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:
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)
3. Ten frames allow children to visualize how numbers add up to 5, 10, 15, and 20 by placing manipulatives within them.
4. Subitizing cards can be used to develop visualization skills around math. Read more below under Four Number Relationships Children Need to Learn.
5. Part-Part-Whole Circles help children decompose numbers. Read more below under Four Number Relationships Children Need to Learn.
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).
Download the FREE PRINTABLES mentioned in numbers 2, 3, 4, 5 and 7!!
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:
Four Number Relationships Children Need to Learn
There are four key relationships children need to learn to become proficient with their addition and subtraction skills. You can read more about them in Four Number Relationships Children Need to Learn. They are briefly listed here:
Subitizing is the ability to “see” an amount without having to actually count the number of objects. You can learn more in:
For some games to practice subitizing (the cards are included in the FREE printable packet above.): 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.
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.
Understanding Part Part Whole
Breaking numbers apart or decomposing is an important skill that will be used at all levels. Learn more:
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:
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 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.
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 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:
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.
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.
Here are lots of ideas for using story problems:
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:
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!
Our Favorite Curriculum
Our favorite math curriculum that develops number sense in children is RightStart Math! You can learn more about it here:
Have a question about number sense? Ask below and we will update this page to include the answer!