the answer was ___ , but I knew that wasn’t the question is was asking.”  #forthewin

Estimate a reasonable solution

becomes “I know my answer should be about…”   I think this is pretty self-explanatory.  We want students to have an IDEA of what an answer should be.  Is the answer supposed to be bigger?  Smaller? Should it be bigger than my starting number?  Is it possible to put 4,288 cookies in the oven at once?  Does it make sense to order 634 pizzas for a party?  By helping model our thinking, students become better at catching errors that simply don’t make sense.

Select a strategy to try first

becomes “I am going to start by…”  We want students to have a bunch of tools in their toolbox.  They can start by drawing a picture.  Grabbing manipulatives.  Choosing an operation to try.  There are tons of strategies to use.  (By the way, CLICK HERE for a blog post with more ideas about this.)  Students need to have enough ideas to get started–and then to readjust if their first strategy didn’t work.  We can model this with our gradual release.  “I started to draw a picture of this problem and realized that the numbers were too big. I think I’m going to try repeated adding to see if that works.  Does anyone have any other starting strategies for me?”

Check your results

becomes “Did my answer make sense or do I need to make changes?”  You know elementary students.  Once they have written a paragraph, read a book, or solved a problem, they are FINISHED.  We need to coach them on going back to study their work to see if they really are done, if their answer is reasonable, or if they need to try a different approach.  Using think alouds as a teacher is key.  “I doubled checked the problem and my answer seems reasonable.  I know that if I had a pan of 24 brownies and I gave 1/3 away, that I will have less than 24 left.  My drawing shows the 24 brownies split into three groups and my labels show which brownies are mine, and which are given away.  I think I’m correct.”

Finish it off

becomes “Do I need labels, diagrams, or explanations to make my work complete?” This final step is one my students struggle with–but I think is key.  It has to do with precision and making work “professional”.  I want students to have their work organized–even if the process is messy along the way when they finish their answer should be clear as a bell.  I talk to students about ways to showcase their answer, perhaps by circling or boxing it.  Sometimes they may need to skip a line and rewrite it.  I also want them to get used to adding labels and drawings to help, and–when needed–explanations of what they did.  Before they say, “I’m DONE!”, I want them to make sure they are proud of what they did and that others can understand exactly what they did.

Problem Solving Anchor Chart

One thing to consider is to have a display…maybe an anchor chart or series of pictures to help students remember all these key steps.  This could be something super informal or something preprinted like the image below.  I would also recommend that each step of this process be explicitly taught, modeled, and practiced–using that Gradual Release method.  Finally, consider giving students a handout to keep as a reference–something they can refer to when they need support.  Shhhh…I may have something that can help!  See below.

A Problem Solving Freebie for You!

So I thought I’d put these strategies into a little freebie for you in case you wanted to try something new with your students!  Feel free to print off these problem solving “steps” and put them together like an anchor chart to be used as a reference tool.  There is also a one-page student sheet that can be given to students as a tool to help them when working through this process.  See what you think by clicking below!

More Word Problems to Help You!

I have never been satisfied with the word problems provided to me in textbook series, so I have always supplemented by writing my own. I thought I’d share some of my favorite resources here in case you are in need of some great problems too!  Just click any image below to learn more about these problem sets.

The first one listed is a bundle of four sets of high interest, content-based problems.  They are called “Amazing Facts” problems because they are meant to capture the attention of students and make them say “WHOA!  That’s SO cool!” The next set is perfect to use all year long when you want to use some seasonal problems–maybe as warm ups or to keep at math centers.

The next two are bundles of TONS of problems that I have written in three formats–clippable problems that can be glued into math spirals, pages with 4 problems on each, and pages with room for students to solve and explain their thinking.  Each bundle has 4 sets of problems on grade-appropriate topics.  These same problems are available in task card format as well. Topics range from multi-step problems to elapsed time to fractions and more!

Finally, I figured out a few years ago that students simply didn’t have enough strategies in their problem solving “tool box” to be successful.  I wanted to give them a foundation of tools such as draw a picture, make a list, and so on–so they always had a way to get a problem started.  Our textbooks simply didn’t do a good job of it, so I created these!  One is a print resource and the other is digital…if you are looking for some explicit problem solving instruction, these may be just what you are looking for.

Well, there you have it!  I hope you found something that might spark some ideas in your mind.  Problem-solving is such a critical skill, and our students need all the help we can give them!

NOTE: Several people have contacted me after this posted asking for good resources about the gradual release of responsibility model.  I highly recommend the work of Fisher and Frey.  One great book is linked below.  It is an affiliate link for Amazon, and it can get you started if you are interested in learning more!

The post Solving Word Problems…a Gradual Release Model appeared first on The Teacher Studio.