Three Simple Shifts to a Reasoning Classroom

Shelley Gray — Sun, 19 Jul 2026 16:09:01 +0000

For years, traditional math instruction has trained students (and teachers) to believe that math is a race to find a correct answer. When students face a problem that doesn’t immediately fit a learned procedure, they often stop, unsure how to proceed.

But true math understanding isn’t about getting a correct answer fast – and it doesn’t happen through speed drills or rote memorization. It happens through tasks that get kids to reason and think deeply. It’s about building flexible thinkers who can think critically and strategically, draw logical conclusions, and analyze numbers with confidence.

Shifting our classrooms away from ONLY rapid answer recall and toward deep, strategic thinking can feel overwhelming. But it doesn’t require a complete overhaul of your curriculum. Instead, it takes a few intentional tweaks to your daily routine.

Here are three simple instructional shifts you can make to build a culture of reasoning in your elementary classroom.

Shift #1: From Silent Calculation to Mathematical Discourse

Think about how many math blocks start: students walk in, sit down at their desks, and immediately begin working independently on a computational worksheet or morning work page. While there is certainly a time and place for independent practice, starting the math block in this way skips one of the most essential steps of mathematical reasoning: discourse.

To shift this dynamic, try dedicating the first 5 to 10 minutes of your math block to intentional, collaborative math conversations. There are many ways to do this:

1. Present a problem and discuss different strategies to solve it – number talk style. The math conversations that happen during number talks will forever transform your classroom. Students will have the opportunity to hear others’ strategies and develop their own reasoning skills as they observe and listen to different ways of thinking.

2. Instead of presenting a problem to solve, display a rich visual prompt—such as a data set, a number line, an array, or a pattern.

Instead of asking, “What is the answer?” change your prompting to open-ended, thought-provoking questions:

“What do you notice here? What do you wonder?”
“How do you know for sure? How could you prove it?”
“What happens if we change [this]?”

Here’s an example from my Math Conversations slides, which encourages students to reason using a number line. There are endless options for answers here! The ultimate goal is for students to reason and justify their thinking.

3. Rather than simple “find the answer” type questions for addition and subtraction, change your questioning to encompass reasoning. For example, look at the part-part-whole models below. Just imagine the conversation that comes from trying to decide what the parts represent!

“I think it’s 60 and 40 because one part is bigger than the other.”

“No, I think it’s more like 75 and 25 because the small part seems to be about one-fourth of the total.”

Questions like this are a goldmine for mathematical reasoning and discourse.

By prioritizing math conversation, students are exposed to multiple ways of thinking. They learn that their classmates might see a problem entirely differently than they do, and that both ways are valid. This simple daily routine builds a strong foundation of vocabulary, flexible thinking, and confidence.

Bring it to your classroom: If you want to implement this routine tomorrow without spending hours hunting down visual prompts, check out my Math Conversations Slides. This zero-prep digital resource gives you an entire year’s worth of visual prompts and discussion starters designed to get your elementary students thinking critically and talking about math the moment your block begins.

Shift #2: From Abstract Practice to Concrete Modeling

Too often, we rush students into memorized procedures, tricks, and algorithms before they truly understand number relationships and develop strong number sense. We ask them to memorize procedures like “carrying a 1” or “just add a zero to the end.” These procedures can get them to a correct answer but completely bypass mathematical reasoning.

When students learn only abstract procedures and rules, they can lose the ability to estimate, self-correct, or visualize what is actually happening with the numbers. Additionally, they may struggle with future math concepts, as it’s more difficult to make connections and develop new understanding when their foundation is based on a memorized procedure.

To break this cycle, we can shift toward hands-on, concrete modeling, even in upper grades. When students can SEE the math they are working with, it’s far easier to understand! This is where tools like Cuisenaire rods become absolute magic at any grade level.

Because Cuisenaire rods are not labeled with any value, they can be used in a variety of ways to represent numbers (even fractions!) They force students to think about numbers in terms of relationships, proportionality, or parts of a whole. Here are some examples of Cuisenaire rod tasks that encourage reasoning. For Cuisenaire rod tasks for fractions, see THIS blog post with tons of ideas.

This shift completely transforms how kids work with the math. Suddenly, they aren’t just mindlessly finding answers; they are physically manipulating, comparing, and visualizing concepts. There are multiple entry points to allow success for all students.

Bring it to your classroom: Ready to dust off your math manipulatives and put them to work? Check out my Number Rod Reasoning Tasks. These task cards are specifically designed to bridge the gap between abstract math concepts and concrete modeling.

Shift #3: Toward Perserverance and Productive Struggle

Imagine a standard math worksheet featuring 50 multi-digit division or multiplication problems. For the students who already understand the concept, this is mindless busywork. For the students who don’t understand the concept, this is simply repetitive mimicking of a learned procedure that is not building any new or deeper understanding.

Traditional computation worksheets often measure speed and the ability to mimic, not deep understanding and the ability to transfer knowledge and skills to new situations. When we overemphasize these surface-level drills, we rob students of the chance to experience productive struggle – the sweet spot where real learning, new connections, and “a-ha moments” actually happen.

Now – this is not to say that computation worksheets have no place in the classroom. I believe they do; however, we need to be mindful of what the foundation of our instruction is being built on. If our instructional foundation is being built on worksheets where students simply mimic procedures, then we need to make a shift.

To make this shift, we can think about how we ask questions.

Instead of “What is 8×3?” try, “Write three different equations with a product between 21 and 24.”

Or elicit connection-making using questions like this one:

Another way to give kids the opportunity for productive struggle is with math puzzles that offer multiple entry points.

Try this Reasoning Puzzle and Logic Puzzle, and notice how you engage in productive struggle while you solve them! The thinking required for puzzles like this is very different than the thinking required for simple answer regurgitation questions.

When you offer tasks that require real thinking rather than just rapid calculation, you build an environment where stamina and making mistakes is just a natural part of the solving process. You teach kids that the goal of math isn’t just to answer questions correctly as quickly as possible, but to build thinking skills and perseverance.

Bring it to your classroom: Want more puzzles like the ones above? Check out these popular Math Reasoning Puzzles and Logic Puzzles. They are the perfect tool for math centers, independent practice, or early finishers, offering the ideal amount of “productive struggle” to keep students challenged but still able to experience success.

Shifting from a math classroom focused on “answer-getting” to one rooted in mathematical reasoning and deep understanding doesn’t happen overnight. It is a journey for both you and your students. But by making small, intentional shifts to your daily routine and the way you ask questions, it will quickly become the norm in your classroom.

Start small. Pick just one shift to try this week, whether it’s a quick 10-minute math conversation at the start of class or a hands-on modeling task with manipulatives during small group instruction. Watch how your classroom transforms into an engaging space where students want to keep learning and challenging themselves!

For More Support

You don’t need any additional resources to start teaching in a way that incorporates reasoning. The only thing you need to do is adjust your tasks and the way you talk about math in your classroom.

However, I know that this can be a tricky shift to make when you’re first getting started. If you’d like support as you begin this shift, I’d love to help! Most of my resources are based on a reasoning and deep thinking approach.

The post Three Simple Shifts to a Reasoning Classroom appeared first on Shelley Gray.

Tackle Problem-Solving, Logical Reasoning, and Critical Thinking With These Fun Activities!

Shelley Gray — Sun, 22 Jan 2023 23:32:07 +0000

When you think of problem-solving, logical reasoning, and critical thinking, do you visualize boring worksheets that students moan and groan about? Well, let’s put a stop to that! Logic problems are an engaging and interactive way to incorporate these essential skills into the math classroom, resulting in increased motivation and interest. They are also an effective way to introduce algebraic thinking and help students develop the skills necessary for success in algebra in later grades. Too often the work that we give students consists of surface level thinking, where they simply regurgitate answers. But logic problems can provide a new type of challenge and encourage them to think in a much deeper way.

How to Complete a Logic Problem Puzzle

To complete the puzzle, students will quickly catch on that they must begin with symbols that they KNOW for certain. For example, in the puzzle below, we begin with solving for the gumball machines, since we know that 5+5=10. Now that we know the gumball machine equals 5, we can solve the second row. The heart equals 10, since 10+5=15. Lastly, we can solve the bottom row. Since we know the heart equals 10, we can conclude that the lollipop must be 6.

Trickier Than They Seem

Although the example above seems simple, it is not always easy for kids to think in this way, particularly once the puzzles get more difficult. When deciding which puzzles to use with your students, remember that if they are not used to doing activities that involve logical reasoning, they will very likely find them challenging. Your grade 3-4 students might be sufficiently challenged with the numbers to 20 puzzles, even though they work with numbers in the thousands in other math activities.

I recommend making several levels of puzzles available to your students and allowing them to choose the ones that challenge their brains “just enough.” I typically find that students are eager to work to their full potential and will generally choose the ones that are best suited to their abilities.

Ideas for Use

There are many ways you can store and use these puzzles in your classroom:

Use at one of your math centers. Place the logic puzzles in the center of the table, and have students choose whichever ones they want to complete. To add differentiation, allow your students to choose between different sets of logic puzzles.
Store on a ring or in a folder and use an early finisher activity.
Post the puzzles around the room and use them for an “Around the Room” gallery walk activity. Have students circulate around the room, completing puzzles as they go! *Pro-tip: Give each student a clipboard if you have them available.
Use them as partner work. You will LOVE the amazing mathematical conversation that will occur as students talk about what each picture represents.

Personally, I prefer to print these in color and laminate each card, but you may also wish to simply make black and white booklets for your students to keep inside their math folders.

Free Sample for Your Classroom

If you’d like to try these puzzles in your classroom, but aren’t sure which set will work best, I’ve made a free sample available for you. Take them to your classroom and see how students respond before committing to purchasing an entire package or the full multi-grade bundle. In the free sample, you’ll receive one puzzle from each package . Download your free sample below!

Full Packages and Bundle

If you are ready to use these puzzles in your classroom, I’ve included the links to the individual packages below. Each package of Logic Problems comes with 20 puzzles. Simply laminate, cut, and make copies of the recording sheets and you’ve got one of your math centers taken care of!

The post Tackle Problem-Solving, Logical Reasoning, and Critical Thinking With These Fun Activities! appeared first on Shelley Gray.

Logic and Problem Solving Archives - Shelley Gray