Preschool Math: What Do Kids Need to Learn?

Preschool math instruction is incredibly important, and how well a child learns the basic concepts during this foundational time can make the defining difference in whether or not a child sees himself as "a math person" or "not a math person."  Research is now showing us preschool math achievement is an even greater predictor of school success than early pre-reading skills!  The article states, “We found that only three of the school-entry measures predicted subsequent academic success: early reading, early math and attention skills, with early math skills being most consistently predictive,” Duncan says."

Since we now know how important preschool math skills are, what should we focus on to make sure that our children are as prepared for Kindergarten as they possibly can be? Based on my own 25 years of experiences teaching the K/1 grade levels, and also on some recent research, I have tried to narrow it down to just a few of the most important preschool math topics to focus on.

1.  Counting Real Objects One by One Accurately

What is it?  This is the skill of counting out objects one by one, without re-counting any of the objects or getting mixed up in any way.  Kids should be able to count out a minimum of ten objects accurately by the time they finish preschool.  If you ask a child to "show me six toys," the child should be able to count out and give you six toys without hesitation.  If you say, "How many are there here?" the child should be able to count out any set of object up to ten and tell you how many there are.  So, if I ask a child to count a group of five objects, he should be able to say something like, "1, 2, 3, 4, 5.  There are five."  Children must understand that the last number they say as they count indicates how many there are.

Why is it important?  It is important for children to be able to count accurately in order for them to add, subtract, or begin to do any kind of "mental math" problems in their heads.  FIRST they must be able to count out sets of objects accurately.  This is a foundational skill in preschool math.  Children must learn to maintain one-to-one correspondence, which means that they accurately count only one object for each number that they say.  This may seem like an obvious thing to many of us, but it is not at all obvious to a young child!  Children also need to learn to figure out a way to count objects without re-counting some of them, such as moving objects to the side once they have been counted, etc.

What to watch out for:  Watch carefully while your child counts to make sure that he or she does not skip any objects or does not count any of them twice.  Children usually are able to first count out small quantities of objects, such as two or three, and then gradually add on a few more little by little over time.

Also, watch for a child that re-counts every time you ask him or her how many objects there are.  So if you give a child a jar of ten stones and say, "How many are there," you would expect the child to count them- but just once or maybe twice to double check.  But after that, the child should remember and know that there are still ten in the jar when he puts them back inside!  If not, it may be that your child does not realize that the last number he says is "the answer."

What can the top achieving children do on DAY ONE of Kindergarten?  The children that do the very best in kindergarten can already count out thirty objects (or nearly thirty) without any help on the first day of Kindergarten.

How to practice:  A great way to practice counting skills in preschool math is to simply write numbers on paper plates, and have them place that number of objects on that plate. Start with very small numbers, such as one, two, and three. Once a child has mastered three objects and gets it right consistently, then add in plate number four.  It's as simple as that! You can change out the objects and even the plates for variety. I used to give my kids farm animals to count with when we studied the farm, little plastic sea animals to count when we studied sea life, etc. Sometimes, they can pick up the objects with tweezers or tongs for an extra fine motor challenge. There are also many more ideas for counting and other math skills on my math centers Pinterest board. And when your child is ready to transfer this skill to paper, we have a really fun little math workbook series to try out called Counting Creatures, as well as counting songs on our Video Streaming Site. My students LOVE them! But children MUST count with real objects FIRST if they are to gain the preschool math skills they really need; THEN they can transfer their skills to paper!

2.  Counting Aloud (By Rote, Not Counting Objects)

What is it?  This skill is not the same as counting objects; it's just counting out loud, strictly from memory.  Children need to be able to count out loud without any help or prompting to at least 20 when they start Kindergarten!

Why is it important?  It is important for children to be able to count accurately in order for them to add, subtract, or begin to do any kind of "mental math" problems in their heads.  FIRST they must be able to count out sets of objects accurately.  This is a foundational skill in preschool math.

What to watch out for:  Watch out for skipping over numbers!  Many, many children will skip over some of the teen numbers when they count, saying things like "11, 12, 13, 14, 16...."  This is a HUGE problem and can be very hard to correct once a habit has been established.  Once a child has internalized and memorized an incorrect counting sequence like this, it affects not just their ability to count out loud, but also their ability to count objects, and eventually to add and subtract, and so on.  I have been told many times by very well meaning parents, "Well, sure, he skips 15.  But after that, he can continue on to 29!!!"

But here's the problem:  none of the numbers "matter" past the first mistake.  So even if the child can keep counting to 200 after that, as far as his report card is concerned, he can only count to 14 (which was the last correct number.)  By the same token, if a child cannot get past 29 without someone helping him or her to say "30," or cannot get past 49 without someone helping him to say "50," then the last correct number that the child was able to say without help is the the number that the child can officially count to.  I have never met a teacher with a different policy than this.

What can the top achieving children do on DAY ONE of Kindergarten?  The children that do the very best in school usually come in to Kindergarten counting WAY past 20; in fact, the very best students usually start off Kindergarten already counting to 100 accurately, without any help at all.

How to practice:  To help children practice at home, make counting things part of your daily life.  Count trees as you walk to school or as you drive by.  Count cracks in the sidewalk.  Preschool math teachers can encourage children to count blocks in towers as they build, toys as they put them away, count leaves on the ground, balls in the ball box, or anything at all. Just keep counting!  After a while, children internalize the pattern of the counting sequence, and then they are off!  I used to always sing the HeidiSongs Counting to 100 song with my class as often as possible (shown below.)  It is in both the Musical Math collection and the Number Jumble collection on our Video Streaming Site.

3.  Recognizing the Dot Patterns on Dice as Numbers

What is it?   This is the skill of seeing a small group or set of objects or dots and "just know" how many there are without having to stop and count them one by one.  For example, when they see three dots come up on a die, then the child should know instantly that it's three, without having to count.  This skill even has a "fancy," official name:  we call it "subitizing."

Why is it important?  One of the greatest strengths a child can develop in the area of preschool math is learning to instantly recognize the dot patterns on dice and dominoes as a certain quantity.  It's knowing deep inside "what three looks like," and so on.  We can be confident that a child can do this up to at least number three when he finishes preschool has a firm idea in his head of "three-ness."  That child will be able to build on this concept and keep it growing to understand what four really is, and so on.  A child that knows that six dots looks like three dots on one side and three dots on the other side will have an easier time remembering that three plus three equals six, so addition for these smaller numbers will be easier to comprehend as well.

What to watch out for:  If you have been playing dice games with your three year old child at home for at least a year, and he or she still doesn't recognize when there is only one or two dots, you may want to have your child's vision checked.  This is particularly true if you are using the regular sized small dice adults use.  Don't fool around with any vision issues!  If you suspect there may be a problem, get it checked out immediately.  If your child really cannot see well, your child's academic development will certainly be affected.

What can the top achieving children do on DAY ONE of Kindergarten?  The children that do the best in Kindergarten can (almost) ALWAYS recognize all of the dice patterns up to number six just as soon as we start playing games with dice.  This might not be until a few weeks into the school year, but since this skill develops over time, I think it is safe to say that they could probably do it on day one.

How to practice:  Children will not learn to subitize, or recognize dot patterns over night.  It takes a lot of practice.  But the good news is that the best way to learn is to simply play games with dice!  Start with a nice BIG pair of dice, if you can get them.  These are easily found online.  Let children count the dots as much as they need, and then after a while, they will probably begin to simply recognize how many dots there are based on the dot pattern alone.  When you notice your child "just knowing" how many dots there are without counting, let him or her know how proud you are!  Some of my favorite games to play at home are "Don't Spill the Beans" and "Hi Ho Cherry-O" (replace the spinner with dice.)  I think you could do this with a Christmas Tree and ornaments, too!!!!  Call it "Hi Hee Christmas Tree!"  Just keep going until someone gets 20 ornaments in a bag, or until all of the ornaments are off the tree.  The last person to remove an ornament is the winner!

4.  Recognizing the Numbers 0-10 Out of Order and the Basic Shapes

What is it?  This is simply the skill of identifying which numeral or shape is being shown on a flash card when they are all mixed up and out of order.  In other words, if you show a child a flash card with a square on it, or a 5 on it, can he tell you what it is without any help?

Why is it important?  Teaching children to recognize the shapes and numbers 0-10 out of order is a very important part of preschool math.  It is a foundational skill that affects nearly every other math skill that comes afterwards.  Without knowing the numbers, children will not be able to measure, tell time, add, subtract, identify fractions, etc. Without knowing the names of the shapes, children will not be able to answer do geometry, or any other activities that depend upon knowing the shapes and being able to create them, such as guided drawing and many other fun art projects.  Learning the numbers and shapes in preschool is also important because it helps the children develop their visual perception as well.  That means that the child will better be able to "see the difference" when shown letters that look similar, such as the b, p, q, and d.

What to watch out for:  Watch out for mixing up numerals such as 6 and 9, since they look alike.  When your child gets to the numbers past ten, watch out for mixing up 12 and 21, 20, 13 and 30. Children should get in the habit of reading from the left to the right, and that includes numbers.  Also, listen carefully to the pronunciation of the teen numbers, which should sound different from the multiples of ten.  For example, if a child says "Thirteen" it shouldn't sound like he said, "Thirty."  By the same token, "fourteen" shouldn't sound just like "forty," and "fifteen" shouldn't sound like "fifty."  A good rule of thumb is to ask a friend that does not have small children to listen to your child say the numbers.  If your friend can tell you what your child said, then all is well!

What can the top achieving children do on DAY ONE of Kindergarten?  The children that do the best in Kindergarten can ALWAYS identify 0-10 without any hesitation at all.  And most of them can identify the numbers up to 30, with just a few mistakes here and there.  They almost always know all of these shapes as well:  square, circle, rectangle, triangle, oval, star, and diamond (also known as a rhombus, but children rarely come up with that word upon their first Kindergarten testing.)

*  Keep in mind that by the end of Kindergarten, they will be expected to know the hexagon as well, and by the end of first grade, they will have to know the trapezoid.  The "flat" shapes that are required under the Common Core State Standards in Kindergarten are:  circle, square, triangle, rectangle, and hexagon.  The trapezoid is added in first grade.  Some school districts also ask children to learn the octagon. One school district that I know of requires the children to refer to the rhombus (the diamond) as a parallelogram in Kindergarten, but so far I have only come across the one school district that does that. You may wish to ask teachers or parents who have older school age children that attend your local schools what they require.

*  Under the Common Core, Kindergartners will also have to learn the three dimensional shapes, also known as "volume shapes," such as the cube, the cone, the cylinder, and the sphere.  The rectangular prism is added in first grade.

How to practice:  The quickest and very best way that I know of to teach children to identify the numerals and shapes is by using an active learning method I developed called Jumpin' Numbers and Shakin' Shapes.  In it, children are taught to associate a movement with each numeral or shape card that has a special picture embedded into that number or shape.  Children are taught an accompanying song to reinforce the number or shape and its motion.  Then they are "weaned" off the special flash card.  Kids really love the songs, too!  Check out the movie below to see how it works.

5.  Sorting

What is it?  When we sort objects, we put things into groups based on their attributes, such as color, shape, size, width, etc.  For example, when we put away toys into their proper boxes, we are actually sorting them into their different categories (also called categorization.)  The cars go here, the blocks go there, puzzles go over there, etc.  But children can also be taught to sort in other ways:  they could put all of the red cars in one pile, the blue cars in another pile, and cars that have more than one color in another pile, etc.  It doesn't matter HOW a child sorts; the most important thing is that the child EXPLAINS how he sorted.  So, when he is finished sorting, he might say, "I sorted these cars by color."  Or, if the big cars go here, but the small ones go there, then the child would say, "I sorted by size."

Why is it important?  Sorting is an important part of preschool math because it helps children learn to analyze groups of objects in a systematic way, and organize their thoughts well enough to be able to tell what they are thinking.  Verbalizing (or telling) how he sorted is ALWAYS the hardest part!

What to watch out for:  Watch for children that switch the way they are sorting before they are done.  For example, children sometimes start sorting by color, putting all of the red shapes in one group and the blue shapes in another, etc.  However, somewhere in the middle of the sort, children tend to get mixed up and, for example, start grouping all of the red triangles in a separate subgroup, and then the blue triangles in a separate subgroup, etc.  Once a child begins to sort by color, they must finish sorting by just that ONE attribute.  Then, after that, they can sort the entire collection by shape, or by size, etc.  In addition, watch out for children who can sort, but cannot tell anyone how they sorted.  This last step is foundational and an extremely important part of preschool math.

What can the top achieving children do on DAY ONE of Kindergarten?  The children that do the best in Kindergarten can ALWAYS sort objects by color, at least.  Many of them can sort by shape as well.  I usually have to get them started so that they know "what I mean," but after that, they can do it.  They often have to be trained to tell how they sorted, but catch on quite quickly.

How to practice:  I always teach my students the Sorting Song from HeidiSongs Musical Math collection to help them practice verbalizing (or singing, at least!) that when we sort, we put things into groups, and three possible ways to sort are by color, shape, and size.  Other than that, kids just need LOTS of practice with lots of different objects, especially Attribute Blocks, which can be purchased online and also in teacher supply stores.

6.  Patterning

What is it?  When children first start learning about patterning, they must recognize patterns in their world and learn to name them.  For example, when they see a candy cane, they may notice that it is usually colored with a two color pattern, such as "red, white, red, white."  A pattern with two colors or parts is referred to as an AB pattern.  A pattern with three colors or parts, such as "red, white, blue, red, white, blue" is referred to as an ABC pattern.

The second part of this skill is extending patterns that are already started.  So if a child sees a pattern such as "square, triangle, square, triangle, square," you could ask him what comes next, and the child would be able to tell you that the triangle comes next.  That is called extending the pattern.  The next level of patterning would be to ask a child to create a specific pattern, such as an AB pattern.  The child would then know that you want a pattern with two elements, such as "sock, shoe, sock, shoe, sock, shoe."

What is it important?  Patterning is an important part of preschool math because our counting system itself is based on a gigantic pattern.  Just look at a chart with all of the numbers from zero to 100, and you will see patterns running throughout the whole thing!  So when children start learning to look for patterns in their world, they are getting their brains ready to understand our base-ten counting system.  Learning to recognize and make simple patterns as young children helps then eventually learn to do "skip counting," such as counting by two's, five's, and ten's, which is the beginning of multiplication and division.

What to watch out for:  Watch for mistakes in the middle of patterns that children make.  Kids often start off patterning, and then get distracted and start laying down the incorrect objects.  Also, when children name patterns, they should always start with the letter A and then proceed to B, etc.  We never would have a "BHBH" pattern.  A pattern with two items is always called an AB pattern, etc.

If you have been working with your (at least) four year old child on AB patterns for at least six months and the child is still not recognizing these two item patterns when he sees them, and cannot tell you what comes next, I would consider this cause for concern.  Talk to your pediatrician about possible developmental delays, because early intervention is the key.  The children that I have seen that could not learn to make a simple two color pattern by the end of Kindergarten nearly always ended up being diagnosed with some type of learning disability later on in their schooling years, unfortunately.

What can the top achieving children do on DAY ONE of Kindergarten?  The children that do the best in Kindergarten have seen patterns and recognize them immediately.  Even if they cannot name them as AB or ABC patterns, they still know a pattern when they see one and can figure out what comes next easily with at least these two basic patterns.

Note:  Patterning is no longer a part of the Common Core State Standards in Kindergarten; it appears in the first grade Common Core standards instead in the form of number patterns, such as skip counting.  However, many kindergarten teachers still teach and test patterning skills in order to prepare children for patterning in first grade and beyond.

How to practice:  The most important thing to do is to point out patterns that you see in your world to your child, and then to practice patterning with things you have at home.  "Body patterning" is also a fun way to practice, such as touching your head, then shoulders, head, then shoulders, etc.  I always teach the patterning songs from HeidiSongs' Musical Math collection to help children learn to identify and name the AB, ABC, and AAB patterns. This is a video from our original Musical Math videos. We have updated the videos with animation and different dancers, but I don't have this patterning song on YouTube, but I thought at least hearing/seeing an example of the song would get the point across! :)

I hope you enjoyed this information and it was helpful to you!

- Heidi

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