*Preschool math is more than just counting! Learn the 4 essential skills that preschoolers need for a strong foundation in math.*

When I began researching preschool homeschool math curriculum when my son was little, I was very disappointed with what I found. Most resources were tedious workbooks with lots of time spent learning to write numbers. Learning how to write numbers is a valuable skill, but it’s handwriting, not math! There were also lots of adorable number crafts available online. Many of them looked fun, but I couldn’t see how sponge-painting a 3 would help him understand the number three much better.

As I dug deeper into the research on how young children’s brains learn math, I found that there are four main skills that young children need to develop:

- Counting
- Subitizing (recognizing quantities
*without*counting) - Comparing
- Connecting quantities and written numerals

#### Counting: more complicated than adults realize

Counting seems very basic, but it is actually very complex. To be able to count accurately, a child has to learn:

- The order of the counting words (“one, two, three,” etc.),
- That any kind of thing can be counted (blocks, sounds, jumps, people, etc.),
- That you have to count each item once and only once,
- That you can count objects in any order,
- That the last number said when counting is the total number. (For example, young children can often point to blocks and say “one, two, three” but aren’t able to say
*how many*blocks there are.)

Because counting is so complex, children need lots of experience with counting activities as they first begin to understand numbers.

#### Subitizing: recognizing quantities without counting

While learning counting strategies is essential, children also need to learn to recognize groups of items *without* counting. This skill is called subitizing. Recognizing small quantities helps children start to think of numbers as groups and understand the relationships between numbers.

One useful tool to help children develop this skill is a five-frame. Take a look at the five-frame below. Notice how you can immediately “see” that there are three circles, and that two spots are empty? When you do this, you’re subitizing. Organizing blocks on the five-frame helps develop this crucial skill and helps children move beyond one-by-one counting to solve problems.

Once your child is familiar with the five-frame, it’s then helpful to use a ten-frame. The ten-frame is especially useful for noticing relationships between numbers. For example, can you tell how many blocks are on this ten-frame without counting?

You might have noticed that there is one empty box and figured that there must be nine blocks. Or, you might have noticed that there are five blocks on the left-hand side and four blocks on the right-hand side, for a total of nine blocks. Either way, you were using relationships about numbers to find the total, rather than one-by-one counting. Learning how to subitize will provide a huge advantage to your child when she first encounters written addition and subtraction problems.

#### Comparing numbers: more, less, or equal?

As children start to visualize quantities and understand numbers more deeply, they learn that the numbers that come later in the counting sequence signify greater amounts than the numbers that come earlier. (I.e., since six comes *after* five in the counting sequence, six is *more* than five.)

Before children are able to reach this level of abstraction, however, they need plenty of experience with concrete materials. Once they’ve spent some time comparing numbers of objects, they’re then ready to begin comparing spoken numbers without counting out the corresponding number of objects.

#### Recognizing written numerals: making the connection between quantities and symbols

Recognizing the written numbers is essentially reading—matching a printed symbol to a spoken word. Before children are ready to deal with the abstract written symbols for numbers (1,2, 3, etc.), they need plenty of experience with quantities and the number words. Written symbols should only be addressed after their basic number knowledge is solid, with lots of time spent making the connections between the written symbols and what children already know about numbers.

**Would you like simple, playful math activities to get your own preschooler off to a great start in math? Check out my book, Preschool Math at Home. Based on the activities I used with my own kids, it will show you how to give your young kids a great foundation with numbers in just five minutes a day.**

So excited Kate! Laura really struggles with subitizing. Some how she understands some basic addition but a few basic concepts really haven’t connected with her yet.

Hi! I just ordered your book and am ordering RSA tonight. I’m so excited! Anyway, I was wondering if RS uses 5 or 10 frames, and if they do not, do you have any favorite resources that I could use to show my son the frames? I was a math teacher (nationally board certified in middle school but I taught 5th for 11 years before I started staying home 3 years ago), but I have been out of the loop and am not sure the best resource for the 5/10 frames. I think they are a great visual strategy for learning math facts!

Hi Julie,

Pressing that “order” button feels great, doesn’t it? RightStart doesn’t use 5 and 10 frames, but the beads on the abacus are grouped by color for similar results. (Groups of 5 yellow beads alternate with groups of 5 blue beads to make it easier to visualize the groups.) Between the activities in Preschool Math at Home and RightStart A, you should be in great shape!

Happy math!

Kate

Hi, Kate, I have a question about subitizing. In your Homeschool Math 101, you say that humans naturally have the ability to subitize up to 5 items (and I have seen this myself to be true.) I have a book called “Jude’s Dots”, the premise of which is that you can teach a child to recognize groups up to 100. Have you heard of this theory, and do you think it is a worthwhile endeavor? Or maybe it is enough to use two colors to get two groups of 5 to make 10, as in the 10-frames. I’d love to hear your thoughts!

Great question! To go a little deeper, there are two different kinds of subitizing: perceptual and conceptual.

Perceptual subitizing is that immediate recognition of quantities up to 5. Conceptual subitizing is when we use other things we know to immediately recognize quantities greater than 5. For example, w e use conceptual subitizing when we recognize a 3×3 grid of dots as 9 dots, or when we know right away that someone who is holding up a whole hand and 2 fingers is holding up a total of 7 fingers.

I’m not familiar with Jude’s Dots, and there’s no preview available on Amazon, but I’d guess that the author is hoping to develop children’s conceptual subitizing ability. RightStart uses a similar approach with the abcus: once children have worked with the 100-bead abacus for a while and are familiar with the color patterns, they learn to immediately recognize how many beads are on the abacus.

I’d definitely say this kind of conceptual subitizing is valuable for building a deep understanding of place value, since place value is so key to the rest of arithmetic. But it’s a concept that takes a lot of time and practice, since place-value is so abstract for small children. So while I’m not familiar with the actual book, I’d guess that it’s best for children in first grade and up who are ready to dive deep into place value.

Happy Math!

Kate

We love Preschool Math! My son, age 4, learned how to subitize up to 5 a lot easier than subitizing 7, 8 and 9! We spent about 2 weeks (we use your book 3 times a week- it’s a gentle preschool schedule!) and have moved on to the next chapter on written numerals. I incorporated subitizing 7,8,9 during the card game activity and that worked well! We have a trial of Dreambox as well and that has activities using the ten frame and subitizing. ( My son likes the game, but I’m undecided since he needs me throughout!) Anyway, should I plan on revisiting the activities using the ten frame before going on to Right Start Math, as you recommend?

Hi Cintia,

Glad to hear that the subitizing activities have gone so well for your son! You’re right–up to 5 is a LOT easier for kids than the numbers up to 10. No need to revisit the activities before you start Right Start. The beginning of the curriculum includes a lot of subitizing with fingers, tally sticks, and the abacus, so your son will get plenty of review.

Happy Math!

Kate

Any math apps you recommend for preschoolers?

Hi Cintia,

Sorry, my kids are out of that range now, and so I haven’t explored what’s out there for preschool apps these days.

Kate

Hi, thanks for the blog. A great helping. I’m Brazilian, and we have two kids, 6 almost 7, and 5 ys. I have read about delay the math until 9 or 10 ys. And don’t use textbooks or formal exercises so early. My kid 6 y loves the math, and asked me to teach her multiplication, but I don’t know how take way. Do I need to begin with the book ‘Preschool math at home’? Or Can I introduce the another book?

Hi Carolina,

That’s wonderful that your daughter is so interested in math! Try just introducing the idea of multiplication at first–that it’s equal groups–and give her lots of practice at finding answers to small, real-life problems.

Multiplication Facts That Stick is for memorizing the multiplication facts from 1×1 up to 9×9. Start with Addition and Subtraction Facts before starting the multiplication book, or else it may be frustrating.

Happy Math!

Kate

Hi Kate

Do you still recommend RightStart after Preschool Math at Home (PSM)? I recently purchased your K Math. We haven’t started it yet as we are still going through comparing and quantities with PSM.

Hi Marie,

RightStart is still a great curriculum, but I’m perhaps a little biased toward Kindergarten Math with Confidence. 😉 Both programs have similar goals, but they just go about them in slightly different ways. I wrote a longer comparison in my response to RB’s comment on this page (halfway down the comments) if you’d like to read more on how they compare.

Happy Math!

Kate

Hi Kate,

I just purchased “Preschool Math at Home,” and it seems like an amazing resource so far! I am curious as to why you chose to present a ten-frame as two five-frames side by side rather than stacked?

Great question! Please see this Facebook thread for my full explanation.

Happy Math!

Kate

Hi Kate,

I have two kids, 6 yearold boy and 5 year old girl (13 months apart). We started TGAB kindergarten math last fall. We need to switch curriculum. Based on what I am seeing and reading, I want to go with your curriculum, but I don’t know which level.

Subitizing and the relationship between numbers just isn’t there. My son has trouble counting up if you don’t start with 1. Can’t tell at this point, if part of his problem is his vision or what. Eye surgery scheduled for next month.

Should we start with level 1 or redo kindergarten. Or do you have suggestions on how we can work on things during the summer?

I’d redo kindergarten, at a brisk pace and skipping lessons if he’s already mastered the content. It will probably go pretty quickly. You might even be able to complete it over the summer and then go straight into first grade in the fall.

Happy Math!

Kate