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Building a Strong Math Foundation with Number Sense

The day has finally come. The foundation of your new home, your dream home, is being poured.  With excitement, you head over to the property to see the big slab of concrete that will literally support everything you have worked so hard for.   When you arrive, you get a glimpse of the shiny, still wet gray material that glistens in the sun.  Your heart skips a beat as you watch your dream start to take shape.  As you walk around you notice that the concrete is a little uneven.  Some spots are lower than others, and there appears to be a small hill right where your living room is.  You also notice that the foundation doesn't come close to filling to mold that was created for it.  You decide it's okay because what really matters is what has yet to be built.
Building a Strong Math Foundation With Number Sense Tips and Ideas

Building a Strong Math Foundation

If you were going to build a house, would you build it upon a foundation that was only 1/3 the depth of concrete that was required by code or recommended by the engineer?  What about a foundation that was uneven with obvious high spots and low spots?  I sure hope not!  Why?  Because we know how important the foundation is to the stability of the structure being built upon it.  Well, in the math world, number sense is this foundation. 

Everything we do in math rests on this foundation.  I know that this is a strong statement to make, but think about it.  Place value . . . number sense.  Algebra . . . number sense.  Even geometry . . . number sense.  That is why helping out students build a strong number sense foundation is so important.  If we look at math in the early years as just learning to count and identify shapes, then we are completely missing the importance of building a foundation.

So What is Number Sense?

Well, that can actually be a tricky question, since number sense is a broad and abstract concept.  One of the best definitions that I have found came from Janette Bobis, a math educator and researcher in Australia.  She defines number sense as "a well organized conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems not bound by traditional algorithms."  It's the ability to see numbers and their relationships in different ways, to work fluidly with numbers, and to be able to easily adapt to number representation without losing meaning. 

Building and Representing Numbers with tally marks is part of number sense

Number sense is what allows students to think about numbers in different ways and solve problems differently, while still reaching the same conclusion.  Number sense is what leads to true mastery and understanding of math.  Check out this short video to see how building a strong number sense in the primary grades can affect a student's math thinking in the future.

What Makes Up Number Sense?

In 1989, the United States National Council of Teachers of Mathematics identified five key components to this abstract notion of number sense:
  1. Number meaning
  2. Number relationships
  3. Number magnitude
  4. Operations involving numbers
  5. Referents for numbers and quantities
It is these skills, when woven together, that create a solid and strong foundation for more complex math concepts.  

Helping Our Students Develop a Solid Foundation

Now that we can better wrap our minds around this nebulous concept of number sense, let's turn to the more important topic of how to help our students get it.  You see, number sense is not something that can really be taught.  It's really something that is learned through experience. And that right there is the key to developing number sense in the classroom - experience.  We need to give our students lots and lots of opportunities to experience numbers.

While we can include some instruction in that equation, without the experience our students will develop that deep foundation that we want them to have.  This is the difference between the "old school" approach of memorizing math and today's (often misunderstood) methods.  Sure, memorization might be an easy way to remember math facts, but it doesn't give our students the underlying problem-solving skills that are developed as number sense strengthens.  

Number Sense Activities for the Classroom

Boy working on building and showing addition problems as part of building a solid number sense

I want to share with you a variety of number sense activities that you can easily add to your classroom.  

1.  Math Centers
Math centers are a great way to give students independent time to experience numbers.  As you prepare and plan your centers and math activities I would encourage you to make sure that you are including variety.  For example, don't just include number identification activities.  Even if identifying numbers to 20 is the standard you are working on, make sure to provide some variety that gets your students experiencing those numbers in different ways.

Building number sense through hands on math centers

2.  Number of the Day
This one is near and dear to my heart because I have used it and seen its effectiveness with students.  Number of the Day is a daily number routine, usually done with the whole class, that gives students with a variety of number sense activities all related to the summer number.  It can be a very powerful tool in helping students develop a strong number sense.  Find out more about how I use Number of the Day in my classroom.

Building Number sense through Number of the Day

3.  Real World Math Connections
Math by nature is abstract.  By connecting these abstract concepts to the real world, we help our students make personal connections.  When they make personal connections, they understand better, and are then able to apply that understanding to future abstract concepts.  You know those word problems that get such a bad reputation (yeah, the ones about two trains heading towards each other)?Well, ty are a great way to connect math to the real world.  Now I will be the first to admit that not all word problems are written well.  But when they are, they can really help students connect to math in a new way.

Another great way to make real-world connections with my students is by sending them out to find math in their world. These days, with technology so readily available, it can be as easy as taking a picture of something that shows 10 and email it to me.  Send them out with a real-world math challenge and I bet they will surprise you and amaze you at what they come back with.

Time to Get Started

So grab your hard hat (I couldn't pass up the opportunity for one more construction connection) and get busy building that foundation.  Our number sense foundation might not be as easy as pouring liquid rock, but over time, we can build it strong by laying it brick by brick.

Don't lose these thoughts and ideas.  Just pin this to your favorite classroom Pinterest board so you will be able to get back here whenever you need to.  And don't forget to check out more number sense ideas.

Building a strong math foundation starts with strong number sense skills.  These tips and ideas will help you incorporate number sense building activities into your classroom.Building a strong math foundation starts with strong number sense skills.  These tips and ideas will help you incorporate number sense building activities into your classroom.

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