• We ask them to solve multi-step problems.
• We expect them to explain their reasoning.
• Finally, we want them to apply strategies flexibly and make sense of complex situations.

But what happens when the foundation isn’t solid?

What happens when students can multiply… but don’t really understand what multiplication represents?
When they can compute… but freeze when the unknown “moves”?
When they rely on keywords instead of relationships?

This is where Cognitively Guided Instruction (CGI) becomes more than an instructional approach. It becomes a powerful intervention tool.

CGI Isn’t Just for Primary Classrooms

CGI is often associated with K–2 classrooms, and that makes sense. The research behind CGI began by studying how young children naturally develop mathematical thinking.

But here’s the truth:

The benefits of CGI don’t “expire” in second grade.  In fact, they become even more important in grades 3–5 — especially when students are struggling.

At its core, CGI is about understanding problem structure and listening carefully to student thinking. It’s about using that thinking to guide next instructional steps.

And that kind of responsive teaching is exactly what intervention requires.

Why Upper Elementary Students Struggle With Word Problems

By the time students reach upper elementary, gaps become more visible.

You might notice students who:

• Automatically subtract whenever they see the word “left”

• Add numbers together because they see two numbers

• Struggle when the unknown isn’t at the end

• Can compute accurately but can’t explain why their answer makes sense

• Shut down when faced with multi-step problems

Often, the issue isn’t computation.

It’s structure.

Many students have learned procedures without deeply understanding how quantities relate to one another. They’ve practiced result-unknown problems (5 + 8 = ?) repeatedly, but haven’t had consistent exposure to change-unknown (5 + ? = 13) or start-unknown (? + 8 = 13) situations.

When those structures reappear in upper elementary — especially inside fraction problems or multi-step situations — the foundation cracks. And as you can imagine, this truly is the foundation of algebraic thinking in later years.

How CGI Becomes a Powerful Intervention Tool

When we use CGI principles in upper elementary, we shift from “reteaching steps” to rebuilding understanding.

1. Diagnose Thinking Before Correcting

Instead of modeling immediately, we give students a carefully structured problem and listen.

For example:

A class collected 248 cans. They collected 63 more cans on Friday. How many cans did they collect before Friday?

This is a start-unknown problem.

You might see students:

• Subtract 63 from 248

• Add 248 and 63

• Draw a diagram

• Write an equation with a missing number

Instead of correcting right away, ask:

• What does the 63 represent?

• What is missing in this situation?

• How could we represent what’s happening?

In just a few minutes, you learn far more about student understanding than you would from a worksheet score.

That’s powerful way to begin an intervention!

2. Rebuild Conceptual Foundations Through Structure

In upper elementary, intervention often focuses on more practice. More worksheets. More computation drills.

But CGI reminds us that struggling students don’t need more of the same structure — they need exposure to varied problem structures.

Even in grades 3–5, intentionally using:

• Start-unknown problems

• Compare problems

• Equal groups problems with different unknown positions

Strengthens:

• Algebraic thinking

• Understanding of operation relationships (and when to choose which operation!)

• Flexibility with equations

• Sense-making

When students analyze structure instead of chasing keywords, they begin to see the relationships between quantities. That is what supports success in multi-step and fraction problems later.

3. Elevate Strategy Discussion

Upper elementary standards demand explanation and justification.  We constantly ask students to “show what you know” or “explain your thinking”.  Do we do enough to give them the experiences and languages to actually do that? Do we model OUR own thinking and explanations?

CGI supports this naturally.

When students share different strategies — decomposing numbers, using compensation, modeling with a number line — we can:

• Compare methods

• Highlight efficient strategies (The goal is to gently nudge students toward more efficiency! We don’t want them to have to carry around pockets full of counters forever!)

• Connect strategies to properties of operations

• Make structure visible

• Even model our own strategies and language

Students aren’t just getting answers. They’re reasoning–and reasoning is what the standards expect.  It’s also where things break down for many of our students.

Intervention Isn’t About Lowering the Level

Sometimes intervention is mistaken for “simplifying” the math.  But strengthening understanding doesn’t mean lowering expectations.

It means strengthening the foundation so students can access grade-level work.

Grades 3–5 demand:

• Multi-step problem solving

• Algebraic reasoning

• Justification of strategies

• Deep understanding of operations and how/when to use them

CGI supports all of that because it centers on relationships, structure, and student thinking.

A Different Way to Think About Intervention

When students struggle in upper elementary, our first instinct may be to show them the steps again.  And again.  And maybe one more time.

But what if instead we slowed down and asked:

• What do you think is happening in this problem? (Or “What DO you know about this problem?)

• How are these quantities related? (“What do you think is happening? Can you visualize what is happening?”)

• What does your strategy show us? (“How can you get started with something?  Did it work?  What else can you try?”)

When we listen first, we teach better.

CGI isn’t about “dumbing down” instruction. It’s about making instruction responsive.

And in upper elementary classrooms — where reasoning, flexibility, and problem solving are essential — that shift can be transformative.

If you have students who are struggling with problem-solving and/or determining what operations to use, you may be interested in my CGI problem resources where I lay it all out for you–with smaller numbers so they can focus on the problem types.  CLICK HERE and see what you think!

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

The post CGI Math: A Problem Solving Intervention appeared first on The Teacher Studio.

On paper, everything looks right. The math skills are there. And yet… the answer doesn’t come. Or the student chooses the wrong operation. Or they give up before they even start.

When that happens, it’s tempting to think, They just need more practice.
But in my experience, that’s rarely the real issue.

The problem isn’t that students need more math.
It’s that they need better opportunities to think mathematically—and that’s exactly what quality word problems provide.

How Word Problems Often Get Pushed Aside

Let’s be honest: word problems are sometimes treated as “extras”, even if we know it’s a bad idea.

They show up:

• at the end of a lesson

• at the end of a unit

• during test prep

• or on Fridays, when we “have time”

And I understand why. Teaching math already feels like a race against the clock. Many math programs emphasize computation and pacing, leaving teachers to squeeze word problem activities and practice in wherever it fits. (And when it’s at the end of a lesson, it’s easy for teachers to skip it or leave it for only the fast finishers.  Eeek!)

The result?

Students don’t get regular, meaningful exposure to word problems—and when they do, the expectations feel high and the confidence feels low.

But here’s the thing: when word problems are optional or “sporadic”, students never really learn how to approach them.

What Quality Word Problem Activities Actually Teach

Strong word problems do far more than check for answers.

They teach students how to:

• make sense of a situation

• decide which math operations are needed

• connect numbers to meaning

• explain and defend their thinking

This is where real math understanding lives.

A page of computation might show whether a student can perform a skill.
A word problem shows whether they understand when and why to use that skill.

In fact, one well-designed word problem can reveal more about a student’s understanding than ten pages of traditional practice.

Why Students Struggle—and Why That Matters

When students struggle with word problems, it’s often interpreted as failure. I see it differently.

Word problems are challenging because they ask students to:

• process language (which we know is a struggle for many students)

• identify relevant information

• successfully choose an operation

• make sense of the answer

That struggle isn’t a sign that word problems aren’t working.
It’s a sign that they’re doing exactly what they’re supposed to do.

Word problems expose misconceptions.
They surface gaps in understanding.
They give teachers insight we’d never get from a worksheet alone.

Avoiding word problems doesn’t protect students—it delays the learning they actually need.

An Important (and Often Overlooked) Piece: Reading Level Matters

This is something I feel strongly about.

Math class should be challenging—but it should be challenging mathematically, not “linguistically”.

I can’t say this strongly enough. If a word problem is written at a reading level students can’t manage, their brains are doing double duty:

• decoding complex language

• and trying to reason mathematically

That’s a recipe for frustration.

Students shouldn’t have to work through dense vocabulary, long-winded sentences, or unnecessary language just to access the math. When reading becomes the barrier, we’re no longer assessing math thinking—we’re assessing reading stamina.

High-quality word problems:

• use clear, intentional grade-appropriate language

• remove unnecessary complexity

• allow students to focus their cognitive energy on the math

This is especially important for:

• multilingual learners

• students with reading challenges

• students who already feel anxious about math

Good word problems don’t water down the math—they remove distractions so students can actually engage with it.

What Happens When Students Get Regular Exposure to Good Word Problems

When word problems are used consistently—and thoughtfully—something shifts.

Students:

• talk more about math

• explain their thinking more clearly

• make better decisions about operations

• grow more confident as problem solvers

Math stops being about speed and starts being about sense-making.

And for teachers, word problems become less of a hurdle and more of a window into student thinking.

What to Look for in a Strong Word Problem

Not all word problems are created equal. When I design or choose them, I look for problems that:

• present a meaningful context

• require students to make decisions

• involve more than just plugging in numbers

• encourage explanation and reasoning

• are written at a reading level that students can manage

The goal isn’t to trick students. The goal is to help them think.

Making Word Problems Doable in Real Classrooms

I know time is tight. Planning is heavy. And no one needs more on their plate. (After more than 30 years in the classroom, I feel I’m pretty qualified to make that statement!)

The good news? You don’t need more word problems.
You need better ones.

When word problems are thoughtfully designed and ready to use, they don’t slow instruction down—they deepen it. They replace piles of practice with meaningful discussion and insight.

That’s why I’ve spent years creating word problem resources that are:

• intentional

• accessible

• rooted in real classroom experience

They’re designed to help teachers see how students think—and help students build confidence as problem solvers. If you want to check them out, you can visit my shop RIGHT HERE or visit my word problem collection on TpT.

The Takeaway

Word problems aren’t an add-on to math instruction.
They’re not something to squeeze in if there’s time.

They’re where math understanding shows up.

When students regularly engage with quality word problems—written with care, clarity, and purpose—they don’t just learn how to get answers.

They learn how to think.

If you are interested in a free problem solving strategy guide, I’ve got you!

Click HERE or the image below.

If you want to explore more word problems in my TpT store, CLICK HERE to see the many different options!

Do you follow me on social media yet? 

I’d love to connect there!

The post Why Word Problems Matter More Than Ever appeared first on The Teacher Studio.

Why a Back-to-School Math Task Might Matter More Than You Think

Instead of focusing solely on review, the first week of math instruction can set the tone for the entire year. It’s the perfect time to introduce the kind of thinking, collaboration, and perseverance you’ll expect from your students moving forward. That’s why I believe in starting the year with meaningful, fun math activities that go beyond rote computation.

Let me explain more about why your first math task should be more than just review—and how one powerful resource has helped ME launch math instruction with intention and engagement. By the way–if you aren’t ready to start thinking about back to school yet, just pin one of the images to revisit later!

Start Strong with Rich Math Tasks

A well-designed math task does more than practice skills. It encourages students to think critically, explore different strategies, and communicate their thinking clearly. Starting the year with a low-floor, high-ceiling challenge invites all students in—no matter their confidence level—and helps you observe how they reason, organize their work, and collaborate with peers.

And when those tasks are built around real-world problem solving? Even better. When that “real world” task is something that is meaningful to them?  Golden.  (No more “Johnny bought 24 watermelons…” problems because–no, indeed, Johnny did NOT!)

A Fun Back-to-School Math Task to Get Students Thinking

One of my favorite ways to kick off the math year is with the Open-Ended Teamwork Challenge: Back-to-School Shopping. This fun math project asks students to help “Mila” (named after a former student, I must admit!) shop for school clothes on a budget—choosing from different stores, weighing deals, and stretching her money as far as it will go.

Why do I love this math task so much? Because it…

• Combines addition, subtraction, and multi-step thinking in an authentic, MEANINGFUL context

• Encourages creativity, decision-making, and accountable math talk

• Is fully differentiated with multiple levels of challenge

• Allows for collaboration OR independent work (whole class, small group, partners, centers, you name it!)

• Includes extension tasks and discussion prompts that deepen thinking and takes all the prep concerns away for you

• Has a digital option, making it easy to assign to different groups

Students aren’t just solving math problems—they’re thinking like mathematicians. They analyze, justify, reflect, and adjust. This is the kind of math classroom culture I want to build from day one.  In fact, by starting the year with tasks that are differentiated, it helps build the culture for that as well!

More Than Math: Setting the Stage for a Growth Mindset

This activity also gives students permission to try, to revise, and to persist—without fear of making mistakes. That’s what makes it such a powerful tool for introducing growth mindset in math.

Some students will overspend. Others will forget an item. Some will go back and find better deals. And that’s exactly the kind of productive struggle we want to normalize. These aren’t just math lessons—they’re mindset lessons.  Is there a single right answer?  NO.  Is there more than one way to solve it?  YES!  What better way to start the year than to help students learn this!

Bring Math to Life Through Accountable Talk

If you’ve ever struggled to get students talking meaningfully about math, this is a great way to practice accountable math talk from the first days of school.  This isn’t something that should be a “unit” or minilesson.  It needs to become a way of “being” in your classroom. To help, this math task includes guiding prompts to encourage math discourse:

• How did you decide what to buy and where?

• What was tricky about this task?

• Was your solution the only possible one?

• What would you change next time?

These conversations not only build math understanding—they build classroom community.

Let’s Stop “Saving the Good Stuff”

Sometimes teachers wait to introduce rich problem-solving tasks until students have “learned the basics.” But here’s the thing: solving problems is how students learn the basics. It’s how they build number sense, logic, and confidence.

So this year, why not start with something meaningful?  To be honest, it may feel uncomfortable.  You may worry that you don’t know enough about your students as mathematicians yet.  I challenge you to think in a different way.  What could you LEARN about your students while doing a task like this?

Try It Yourself!

If you’re looking for a flexible, engaging, and standards-aligned math activity to launch your year, I highly recommend the Open-Ended Teamwork Challenge: Back-to-School Shopping. It’s more than just a math activity—it’s a way to build habits of mind that will serve your students all year long. Having a task like this is project based learning–especially when you get into the extension options I’ve included.

Let’s give our students a strong start—not just in content, but in mindset, collaboration, and a love for problem solving.  Don’t worry–there is PLENTY of time to work on the “basics”.  I promise.

Want to read more about growth mindset at the beginning of the year?

How about this post about some great back-to-school reading lessons?

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 Using a back-to-school math task along with your review? YES! appeared first on The Teacher Studio.

The good news is that the winter months are an opportunity to breathe new life into your classroom with creative, seasonal strategies. By incorporating winter themes and interactive activities, you can reenergize your students and spark excitement for learning.

In this post, I’m sharing a toolbox of ideas to help you keep your students motivated all winter long.

Incorporate Seasonal Themes into Lessons

One of the easiest ways to capture students’ attention is to connect learning to their environment. Winter-themed lessons add a little “fun” and relatablity to your usual routines and make learning feel more relevant.

Use winter-related topics in reading and writing assignments.

• Try a creative writing prompt like “Imagine you’re stuck in a snow globe—what happens next?” or “What would you do on a snow day?”.  If you live in an area where you don’t see snow, how about “If you could spend a day in a snowy place, what would you do?”
• Have students write persuasive essays on topics like “Should schools close for snow days?”.

Integrate seasonal math problems.

• Create word problems about building snowmen or calculating snowfall totals.  I have a ton of winter word problems to help you out if you are interested in having some ready to go!

• Use real-world math, such as budgeting for winter gear or calculating the area of an ice skating rink. I love using this set of winter math challenges to do just that.  From skating to snow days to baking cookies–these tasks are SUPER engaging for students.

Try This! Add a visual element by displaying student work with a winter-themed bulletin board—snowflakes, mittens, or snow globes make great backdrops. My students LOVE our snowman book report project, and others in the building love to stop by and check them out!

Implement Interactive Activities

Interactive, hands-on activities engage students’ minds and bodies, which is especially important during winter when energy levels can dip.

Organize classroom debates on winter topics.

• Let students discuss fun “what if” scenarios, like “What’s the best way to survive in the Arctic?”  These are great discussions to have as part of a classroom community circle or when you have just a few minutes in your schedule.  They could even turn into great “quick writes”!

Set up science experiments related to snow and ice.

• Conduct a simple experiment on the freezing and melting points of water.
• Have students make “fake snow” using household materials and observe its properties.
• Search for cool short videos that talk about the science of winter, from snow to hibernation, to the changes in seasons.  These are also great little transition breaks in your schedule!

Try This! Bring winter indoors by challenging students to create paper snowflakes and discuss the science of symmetry as they work.  There are some amazing websites that show detailed photos and videos of snowflakes.  My students are always wow’ed by them!

Incorporate Technology

Technology can bring fresh excitement to your lessons, especially when paired with seasonal themes.

Utilize educational apps with winter-themed games.

• Many math and language apps include seasonal updates or challenges—look for options that align with your curriculum.
• If you don’t have access to these, even creating your own digital “menus” can be a fun way to incorporate a little fun.  CLICK HERE to grab a free copy! (I even included a few other free winter activities for you!)

Create virtual field trips to explore polar regions.

• Visit places like Antarctica or Alaska to learn about extreme climates, animals, and geography.
• Use Google Earth to “travel” to snowy destinations around the world.
• Research temperature changes around the world–or compare your current location to the coldest on the planet!

Try This! End a virtual field trip with a student reflection—ask them to write or draw their favorite part of the experience.

Foster a Cozy Classroom Environment

Your classroom environment plays a big role in student motivation. A warm, inviting space can make all the difference during the cold months.

Fill your classroom with winter themes.

• Add simple touches like string lights, snowflake cutouts, or a cozy winter banner.
• “Book talk” books from your classroom library (or school library) that have a winter theme and challenge students to read a certain amount.
• Use winter words when making groups.  The “snowmen”, “icicles”, and “frosties” is more fun than “red”, “yellow”, and “blue”!
• Have a reading afternoon where students bring in blankets or stuffies and put a fake fire on your smart board and ENJOY!

Try This! Pair a cozy reading corner with a winter-themed book list and winter bookmarks to inspire students during independent reading time.

What else can help with student engagement in winter?

Keeping students motivated during winter doesn’t have to be a challenge. With seasonal themes, interactive activities, and a cozy classroom environment, you can create engaging experiences that capture their interest and keep them excited about learning.

Ready to take these ideas to the next level? Download my Winter Bundle—it’s filled with everything you need for a low-prep, highly-engaging winter season!  I love to sprinkle these activities in for the entire winter to keep things fun while the weather is miserable here in Wisconsin!

Don’t miss THIS POST for more ideas on student engagement in winter–through rebuilding classroom routines!

The post Student Engagement in Winter: Motivating Learners in Upper Elementary 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.

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

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

Here’s what I mean.

We know students have been solving problems since kindergarten (we hope!), but often in the primary grades, we don’t showcase different strategies and help students learn to recognize different word problem types and the strategies that can be useful in tackling them.  Here’s where a boot camp can come in handy!

Most students have been exposed to strategies for solving word problems such as “draw a picture” or “make a table”.  (Sidenote:  Not ALL students have, so do some digging to see what background YOUR students really have!)

Unfortunately, these lessons may have been sprinkled in here and there over the years and rarely revisited.  What can solidify these strategies in students’ minds is to really study them, first one strategy at a time and then later in a more “mixed” setting.  When students do an in-depth study of the different problem types, practice the strategy, and then later have to apply those strategies on their own, we have a perfect example of how a gradual release model can make a huge impact.

Getting Started With Problem Solving Strategies

So here’s what I do!  First, decide which strategies are important for you to explore.  Here’s a list to get you started!

• Make a list
• Guess and check
• Use objects to model
• Make a table
• Find a pattern
• Work backward
• Draw a picture

Now, these strategies are all useful in different types of problems, so we need students to understand how and when they are effective.  We also want students to recognize that there is no “right” strategy.  If students have a full “toolbox” of strategies to try, they have a much better chance of selecting a good starting point for their problem.

Some of these strategies are more sophisticated than others as well.  Let’s look at two: “Use objects to model” and “Draw a picture”.

Helping Push Students to Think Deeply

One of the most useful strategies we can teach is to “use objects to model”.  We begin this when children are very young. When we use real objects (ex. crackers) to model a problem such as, “Benny has 3 crackers.  His teacher gave him 2 more. How many does he have now?”, students can “see” the problem.  They can see the “joining” action.  We gradually move student to realize that objects such as unifix cubes can represent objects like crackers.  This is still modeling and is a very tangible, concrete way for students to solve problems.

Unfortunately, we often move past this modeling as students get older and the numbers get larger.  Students in upper elementary see using objects as “babyish” instead of a useful tool that can help them get unstuck! Having manipulatives handy and modeling their use can be exceptionally beneficial.

Now, do we want students having to pull out a bag of plastic cubes forever?  Absolutely not.  One strategy to start to move them past the concrete objects is the “Draw a picture” strategy which is one level more abstract.  Instead of having crackers or cubes to represent the problem, students can learn to make tallies or other marks to represent the problem.  This becomes exceptionally useful as the problems get more advanced.  Check out this problem geared for third and fourth graders.

Think about how using objects (scraps of paper, plastic cubes, etc) could help a student model exactly what the problem is asking.  Now check out this one!

Do you see how a drawing would be an excellent way for students to “show” the action of the word problem.  This is certainly not a problem that can be done effectively in one’s mind, and the numbers in the problem are only a part of the story.  Using problems like these to show students the strategies helps students understand the value of adding them to their own problem solving toolbox to access for ANY type of problem they encounter through the years.

Modeling Our Thinking

So let’s chat about modeling.  So often we skip this step entirely or don’t dedicate enough time to it. Whether you are working with your entire class or small groups, modeling different problem solving strategies and tools (like manipulatives) is key.  In a boot camp like this, you will want to make sure to take your students through each and every strategy you want to teach and go through the gradual release.  Model your thinking, have them work together, and then try it on their own.  This may take several days–especially if the strategy is new.

If you are working with a large group, consider projecting problems onto your Smartboard or device and walk through the steps you use to make sense of the problem and dig in.  Use a document camera and show the same thing.  No technology?  Print a copy of the problem out nice and big and bring the students close to watch you think, talk, and solve.  The key here is to let them in on the secrets!

• Let the students know what you notice when you read the problem.
• Show them confusing parts.
• Wonder aloud about what strategies might be useful.
• Ask them for their input.
• Showcase how you keep track of your work and organize it.
• Reflect on your answer and whether or not it seems reasonable.

All of these stages are intuitive to us as adults–but certainly are NOT to most elementary students.  The more they see it, the better chance they have of applying it to their own work.  This leads me to…

Students Solving Word Problems Together

The “we do together” step is such a powerful intermediary step.  After seeing a teacher model a strategy, letting partners or trios try it together gives the perfect blend of “I’ll try now!” and the support of peers.

Of course, it is essential to help students learn how to work together. (I talk about this a little more in THIS POST if you want some details.) Once you have established expectations, it’s great to take problems similar to what you have just modeled–whether working on drawing pictures or making tables or guessing and checking–and then have students work together to try some.

One tip I love to give is simple but SO powerful.  Before you let the partners work together, give them a few minutes of alone “think time”. This can help students who tend to be more reserved collect their thoughts and wrap their heads around the problem.  Without this wait time, some students tend to take over a partnership.  You know you’ve seen it!  This gives everyone a little chance to get their background–and gives you a few minutes to walk around, coach, get students started, or even “prime the pump” with students who you know are slow to get going or who may need a hint to get started.qx

Students Solving Word Problems Alone

Once students have had some practice with a specific strategy, feel free to send them off to try on their own.  If needed, bring a small group together for additional coaching and modeling.  Ideally, we want to get to a place where students can apply what they have learned in their “boot camp” to any problem they encounter.

I also think it’s important to find ways to work problem solving into every single math class.  Consider…

• A problem every day as a warm up
• Math centers with differentiated problems set up
• Partner problems
• Small group interventions or challenges for students needing differentiation
• Problems on a variety of topics and skills–not just what you are working on at the time.  This forces students to use those tools you taught them!

Need Some Help?

I know this can seem like a lot, so over the years I have worked to create a collection of problems that are perfect for this “Solving Word Problems Boot Camp”!  If you are interested in having problems that are geared toward each strategy listed above with enough problems to model, have partners work, and have some for independent work, check it out.  It even includes a collection of problems at the end where no strategy is identified so students need to reach into the toolbox and choose on their own!  The cards can be printed as task cards (color or black and white), projected, or even used digitally through Google Classroom.  CLICK HERE or the image below to check it out.

Want to read another post about teaching problem-solving?  This is a great one–and there’s even a freebie waiting for you!

The post Solving Word Problems: A Boot Camp! appeared first on The Teacher Studio.

Word problems are a key part of rigorous standards everywhere, but teachers and students alike often dread tackling them.  Even textbooks sometimes save them for the bottom few problems on a page or a separate lesson toward the end of a chapter.  The thing is–word problems (at least good ones!) are the “real world” part of math.  One type of word problems, comparison problems, can be particularly challenging for students.  Let’s look at some teaching tips that might make them more accessible!

Critical Reading of Math Problems

As educators, we should always be striving to help our students understand that the skills we are teaching are them are FOREVER…not just to complete a math page or worksheet.  One skill that we really want to make sure our students understand is the need to critically read math problems to figure out what is being asked, what information is given, and to make a plan for solving.  So often we do the thinking and hard work for our students.

For example, just consider how many of our math books are organized.  A lesson entitled “Solving Addition Stories” doesn’t leave much room for student thinking, does it?  It seems pretty clear what operation students will need to choose! Providing students with a constantly spiraling variety of problems forces them to think for themselves, learn to look for key information in problems, and make solution decisions accordingly.

One idea?  Use highlighters to find and notate important information.  Underline or circle the question.  One thing I do NOT recommend? Looking for key words like “fewer” or “total”.  These words may seem like a quick fix for students…but they can lead them down the wrong path.  How?  How about this problem…

“Larry has 14 baseball cards.  This is 25 fewer than his sister Kara has.  How many cards does Kara have?” 

By teaching “fewer” as a signal word that indicates subtraction, a student will certainly not think through this problem correctly!

Visualization and Modeling with Comparison Problems

One strategy that can really help students make sense of problems is to be able to visualize and draw models of different problem types.  Comparison problems–sometimes represented with “tape” or “strip” diagrams are a GREAT way to help students visualize the math!  I thought I’d share a few ways that these can be super helpful for students–whether used as whole class lessons or for intervention groups.

Using a blank “template” or outline of a tape diagram with manipulatives can really help students see the comparison that appears in a problem.  The photo below showcases a visual representation of the following problem:

Next Steps with Comparison Problems

As students get more adept at these problems, you might see that a sketch with only numbers placed in the diagram is appropriate.  Check out this lesson where we “filled” a diagram and then brainstormed a ton of different questions that could work with this problem.  Again, part of making sense of problems is realizing that the QUESTION matters..  Students need to learn to be detectives as they problem solve.  Finding the missing part is the first step!

Another strategy to get students really visualizing is to take a blank diagram and create different stories to go along with them.  This is a fantastic way to help students get flexible with their thinking.  I start with modeling some problems and then have students progress to writing and sharing their own.  It truly helps them understand the problems at a deeper level.

Hope you found this information valuable!  These problems don’t HAVE to be as challenging if we help students bridge the gap between the problem and a meaningful strategy to solve them!

Looking to try some of these on your own?

Click the image below to see more!

The post Comparison Problems with Tape Diagrams/Strip Diagrams appeared first on The Teacher Studio.

Gets students tackling problems that have more than one solution

So often we give students problems where there truly is one solution.  They get very accustomed to “filling in the box” and seeking the right answer rather than digging in and finding the complexity of the math.  Finding quality open-ended math tasks can help them see that math is far more intricate than merely finding a quick answer!

Helps students learn to make sense of a complex problem

Indeed, one of the Standards for Mathematical Practice involves students tackling a problem to determine what it’s asking.  If we consistently give students simple word problems that accompany our units, we take away all that thinking.  For example, when I teach a unit on multiplication if I only present word problems that involve multiplication–I’ve taken the thinking away.  Using more complex tasks forces students to think about what type of math they need to do and to dig in to get started.

Allows students to choose from multiple strategies or entry points

Similarly, these open-ended math tasks are perfect for giving students an entire arsenal of strategies–many of which can work in any given situation.  When there are multiple steps and lots of information, there are different places for students to dig in and get started.  Similarly, students can move back and forth between different parts of the task as they work and made progress toward understanding.  When given a task like designing a new library display, students can collect all the different pieces of information in the task and CHOOSE what makes sense to get them started.  They may start with a sketch or an estimate or any number of other strategies, but there is a LOT to grab onto as they begin.

Encourages math talk and discourse

This is pretty self-explanatory!  When you assign a rich math task, there is a lot to talk about.  When we ask students to tackle them, it only makes sense to give them “talk time”.  This is truly one of the best parts about using quality problems.  The opportunity to share thinking and help get classmates “unstuck” is invaluable.

Allows students to see real-world applications of math

We’ve all seen the memes making fun of word problems.

“If Lois buys 16 watermelons…”

“There are 693 kittens…”

(You get my drift.)

Quality open-ended tasks are MEANT to be real-world math.  Students are asked to solve real-world problems.  They may be working with a budget.  They may need to make decisions about “how many” or “which ones”.  Students may need to design something.  THIS is math.  When you find math problems that mimic students’ real lives, it’s priceless.  Our students eat lunch in the cafeteria.  They go on field trips.  They have sleepovers.  This is engaging math.

Helps students see the interconnectedness of math concepts

Like I mentioned before, teaching math in isolation takes away the thinking and deep understanding.  By using rich math tasks, students are forced to examine ALL the math they know as they look for ways to accomplish their goal.  They may need to add and subtract.  They may need to make a chart.  Sometimes they may see that drawing an array can help them solve a multiplication problem. In a great task, they may need to do all of these things for one problem!  So often, we fail to give students enough credit for being able to do this kind of work, and we do them a disservice when we don’t give them those opportunities.

Immerses students in the Standards for Mathematical Practice along with the math content

As we rush to work through the endless list of standards for our grade levels, we cannot forget to include the math practice standards in our plans.  When you read through these 8 standards, you can see the role open-ended math challenges play.  In fact, every single one of those standards can be met when we provide students with this type of math work.

Provides an excellent forum for partner and small group work

As I mentioned before, providing students with these rich tasks encourages accountable talk.  They are perfect for partner and small group work.  In fact, using these to explicitly teach students HOW to work together, how to coach each other, and how to encourage each other is invaluable.  Building relationships and adopting a growth mindset is a critical piece of learning productive struggle.  Learning to struggle and overcome challenges TOGETHER is a key part of our math coaching.

Naturally differentiate as students take “just right” approaches to solving them

Unlike more simplistic math problems, open-ended tasks can naturally differentiate.  Some students may want access to calculators.  Some may draw pictures.  There may be a time when groups of students choose to use manipulatives to model their math thinking.  As teachers coach, they can give math “hints” as needed to students based on their needs.  I have used countless math tasks where I have assigned the same task to ALL students but have provided differing levels of support as they tackle them.  Remember, students can still work on problem solving skills and strategies if they haven’t yet mastered algorithms.

A perfect example is a back-to-school shopping challenge where students have a budget and a set list of things to purchase.  There are multiple things to consider–from the number of items required to the different prices at different stores.  Should we save this rich task for students ONLY when they have mastered the additional algorithm with decimals?  Of course not.  We can have students work in teams, give calculators or other tools–or anything that will make the task more accessible.  This is an example of providing QUALITY education to all students and is a powerful way to build math confidence and self-esteem.

Allows teachers to serve as coaches as they watch and interact with students as they solve them

This is big.  Rather than teachers being the lecturer or “provider of knowledge”, these tasks naturally lend themselves to teachers serving as coaches.  So what?

• We learn so much about our students’ thinking as we watch.
• We have the power to differentiate on the fly as needed.
• Some students benefit from having more direct teacher contact while others thrive on being more independent.
• Learning to ask good questions to get students “unstuck” is so much more powerful than merely “showing them how”.
• Teachers can truly maximize their time to reach WHO needs help, WHEN they need help.
• We can help show students how to coach each other, making a room full of places for students to get coaching and guidance.
• We can notice when “a ha” moments happen and recognize them.
• This coaching time is perfect for finding work samples to share and discuss
• And so much more!

Encourages creative thinking and strategies

I think this point is being made throughout this post, but I’ll reiterate it here.  When there is more than one solution, there are countless solution paths.  When there are multiple solution paths, students see the value in thinking differently and there is not one “right” way to do business.  What a powerful message!

To make it even more powerful, make sure you build in time to SHARE strategies.  Whether you have students showcase their work under a document camera, share their ideas in small groups, project their work, or hang it up–celebrate the amazing solutions students come up with!  Even more valuable?  Make sure students know that the final answer is less important than the process to get there.

Do we want students to realize that we value their thinking?  You bet.  Learning to think independently and creatively is another one of those life lessons that will extend far beyond your math class.  It’s how REAL problems get solved.

Encourages students (and teachers) to focus on the PROCESS over the solution

As I stated before, of course, we want students to do math accurately and get correct solutions.  The truth is, when students tackle these complex tasks, there are lots of places where errors can occur.  If we stress getting a correct answer over the complex processes, all value is lost.  The value in these tasks is the process of understanding the problem, choosing strategies, modifying strategies when needed, selecting models or tools to use, estimating, reviewing answers, organizing work, and so much more.

When students know that WE value their hard work as much as correct answers, it’s so freeing for them!  They see that we value their thinking and strategies and even their mistakes.  This takes away any compulsion to get the answer from others or to shut down due to frustration.

As you can see, the power of these tasks is obvious.  Unfortunately, very few math programs provide enough of them to really help students develop these skills.  Because of that, one role I have taken on as a curriculum designer is to try to fill this gap by creating tasks like this for different age levels.

Convinced?  Give some a try!

CLICK HERE to grab a free guide that summarizes this blog post AND tells exactly what skills some of my open-ended tasks cover.

CLICK HERE to see a bundle of tasks for grades 2/3 (or for beginning problem solvers in grade 4)

Looking for tasks for experienced grade 3 problem solvers and grades 4/5?  CLICK HERE!

Finally, looking for some even more in-depth tasks that are differentiated and have tons of extensions?  These tasks can last multiple days and can be used with your entire class or with small enrichment groups or for fast finishers.  CHECK THEM OUT HERE!

(NOTE:  All tasks are AVAILABLE IN PRINT AND DIGITAL FORMATS)

The post Open-Ended Math Tasks: The Benefits appeared first on The Teacher Studio.