anna by anna May 16, 2016

Three Important Number Sense Concepts For Children to Practice

“Number sense is an emerging construct that refers to a child’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.”

Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities, Russell Gersten and David J. Chard (2001)

As a parent of two elementary age children, math and especially developing number sense is an integral part of our lives. From the moment my children were born, I was counting toes. Oh those cute toes! We count down from 10 before blasting off as their daddy throws them into the air. We write numbers alongside ABCs at the kitchen table. And, of course, we relish our time to play Todo Math together on the living room couch.

When it comes time for intentional practice to hone number sense, there are a few important concepts that may not get the attention they deserve. Here is my list of three important hard to practice number sense concepts and a few fun activities.


My youngest and I walked along a pier of sailboats. In my mind I estimated about 80, possibly up to 100 sailboats. I wondered what my youngest thought so I turned to her and asked “how many boats do you think there are? Don’t count, just use your super powers of estimation.” She said “100 million” stretching her arms out big. Clearly, she just knew it was a number bigger than 10 but without much “sense” of number she over estimated. Her answer is totally typical of 3 – 5 year olds. With the following tips, you can help your child hone their magnitude skills without having to change your daily routine or schedule.

  1. Estimate, estimate, estimate! Practice estimating out loud the time it will take to get to school, the number of steps between your front door and the mailbox, or the number of skittles in a candy bag. After you estimate, count the minutes, steps or candies to see how close you are to your estimate. Kids LOVE this activity. You can make it more intriguing to them by over estimating or under estimating.
  2. There is a lot of language in math. And for children who have speech and language delays, intentional practice of math language is critical to mastering the related mathematical concept. Here is a list of different terms to describe magnitude. Use them with your children to help them familiarize with the concept.
Less More
Fewer Greater
Smaller, Smallest Bigger, Biggest
Decrease Increase
Tiny Huge
A little A lot


Unitize and Place Value

The ability to unitize means your child can understand that groups of ten are both equal groups of ten and equivalent number of units (ones). For example, 20 is 2 groups of ten and 20 units. In 25, the two means 2 groups of tens or 20 ones plus 5 additional ones represented by the 5. Unitizing is a HUGE shift in a child’s thinking and giving them lots of opportunities to explore this concept will help them make this shift. Here’s an activity you can do with straws and rubber bands.

  1. Take a box of straws and spread the straws out onto the table. Ask your child “How many straws are on the table?” After your child answers, invite them to check how close they are by counting by ones. For this example, let’s say there are 65 straws on the table. Now ask your child, “I wonder how many bundles of 10 there are? Can you guess?” At this moment, your child may be a little confused and answer a number other than 6 tens. That’s OK. Avoid explaining why their answer is unreasonable and instead, invite your child to count by 10s. Start bundling up 10 straws at a time and tying them with a rubber band. You can model one group of 10 and let your child bundle the rest of the straws. Once bundled, ask your child to count how many 10s there are. Answer “6 tens!” You can extend the activity to 100s, 1000s. Unifix cubes are also a great substitute for straws.


Addition – Part Unknown Puzzles

One of the lesser common but more intriguing types of addition problems is the “part unknown” problem. Some of you may know them as a missing addend addition problem. For example, 1 + ? = 2. Solve the unknown. This type of question is important to help children develop part/whole thinking. Here are a couple of fun activities to help hone their addition skills.

  1. While sitting at the table with your child, tell them that you notice there are 20 toes under the table. Tell them “I have 10 toes, how many do you have?” If you have different eye color from your child you could say, “I notice we have 4 eyes, 2 eyes are green and how many are brown?” Use other examples from your surroundings like number of family members and the number of boys and girls in the family. Represent your thinking in pictures and in equations like 20 = 10 + ?, 4 = 2 + ?.
  2. There are so many great games in Todo Math but one of my most favorite games is Domino Math because it helps my children part/whole thinking. Levels 6, 9 – 12 are all “part unknown” puzzles. Here are a few screen shots of the puzzles.


Make 6 Make 9 Make 10 v2 Make 10 Make 12 Make 18


I hope you enjoy these activities and if you have a few of your own, please share! We’d love to hear from you.