More to Math Fluency

Ideas for teaching math fluency and number sense

Today we’re talking all about fluency – math fluency to be specific. Much like fluency in reading, developing fluency in math is just as important. There is some confusion, however, about what math fluency REALLY is. Many teachers are just teaching basic fact recall and calling that instruction math fluency…. They believe math fluency is simply the ability for students to automatically recall basic math facts (addition, subtraction, multiplication, division) without hesitation. However, there is so much more to fluency besides basic fact knowledge! While fact recall is certainly part of it, that’s not all there is to it! It’s really just one tiny piece of true math fluency. Now you may be asking, “What does it mean then for students to be fluent in math?” Let’s dig in!

Math Fluency Means Number Sense

Before students can attain fact fluency, they first need to develop their concepts of number. This begins at a very young age for most children with parents or other family members teaching children to count everything in the world around them – fingers, toes, and toys. What seems like routine practice for toddlers is actually the beginning of their overall number sense development. 

 

As children grow in their number sense, developing children’s early number concepts can take place through a variety of activities that address these skill sets:

          ➜ Quantity Discrimination – Ideas of More, Less, and Same

          ➜ Counting Activities, including Counting On and Counting Back and Missing Numbers

          ➜ Number Relationships and Patterns

activities and resources for teaching math fluency

Young students need concrete methods of learning in terms of number sense. This can be accomplished in a wide variety of ways, but hands-on-learning is typically the best. Math stations or centers make great opportunities for students to use manipulatives and models to gain a concrete idea about an abstract concept like numbers. This model for delivering math instruction and practice also allows for you to differentiate to meet the needs of all of your learners. Before math automation can occur, students first need a solid understanding of numbers, counting and relationships between numbers, and we all know that everyone does not learn at the exact same pace. Differentiated math instruction and practice is a must if you truly want to develop students math fluency!

Math Fluency Means Flexible Thinking

To gain fluency and understanding of numbers, students also need flexibility when composing and decomposing numbers. This means that students come to identify and understand relationships in numbers. This is so much more than 3+2=5. This is truly understanding what 5 means… the quantity that 5 represents… what it IS to be 5. Students must have many opportunities to see, touch, manipulate, and otherwise interact with the number 5. Dot cards, rekenreks, five and ten frames,  number bonds, number lines, etc.

represeting numbers in different ways for number sense and math fluency

There are a so many hands-on activities that allow students to grow and strengthen their awareness of numbers and counting! I think as a teacher, it is so very important that you provide students with multiple tools, variations, and opportunities to compose and decompose numbers. Students must build flexibility in their math thinking that will extend far beyond the primary years. These foundations of number concepts will extend into multi-digit operations with addition and subtraction, as well as into their knowledge and understanding of multiplication, division, fractions, decimals— the list goes on and on.  

Each student learns differently, so be prepared to offer multiple means of instruction. A simple concept such as addition can be taught using tape diagrams, but it can also be instructed with rekenreks and number bonds. Present students with many different representations so that they can succeed and build a strong math foundation. I promise, it’s not something that should be overlooked in the primary grades. It IS THAT important! I’ve experienced upper elementary students struggle firsthand with fractions because they did not have a solid foundational understanding of whole-number relationships. Of course numbers less than one blow your mind when you don’t really “get” the relationships that numbers have!

The Importance of Math Fluency Foundations

Once the foundation has been laid for students, they are ready to start gaining math fluency. Early number concepts are so important when learning math. These are the building block topics that all other math understanding will be built upon, so it is especially significant that students create a strong math foundation and concept of number sense. Without it, students will fall behind or be unable to gain automaticity. 

 

As students grow and move up in grade levels, math automaticity becomes that much more important. Before students can move onto subtraction, they must first successfully understand addition. Before they understand addition, they must understand parts of a whole. The same goes for multiplication and division, fractions, decimals, exponents, irrational numbers- you get what I’m saying?!? Students need a strong number sense, and automaticity to be successful and grow in math skills even beyond their elementary years. 

Activities for Building Math Fluency

When you think about math fluency, I’m sure your mind wanders to the days of addition flash cards for homework, or even the dreaded (by some) timed multiplication quiz. While these are not bad options, there is so much more to math fluency than just basic computation drills

Break out some fun manipulatives for students to use that are engaging but also easy on the bank account. My personal favorites are rekenreks, ten frames, two colored counters, and oh-so-fun seasonal erasers or other fun trinkets. Remember the importance of offering students flexibility? This can be accomplished by the activities that you provide in the classroom. Use dot patterns on paper plates, decks of cards (printable or even digital), online games like Kahoot, math notebooks, and even a game of Around the World. These options are so easy to use, and students will love them as well!

How do you teach math fluency in your classroom? I’d love to chat with you! Drop a comment below or connect with me on social media! 

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2 Responses

  1. Thank you for the enlightenment on math fluency. I’d like to know how to create and incorporate math stations for all learners and keep them engaged but for less work and money and prep.

    1. Hi! I’m working on an upcoming post about how to make differentiation work for math teachers. Math stations are my go-to for differentiation! More info coming soon!

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