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Number Sense: The Key to Math Success

Free your child's inner mathematician and free yours as well!

Math and I were not friends.

In fact, I loathed and feared math up until my early adulthood. I struggled through every problem, hoping that I was doing it correctly, following the examples intently, only to repeatedly get the wrong answer. I would beg people to show me how to do the problems the right way, only to find that my mistakes were always simple ones; ones I should have seen.

I didn’t know I should have simplified at Step 1 or that the fraction that gave me so much trouble in Step 3 could have obviously been written as a decimal and then it would have been easy.

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I just didn’t see numbers like that. I didn’t understand them at their most basic level, and so every subsequent level seemed impossible. Math made me feel stupid. I even chose my college in part because of its limited math requirements.  

It wasn’t until I became a teacher and had to teach math that I actually understood what it was that I lacked, what made math so difficult for me.

I lacked number sense.

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At the most basic level, math comes down to a simple understanding of numbers; what they mean, how they can be combined and used in different ways. My idea of numbers was always so inflexible. A six was a six, and only a six.

My rigid thinking of numbers crippled me when it came to higher level mathematics and science. For example, the step into fractions depends on a flexible understanding of numbers and number relationships. Six is not just six; it is also two plus four, three plus three, four less than 10, two times three, and half of 12.

Number sense is internalizing this number diversity and being able to think of numbers in creative ways for problem solving. It is an essential knowledge for math success, because when kids internalize numbers, they become free to think beyond basic calculations to higher-level problem solving.  

Things you and your child can do at home to build number sense:

  • Relate numbers to everyday life. Numbers are everywhere when you get past the rigidity of six means six and only six. Number sense lies in patterns and rules and relationships. Look at the world for patterns and share what you find. What do you see while driving? Walking to the park? Watching T.V.? Encourage a discussion about numbers, patterns, and relationships between seemingly unrelated things.   
  • “Mathematize” everyday experiences. When numbers become part of everyday life, you remove the stigma of math being skills only needed for school. Integrate math when reading a story book. Count while climbing stairs and skip count when skipping stairs. Ask questions such as “How many children are on your team and how many cookies would we need to make if everyone was to get two?” Cook and shop together and use recipes as a way to understand fraction relationships and problem solving.  
  • Give your child meaningful responsibilities that require using numbers such as finding the tip at a restaurant, making and verifying change in a store, finding the percentage off of a sale item. When children use math in meaningful ways, they learn to value its importance in becoming a successful adult.  
  • Discuss different ways to solve problems. Flexibility in thought leads to more creative problem solving. Discussing different solutions to the same problem teaches that no matter how we get there, the right answer can be found and that if one way of solving doesn’t work for us, we can try another way, our own way, until we reach the answer. This is true in problems that do not involve numbers, too. Being able to see multiple perspectives is a great tool for being a diplomatic citizen as well.  

Online resources for number sense practice and cool tricks to learn:

  • Skip Counting – Essential for multiplication. One trick for visualizing this is “putting a number on your finger.” If you are skip counting by three, imagining a three at every finger tip.    
  • Patterns - This site has great suggestions for teaching pattern recognition for higher-level number sense.    
  • Create a 10 then Add On – Thinking in groups of 10 makes quick computation easy.  
  • Mental math – Being able to do simple calculations in our head frees us from feeling like we always need pencil and paper to do math. Much of day-to-day math is done in our heads.    
  • Multiplication and Division Songs – Music makes memorizing easy and fun. Here are songs for learning math facts.
  • Multiplication Rock – More songs for learning math facts.
  • Touch Math – This method allows kids to visualize and count numbers in a tactile way. Although this company would like to sell you their product, there are free resources on their site and the learning of the numbers is all you really need.
  • 10 Easy Math Tricks – These are so COOL! Takes a little practice, but very neat.

I am always impressed when my students come back to school after a math lesson and tell me their mom or dad taught them a different way of doing the lesson than I showed them. I encourage them to teach the class their trick and for the rest of the students to use whatever makes most sense to them. I don’t remember this sharing of methods being encouraged when I was in school, but I find, the more tools a child has in his tool belt to select from, the better!  

For those of us who are not number savvy, it is crucial that we have as much exposure to different ways of thinking about numbers as possible to give us success. I often hear parents say, “Math just isn’t my thing.” Unfortunately, what you are telling your child is that it is OK for you to give up on math because it is hard.

What we need our kids to hear is that they can be successful at math with practice, patience, and tricks for internalizing number sense. Accepting our weaknesses is fine, but not when we decide we do not need to improve upon them. Lead by example. Take this opportunity to relearn your own number sense. I did it when becoming a teacher, and life is much more meaningful now that I have.

Be sure to read next week’s article on Patch for more on math help.

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