The inclusive classroom. Teaching tips for elementary schools.

Why I Love Inclusion

When I first started teaching in an inclusive classroom I was nervous. I didn’t know how I would be able to differentiate for every student, meet their diverse needs, and remain sane and happy.


I grew to LOVE inclusion. 


inclusive classroom strategies for teachers


One lesson I learned is that a learning disability is just one strand of who a student is.


I am constantly impressed with the wide variety of strengths and challenges my students present.


The rich insights from dyslexic students into the plot of read-aloud books have left me in awe.


The spot-on recommendations I’ve heard from a student for how we can solve class-wide social problems have opened my eyes to his future. I see him in a successful career, respectfully solving problems and leading a team of employees.  It now breaks my heart to think that in a different setting that student would be left out of this social experience because he needs to dictate written work.


inclusive elementary classroom


Learning about all these STRENGTHS has tuned me into how inaccurate the message about learning disabilities often is.


inclusive classroom teaching strategies



Even a kid who can’t read, write, or solve math problems on grade level can be incredibly intelligent in so many other areas that are just as or MORE important in real life.


I have seen mind-blowing artwork and ingenious math strategies come from students who have pushed themselves to be great in spite of tremendous challenges.


Those students need to be allowed the space and time to do this.


As teachers in inclusive classrooms it’s not our job to say, “Well, you have strengths in other areas.”  It’s our job to provide activities with multiple entry points, provide blocks and visuals and oral instruction, and perhaps most importantly, reflective debrief at the end of these activities.


Sometimes we have to be really creative about how reach all students.


inclusive classroom teaching math strategies for elementary teachers and students

In math, I’ve found that stations are especially effective. The structure helps me hold myself accountable.


I plan in best practices by always having a station with a hands-on activity, a station that requires logic and reasoning, and a station where students are pushed to persevere in solving a complex problem they haven’t seen the likes of before.


math stations for elementary students in an inclusive classroom


The kids are spread out in 3 areas of the classroom, and I’m free to walk around, listen in, support those who need it, and sip my coffee!


When there are a few minutes left, we gather around the circle and discuss math strategies we used and character traits that helped us, like perseverance and for teaching in an inclusive classroom


My students know where math tools are, and they recognize that my expectation that they be fairly independent is part of the respect I have for them.


For the most part, I differentiate by providing time, tools, and an environment of perseverance and problem solving. Only occasionally do I alter work for a student.


I find that very few students can’t grasp grade-level math concepts, even if they’re challenged by accurately solving the corresponding problems. For example, most students who struggle with dividing large numbers can tell you exactly what division is.


It is most often not going to help them to dumb-down a math problem. Instead, we work together to figure out what strategies and tools will work for matching accuracy to conceptual understanding.


Why I love inclusion. Elementary teaching tips.

I love inclusion because it benefits ALL students.


When my class shares at the end of math, we hear about the struggles of perfectionists, kids with learning disabilities, and kids who have trouble working collaboratively. We also hear about successes, and the work that went into them.


An inclusive classroom is well-rounded, and that means it’s a classroom that is balanced by kids with strengths and challenges in all different areas. Some students  (with or without IEPs) have trouble with social skills, while others shine with exceptional interpersonal skills.


I try my best to help my students see that we’re a community there to support each other. We can all grow if we share our strengths and empathize with each other’s challenges.


They key is the way we, as teachers, support all students in embracing the differences. Inclusion is a way to build empathy and tolerance in children. Not surprisingly, it’s open communication and respect that fosters understanding instead of stereotyping and teasing.


improve math education at elementary schools
I work with teachers and schools to implement math stations. Recently I bumped into a local teacher. She told me that using my structure for planning and facilitating math stations has made a world of difference at her school. Please click here to learn more about how I can support you and your school!



Why Do Students With Dyslexia Struggle With Math?

If you have read Why I Love Inclusion, well, then you know that I love inclusion.


Unfortunately, I find that by the time some students get to me in 4th grade, they feel they can’t do things that I believe they can do. They have generalized their own learning disability too broadly, and given up on being “good” at skills for which I feel they have potential.


One example that comes up over and over again is welcoming a student with dyslexia into my classroom, and learning that he or she also has a generic IEP goal for math.


Why is it that so many students with dyslexia struggle in math?

dyslexia and elementary math

I have a theory, but first let’s talk about what dyslexia is.


The Yale Center for Dyslexia and Creativity says, “One thing we know for certain about dyslexia is that this is one small area of difficulty in a sea of strengths.”


The following are some quotes from an article by Sally E. Shaywitz, M.D. that appeared in Scientific American. The full article can be found here.


“Testing the youngsters yearly, we found that dyslexia affects a full 20 percent of schoolchildren…”

“This basic deficit in what is essentially a lower-order linguistic function blocks access to higher order linguistic processes and to gaining meaning from text. Thus, although the language processes involved in comprehension and meaning are intact, they cannot be called into play, because they can be accessed only after a word has been identified.”

“Linguistic processes involved in word meaning, grammar and discourse—what, collectively, underlies comprehension—seem to be fully operational, but their activity is blocked by the deficit in the lower-order function of phonological processing.”

“The phonological model crystallizes exactly what we mean by dyslexia: an encapsulated deficit often surrounded by significant strengths in reasoning, problem solving, concept formation, critical thinking and vocabulary.

“It is true that when details are not unified by associated ideas or theoretical frameworks—when, for example, Gregory must commit to memory long lists of unfamiliar names—dyslexics can be at a real disadvantage. Even if Gregory succeeds in memorizing such lists, he has trouble producing the names on demand, as he must when he is questioned on rounds by an attending physician. The phonological model predicts, and experimentation has shown, that rote memorization and rapid word retrieval are particularly difficult for dyslexics.


I’m worried. Are our dyslexic students struggling in math because they are being taught through memorized procedures, rote memorization of facts, and without connecting math strategies to conceptual frameworks?


That is my theory.


I have worked with enough teachers and parents to know that there are 2 major issues at hand here:


1. We are teaching the way we were taught.

Most of us were taught to memorize times tables, memorize the standard algorithms, memorize the steps of long division.


Most of us were not given opportunities to problem solve, figure out strategies on our own, or put math into context.


Many teachers are still teaching this way.


2. We are focusing on deficits instead of strengths.


Students with IEPs are often provided remedial help.  If she doesn’t have facts memorized, she’ll have help memorizing them. If she can’t keep a procedure straight, she’ll get extra practice doing it over and over again.


This all seems like common sense. But teachers are missing so many opportunities to allow her to internalize higher level math concepts through her strengths: visual spatial strengths, reasoning strengths, conversational strengths, and, critically, the ability to form conceptual frameworks.


She is being pulled aside and being held back.


So what can a teacher do?


Teachers can help students with dyslexia use their strengths to overcome their challenges. Math is actually the perfect subject for this.


Through hands-on experiences and rich math discussion, students with dyslexia can reach and exceed grade level expectations of math concepts.


inclusive classroom teaching math strategies for elementary teachers and students


Teachers can encourage students to figure out how to solve math problems on their own, suggesting that they use math strategies they are already comfortable with. For example, holding back on showing a more efficient strategy, and allowing kids to use repeated addition, blocks, or some other well understood strategy to solve newly introduced large multiplication problems. Is this time consuming? Yes? Does this allow for seamless understanding? Yes.


hands-on math for students with dyslexia


Teachers can offer activities that require students to practice math in context. For example, ask students to work together to solve a complex word problem that is realistic. The word problem should be written and read aloud several times – as many times as needed – throughout the activity.


Stolen pendant elementary math STEAM activity


Teachers can ensure that conceptual understanding becomes solid by providing time EVERYDAY for students to share strategies they used, and discuss similarities, differences, and patterns among their classmates’ work.


reflection questions for elementary math teachers


Teachers can create activities in which students must use several models to represent the same math problem. This helps all students see the connections between visual models, written equations, and physical models.



inclusive classroom teaching math strategies for elementary teachers and students

There are so many things we can do to serve our students with dyslexia. And guess what? All of these instructional practices benefit EVERY STUDENT!

What other ideas do you have for meeting the needs of every child?


improve math education at elementary schools

teaching growth mindset to elementary math students

Reset Math Mindsets

Today I want to talk about giving kids a clean start in math. We can do it with fun, hands-on activities.


STEAM Math Art Tile Design Activity for 4th, 5th, and 6th graders

When kids get to have an experience like this tile design activity, sometimes they forget they’re doing math.  The math is so in context, so authentic, that it just feels like a seemless part of the design process.


They’re moving, talking, and having fun. And at the end, it’s the teachers job to host a reflective discussion that helps students realize that they just tackled a complex math challenge. That last reflection component is the key to resetting kids’ math mindset.


To give students a fresh start, provide activities that have these 3 components.

1. Get Them Up And Moving!

Hands-on learning helps students make their own sense of math. Activities with blocks or fraction tiles boost proportional reasoning. Activities with counters can support number sense and organization. Dice activities foster subitizing, and games motivate efficiency and fluency.


STEAM math art elementary project
With this STEAM activity, students are given a checklist and pattern blocks. The kids work in partners to create a tile design within budget for their client, Mr. Buzz. A checklist provides students with a feeling of independence and frees up the teacher to move around the room, asking questions and observing problem solving. (Click image to learn more about this tile design activity.)


Set up math stations so even when students are sitting and working, they’re not at their usual work space. Even that small novelty changes the dynamic of the classroom.


Beginning class in a circle on the floor to introduce activities and ending class with a reflection circle of questions and shares means students are moving to at least 3 spots during their math period.




2. Get Them Talking!

Help students make strong math connections through talk. As they work, ask questions that connect physical reality to abstract math. Explaining concepts helps us process information at a deeper level – so take a break from teaching and leave the explaining to the kids!


STEAM math art tile design elementary turn and talk
In this tile design activity, kids need to communicate with their partner to choose tiles (pattern blocks) within a given budget, agree on a design, figure out each shape’s fraction of the whole, and measure the area of their creation. Talking about each step helps them process the math, and recording their work in a data table helps them see patterns and connect concrete concepts to abstract symbols. (Click image for details about this tile design activity.)


Here are some questions that get kids talking:

What symbol can I use to represent pushing two sets of blocks together? (addition +)
What are my choices if the two sets have the same number of blocks? (x or +)
What if I break a set of blocks into equal groups? (division ÷)
How would this be different if you had 10 more counters?
How many more counters would you need to get to the next 100?
How is your strategy different from your partners?
How is multiplying with 2 digit numbers different from 1 digit numbers?


3. Reflect On Fun!

Take advantage of the fun of hands-on activities and games to steer students towards a growth mindset. When kids are having fun, they don’t always realize the perseverance and problem solving skills they’ve used. Highlight those skills, and help students see that they have what it takes to work through challenging problems, whether they’re part of a game or an assessment.


At the end of class, ask direct questions about perseverance and problem solving:
Who got stuck and had to change gears at some point?
Who figured out strategies during the game that helped them do better and better?
How did you use math you already knew to solve this more complex problem?
What did it feel like to get stuck, and what did you do?
How can you use the perseverance strategies from this game to help you do math in the future?

Let’s finish the school year strong, with high-quality activities that promote positive attitudes and deep mathematical understanding!



Click here to check out one such activity:


STEAM Math Art Tile Design Activity for 4th, 5th, and 6th graders


Take care everyone! Happy New Year!

Jeannie Curtis

 teaching growth mindset to elementary math students

SALE! All of my teaching materials are 20% off Monday and Tuesday!


math teaching activities and materials



Hi friends,


This Monday and Tuesday, November 28 and 29, all of my teaching materials on Teachers Pay Teachers are 20% off!




I’m giving away a $10 gift card!


All you need to do to enter to win is sign up for my monthly newsletter by clicking the link below:


math freebies and teaching tips



I’ll choose a winner at random on Wednesday, November 30, 2016. GOOD LUCK!


PS: I suggest you use this sale to purchase this DIVISION STRATEGIES video. The video shows parents and teachers 6 methods for dividing large numbers by one-digit divisors. These strategies are perfect for 3rd, 4th, and 5th graders.




See you at the sale!


math teaching activities and materials




Effort and Accuracy in Math Class

In 2014 I did some action research for the Governor’s Teacher Network. I was researching perseverance in elementary students, and I created a plan to gather data every few weeks.


I developed a rubric for perseverance, and I was clear with my 4th grade students about how I would be scoring their math assessments. I scored every problem separately, using a 4, 3, 2, 1 system:



That was it. Clearly explaining how they could score points on every problem encouraged students to put forth effort so effectively that it almost ruined my research project.


Why? Because on the very first assessment, before I could implement the other aspects of my plan, the students out performed any normal group of beginning-of-year 4th graders. Almost all of them tried to earn a “4” on every problem, attempting to solve each problem with two strategies.


So why does explaining this simple grading rubric to students work so well?


For many students, grading is a mystery.


Combine that mystery with a fixed mindset of “I’m not great at math,” and you have students who look like they’re not willing to try for that “A,” but they actually just don’t know how. They feel that the “A” is not for them. Clearly explaining how students earn points invites more of them to try.


grading math for elementary teachers

It’s not just students who feel that grading is a mystery. Many teachers are overwhelmed by creating their own grading system. And parents LOVE the clarity of this rubric.

With this rubric, all strategies are valued equally… with a few caveats.


I gave students a “4” for accurately using ANY two strategies; abstract, representative, and concrete strategies were OK. Even on assessments, students could use hands-on tools, like base ten blocks, counters, or other manipulatives.


This practice does not only improve the number score on their assessments, it makes use of every moment of math class for students to practice problem-solving and self-differentiating. This helps students grow faster as mathematicians.  By allowing a student who only understands a concept in a concrete way to use a concrete solution, he is not being left out. 


Caveats: as the year progressed, I was clear about changing expectations. For example, by the end of 4th grade, the Common Core Standards require 4th graders to use the standard algorithms for addition and subtraction. Therefore, by the end of the school year, I required students to use the standard algorithm as one of their two strategies in order to earn a 4.  Also, throughout the year I continually showed students when strategies were too similar to count as 2 different strategies. Dividing 84 by 4 by separating 84 ones blocks into 4 groups and then drawing the same process did not count as 2 strategies (even though that step of moving from concrete to representative is important and valuable during math practice!).

Solving problems with 2 strategies is a better accuracy check than using the inverse operation.


Have you seen some of the end of grade test questions elementary students need to solve these days? They can be REALLY complex, and more often than not they are multi-step problems.


Checking solutions with inverse operations works well sometimes, but kids get mixed up working backwards from their solution to a multi-step problem. Also, sometimes kids miscopy the numbers from their word problems, and checking with the inverse operation won’t help them find that mistake.


Students catch many of their mistakes when they solve a problem once with one strategy, and then start all over again with a different strategy.  


elementary school math accuracy check



This is especially helpful for advanced students who sometimes rush through solving problems or those who are overly confident and don’t check their work. When they know that the only way they can get the highest score is to solve the problem twice, they are more likely to catch mistakes they made the first time. Also, pushing these students to come up with a second strategy is a great way to engage those students who sometimes feel bored with problems they think are “too easy.”


When students use multiple strategies, they make strong connections between operations… and this makes the teacher’s life easier.


Students who are frequently asked to use 2 strategies begin to see patterns and structures in math that make sense to them. They begin to understand how numbers work.


Over and over again, I see students using place value-based methods throughout the operations. Once students realize they can break down an addition problem by place value, they try a similar method for subtraction. They break up multiplication problems by place value, and when division is introduced they break apart place value again.


place value strategies for elementary school math teachers


I notice similar trends for students who like using math tools, like base 10 blocks. They realize that using manipulatives turns the abstract into concrete… the numbers in equations become blocks, and the operation symbols become actions (separating blocks, bringing them together, etc.).


These connections are exactly what’s missing when students rely mostly on standard algorithms. When they use multiple strategies regularly, students begin to see the relationship between all 4 operations on their own, which cuts down on teaching time.


I hope that using this simple grading rubric helps you as much as it’s helped me. It’s all about empowering students, right? If they know how to reach their goals, they’re much more likely to try.


Freebie: Find a free assessment reflection that fits this rubric on my Teachers Pay Teachers page. Just click the Download Now button under the words Free Download. 

elementary math teachers pay teachers store


how to teach fractions

Teaching Fractions: How To Introduce Fraction Concepts

I find it to be very interesting that many people, adults and kids alike, are scared of fractions.


Each year of teaching, I encounter students who are in one of two camps: they are overwhelmed by how abstract fractions are, or they enjoy fractions because of how concrete they are!


Wow! What a huge divide (pun intended)!


I love investigating this type of difference.


What I have found is that students’  attitudes towards fractions can often be traced back to their introduction to fractions.


When parents or teachers introduce fractions in a way that pushes new symbols and vocabulary too soon, kids are turned off. Think about it, most kids are exposed to fractions even before division.  If their first fraction experiences are with written fractions, all at once they are…

  • dividing numbers into equal pieces for the first time,
  • thinking about values between zero and 1 (talk about abstract!),
  • learning words they never hear in everyday conversation (e.g. numerator and denominator),
  • seeing numbers written in a new way (one on top of the other), and
  • seeing a new symbol that looks like a subtraction sign but isn’t (it’s called a vinculum, by the way. I had to look that up!).


YIKES!  That’s introducing wayyyy too much at once! 


On the other hand…

When students begin their fraction journey with hands-on activities, they seem to feel that fractions are a natural part of life.


Fractions are all around us. Kids have heard about sharing for years by the time they learn about fractions in school. They have felt cheated when given less than exactly one half of a cookie. Many of them know there are 4 quarters in a dollar. Most of the time, they have played with plenty of blocks, which has built their proportional reasoning.


We see many cutesy activities with pizzas and candy bars representing fractions, and while that’s a good start, it doesn’t guarantee the authentic experience students need.  If you know me well, you know I’m often skeptical of cutesy educational products! I appreciate the real-life connection, but it’s what students are doing with the pieces of pizza and candy I pay close attention to.


We want students getting their hands on fraction pieces, exploring proportions, and sharing aloud the patterns and connections they find.fraction-tiles


Before any other fraction work, students need many activities that simply require them to observe what happens as they work with physical, concrete fraction tiles or pieces.


This is why I created the game Fraction Swap.




Playing Fraction Swap is super fun, and it gives students the hands-on experiences they need to understand fractions in a concrete way.


As they play, students physically compare fraction pieces to see if they can make equivalent fractions.


4th grade 5th grade fractions math game


Fraction Swap works for everyone because it’s a game of strategy. It lets kids who are new to equivalent fractions learn by using the size and shapes of the blocks. It’s also engaging for kids who are ready for operations with fractions. They play strategically and have rich discussion afterward about how to represent their moves with equations.


The goal of the game is to completely cover 2 whole rectangles with the fewest number of fraction pieces. Players strategically swap groups of small fraction pieces for larger, equivalent fraction pieces.


fraction math for elementary teachers


These hands-on actions are essential for building a strong foundational understanding of fractions.


Kids build and deconstruct fractions over and over during this game. Teachers can take this activity as far as they like with the discussion questions included in the provided lesson plan:

  • Share a strategy you used in this game.
  • How did you know when fractions were equivalent? Show and explain, please.
  • What patterns or connections do you see between equivalent fractions? (On the board, write some equivalent fractions. Ask class to call out patterns they notice.)
  • What factors helped you win or lose a round?
  • Which cards were best or worst to pick and why? (This gets kids talking about larger and smaller fractions. Larger fractions help you cover the board, smaller fractions (1/12 for example) are useful in making “swaps” that help you get larger fractions eventually.)
  • When did you multiply a fraction by a whole number? (“Swapping” two 1/4 pieces for a 1/2 piece is 1/4 x 2 = 1/2)
  • When did you divide a fraction by a whole number? (“Swapping” 1/2 piece for two 1/4 pieces. 1/2 ÷ 2 = 1/4)
  • How could I represent this game board (put some fractions on a board) as an equation? (This can be an addition or multiplication equation.)

fraction game for teaching elementary math


Fractions don’t have to be scary. Elementary students learn so much from hands-on play. It is fun for kids, easy on the teacher, and highly effective. Win-win-win!


fraction game for elementary math students

improve math education at elementary schools

Elementary Teachers Can Be Excited About Teaching Math For These 4 Reasons

Math anxiety is real. And many elementary teachers experience it. Big time.


Teachers are not only stressed about the content their teaching, but the timeline they’re held to for teaching it.


Most elementary teachers are underprepared to teach math. Even those who like doing math haven’t had sufficient training to teach math. Especially not Common Core math.


All of this can lead to low morale and teacher burn out. And that’s bad. But there are a few things teachers can get excited about when it comes to teaching math nowadays.


The following are a few points I like to hit with teachers during my professional development workshops:


1. Efficiency Is Less Important Than It Used To Be

elementary math teaching ideas

Not too long ago, the “best” elementary math students were the ones who could solve problems quickly and had their facts memorized. These little calculators were praised and identified as smart – until middle school. Studies show that that’s when students who have been memorizing their way through math hit a wall. The fixed mindset they’ve developed affects their math and their self-esteem.


These days, however, conceptual understanding is king. 


Efficiency does not equal understanding or mastery. The Common Core says that fact fluency should not come at the expense of understanding. Plenty of research shows that timed tests are actually detrimental to students’ future math success.


As we follow students through the grades, we can see that those students who have strong conceptual understanding (read What Is Conceptual Understanding?) and work harder to learn math continue to persevere and do well throughout upper grades.


Many teachers become frustrated when students solve math problems inefficiently.

This is one stressor teachers can let go.


Allowing students to work longer on fewer problems

  • allows students to take ownership of their solution,
  • provides the teacher with lots of information about how each student is thinking, and
  • helps teachers pinpoint where misunderstandings are occurring in the problem solving process.


Instead of judging students’ math ability on speed, teachers can create clear grading guidelines that will make life easier for themselves, the students, and parents.


If a student can regularly solve a problem with 2 different strategies (no matter how efficiently), she gets a “4” or “A” for that skill.

If a student can regularly solve a problem with 1 strategy (no matter how efficiently), she gets a “3” or “B” for that skill.

If a student can show work and is on the right track to solving a problem with 1 strategy (no matter how efficiently), but cannot regularly find the accurate solution, she gets a “2” or “C” for that skill.

If a student does not show work or uses the wrong operations to solve a problem, she gets a “1” or “D” for that skill.


You will be amazed how this grading scale affects students’ math work!


Students who are encouraged to solve problems with 2 strategies catch their own mistakes and create incredible math connections.


Providing less work and more time for problem solving, efficient or not, will help teachers and students enjoy math class.


2. Interleaving Helps Teachers Get Through Their Curriculum

interleaving elementary math teaching

Something I hear from teachers all the time is that they can’t get through their curriculum in a school year. Definitely not with time for review before end-of-grade standardized tests.


When I ask teachers what the problem is, they often have one of two (or both) issues:

  • they wait for mastery of one concept before moving onto the next, or
  • behavior problems in the classroom slow down teaching.


Interleaving is here to save the day! What is it, you ask?


Interleaved practice is when students practice one concept and then another and then another, and then finally come back to practice the first again. They problem solve and learn in an ABCABCABC format.


“Blocking” is the opposite, where students practice the same concept over and over again. Blocking is the most common way we try to teach students, but it is far less effective. Blocking is when students practice AAA before BBB before CCC.


What’s crazy is that most textbooks are organized by blocked units.


(Scientific American has a great article about interleaving if you want to read more and see some statistics.)


There are a few theories as to why interleaving works so much better than blocking. 


Spacing: Memory researchers have found that deeper learning takes place when students have breaks, or space, between practice. If students are introduced to adding fractions on Tuesday, their understanding will actually grow in they practice a different math skill Wednesday and then return to adding fractions later that week.


Discrimination: Our brains are great at picking out differences. When students add and then multiply and then subtract, their brains have a chance to find all the similarities and differences between those operations.


Retrieval: When students participate in blocking, or learning one unit at a time, they are able to keep information in their short term memory. They might appear to be doing well during the unit, but forget much of what they knew by the end of the school year. With interleaving, students’ brains are constantly asked to retrieve information needed to solve problems, which creates strong and lasting memory pathways.


Interleaving leads to better class engagement and helps students master concepts with less practice!


In fact, teachers should move on from one concept to the next before most students have a chance to master the first. When the concept is revisited later, the class will make greater gains in the area because of the break from it. Isn’t that fascinating?!


Get interleaved stations here.


3. Exploration Is One Of The Most Effective Ways For Students To Learn, And It’s Easy On The Teacher

elementary math teaching strategy: exploration

What’s the best way to help students develop seamless understanding? Give them time and tools to build knowledge on their own.


If you want an engaged class of motivated learners, set up stations where they work together or independently to solve problems without teacher help. Kids feel the respect from teachers who let them hash out problems with their own unique strategies.


Teachers understand how powerful exploration is when they participate in activities at my professional development workshops. In less than 10 minutes of solving large division problems with base 10 blocks, I always hear exclamations from teachers who never truly understood the concepts behind long division.


Teaching through exploration first saves teachers so. much. time. 


The best part is, the problem solving strategies that students come up with are based on the math they know and the ways of solving problems they’re comfortable with.


When we show students a strategy for solving a problem without providing lots of exploration time first, we are creating learning gaps for most students. If I show you my way of multiplying 2 digit numbers before I’ve let you create your own, you’re…

a) missing out on authentic problem solving practice,

b) focused partly on the context and partly on trying to think like me,

c) learning a procedure and not the concept, and

d) less motivated by the efficiency of my strategy because you haven’t had time to create your own inefficient one first.


Some teachers may fear that “Exploration” is some free for all time where students may or may not learn something. This is certainly not what I’m pushing for.


Exploration activities should be thoughtful and well planned. Here is an example of an exploration with pattern blocks that helps students build area, multiplication, proportional reasoning, and ratio skills.


Through exploration activities, teachers spend less time (if any!) in front of the class, and more time circulating, listening to math discussion, supporting struggling students, and taking informal assessment notes.


Exploration activities are fun for everyone. Including the teacher.


This set of math stations includes two exploration activities: a multiplication exploration with base 10 blocks, and a challenge for students to create word problems for given equations. 


4. Math Talk and Math Discussions Lead To Better Understanding, And Make Use Of Teachers’ Language Arts Skills


Did you know that most elementary teachers have a language arts background and/or preference?


Because of this, many elementary teachers are uncomfortable teaching math.


The good news is, hosting a discussion about math everyday will dramatically deepen students’ understanding of the concepts and strategies they’re learning.


Just like you would lead a discussion about a novel, you can ask students what connections they made, what patterns they noticed, and how the math made them feel.


Using the last 10 minutes of class to discuss the day’s math is well worth the time. It isn’t lost teaching time, it’s extra effective teaching time.


elementary math professional development workshop



Exploration with Hands-On Math Tools (Manipulatives, Blocks, Tiles) Part 1

In your school you probably have access to math manipulatives – blocks, fraction tiles, clocks, Cuisenaire rods, pattern blocks, compasses, rulers, base ten blocks, even building blocks like Legos. You might not have all of these hands-on tools in your classroom, but you can probably find lots of them in other classrooms or stored away on shelves and in closets – don’t be afraid to borrow!

Math exploration for elementary teachers.

Math manipulatives are our best friends!


There are tons of structured activities out there that help students gain concrete, conceptual understanding through using manipulatives. You can find a bunch here.


But right now I want to talk about the benefits of unstructured exploration and play with the blocks and other manipulatives in your school.


Some kids grow up playing with all kinds of toys and blocks from the moment they’re old enough to hold them.


Playing with blocks has so many benefits, and children make different kinds of connections through playing with blocks at each different stage of their development.


Through play with blocks, young children make important math connections that later help them with:




Visual/Spatial Understanding



Hand-Eye Coordination


Accuracy and Precision

Problem Solving


Think of playing with blocks as building mathematical background knowledge.

Developing the skills listed above sets kids up for mathematical success.


But not all students come to school with these background experiences. Giving your elementary students time for low-structure play with base ten blocks, Cuisenaire rods, Lego-style blocks, and pattern blocks helps them with elementary math!


Without even knowing it, during unstructured math exploration they’re learning:


Fraction concepts



Unit conversion

Problem Solving


Geometry concepts

Proportional reasoning


Even if it’s just a few minutes of free play time before a structured lesson…

Students are excited and motivated by math tools. They love to feel the wooden blocks, stack the plastic ones, and ogle over the  designs and patterns they can create with the multi-color blocks.


Here’s a classroom management tip:


Before a structured math activity with manipulatives begins, provide free time for exploration.


It’s so hard for little dudes and dudettes (or even big dudes and dudettes!) to stop themselves from building towers of ones blocks or crafting beautiful designs with pattern blocks, so give kids a few minutes of creative free time before asking them to use the tools for specific activities.


Say, “OK I’m going to let you explore this math tool for 5 minutes before we start our math activity. That means that at X o’clock we’ll stop free time and begin the math activity.”


You’ll be amazed at how engaged students become when they are allowed to experiment with manipulatives. And because they’ve been given a little time to scratch their creative and curious itch, they’ll be better able to use the tools appropriately during a math activity.


Read Part 2 and Find a free Math Manipulatives Activity here!


improve math education at elementary schools




Exploration with Hands-On Math Tools (Manipulatives, Blocks, Tiles) Part 2

(Read Part 1 here!)

Exploration as a math activity…

Sometimes as teachers we have a hard time giving up control. OK, lots of times as teachers we have a hard time giving up control. That’s why we so often skip taking a day off just to avoid writing lesson plans and searching for a capable sub.


It’s hard to give up control, but sometimes it’s the best thing we can do to foster engagement and authentic learning.


Facilitating exploration activities means that you cannot predict all of the learning outcomes for your students and you cannot formally assess the accuracy of your students’ work.

However, you can count on engagement, curiosity, and valuable, self-differentiated learning.


exploration math activity with pattern blocks for elementary studentsHere’s an example of an exploration activity with pattern blocks:

“I’m going to give you 20 minutes to explore the pattern blocks. You can work together or alone. What are some guidelines we can write on the board for this exploration time?” (Students brainstorm and you help: share the blocks, don’t touch other kids’ blocks unless you’re working together, don’t throw blocks or knock over towers, keep the noise level reasonable, etc.)


After 18 minutes: “You have two more minutes until we’re going to pause. You won’t have to clean up, but you will need to take your hands off the blocks and listen to directions in 2 minutes.”


“OK go ahead and put both of your hands on your head so that I can see that you’ve stopped exploring and you’re ready to listen in 5, 4, 3, 2, 1.


elementary student math pattern block activity for teachers“Most of you have a design of some sort in front of you. Some are built vertically, some horizontally. I’m going to give you 1 more minute to make sure you have some sort of design made of 10-20 blocks for this next step. No less than 10, no more than 20.”


“Hands on heads in 5, 4, 3, 2, 1. What I want you to do is figure out how many green triangles you would have if your design was made of only green triangles. I’ll give you a few minutes to work this out, and then we’ll share.”


Walk around while students are working. Listen to conversations and observe. Try not to help! If students are stuck, ask them to look around for strategies that other students are using.


“1 more minute! It’s OK if you don’t finish. What’s most important today is that we share some strategies.”


At this point you may choose to move students from their work spaces to a place where they can have a discussion with empty hands. Provide a few blocks to help students show their strategies.


You will not know whether students came up with the correct answer to the challenge you gave them, but that is not the point of this activity.


Tell students that some of them will have a chance to share their strategies.  Provide them with some sort of silent hand signal that they can use as they listen to each other to show if they agree or used a similar strategy (this can be a thumbs up or the sign language sign for “same”).


Allow several students to talk about their experience figuring out how many triangles it would take to create their design.

It is important to allow for some reflection time at the end of EVERY lesson, including this one.


Ask students to share out what they learned during this activity. This is when you’ll be able to find out the learning outcomes for each student.


You may hear students talk about…

  • multiplicative reasoning (for every red block I counted 3 greens),
  • ratios (1 hexagon: 6 triangles),
  • geometry (these corners were equal angles, two smaller angles fit in this bigger angle),
  • equations that match actions (I had 4 blue blocks, so I did 2 x 4 = 8 to figure out how many green blocks that would be),
  • comparing and contrasting,
  • conversions,
  • endless other important math concepts!


This reflection time is important and exciting.


Write each idea on a poster and return to these concepts throughout the year.

Teacher or parent questions for the elementary math consultant.