Subitizing, Number Sense & Fluency

I worked for several years as a numeracy teacher, meaning I spent a lot of time making sure that students can subitize numbers accurately and quickly.  I soon became know as the dot lady because counting dots quickly by grouping them is what we did a lot.  Since that time many website have lots of activities that help students improve their number sense.

The same is true for subitizing numbers when adding or subtracting.  There are not very many ways to make ten, yet students are still struggling with adding and subtracting past third grade.  Even the adding by nine's trick where you move one number over to make the nine a ten, therefore only having to add a ten to the other number making it easier is a struggle for students.  How many students do you know that have trouble adding ten to a number. Below is a nice video that explains the 9's trick.

From Walmart site,
 Students taught me this game.

From Rainbow Resource website
Kids of all ages love this game.

from Really Good Stuff website
This is a great game because it teachers number sense, vocabulary and kids love it.

From Target website
Old school, not too many kids are familiar with this game.

From Target Website
Competitive Kids stop counting on their figures after a few days playing this game.

There are a lot of board games that help students learn number sense that I have had great results using.  Below are just a few ideas I have used that students seem to enjoy and learn from.

•  Mexican Train Dominoes.  
• Yahtzee
• Make 7
• Card games with Ten Grids on them  Teachers Pay Teachers Ten Frame Card Game
• Build and Block board game
• What's my Number 

Image from Greg Tang Math Website

Here are some online sites.  Just click on to link to webpage.  Let me know what you think!

• Greg Tang Math
• Arcademics Jumping Chicks
• Speedy Numbers
• Learning Box
• Making Bonds
• ABCya Sum of Dice
• ICT Games Shark
• Illuminations NCTM

And just a fun, rewarding site kids love (it also makes them think!)

• Hooda Math

Why do I need to learn this..... I am never going to use it!

I am going to guess that many of you have either said or heard those words.  I remember saying them myself in school.  For years I would try to make sure that my math lessons were relevant to the students' lives and although I was often successful I still heard these words.  I have also heard students say they didn't need to learn what I was teaching because  their mom, their wife or they just planned on hiring someone to do their bills or another life skills or math lesson I was teaching. Since then I have one answer.  Don't you want to grow dendrites?  That answer seems to actually motivate them to learn and try harder.  When new students as why they have to learn something, the other students fill him or her in on dendrites for me.

Neuron

Dendrites grow in your brain, the more you use your brain the more dendrites and the stronger dendrites you will grow. Even though it has been argued that worksheets definitely aren't the best way to grow dendrites, when I see someone cheating, or copying another students answers instead of struggling a bit and figuring it out on his own.  I tell the student that the person he or she is copying from won't be around to solve his problems forever, I then ask them don't you want to grow your own dendrites so you can problem solve for yourself?

Who wants to play chess?

Even though you may not use the math you are specifically studying, don't you want your brain to have lots of these great problem solving dendrites?  Now as a parent you might think this is all school related.  You can do puzzles, play chess or even have your child figure out how to increase a recipe she is cooking are all ways that you can all help your child grow dendrites.  Don't worry about your child making a mistake or having to start over, this is part of the learning process.  Figuring out how to fix a mistake challenges the brain. Challenging the brain is what learning is all about. Let you students and own children know that making mistakes is all about learning, nothing to get upset about.  We know when a person is upset their brain actually has trouble connecting all the pieces due to being stressed out.  When students feel confident and don't worry about making a mistake it helps learning be at its best.

There has been talk about the brain having plasticity.  This basically means that your brain can grow and change all your life.  Carol Dweck has coined the term "growth mindset".  where a person can continue to learn, their brain will continue to get smarter.  In 2013 I took  Jo Boaler's online class at Stanford University, "How to Learn Math".  Jo Boaler recently co-founded  the website  www.youcubed.org  One of the things Jo talked about was students learning from their mistakes and not being afraid to make mistakes. Although I had already been doing this a bit, I took it a step further from what I learned in her class.  One way was when we worked out a difficult problem I would call on several students to tell me what answer they got and how they got it.  As I went from person to person I didn't say who was correct or who was incorrect.  Students listened to each other, figured out how they went wrong or why several people might be correct and how different students arrived at the same answer using a different technique.  Other times I would have students document words, pictures and symbols on paper and take turns going up to the Elmo and showing the class what they got for the answer and how they solved it.  Students loved the fact of self-discovery teaching them another way to do a problem, or figuring out where they missed a step.  

I recently found online that Jo Boaler has developed a reference card that gives you great ways to encourage mindset growth when you are teaching or with your child.  Mindset Cards

One of the lesson Jo Boaler showed a video on when I took her class was students telling how many squares around a numbers chart (like the picture frame on the outer number boxes).  So how many squares are around a 10x10 hundreds chart?  A 8 x 8 chart? This is a great activity.  How many of you said 40 squares? 38 squares? 36 squares?  I get all those answers, we then discuss and go on and do a few more squares.  When we do our final discussion, students have come up with different formulas to figure out how to be correct each time without having to count all the squares.

Competitive and Engaging Rote Learning

Okay, I know, rote is a four letter word in education.  I wrote my master's thesis on the benefits of rote learning.  My instructor told me her view on it but I still thought it was important.  My study group that I used was sixth grade math students who had an F or D in math.  After eight weeks of rote learning their math grades went up to either a B or a C without any tutoring in their daily lessons from their math teacher.  I basically had them memorize their multiplication tables in a variety of ways.  Any math teacher that has ever tried to teach a student to reduce a fraction, find a common denominator or factor an algebraic expressions can tell you that if the student does not know his or her basic multiplication facts it turns into a frustrating lesson for both the student and the teacher.

The same could be said for reading.  Sight words are usually not easy to decode, sound out or figure out in context (whole language).  By third grade students that do not know their sight words really start to struggle in school.  Think about how important reading is in every subject.  A student that has difficulty reading will have a challenging time in middle school, high school and college.


One of my favorite sites for rote learning is Arcademics.  It is a free site to use if you don't mind the ads and let your students know that is not part of the site, or you can pay to use it ad free along with the benefits taken directly from their website are show below.

On the free version up to four students can compete against each other,  I also have done something the kids really love.  My students often complain about having to not only do grade level work, but become efficient in their basic skills (memorize them!).  I tell them if they can beat me in a race I will consider their complaints.  (Thank goodness in all my years teaching I haven't had a student beat me yet!).  So they line up at the SmartBoard to take turns racing me while I play on my desk computer. It is a lot of fun.  I do the counting coins or multiplication one.  Once the students see how fast I am they actually want to improve.  I think up until that point they really didn't see a need to memorize their basic facts or think that they could recall them quickly by memorizing them.  I even allow several students at the SmartBoard to help each other and occasionally allow them to have a calculator.  

Screen shot from www.arcademic.com

Besides math the site also has a typing, language arts, spelling and geography section.  And if you homeschool or have only one or two students playing, they can either play against the computer or students from other schools. Students use either an assigned player123 screen name or you can have your student create an appropriate fake screen name.  There is no chatting or texting while playing against students from other schools, which is really a nice safety feature.  I have used this website for almost a decade, and they continually improve it.  The site has won numerous awards in the past few years, and I can see why.  Take the time to try this site out, I know you will love it!