Math Facts for Kids

Math facts are the addition facts of two one-digit numbers, from 0 + 0 to 9 + 9, and the subtraction facts that go with them, such as 13 − 5 = 8. Fluency means answering them quickly and correctly. The Common Core expects fluency within 5 in kindergarten and within 10 in first grade, and it expects children to know these sums from memory by the end of second grade. A child gets there in three stages: counting a fact, then working it out from a fact they already know, then simply knowing it. Speed comes last.

The most useful move at home is to practice the facts your child can already work out, a few minutes at a time. Teach the strategy first for the rest. Free flash cards sorted by strategy, with each answer on the back, are on our addition and subtraction facts page, and a free addition chart shows which facts are already known.

What are math facts, and what is math fact fluency?

Math facts are the basic addition facts of two one-digit numbers and the subtraction facts that go with them. Teachers also call them basic facts or number combinations. They are the facts of kindergarten to second grade, and multiplication and division facts follow from third grade. Our page on the addition and subtraction facts to 20 counts them and sorts them into the strategy families they are learned in.

A math fact is one answer to know, and a math concept is the idea that lets a child find it. The fact is 8 + 5 = 13. The concept is that 8 + 5 is 8 and 2 more, which makes 10, and then 3 more. A child needs both, because the concept is how a forgotten fact gets found again.

Math fact fluency means answering a fact quickly and correctly. The Common Core Standards Writing Team defines fluent as “fast and accurate” in its progressions document. It describes fluency as “a mixture of just knowing some answers, knowing some answers from patterns (e.g., ‘adding 0 yields the same number’), and knowing some answers from the use of strategies” (pp. 18–19). A child who answers 8 + 9 by thinking “8 + 10 is 18, so 17” without hesitating is fluent. A 2025 review by McNeil, Jordan, Viegut, and Ansari widens the word the same way. According to the Association for Psychological Science’s summary of the review, its authors propose a definition of fluency that includes “noticing and using number relationships to solve problems”.

When should kids know their addition and subtraction facts?

Under the Common Core, children are expected to be fluent within 5 by the end of kindergarten and within 10 by the end of first grade. By the end of second grade, they are expected to know all the sums of two one-digit numbers from memory.

Grade	What children do	Common Core	Texas (TEKS)
Kindergarten	Add and subtract within 5 fluently; work out facts to 10 with objects and fingers	K.OA.A.5	K.3(A)–(C): within 10, no fluency target
1st grade	Use strategies within 20, such as counting on and making ten; fluent within 10	1.OA.C.6	1.3(D): strategies, no fluency target
2nd grade	Fluent within 20 using mental strategies; all sums of two one-digit numbers from memory	2.OA.B.2	2.4(A): “with automaticity”
3rd grade	The facts are used, not learned: adding and subtracting within 1,000, and multiplication facts	3.NBT.A.2, 3.OA.C.7	3.4(A), 3.4(F)

Texas sets no fluency target before second grade. Its first graders “apply basic fact strategies” within 20, “including making 10” (1.3(D)), and its second graders “recall basic facts to add and subtract within 20 with automaticity” (2.4(A)). The Common Core asks second graders to know only the sums “from memory”, while Texas names subtraction in its recall standard too.

Learning the facts takes three school years, so a first grader who still counts on for 8 + 5 is on time. The progressions document calls knowing the sums from memory “an outcome of a multi-year process that heavily involves the interplay of practice and reasoning”. Fingers are a normal tool along the way, and the guide to counting on fingers explains when children usually stop using them.

Why do math facts matter?

A fact a child knows takes no effort to recall, so the child’s attention is free for the new step in a harder problem. In 47 + 38, a second grader who knows 7 + 8 = 15 can think about the new ten instead of counting. The What Works Clearinghouse guide Assisting Students Struggling with Mathematics (2021) says that quick recall of facts “gives students more mental energy to understand relatively complex mathematical tasks and execute multi-step mathematical procedures”.

Second grade builds on the facts at once. Second graders “fluently add and subtract within 100 using strategies based on place value” (2.NBT.B.5), and every two-digit problem is made of one-digit facts. A fact that still has to be counted slows every step. Adding with regrouping and subtracting with regrouping both start from the facts, and the same facts come back inside multiplication, division, and fractions. Every fact a child knows by heart is one less step to count inside each of those problems.

Memorizing math facts or understanding them? Strategies first, then memory

Children need both, in that order: a strategy first, then practice that turns it into memory. McNeil and colleagues’ 2025 review presents memorization and thinking strategies “not as opposing methods but as complementary forces”.

Children learn a math fact in three stages: counting, reasoning, and knowing. Arthur Baroody describes the three phases children typically go through in Teaching Children Mathematics (2006, p. 22), calling them counting strategies, reasoning strategies, and mastery. Take 8 + 5:

1. Counting. The child counts on from 8: nine, ten, eleven, twelve, thirteen.
2. Reasoning. The child works it out from facts already known: 8 + 2 is 10, and 3 more is 13. That is the make ten strategy.
3. Knowing. The child says 13 at once.

Speed belongs to the third stage, and the third grows out of the second. Baroody writes that “practice should focus on making reasoning strategies more automatic, not on drilling isolated facts” (p. 29).

Reasoning cuts the number of facts a child has to memorize. First-grade standard 1.OA.B.3 says “If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known”, which takes the 100 addition facts to 55. On a 0–10 addition chart of 121 facts, a strategy covers all but 26, and the chart’s patterns show which ones.

The strategies, in the order Eureka Math’s first grade teaches the addition ones, with think addition, which Eureka teaches between the doubles and making ten, last here:

• Count on 1, 2, or 3 from the bigger number: 8 + 3 is “nine, ten, eleven”.
• Doubles: 6 + 6 = 12.
• Near doubles: 6 + 7 = 6 + 6 + 1 = 13.
• Make ten: 8 + 5 = 8 + 2 + 3 = 13.
• Adding 9 and 10: 9 + 6 is one less than 10 + 6, so 15.
• Think addition, to subtract: 13 − 5 asks what goes with 5 to make 13.

Each is taught step by step in doubles, near doubles, and make ten, and the addition strategies in the order kids learn them sets out the full sequence. Subtraction facts are learned through the addition facts, not as a second list, and how kids learn subtraction facts shows the three ways in.

Memorizing and understanding are two halves of one job. The standards ask for the sums “from memory” by the end of second grade, and the strategy is the shortcut to that memory, not a detour from it. A child who can work out 8 + 5 has something to practice; a child who cannot can only guess or count. Making ten can be seen on two ten frames or as a number bond. Number talks, where children solve a sum in their heads and say how, practice the reasoning stage out loud.

Math fact games to play at home

These five math fact games need only a deck of cards or two dice, and each one ends with your child saying the fact aloud. Take out the face cards and 10s, and count an ace as 1.

• Addition war. Each player turns over two cards and says the sum, and the bigger sum takes all four. For subtraction war, take the smaller card from the bigger, and the bigger difference wins.
• Salute. Three players. Two each hold a card to their forehead without looking at it, and the third says the sum. Each card holder works out their own card from the sum and the card they can see: a sum of 13 and a 5 means 8.
• Roll and cross off. Each player writes 2 to 12 in a row. Roll two dice, say the sum, and cross it off. The first to cross off five numbers wins.
• Make ten Go Fish. A pair is two cards that make 10, such as 7 and 3, and the number bond games explain how to play.
• Beat your own score. With a small pile of quick cards, count how many your child answers in one minute and write it down. Next time, the goal is the same score or one more.

Subtraction war and salute are the subtraction games. More games with dice and cards are in math board games.

How to practice math facts at home: a few minutes a day

Practice math facts in short sessions on most days, one strategy family at a time, starting from the facts your child already knows. The WWC guide’s advice on timed practice is written for intervention teachers, and these six steps adapt it for a kitchen table.

1. 1

   Find what is already quick

   Go through the flash cards once with no timer and sort them into two piles: the cards your child answers at once, and the ones that take a while. Or tick the facts your child knows on the blank addition chart.

2. 2

   Pick the next family

   Take the strategy families in order: counting on 1, 2, or 3, then doubles and near doubles, then making ten, then the subtraction facts of each. Before practicing a family, check that your child can work out its facts with the strategy.

3. 3

   Practice for about five minutes

   Mix a few cards from the new family with cards that are already quick, and have your child say each fact aloud, the answer included. A game with cards or dice counts as practice too.

4. 4

   Most days, not one long session

   Keep each session short and come back on most days of the week, rather than practicing for half an hour once a week. Stop while it is still going well.

5. 5

   Move a fact to the quick pile

   A card moves to the quick pile when your child answers it at once on two different days. Add the next family when most of the current one is in the quick pile.

6. 6

   Time it only once it is accurate

   Once your child gets a pile right every time, set a timer for one minute and count the cards answered. Write the score down, and next time the goal is to meet or beat it, never another child's score.

The WWC guide recommends including timed activities regularly, each lasting “between 1 and 5 minutes”. For step 1, the flash cards and the four rules for a card session are on our facts page, and the blank chart is on the addition chart page. For step 2, each family’s strategy is in how to teach doubles, near doubles, and make ten at home. For written practice beside the cards, the worksheets within 10 and within 20 mix the facts in each range. Praise the strategy and the improvement: “You used the double” tells your child what worked, and a score that climbs is a reward your child can see.

Are timed math tests bad? Speed, stress, and math anxiety

Parents who worry about timed math tests have reason to: math anxiety is real in young children. Ramirez, Gunderson, Levine, and Beilock (2013) measured math anxiety in 154 first and second graders. Sian Beilock and Daniel Willingham describe the study in American Educator (2014): “nearly 50 percent of the students reported medium to high levels of math anxiety”. The link between anxiety and lower scores was strongest in the children with the most working memory. The column adds that “math anxiety is more strongly linked to poor performance when students take a timed test.”

Jo Boaler of Stanford argues that timed tests should not be used. Her essay Fluency Without Fear (YouCubed, 2015) calls them “a major cause” of math anxiety and says they “prompt many students to turn away from mathematics”.

The WWC guide rates brief timed activities as having strong evidence for children who struggle with math, from 27 studies, with conditions. Each activity lasts “between 1 and 5 minutes”, is added once students have worked on a concept over many lessons, and is never used to introduce one. The goal is to “meet or beat” a previous score, and “accuracy is the goal”, not how many problems were attempted. McNeil and colleagues recommend “introducing time-limited practice only after students demonstrate accuracy”.

The two positions describe different activities. Boaler writes against tests that teachers give to measure number facts against the clock. The WWC’s is a round of a few minutes on a concept already taught, where the goal is to meet or beat a previous score. Timed tests are also “commonly used” to show which facts children know from memory, write Gina Kling and Jennifer Bay-Williams in the National Council of Teachers of Mathematics journal Teaching Children Mathematics, though they argue such tests show little about which strategy a child used.

The alternatives to a timed test are an untimed round sorted into a quick pile and a slow pile, a one-minute personal best, and a game score. The WWC guide was written for children who struggle, including children with learning disabilities, and still recommends brief timing on its conditions. If timing is the barrier for your child, ask the teacher about an untimed version.

When school sends home a timed test, practice the facts untimed first, then do a one-minute beat-your-score round with a small pile. If the test is causing tears, tell the teacher.

What if my child cannot remember math facts?

When a child cannot remember math facts, go back one stage: to the strategy, or to counting on and pictures. Arthur Baroody gives two reasons many children struggle with the facts (2006, p. 27). They “lack adequate informal knowledge”, such as how numbers split and combine, and “the conventional approach makes learning the basic number combinations unduly difficult and anxiety provoking”. Four patterns, and the way back from each:

• Still counting from 1. Go back to counting on from the bigger number, and to pictures of the numbers, such as ten frames for making ten and number bonds.
• Guessing. The facts are being practiced before the strategy is there. Work a few facts out together with the strategy.
• Right at home and wrong at school. Speed pressure is the likely cause. Practice untimed, and time only against your child’s own score.
• Known one week and gone the next. The pile is too big. Make it smaller and spread it over more days.

When it is more than practice, talk to your child’s teacher. A second grader who still counts every fact from 1, or a third grader who has not moved on after weeks of steady practice, is worth raising.

Free printables for math facts practice

The flash cards and charts the routine above uses are free PDFs, with no account and no email. The addition and subtraction flash cards, sorted by strategy family with each answer on the back, are hosted with the facts they hold, and the free addition charts, filled and blank, with how to read one. The Take From Ten sheet and the within-20 worksheets are for written practice of the same facts. Every PDF ends with a page for grown-ups on how to use it.

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Free printables for math facts practice

Seven free PDFs in black and white, with no account and no email, from our other math pages: the addition and subtraction flash cards, the addition chart, the blank addition chart, Take From Ten, and the within-20 addition and subtraction worksheets. Every PDF ends with a page of instructions for grown-ups on why, what for, and how to use it.

1. 1
   Addition Flash Cards (PDF)45 cards · answer key included · 9 pagesDownload

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2. 2
   Subtraction Flash Cards (PDF)81 cards · answer key included · 17 pagesDownload

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3. 3
   Addition Chart (PDF)477 facts · 5 pagesDownload

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4. 4
   Blank Addition Chart (PDF)227 facts · answer key included · 8 pagesDownload

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5. 5
   Take From Ten (PDF)52 facts · answer key included · 9 pagesDownload

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6. 6
   Addition Within 20 (PDF)144 problems · answer key included · 11 pagesDownload

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7. 7
   Subtraction Within 20 (PDF)144 problems · answer key included · 11 pagesDownload

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