I was the product of lots of drill-and-kill practice and timed tests in my own school experience. I could follow steps. I could memorize. I could get through the assignment.

But deep problem-solving?
Flexible thinking?
Real conceptual understanding?

That came later.

And once I started teaching, I began to see the same thing with students.

Some students could memorize facts quickly. Some could not. Some could fly through a timed test but had no idea how to explain their thinking. Others understood the math, but froze the second a timer started.

That is when I started asking a bigger question:

Are we building fact fluency, or are we only training students to answer quickly?

Because those are not always the same thing.

Fact fluency matters. Of course it does. Students need to know their basic facts. But if we want facts to stick, we have to build them on something stronger than memorization alone.

We need number sense.
We need visuals.
We need strategies.
We need math conversations.
We need repeated practice that actually helps students understand what numbers are doing.

So let’s talk about three common myths about fact fluency, and what to do instead.

Myth #1: Math Is Mostly About Memorizing Basic Facts

Let’s start with the big one.

Students absolutely need to know their math facts. I will never argue against that.

But memorizing facts is not the same thing as mastering facts.

There is a difference.

Memorization says, “I know the answer.”

Mastery says, “I know the answer, I understand why it works, and I can use what I know in other problems.”

That is the goal.

When students only memorize facts in isolation, they may struggle when numbers appear in a different format. They may forget facts quickly. They may not know what to do when they get stuck.

But when students learn facts through strategies, models, and visuals, they begin to see relationships between numbers.

They notice that 6 x 8 is connected to 5 x 8.
They see that 9 + 6 can be solved by making a ten.
They understand division as equal groups, not just a symbol on a page.

That is where real fluency starts.

What to Do Instead: Help Students Build Mental Images

Students need to see math before they are expected to manipulate it mentally.

Most often, students are presented facts in symbolic form only.

5 + 3
8 x 7
24 ÷ 6

But symbols mean very little if students cannot picture the quantity behind them.

That is why visuals matter so much.

Students need practice with:

• Subitizing images
• Ten frames
• Arrays
• Equal groups
• Number bonds
• Bar models
• Multiples
• Word problems
• Fact strategies

These models help students form mental images of numbers and operations.

And once students can picture the math, they are much more likely to remember it.

For multiplication practice that goes beyond symbolic facts, add visual fluency booklets to your small group, math center, or independent practice routine.

Multiplication booklets include 16 ready-to-print 8-page booklets, with one booklet for each fact group from x1 to x12 and five mixed fact booklets. The activities include arrays, subitizing images on ten frames, multiples, fact strategies, number bonds, word problems, and equal groups.

Myth #2: Timed Tests Are the Best Way to Assess Fact Fluency

Timed tests are efficient.

I understand why they are used.

They are easy to give.
They are easy to grade.
They give you quick data.

But quick data is not always complete data.

Timed tests usually measure one part of fluency: speed.

And speed alone does not tell the full story.

A student can answer quickly without understanding the math. Another student can understand the math deeply but perform poorly when a timer creates pressure.

That is why we need to be careful.

Fast math is not always strong math.

Strong math includes:

• Accuracy
• Efficiency
• Flexibility
• Strategy use
• Conceptual understanding
• The ability to explain thinking

If we only measure speed, we may miss the most important parts of fluency.

What to Do Instead: Listen to Student Thinking

One of the best ways to assess fact fluency is to listen.

Ask students how they solved. Ask what they noticed. Ask if they can solve the problem another way.

You can learn so much from a simple math conversation.

Try prompts like:

“How did you see it?”
“What strategy did you use?”
“What fact helped you solve this one?”
“Can you solve it another way?”
“How do you know your answer makes sense?”
“What do you notice about the numbers?”

These questions help students move beyond answer-getting.

They also give you better information as the teacher.

You can hear whether students are counting one-by-one, making tens, using doubles, decomposing numbers, applying place value, or using related facts.

That is powerful data.

Myth #3: Improving Fact Fluency Means You Have to Overhaul Your Entire Math Block

This myth keeps too many teachers stuck.

Because when something feels too big, it becomes easy to do nothing.

But building fact fluency does not require you to throw out everything you are already doing.

Small changes can make a big difference.

You can begin by adding:

• A 5-minute visual number sense routine
• One number talk a few times a week
• Visual flash cards during small group
• Fluency booklets during centers
• Subitizing practice beyond primary grades
• More questions that ask students to explain their thinking
• A strategy review routine once a week

That is manageable.

And manageable matters.

The goal is not to create a Pinterest-perfect math block. The goal is to give students consistent opportunities to see numbers, talk about numbers, and use numbers flexibly.

What to Do Instead: Build a Simple Weekly Fluency Routine

Here is a simple way to make fact fluency practice feel doable.

Monday: Start With a Visual Number Sense Routine

Show students a dot image, array, number bond, or ten frame.

Ask:

“What do you notice?”
“How do you see the number?”
“Can you see it another way?”

Subitizing is one of the most important foundational skills for building number sense, and it should continue well beyond the primary grades.

Tuesday: Use Visual Math Cards

Choose cards based on the operation your students need most.

You can use them whole group, in small groups, with partners, or as a quick warm-up.

Wednesday: Add Fluency Booklet Practice

Let students practice with models that help them make sense of the facts.

For multiplication, this might include arrays, ten frames, equal groups, number bonds, fact strategies, and word problems.

Thursday: Strengthen Number Talks

Use number talks to help students explain their thinking and hear strategies from classmates.

This is where students build flexibility.

Discover Number Talks Resources

Friday: Review Strategies and Let Students Explain

End the week by asking students to reflect.

Try:

“What strategy helped you most this week?”
“What fact feels easier now?”
“What visual helped you understand the math?”
“What is one fact you can solve in more than one way?”

This is also a good day for spiral review or a quick student explanation activity.

Want to Go Deeper With Number Sense?

If you are ready to make number sense and fact fluency a bigger part of your instruction, this is where Number Sense University fits beautifully.

This is not just another resource to print.

It is the deeper support system for teachers who want to understand the strategies, build better routines, and strengthen fact fluency with more confidence.

If you’re ready to move beyond quick fluency activities and start building a stronger foundation for your students, Number Sense University is where I can help you do that.

Inside Number Sense University, I walk you through the number sense strategies students need in order to build true fact fluency, not just memorize facts long enough to pass a timed test. My goal is to help you strengthen your students’ understanding of numbers, operations, and strategies so they can solve with more accuracy, flexibility, and confidence.

You’ll get training on 29 different number sense strategies organized by grade level and operation, along with more than 1,100 pages of classroom-ready resources you can use to bring these strategies into your math block.

This is perfect if you’ve been wanting to build stronger fact fluency routines, but you don’t want to keep piecing everything together on your own.

Because when students understand numbers deeply, math facts don’t just become something they memorize. They become something they can see, explain, and use.

Ready to build stronger number sense routines in your classroom?

Fact fluency does not have to be a race.

It does not have to be all timed tests.
It does not have to be endless drill.
It does not have to be one more overwhelming thing added to your math block.

Students need to know their facts, yes.

But they also need to understand numbers.

They need visual models.
They need strategies.
They need conversations.
They need opportunities to explain their thinking.
They need practice that helps them build confidence, not just speed.

When students build fact fluency through number sense, the memorization starts to make more sense.

And that is where the magic happens.

Start small this week.
Choose one visual routine. Ask one better question. Add one model. Let students explain one strategy.

Those small shifts can change the way your students see math.

The post 3 Fact Fluency Myths That May Be Holding Your Students Back appeared first on Tanya Yero Teaching.

Flash cards have been used in classrooms for years.

And I get why.

They are quick.
They are easy to use.
They give students repeated practice with math facts.

But traditional flash cards have one big problem.

They are usually only symbolic.

Students see something like:

6 x 4
8 + 7
24 ÷ 6

Then they are expected to recall the answer.

For some students, that works. They memorize the facts, move on, and everything feels fine.

But for many students, those symbols do not create enough meaning. They may memorize a fact for a short time, but they do not truly understand what is happening in the operation.

And when students do not understand the math, fact fluency becomes much harder to build.

That is exactly why visual math flash cards can be such a powerful tool.

Students Need to See the Math

Children do not learn from symbols alone.

They learn from experiences, hands-on activities, conversations, and visuals.

Before students can confidently manipulate numbers, they need opportunities to see and understand quantities. They need to build mental images of numbers and operations.

Think about it this way.

If a student sees 5 + 3, that is a symbolic representation.

But if that same student sees five dots and three more dots, they can begin to subitize, count on, make a group, or compose the total.

If a student sees 6 x 4, that is symbolic.

But if they see an array with 6 rows of 4, they can begin to understand multiplication as equal groups.

If a student sees 24 ÷ 6, that is symbolic.

But if they see 24 objects split into 6 equal groups, they can begin to understand division as fair sharing or grouping.

Visuals make the math come alive.

And when students can see the math, they are more likely to understand it.

This is exactly why visual math cards work so well. Instead of asking students to memorize symbols in isolation, students get repeated exposure to the image, the value, and the operation at the same time.

For younger students building addition and subtraction fluency, start here:

What Makes Visual Flash Cards Different?

Visual math flash cards are not your typical flash cards.

Traditional flash cards usually show only the equation.

Visual flash cards show the operation through an image.

That means students are not just practicing recall. They are building connections between the symbolic part of math and the conceptual part of math.

They can see:

• Addition as combining quantities
• Subtraction as separating or finding the difference
• Multiplication as equal groups or arrays
• Division as sharing or grouping
• Numbers as values, not just digits
• How quantities can be composed and decomposed

This matters because symbols and digits do not hold much value if students cannot mentally visualize what they represent.

A student may memorize that 8 x 7 equals 56.

But if they can also picture 8 groups of 7, an array, or a related fact, they have a stronger foundation.

That is the kind of fluency we want.

If you teach upper elementary, the multiplication and division visual math cards are especially helpful because students can actually see arrays, groups, and division models instead of only memorizing facts.

Visual Flash Cards Support Mental Math

One of the biggest benefits of visual flash cards is that they help students create mental images.

And mental images are powerful.

When students can picture quantities, they can start using strategies instead of relying only on memorization.

For example, a student looking at a visual for 9 + 6 might think:

“I can make a ten.”
“I can move one from the 6 to the 9.”
“That makes 10 + 5.”
“So the answer is 15.”

That student is building flexibility.

A student looking at a multiplication array may think:

“I know 5 x 4 is 20.”
“One more group of 4 makes 24.”
“So 6 x 4 is 24.”

That student is using a known fact to solve an unknown fact.

This is how students begin to move from counting to reasoning.

And reasoning is what makes fact fluency stick.

Want to help students explain how they see the math?

This would be a great place to offer a simple student page with prompts like:

• I see…
• The equation is…
• My strategy is…
• Another way to solve it is…

Visual Flash Cards Help Students Build Conceptual and Procedural Understanding

In math, students need both procedural understanding and conceptual understanding.

Procedural understanding helps students know the steps or recall the facts.

Conceptual understanding helps students know why the math works.

Some classrooms focus first on procedures. Others focus first on concepts.

But students benefit when they are exposed to both at the same time.

That is especially true with multiplication and division.

Students need to know the fact, but they also need to understand what the fact represents.

For multiplication, they need to see equal groups, arrays, repeated addition, and patterns.

For division, they need to see equal groups, sharing, related multiplication facts, and how quantities can be separated.

Visual flash cards allow students to practice facts while still seeing the meaning behind the operation.

That is a win.

Ways to Use Visual Flash Cards in Your Classroom

Visual flash cards are low prep and easy to use, which is exactly what busy teachers need.

Here are a few simple ways to add them to your math block.

1. Use Them as a Daily Warm-Up

Display one visual flash card at the beginning of your math block.

Ask students:

“What do you notice?”
“What equation matches this image?”
“How do you see the total?”
“Can you solve it another way?”

This turns a quick warm-up into a number sense routine.

2. Use Them During Small Groups

Visual flash cards are perfect for small group instruction.

You can use them to target specific facts, operations, or strategies.

For students who need support, focus on connecting the visual to the equation. For students who are ready for more, ask them to explain multiple strategies or write related facts.

Small group is also a great time to choose cards based on the operation your students need most.

3. Use Them for Partner Practice

Students can work with a partner and take turns explaining what they see.

One student can hold up the card, while the other explains the equation, strategy, and answer.

This gives students practice with both fluency and math language.

If your students need help naming and organizing their number sense strategies, pair partner practice with this free flipbook.

4. Use Them for Math Centers

Add visual flash cards to a fact fluency center.

Students can sort cards by strategy, match images to equations, write related facts, or record their thinking on a response sheet.

If you want students to keep building visual fact fluency during independent practice, pair the cards with fluency booklets. The booklets give students repeated exposure to visuals like arrays, subitizing images, bar models, and number bonds.

5. Use Them to Build Math Conversations

Instead of asking only, “What is the answer?”

Try asking:

“How did you see it?”
“What strategy helped you?”
“What fact do you already know that helped you solve this one?”
“What related fact can you write?”
“How does the visual match the equation?”

These questions help students think more deeply about numbers.

If you want to make math conversations easier to plan, try ready-to-use number talk prompts.

Why This Works Better Than Traditional Flash Cards Alone

Traditional flash cards can help some students memorize facts.

But visual flash cards do more.

They help students:

• Build number sense
• Form mental images
• Understand operations
• Connect symbols to visuals
• Practice facts in a meaningful way
• Develop flexible strategies
• Strengthen math conversations

This does not mean students never need symbolic practice.

They do.

But when students only see symbols, they miss important opportunities to understand what those symbols mean.

Visual flash cards help bridge that gap.

Fact fluency should not feel like a race to memorize.

It should feel like students are building a stronger, deeper understanding of numbers.

Visual math flash cards give students a way to see the math, talk about the math, and eventually recall the math with more confidence.

Because when students can visualize a fact, they are much more likely to understand it.

And when they understand it, memorization becomes much more meaningful.

Ready to ditch traditional flash cards and help students actually see the math?

Shop Visual Fact Fluency Math Cards:

The post How Visual Math Flash Cards Help Students Build Fact Fluency appeared first on Tanya Yero Teaching.

For many years now, the words fluency and fluently have been sprinkled all throughout elementary math standards.

And yet, if you ask ten teachers what fact fluency means, you may hear ten different answers.

Some will say it means students can answer quickly.
Some will say it means students get the answer correct.
Some will say it means students have their math facts memorized.

And yes, speed and accuracy are part of fact fluency.

But they are not the whole story.

True fact fluency is so much more than students being able to shout out answers quickly or complete a timed test in under a minute. When students are truly fluent, they can solve accurately, choose efficient strategies, think flexibly, and explain how they got their answer.

That is the part we cannot skip.

Because if we only focus on fast answers, we may miss whether students actually understand the math happening behind those answers.

And that matters.

Fact Fluency Is More Than Fast and Accurate

The most common definition of fact fluency is “fast and accurate.”

That definition is not completely wrong. We do want students to solve math facts with accuracy. We also want them to become more efficient over time.

But if we stop there, we are only looking at the surface.

Fact fluency also includes:

• Efficient methods for solving
• Flexibility in computation
• Conceptual understanding
• The ability to explain solving methods
• An understanding of operations and place value
• The ability to check if an answer makes sense

That means fact fluency is not just about what answer a student gives.

It is also about how they think.

A student who knows that 8 + 7 equals 15 because they memorized it has one pathway. A student who knows 8 + 7 equals 15 because they can make a ten, decompose 7 into 2 and 5, and explain that 8 + 2 + 5 equals 15 has a much deeper understanding.

That student is not just recalling.

That student is reasoning.

And reasoning is where real fluency begins.

If your students need help organizing the strategies they can use to solve mentally, this is a great place to introduce a number sense strategy tool.

This freebie is a great support for helping students understand what different number sense strategies mean and what they can look like in action.

Why Memorization Alone Is Not Enough

Let’s be honest. Math facts do need to become automatic.

Students should not have to spend all of their mental energy figuring out basic facts forever. Automaticity helps them tackle larger, more complex math concepts with confidence.

But memorization should not be the only goal.

When we rely only on repetition, students may memorize facts without understanding them. They may know an answer one day and forget it the next. They may freeze when the problem looks even slightly different. They may become dependent on tricks instead of building number sense.

That is why students need more than repeated exposure to symbolic equations like:

5 + 3
6 x 4
24 ÷ 6

They need to see what those numbers mean.

They need visuals.
They need number conversations.
They need hands-on practice.
They need opportunities to compose, decompose, compare, group, and reason.

That is how math facts begin to stick.

Number Sense Builds Stronger Fact Fluency

If fact fluency is the goal, number sense is the foundation.

Students need to understand how numbers work before they can confidently manipulate them.

That means they need practice seeing numbers in different ways. They need to recognize patterns, use friendly numbers, break numbers apart, and put them back together.

For example, a student working on addition facts may need to see 9 + 6 as:

9 + 1 + 5
10 + 5
15

A student working on multiplication may need to understand 6 x 4 as:

6 groups of 4
4 groups of 6
An array
Repeated addition
A visual model

A student working on division may need to see 24 ÷ 6 as:

24 split into 6 equal groups
How many are in each group?
The inverse of 6 x 4
A model with equal groups

These visual and strategic connections help students build a mental library of numbers.

And once students have that mental library, they are much more prepared to recall facts with confidence.

Want students to see these strategies in action? Visual math cards are a simple way to connect symbolic equations to the quantities students are actually working with.

Why Timed Tests Can Be Tricky

Timed tests are often used to measure fact fluency, but they do not always give us the full picture.

A timed test may tell us whether a student can answer quickly under pressure.

But it may not tell us whether the student understands the operation, can explain their thinking, or has flexible strategies for solving.

For some students, timed tests create anxiety. They may know the math, but the pressure causes them to shut down. For others, timed tests reward memorization without revealing whether the student has conceptual understanding.

That does not mean teachers should never measure speed.

It just means speed should not be the only thing we measure.

When assessing fact fluency, we also want to look for:

• Can the student explain their thinking?
• Can they solve the problem another way?
• Can they use a visual model?
• Can they recognize an unreasonable answer?
• Can they apply the fact in a different context?

Those questions give us a much stronger picture of true fluency.

Simple Ways to Build Fact Fluency in Your Classroom

The good news? Building fact fluency does not have to take over your math block.

Small, consistent routines can make a big difference.

Here are a few ways to get started.

1. Add Daily Visual Number Sense Routines

Give students quick opportunities to look at numbers visually.

You can use dot images, ten frames, arrays, number bonds, bar models, or visual flash cards. Ask students what they notice. Let them explain how they see the number.

This helps students move beyond symbols and begin forming mental images of quantities.

For upper elementary classrooms, Array Talks are a great way to bring visual multiplication practice into quick number sense routines.

2. Use Number Talks

Number talks are one of the best ways to hear student thinking.

Display a problem, give students think time, and then ask them to share different strategies. The goal is not just the answer. The goal is the conversation.

Students learn that there is more than one way to solve a problem, and they begin adding new strategies to their own math toolbox.

Need ready-to-use prompts instead of creating your own from scratch?

3. Connect Symbols to Visuals

When students see only equations, they may miss the meaning behind the math.

Try pairing symbolic facts with visual representations.

For example:

6 x 4 can be shown as an array.
18 ÷ 3 can be shown with equal groups.
7 + 5 can be shown with ten frames or number bonds.

This helps students connect the abstract math to something they can actually see and understand.

4. Let Students Explain Their Thinking

When students explain their strategies, they deepen their understanding.

A student who can explain why 9 + 8 equals 17 is showing more than memorization. They are showing flexibility, reasoning, and understanding.

Try asking:

“How did you see it?”
“Can you solve it another way?”
“What strategy did you use?”
“How do you know your answer makes sense?”

These questions help shift the focus from answer-getting to sense-making.

Fact Fluency Takes Time

Fact fluency does not happen overnight.

It is built through repeated, meaningful experiences with numbers.

Students need time to see numbers, talk about numbers, move numbers, break numbers apart, and put them back together. They need chances to make connections between visual models and symbolic equations.

And yes, over time, many facts will become memorized.

But the strongest memorization happens when students understand what those facts mean.

That is the sweet spot.

Fact fluency is not just about speed.

It is about accuracy, flexibility, efficiency, and understanding.

When we give students opportunities to build number sense, visualize quantities, and explain their thinking, we help them become more confident mathematicians.

So instead of asking, “How can I get my students to memorize their facts faster?”

Try asking:

“How can I help my students understand numbers better?”

That shift can change everything.

For more ready to use resources shop https://www.teacherspayteachers.com/store/tanya-yero-teaching

The post What Is Fact Fluency? A Better Way to Build Math Confidence appeared first on Tanya Yero Teaching.

Here is the caption that accompanied the post:

“I used to think that a student’s ability to quickly recall a math fact was important. I regret that decision and every timed test I ever gave my students.

Today I define fluency in three parts: efficiency (quick recall and/or ability to use a strategy), accuracy, and flexibility.

Math celebrates creativity and diversity in solving problems. I now see fact fluency in the same light.”

The post gained comments quickly… with some supporting what I said, and others upset with the post. I received many messages reminding me of the importance of fact fluency. If we don’t assess our students’ fluency then we are failing them. Some commented that they taught middle and high school and that their students didn’t know their facts, thus hindering their work when solving various computation problems. 

I agree with all of this. Fact fluency is very important to me, and should be on every teacher’s radar. Just because I don’t administer timed tests doesn’t mean I don’t teach and check for fluency. I simply choose to define and assess it differently. 

There are two ways to define fact fluency: memorization vs. automaticity. 

What are timed tests really assessing?

The simplest answer is math facts, but with timed tests the child is strictly relying on memorization. Memorization of facts is rote learning; pulling information from memory with speed. There is no time to make deep conenctions. The child is pulling an answer from their mental filing cabinet due to repetition with that particular fact. There were many cases where a child who struggled in my class to conceptually understand math content would then score an A on a timed test because the two tasks required a different level of understanding. Memorization is the most basic level of learning. What’s more important…memorizing the date of the War of 1812 or understanding the causes and effects of that war?

When I administered timed tests, we would collectively grade our assessments afterwards. It would baffle me how many students had to tangibly write out 100 subtracted by however many questions they missed to find their scores. Students that were getting A’s and B’s on a timed test had to then write out 100-12= 88 to calculate their score on an assessment that is evaluating FLUENCY. This proved to me that they were pulling directly from memorization and nothing else. 

What’s the alternative then?

I see math fluency the same way I see number sense and teaching standards conceptually; all can be promoted through purposeful questioning. Instead of using memorization I want my students to use automaticity. Automaticity is the ability to produce an answer with adequate speed while still thinking about deep relationships and/or connections. Automaticity doesn’t mean I let my students spend 5 minutes trying to solve 7 x 7, but it can look something like this:

My students see math as a subject that works for them, not the other way around. They are expected to manipulate numbers, make connections, and seek alternative ways of solving. Why not incorporate these ideas into fact fluency? To this day I will still sometimes use a mental strategy for solving 8 x 8 and 9 x 6; these two facts I cannot commit to memory even well into my 30’s. Is this bad? I don’t think so. It just makes me human, just like your students.

Memorization and automaticity sound very similar, and they are, but automaticity promotes number sense. Introduce your students to various strategies that can be used mentally to solve problems.

How I assess fluency: 

My students complete fluency assessments that focus on number sense strategies and/or mental math. I also conduct fluency interviews. Fluency interviews are quick four to five minute discussions. They can be made even shorter by simply asking the child one question. You’ll be able to tell if the child doesn’t know the solution at all. You’ll also be able to see if they are pulling the answer from memorization or automaticity.

What happens if I have a child that is relying on memorization?

Nothing! Using memorization for fact fluency isn’t wrong, but math teachers should expose students to number sense and mental strategies. I use number talks in my classroom as daily practice. Students need exposure to mental math. Your students need to see the components of math in the deepest forms as much as possible.

Head here to watch a presentation I did for an upper elementary teacher conference on how to promote number sense in your classroom.

To read more about how I incorporate meaningful fuency into my classroom head to this five part blog series.

The post Why I’ll Never Use Timed Tests To Assess Fact Fluency Again appeared first on Tanya Yero Teaching.

Then my first year turned into my second year and by the time the third year rolled around I realized I was creating robotic math students that were simply trained to take a test. They weren’t problem solvers. They lacked number sense and basic strategies that I knew they would need in the real world. They understood procedural learning more than conceptual understanding. 

What REALLY is number sense?

Number sense is a child’s set of skills when working with numbers. More importantly, number sense is one’s ability to see the flexibility in numbers. Children with number sense understand quantities, grasps basic concepts, and understand key operations and symbols. But this all leads to the bigger picture of what number sense really is. A child with a strong foundation in number sense can identify multiple ways to solve problems. Number sense supports the beauty and creativity of each child’s mind and how they interpret a question. 

The Questions You Ask (And Don’t Ask) Will Affect Your Students’ Number Sense

It’s not enough to teach your students basic algorithms and train them to memorize the steps. When I teach a new math concept the algorithm is the LAST thing I introduce. Why? I want to strengthen my students’ number sense. Math is designed to be fun and exploratory and more often than not we take the drill and kill approach. This approach leaves out the opportunity for good quality questioning. 

At the beginning of the year I introduce strategies for manipulating numbers and equations. Expect your students to come to you lacking number sense tools. You have to teach them this style of math and how it works. The posters below stay up in my classroom all year.

I spend time modeling my own thinking, providing opportunities for peer discussion, and integrating manipulatives whenever I can. With time, students will organically begin to manipulative numbers on their own.

The following pictures are samples that I have pulled from student responses when asked to solve 24 x 9. Students that have the ability to see various ways to solve one problem have strong number sense.

Below is the complete list of strategies we came up with together as a class:

24 x 9 is close to 24 x 10 which I know is 240, so 24 x 9 must be one 24 less than 240. Answer: 216

25 x 10 is 225 so 24 x 9 must be 216.

12 x 9 is 108, so 24 x 9 will be double or 219.

20 x 9 is 180. 4 x 9 is 36. 180 + 36 = 216. 

24 x 4 equals 96. 96 + 96 = 192 plus one more set of 24 equals 216.

Area model of 24 x 9

Asking questions such as “Does this mathematically make sense?” And “What does this look like in visual form?” will force your students to justify their answers and use multiple strategies. Never accept only one way of solving a problem. Encourage students to share their methods and celebrate the diversity of strategies. Push student thinking and ask meaningful questions. I used the following questions to steer my students towards the equations above.

“How can we use doubles to solve this problem?”

“How can an area model help us solve a multiplication equation?”

“How can we use multiples of 10 to help us solve this problem?”

What Does Number Sense Practice Look Like In The Classroom?

A class that is heavy in procedural questioning lacks the practice of number sense. Students are relying on the memorization of algorithms to solve problems. I provide questions, especially word problems that are rigorous and deep in conceptual understanding. These sorts of questions lend themselves beautifully to discussions that build number sense. 

I also integrate Number Talks into my math block for extra practice that is specifically designed for number sense practice. Number Talks is a quick 5-7 minute discussion that builds mental math and number flexibility. CLICK HERE to read more.

The post The Power Of Number Sense In The Classroom appeared first on Tanya Yero Teaching.

What is number sense?

Number sense is one’s ability to manipulate numbers mentally. Flexibility is at the heart of number sense. Students with strong number sense can solve a problem in more than one way. The ability to problem solve is also connected to number sense. The four operations of math require the manipulation of numbers. Students need to have strong number sense if they are going to conceptually understand what they’re doing in your classroom.

How do I teach my students number sense?

To build number sense I implemented daily number talks into my math block. A number talk is a short (5-8 minutes) exercise designed to build number sense. During this practice students share how they solved a particular problem mentally. Implementing number talks in your classroom can feel overwhelming. Getting started with any new practice is always the hardest part. Here are 3 tips for implementing number talks in your classroom.

1.) MODELING is key.

You can’t expect your students to successfully complete a number talk if they have never seen what it looks like. Model how to “talk math.” Show them the different mental strategies that can be used to explain ways to problems. Spend some time at the start of your math block completing a number talk with your students. At first you will be doing the talking. After the first few weeks of school gradually release the responsibility over to your students. Have them work in groups or pairs initially and later have them complete a number talk independently.

2.) PREP as much as you can in advance.

Number talks are daily exercises so you will go through materials quickly. You need daily questions on hand. I keep my Grab and Go Number Talks on a binder ring and just pull a card for each day. Easy and quick!

3.) PUSH your students

Most students aren’t accustomed to doing math in this format. They are used to paper/pencil and step by step procedures. Asking them to think independently and innovatively will be hard at first. Expect silence. Expect not a lot of volunteers at first, but do praise those that step up to the plate. Praise the idea of solving one question in different ways. Your students will respond and start thinking independently.

Implementing number talks into my math block made my students better problem solvers. If you’re looking for an already made set of prompts and questions CLICK HERE.

The post 3 Tips for Implementing Number Talks in Your Classroom appeared first on Tanya Yero Teaching.

A few years ago I started integrating fluency interviews into my schedule. These 5 minute chats were a great way to interact with students one on one and get a better understanding of their mastery of fluency. It provided far more insight into my students’ thinking than any timed test could. My students enjoyed an alternative to timed tests. It diminished anxiety and brought a new level of understanding to my classroom.

Because I was taking a flexible stance on fluency that meant my assessments had to integrate flexibility as well. I created 10 question mini assessments that focused more on number sense than speed. My students completed these assessments on Friday’s. They took no more than 15 minutes and provided great insight into student performance. With the weekly alternative quizzes and the bi-weekly interviews, along with classroom observations, I had enough resources to track the progress of my students.

I found my students more relaxed when it came to fluency. It was part of our everyday routine so they were getting ample practice. This new approach built problem solvers versus stressed out children. Gone were the days where my students could only depend on memory alone.

Be sure to check out my Alternative Math Fluency Curriculum. Ready to go weekly quizzes and interviews are included in this curriculum.

The post Week 5: Implementing Alternative Forms of Assessment Math Fluency appeared first on Tanya Yero Teaching.

Students learn from one another. One of the most underused teaching strategies is peer coaching. If done properly misconceptions and clarification can be given to students in a peer setting. You are one person. You are grossly outnumbered in a classroom. As educators we want to be everywhere and help all, but we physically can’t.

I want activities that are quick, simple, and effective. I opt to use weekly fluency games so students can collaborate with one another and I can pull students that need more intensive instruction with fluency. The games usually last no more than 15 -20 minutes and everyone is productively working.

I also use fluency chats daily. Fluency chats are initiated with prompts that focus on building number sense. They can be used in partner or group settings to facilitate discussion amongst peers.

Student interaction will make your job easier. My Math Fluency Alternative Curriculum has ready to go activities for grades 4-5. Click here to see more about this product.

The post Week 4 – Providing Opportunities for Student Practice with Peers appeared first on Tanya Yero Teaching.

I love to talk. Do all teachers love the sound of their own voice like me?

It took me years to learn to stand back and let my students do most of the work. Thru trial and error I learned that the most authentic learning comes when I pose a question and let my students devise and execute a plan to solve it with minimal help from me.

I have my students sit in groups so collaboration is a quick transition. I use daily fluency chats so my students have practice with math talk. I want to hear rich vocabulary and concise explanation of different number sense strategies being used from my students. Not only is their understanding strengthening, but I am able to formally assess my students on a daily basis. Like writing, verbal explanation takes time for students to master. The more practice students have the more accountable talk you will hear.

For the first few weeks model your own thinking. Encourage students to find alternative ways of solving one problem. Teaching math fluency thru number sense is a great topic for accountable talk because of its diversity. There are countless ways to solve problems which naturally promotes discussion.

Below is a prompt my students completed and their responses.

Student A: I subtracted 33 from each number to get an equation of 300 – 134. Then I was able to mentally subtract because I made a multiple of 100 (300). I got the answer of 166.
Student B: I added 67 to each number, to make 400 – 234. My answer is 166.
Student C: I added 67 to just 333 to make 400. Then I subtracted 167 from 400 to get 233. Then I subtracted 67 from it to get 166.
Student D: I changed 330 to 300 and 167 to 170. 300 – 170 = 130. I then added back the adjusted amounts of 33 and 3 to equal 166.

This discussion is far more meaningful than any “drill and kill” worksheet containing math facts. Students are mastering facts and building problem solving skills.

My Math Fluency Alternative Curriculum contains resources for implementing accountable talk in your math block. Click here to view this resource.

The post Week 3 – Promoting Accountable Talk Centered on Fluency and Number Sense appeared first on Tanya Yero Teaching.

Writing is hard. Writing in math can be even harder. I can think back to many times I told my students we were going to work on writing and there was a collective groan. They would rather do 100 chores at home than write.

I teach at a school where we departmentalize. I’m responsible for providing instruction in the areas of math and science; however, I still hold my students accountable for writing in these content areas.

My school provides full-time gifted services. The majority of my students can procedurally solve a basic problem without any issues. When asked to explain their reasoning or the process they used to solve the problem, many of my students struggle. Anytime a student is learning something new writing can lead to deeper understanding of the material. Writing is not for the faint of heart. It takes critical thinking. The same is said for math fluency using number sense.

The picture below shows samples of different possible responses for approaching the 4 questions on the printable. I love the flexibility of number sense. There are so many ways to solve one equation. Because of this variety students of all different ability can connect and contribute.

I use these fluency chat prompts (found below) every day to start our math block. Students write their responses on whiteboards and then share out within groups or partners. It’s a way for students to learn from one another and gain new perspective on how to use the different number sense strategies.

If you want to start using these resources in your classroom my Math Fluency Alternative Curriculum offers these and so much more!

https://www.teacherspayteachers.com/Product/The-Math-Fluency-Alternative-Curriculum-BUILD-NUMBER-SENSE-for-Big-Kids-3446873

The post Week 2: Integrating Writing into Daily Math Fluency appeared first on Tanya Yero Teaching.