Developing Number Sense in Your Children

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Math can be a difficult subject for many people.  Often this is because math has been learned as a series of steps without learners understanding the ‘number sense’ behind what they are doing.  Below you will learn what number sense is and find several articles about how to develop it in your children.  This post is updated as more articles are added.

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What is Number Sense?

Number sense is fully understanding numbers and how they relate to each other.  It involves flexible thinking and seeing different ways that problems can be solved.  Here is a good overview:

How to Stop Your Children From Doing Math on Their Fingers

Boy counting on his fingers

Math Manipulatives for Building Number Sense

These are the seven manipulatives we consider critical to learning math in our homeschool.  Five of them can be printed for FREE at the end of this section.

1. The best math manipulative we have is our abacus.  Read here to find out what kind to buy and how to use it: Using an Abacus to Build Number Sense

2. Number paths and lines are helpful for seeing the linear relationship between numbers.  Learn more: Stop Using a Number Line (Before 2nd Grade)

Number path and number line together.

3. Ten frames allow children to visualize how numbers add up to 5, 10, 15, and 20 by placing manipulatives within them.

Ten frames showing 1-10

4. Subitizing cards can be used to develop visualization skills around math.  Read more below under Four Number Relationships Children Need to Learn.

Six different cards showing different numbers in various ways.

5. Part-Part-Whole Circles help children decompose numbers.  Read more below under Four Number Relationships Children Need to Learn.

Whole circle with 17 written in and part circles with the number tiles 10 and 7 written in

6. You will need some type of manipulative such as tiles, beads, rocks or anything else small that you can have a lot of for modeling problems.

7. Number tiles allow children to see how numbers with more than one place value are ‘built’. (Shown above with Part-Part_Whole Circles).

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Developing Early Math Skills

If you have preschoolers, then here are the math skills your children need to develop so they are ready to learn addition and subtraction when they start the elementary school years:

The 5 Math Skills Kids Need Before Learning Math Facts

blocks in groups with the number of how many in each group next to it

Four Number Relationships Children Need to Learn

There are four key relationships children need to learn as they start on their math journey in the early elementary school years.

1. Subitizing

Subitizing is the ability to “see” an amount without having to actually count the number of objects.  You can learn more in:

Visualizing Numbers: A Key Skill to Learning Math

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For some games to practice subitizing (the cards are included in the FREE printable packet above.): Subitizing Games

Pinnable cover for blog post Subitizing Games

For a number routine to practice subitizing: Show Me Routine

One and Two More or Less

Learning one and two more and less allows children to be flexible thinkers and have a variety of strategies for solving problems.  For example, if a child needs to add 39 + 5 and they understand that 39 is one less than 40, then they know that the answer is one less than 40 + 5, which is a much easier problem to solve in one’s head.

Make Friendly 5 and 10

Learning the numbers that add to 5 (e.g., 1 +4, 2+3) and 10 (e.g., 3+7, 2+8) also allows children to be flexible thinkers and solve problems in a variety of ways since we use a Base 10 system.  If a child knows 3+7 = 10, it makes a problem like 53 +7 very easy to solve.

Understanding Part Part Whole

Breaking numbers apart or decomposing is an important skill that will be used at all levels.  Learn more:

Build Number Sense with Part-Part-Whole Circles

Whole circle with number 10 and part circles with 9 and 1 and a child working the problem next to the circles.

Teaching Math Facts

Teaching children to move from counting to solve math facts to having their facts memorized is a key part of math during the elementary years.  Follow these progressions to make this process as painless as possible:

What Order Should We Teach Addition Facts In?

Addition fact chart highlighted in different colors

What Order Should We Teach Multiplication Facts In?

Chart of multiplication facts with highlighting

Activities for Practicing Number Sense

It is one thing to know what number sense skills our children need to learn, but how do we go about developing these skills?  Check out these activities:

Number Routines

Number routines are simple number activities that children can easily learn that can then be varied to work on the number sense skill children need to learn at the moment.  Here are a few to get you started.

A Simple On-the-Go Number Routine

What comes before, what comes after?: This simply means you give the child a number and ask them what comes before that number (or after that number) so they can visualize in their head the sequence of numbers.

Figure out the pattern: You give 3 numbers and the child has to figure out the pattern and say what comes next.  Some examples would be: 5, 10, 15 (20) or 10, 8, 6 (4).

Number Talks

Number talks are math discussions around a particular question or problem. They are designed to have a variety of solutions to help children stretch their thinking in different ways.  Here is an overview of how you can use them in your homeschool:

Nine Ways to Incorporate Number Talks in Your Homeschool

Cover for blog post about homeschool number talks

Here are more details on the specific type of number talk, How Many Do You See?  This is great for targeting subitizing along with all sorts of early math skills.

Homeschool Number Talks: How Many Do You See?

Story Problems

Story problems give children context to the math equations they are trying to solve.  They can be used to help children generalize their math skills or as a support to help a child see the relationship between numbers when he is stuck.  For example, when my youngest son is stuck on a new concept, I always talk about it in terms of cookies.  9 – 5 = ? becomes “If you had 9 cookies and you gave 5 to me, how many would you have left?”  With older children turning problems into money transactions can help them see the relationship between the numbers.

Games

Games are a great way for children to practice math skills they are developing and/or use the mental math skills they have developed!  Here are some fun games:

13 Math Games Your Children Will Love to Play

Nine Games for Practicing Math Facts

Books

These five book series are a fun way to build number sense and your children may not even know that’s what you are doing!

Books to Get Your Child Excited About Math

Our Favorite Curriculum

Our favorite math curriculum that develops number sense in children is RightStart Math!  You can learn more about it here:

Math balance, books for RightStart math Level B and an abacus

Have a question about number sense? Ask below and we will update this page to include the answer!

 

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