Number Sense for Kids

Number sense is a child’s understanding of what numbers mean: how many a number stands for, which of two amounts is more, and how a number changes when you add one or take one away. It is not the same as counting out loud. A child can recite the numbers to 20 and still count a pile all over again from the start when you ask “how many?”. Number sense grows in steps, mostly between ages 3 and 6: seeing small amounts at a glance, counting each thing once, knowing the last number counted is how many, then comparing amounts and naming numerals.

The most useful thing you can do is ask “so how many are there?” after your child counts something. Answering without counting again is the step that turns counting into number sense. A two-minute check-in shows where your child is in that order, and seven everyday moments at home build each part.

What is number sense?

Number sense is a child’s understanding of what numbers mean and how they relate to each other, not just the ability to say them in order. The Texas Prekindergarten Guidelines define it as “the deep understanding of how numbers work” and list what it includes: “counting, number recognition, understanding quantities, composing, and decomposing numbers, and making number comparisons.”

The line between number sense and counting is the one a parent sees first. A 4-year-old counts seven toy cars, “one, two, three, four, five, six, seven”, and when you ask how many cars there are, starts again at one. The counting is right. What is missing is the idea that the last number said tells you how many, and that idea is number sense.

Four everyday examples of number sense in a young child:

• Knowing there are three apples on a plate without counting them.
• Knowing that 8 cookies is more than 5 cookies.
• Knowing that one more than 6 is 7, without starting again from 1.
• Knowing that 5 fingers and 2 more fingers make 7.

The term is confusing because it has two meanings. The cognitive scientist Stanislas Dehaene uses “number sense” for the inborn feel for rough amounts that babies and many animals share. Schools use it for the learned skills in the list above, which are the ones a teacher means on a report card. Number sense is also not the same as mental math, though mental math depends on it: a child who knows 9 is one less than 10 can add 9 without counting by ones.

How does number sense grow from preschool to first grade?

Number sense grows in a rough order, and it starts before school, from about age 3. The What Works Clearinghouse practice guide Teaching Math to Young Children (Frye and colleagues, 2013) gives the order in its first recommendation, which it rates as having moderate evidence: recognizing small collections without counting, then one-to-one counting, then comparing amounts, then labeling them with number words and numerals, then solving simple problems. Children overlap the parts, so a child can be strong on one and still building the one before it.

The table puts each part of number sense in that order, with what it looks like at home, when the standards expect it, and the page that teaches it. “End of age-3 preschool” means the end of the year a child spends in a class for 3-year-olds, not a third birthday.

Part of number sense	What it looks like at home	Usually by	Common Core	Texas	Page
Seeing small amounts without counting (subitizing)	Says “three” for three crackers at a glance	Up to 3 by the end of age-3 preschool; up to 6 by the end of pre-K (Texas)	None	PK4.V.A.4, K.2(D)	Subitizing
Counting each thing once	Touches each toy once while counting, with no skips or doubles	5 objects by the end of age-3 preschool; 10 by the end of pre-K	K.CC.B.4a	PK4.V.A.2, K.2(C)	How children learn to count
Knowing the last number is “how many”	Counts 7 cars and says “seven” when asked how many, without counting again	10 by the end of pre-K; 20 in kindergarten	K.CC.B.4b, K.CC.B.5	PK4.V.A.3, K.2(C)	Counting and cardinality
Comparing amounts: more, fewer, the same	Says which plate has more grapes, by matching or counting	Groups to 10 by the end of pre-K; numerals to 10 in kindergarten (20 in Texas)	K.CC.C.6, K.CC.C.7	PK4.V.A.8, K.2(G), K.2(H)	Greater than, less than
Naming and writing numerals	Reads the 7 on a door; writes 0–20	Reads 0–10 by the end of pre-K; writes 0–20 in kindergarten	K.CC.A.3	PK4.V.A.5, K.2(B)	Writing numbers
One more and one less	Knows one more than 5 is 6 without starting at 1	Kindergarten	K.CC.B.4c	K.2(F)	One more, one less
Counting on, and counting to 100	Starts at 8 and keeps going; counts to 100 by ones and tens	Kindergarten; to 120 in first grade	K.CC.A.1, K.CC.A.2, 1.NBT.A.1	K.2(A), K.5, 1.5(A)	Counting to 100, hundreds chart
Breaking numbers apart and putting them together	Shows 6 as 5 fingers and 1 more	Begins in pre-K; numbers to 10 in kindergarten	K.OA.A.3	PK4.V.A.7, K.2(I)	Number bonds

The ages come only from the standards and the Texas outcomes for 3- and 4-year-olds (PK3 and PK4), so each one marks the end of a school year, not a deadline. A 4-year-old who counts each toy correctly but counts again when asked “how many?” is in the middle of the pre-K rows, not behind.

Texas makes number sense the first skill area of its pre-K math domain, asks preschoolers to recognize up to 6 at a glance, and in kindergarten asks for counting forward and backward and comparing up to 20 rather than 10 (TEKS kindergarten math). In both Texas and the Common Core, kindergartners compare amounts in words, and the greater than and less than signs arrive in first grade.

Three more pages help a child into the same skills without being parts of their own. Ordinal numbers (first, second, third) name a position rather than an amount. Counting on fingers is a normal tool at these ages. And board games with a number path practice several parts at once.

Why is number sense important?

The number skills children bring to kindergarten predict their later school achievement more strongly than their early reading skills do. Greg Duncan and colleagues (2007) analyzed six long-term studies of children in the US, Canada, and Great Britain. The math skills children had when they started school, which the authors describe as “knowledge of numbers and ordinality”, were the strongest predictor of their later school achievement, ahead of early reading skills and attention. That is a link, not proof that teaching numbers earlier causes later success, and the authors write that their math result may “overstate causal impacts”.

Two studies measured number sense more directly. In the first, Nancy Jordan and colleagues (2009) found that number competence in kindergarten predicted both the level of children’s math achievement through third grade and how fast it grew from first to third grade. In the second, Jordan, Glutting, and Ramineni (2010) found that a short number sense screen given at the start of first grade predicted math achievement at the end of first and third grade.

Number sense is taught, not fixed. The whole first recommendation of the What Works Clearinghouse guide is about how to teach it, in the order from seeing small amounts to solving simple problems, so a parent who knows which part their child is on knows what to practice next.

Number sense check-in: where is my child?

A quick check of where to start. Not a screening or diagnostic tool. It takes about two minutes. You need ten small objects (blocks, buttons, or crackers), and a few cards with the numerals 0–20 written on them.

Pick the items for your child’s age, ask them in order, and for each one decide whether your child did it easily, with some help, or not yet.

Age	Items to ask
3, or first year of preschool	1–4, with up to 3 objects for item 1 and 5 objects for items 2–4
4, pre-K	1–6, with up to 6 objects for item 1, 10 for items 2–4, and numerals 0–10
5, kindergarten	2–8, with up to 10 objects and numerals 0–20
6, first grade	5–9

1. Seeing small amounts. Show a few objects, or a die face, for about two seconds, then cover them: “How many?” Easily means your child says the number without counting. The page on seeing amounts at a glance teaches this part.
2. Counting each thing once. Put out a row of objects: “Count these for me.” Easily means your child touches or points to each one once, with no skips and no doubles.
3. Knowing how many. Straight after item 2: “So how many are there?” Easily means your child answers with the last number counted, without counting again.
4. Counting out an amount. From a pile: “Give me 4” for a 3-year-old, “Give me 6” for an older child. Easily means your child counts out exactly that many and stops. Items 2–4 are all taught on the page about counting objects and knowing how many.
5. Comparing. Make two groups, 7 and 5, and spread the 5 out wider: “Which has more?” Easily means your child picks the 7, by matching or counting, not by which row looks longer. See comparing amounts.
6. Naming numerals. Show the numeral cards in mixed order: “What number is this?” Easily means your child names 0–10 in pre-K, or 0–20 in kindergarten. See reading and writing numerals.
7. One more. “You have 5 blocks. I give you one more. How many now?” Easily means your child says 6 without counting all of them again. See one more and one less.
8. Counting on. “Start at 8 and keep counting.” Easily means your child carries on from 8 without starting at 1. See counting on and counting to 100.
9. Ten more. For a first grader: “What is ten more than 34?” Easily means your child says 44 without counting by ones. A 1–100 chart shows why: 44 sits one square below 34.

Start with the first item that was not easy, not the hardest one your child missed. If it went “with some help”, the skill is on its way, and a few weeks of everyday practice with it will firm it up. If it was “not yet”, that is the place to begin. If your child did every item easily, try the first item for the next age up, or start seeing numbers in groups of five and ten, as in number rods and seeing groups. “Not yet” is expected for a child younger than the age the standards give for a skill: the Texas pre-K outcomes put seeing up to 6 at a glance and counting 10 objects at the end of pre-K, and the Common Core puts counting on in kindergarten.

This is a quick check of where to start, not a screening. If you are worried about how your child is doing with numbers, talk to their teacher or pediatrician. For reading, the same kind of quick check is on is my child on track with reading?.

How can parents support number sense at home?

Parents can build number sense inside routines the family already has, a few minutes at a time, with nothing to buy. The seven moments in this list are organized by the time of day, and each one builds a different part of number sense.

1. 1

   At snack: ask "how many?" after counting

   Count crackers together, touching each one, then ask "so how many are there?" If your child counts again from the start, say "seven, we counted seven" and move on. Answering with the last number counted is the step that turns counting into number sense.

2. 2

   On the stairs or in the car: count on and count back

   Start from the middle: "We are on step 4. Keep going!" Then count back down to 1. Counting on from a number other than 1 is a kindergarten standard, and Texas kindergartners also count backward from 20.

3. 3

   At play: flash small amounts

   Hold up three fingers or show a die face for about two seconds, then hide it and ask how many. The goal is to say the number without counting. Start with 1–3 and go up to 5 or 6 as it gets easy.

4. 4

   When sharing: compare

   Ask whose plate has more grapes, then check by lining the two sets up one opposite one, so the extra grapes stick out. Use the words more, fewer, and the same, and later greater than and less than.

5. 5

   Out and about: point at numerals

   Read house numbers, prices, bus numbers, and the oven clock together. Ask your child to find a 7 on the page of a book, or to read the number on a door.

6. 6

   One more, one less, out loud

   With a few blocks or spoons, ask "You have 5. If I give you one more, how many now?" and then take one away. The goal is to answer without counting the whole pile again.

7. 7

   Read a counting book or play a board game

   Choose a board game whose squares are numbered in one straight line, and have your child say each number as the piece moves. Counting books work the same way when you stop to ask how many.

Each moment practices one part of number sense. Asking “how many?” at snack builds cardinality, knowing the last number is how many. Counting on and back on the stairs is counting forward and backward in small pieces. Flashing fingers and die faces builds subitizing skills, and using fingers to count is a normal tool, not a crutch. Comparing plates is the start of greater than and less than. Pointing at numerals builds number recognition. Giving one more block is one more, one less practice out loud. And a number path board game practices several parts at once.

The What Works Clearinghouse guide recommends math every day, built into routines. Its fifth recommendation, which it rates as having minimal evidence, is to “dedicate time each day to teaching math” and to “embed math in classroom routines and activities”. It was written for preschool and kindergarten teachers, and at home the same advice puts the math inside snack time, play, and errands rather than in a separate lesson. The guide does not set play against teaching: the same recommendation asks for planned daily instruction and for games.

Number sense games with cards and dice

Four number sense games need nothing more than a deck of cards or a pair of dice, and each ends with your child saying a number sentence out loud. Use the cards ace (1) to 10.

• Dice flash. Roll one die and cover it after a second. Your child says the number without counting the dots. Swap roles so your child rolls too.
• More wins. Each player turns over a card, and the player with more takes both, saying “seven is more than four”. Equal cards mean each player turns over another. This is the card game War with a sentence added, and comparing numbers has more games like it.
• One more. Turn over a card and say the number that is one more. A 6 means your child says 7. Later, play it as one less.
• Make 10. Lay out eight cards face up. Your child finds two that make 10, such as 7 and 3, and says “7 and 3 make 10”. Refill the gaps and keep going.

For games on a board, the page on board games for math explains why a straight number path matters and has printable boards.

What if my child is struggling with number sense?

Much of what looks like a struggle with number sense in a young child is an ordinary stage. Counting a pile again, skipping an object, or losing track past 10 are all things children do while counting is still new, and the Texas pre-K outcomes expect accurate counting of 10 objects only by the end of pre-K.

Two things are worth mentioning to your child’s teacher, because each is a skill the standards place in pre-K. One is still counting a small pile all over again every time you ask “how many?” well into kindergarten. Texas expects 4-year-olds to answer “how many?” for up to 10 objects. The other is not yet seeing 1, 2, or 3 objects at a glance by kindergarten. Texas expects that by the end of age-3 preschool. A worry of your own that does not go away is reason enough too.

Talk to your child’s teacher first, since they see your child count every day. For a child under 3, ask the pediatrician. A teacher can also tell you whether the school uses a number sense screener, which is given by school staff and is different from the check-in on this page.

Number sense worksheets and printables

Number sense worksheets live on the page that teaches each part, so the sheet and the advice on using it stay together. Pick the sheet that matches the first part your child is still building.

• Seeing small amounts: dot cards, on subitizing activities.
• Counting and knowing how many: count and match, count and color, and ten frame counting sheets, on counting and matching.
• Comparing: pictures to circle, sign cards, and comparing numbers to 20, on greater than and less than worksheets.
• Numerals: number tracing 0–20 and number bingo, on number tracing worksheets.
• One more and one less: practice sheets, on one more, one less worksheets.
• Counting to 100: filled, blank, and missing-number charts, on the printable hundreds chart page.
• Number paths: number path board games to 10 and to 100, on math board games.
• Ten frames: ten frame mats and cards, on free printable ten frames.

Use a sheet after the everyday version is going well, not instead of it. A child who can say how many crackers are on the plate gets more from a count-and-match sheet than a child meeting the idea for the first time on paper.