Addition and Subtraction for Kids

Addition is putting two amounts together to find the total, as in 3 + 2 = 5. Subtraction is taking an amount away, or finding how many more one number is than another, as in 5 − 2 = 3. Children learn both in stages: counting every object, then counting on from the bigger number, then strategies that turn a hard fact into an easier one, such as doubles and making ten, and finally knowing the fact by heart.

The Common Core asks kindergartners to add and subtract within 5 fluently, first graders within 10, and second graders to know every sum of two one-digit numbers, such as 7 + 8, from memory. Each strategy, with an example, is in the teaching order, and each grade’s goal is in the grade-by-grade standards. Subtraction’s three parts and its four strategies within 20, from counting back to counting up, are on our subtraction page.

What are addition and subtraction?

Addition puts amounts together, and subtraction takes an amount away or finds the difference between two amounts. The Common Core’s kindergarten standards define both in one line: “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.” In 3 + 2 = 5, the numbers being added, 3 and 2, are the addends, and the answer, 5, is the sum or total.

Subtraction has two meanings, taking away and comparing, and a child meets both. Five, take away two, leaves 3; and 5 is 2 more than 3. Both meanings, with a picture, are in what subtraction is.

First-grade story problems use five situations. The first-grade standard 1.OA.A.1 names them: “adding to, taking from, putting together, taking apart, and comparing”.

Situation	A one-line story	Number sentence
Adding to	Three cars are parked, and two more drive in. How many now?	3 + 2 = 5
Taking from	Five crackers, and two are eaten. How many are left?	5 − 2 = 3
Putting together	Four red apples and three green ones. How many apples?	4 + 3 = 7
Taking apart	Seven children, and four wear hats. How many have no hat?	7 − 4 = 3
Comparing	Mia has 5 stickers and Sam has 3. How many more does Mia have?	5 − 3 = 2

Children meet addition first, but kindergarten teaches subtraction beside it. K.OA.A.1 and K.OA.A.2 both name addition and subtraction from the start, and subtraction gets easier once a child sees it as the missing part of an addition. The first-grade standard 1.OA.B.4 asks children to “subtract 10 − 8 by finding the number that makes 10 when added to 8”. The facts 8 + 2 = 10 and 10 − 8 = 2 use the same three numbers, which is what a fact family shows. The names of a subtraction’s three parts, the minuend, the subtrahend, and the difference, are in the parts of a subtraction problem.

Addition strategies, in the order kids learn them

An addition strategy is a way to work out a fact a child does not know yet from one the child does. The Common Core’s progression document for operations describes three levels for single-digit addition and subtraction: “Direct Modeling by Counting All or Taking Away”, “Counting On”, and “Convert to an Easier Problem”, such as a double or a ten. The National Research Council calls this “a well-documented progression of procedures used worldwide by many children”. Within it, Eureka Math’s first grade teaches counting on, then doubles and doubles plus 1, then making ten, with think addition (step 6 below) between the doubles and making ten. The addition strategies, in teaching order:

Step	Strategy	Example	Grade	Standard	Taught on
1	Count all, with objects or fingers	3 + 2: count three, count two, then count all five	Kindergarten	K.OA.A.1, K.OA.A.2; TEKS K.3(A)–(B)	Learning to count, counting on fingers
2	Count on 1, 2, or 3 from the bigger number	8 + 3: “eight … nine, ten, eleven”	1st grade (counting forward from a number is kindergarten, K.CC.A.2)	1.OA.C.5, 1.OA.C.6	This page; one more, one less
3	Doubles	6 + 6 = 12	1st grade	1.OA.C.6; TEKS 1.3(D)	Doubles
4	Near doubles	6 + 7 = 6 + 6 + 1 = 13	1st grade	1.OA.C.6	Near doubles
5	Make ten, including adding 9	8 + 6 = 8 + 2 + 4 = 10 + 4 = 14	1st grade	1.OA.C.6; TEKS 1.3(C)–(D)	Make ten, on two ten frames
6	Think addition, to subtract	12 − 8: 8 + 4 = 12, so 4	1st grade	1.OA.B.4, 1.OA.C.6	Subtraction strategies; fact families
7	Know it	7 + 8 = 15, without working it out	End of 2nd grade	2.OA.B.2; TEKS 2.4(A)	Math facts; practice by range

Turnaround facts shorten every step. Because 3 + 8 is the same as 8 + 3, a child counts on from the 8. The first-grade standard 1.OA.B.3 asks children to use properties like this “as strategies”, and adds that “students need not use formal terms for these properties”.

Children move up and back down the steps. A child who knows doubles may still count on for a fact that feels hard, and that is normal. The progression document says the press toward fluency “should also allow students to fall back on earlier strategies when needed”.

Past 20, the same ideas work in tens. First and second graders add tens to tens and ones to ones (1.NBT.C.4, 2.NBT.B.5), regroup when the ones make a new ten, regroup to subtract when there are too few ones, and add and subtract in their heads. The standard algorithm, the carrying and borrowing method, arrives by name in fourth grade, as our guide to new math explains.

Counting on means starting from the bigger number and counting the smaller one onto it. For 8 + 3, a child says “eight” and counts three more on fingers: nine, ten, eleven. Stretching the first word, “eiiiight”, is natural, and it shows the child is holding the 8 without counting it again. The standard 1.OA.C.5 describes the move as “counting on 2 to add 2”. The progression document calls counting on “a thinking strategy, not a rote method”, because the child has to see the 8 inside the total. Fingers are the normal tool for it, and counting on grows out of knowing one more. Counting on is quickest for adding 1, 2, or 3, and past that a double or a ten takes fewer steps.

Subtraction has four strategies of its own within 20: count back, count up, think addition, and down over ten. Counting up from the smaller number is the one the progression document says “makes subtraction as easy as addition”. Each of the four, with an example and its standard, is in the subtraction strategies, from counting back to counting up.

What grade do kids learn addition and subtraction?

Children add and subtract with objects in kindergarten, learn the strategies in first grade, know the facts within 20 by the end of second grade, and add and subtract within 1,000 fluently in third grade. The grades in the Common Core and in Texas:

Grade	What children do	Fluency by the end of the year	Common Core	Texas (TEKS)
Pre-K	Show adding up to 5 objects, and taking objects from a set of 5, with objects, pictures, or a story	None set	None (the Common Core starts in kindergarten)	PK4.V.B.1, PK4.V.B.2
Kindergarten	Act out the meanings with objects, fingers, and drawings; story problems within 10; split numbers to 10; find the partner that makes 10 (sheets within 10)	Within 5	K.OA.A.1–5	K.2(I), K.3(A)–(C); count backward to 20, K.2(A); no fluency target
1st grade	Count on, doubles, make ten, and think addition within 20; story problems with the unknown in any position; add a two-digit and a one-digit number with models (sheets within 20)	Within 10	1.OA.A.1, 1.OA.B.3–4, 1.OA.C.5–6, 1.OA.D.8, 1.NBT.C.4	1.3(A)–(F), 1.5(F)–(G); strategies “including making 10”, no fluency target
2nd grade	Facts within 20 fluently, and every sum of two one-digit numbers from memory; add and subtract within 100 by place value, with regrouping (addition, subtraction); within 1,000 with models (sheets within 100)	Within 20, with every sum of two one-digit numbers from memory; within 100	2.OA.A.1, 2.OA.B.2, 2.NBT.B.5–7, 2.NBT.B.9	2.4(A) “with automaticity”, 2.4(B) “mental strategies and algorithms”, 2.4(C)–(D)
3rd grade	Add and subtract within 1,000; two-step word problems	Within 1,000	3.NBT.A.2, 3.OA.D.8	3.4(A), 3.5(A)

Texas asks for the same strategies, on a different schedule. TEKS 1.3(D) asks first graders for basic fact strategies “including making 10”, Texas sets no fluency target in kindergarten or first grade, and TEKS 2.4(A) expects second graders to recall the facts within 20 “with automaticity”. Texas also names “algorithms” from second grade, two years before the standard algorithm’s grades in both frameworks.

The fluency column is an end-of-year goal, so a first grader who still counts on for 8 + 5 is on time. First grade’s fluency line stops at 10, and the facts within 20 are second grade’s. Underneath the pre-K and kindergarten rows is number sense: knowing that 5 is one more than 4, and seeing small amounts without counting them.

From objects to pictures to numbers: how kids move to abstract addition

Children move from real objects, to a drawing or model, to numbers alone. Concrete means real things a child can move, such as counters, crackers, or fingers. Pictured means a drawing or a model on paper, such as dots crossed out or a ten frame, which is what “subtraction with pictures” worksheets are. Abstract means the number sentence alone, 8 + 6 = 14.

Objects and pictures carry strong evidence for children who find math hard. The What Works Clearinghouse recommends “a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures” in its 2021 practice guide. It rates that recommendation as strong evidence, from 28 studies of children from kindergarten to sixth grade who struggle with math. The guide was written for teachers giving that extra help, and this page adapts it for home. The Common Core’s progression document calls the methods that show every object “Level 1 methods”. The standards keep pictures in use for years, and second graders still add and subtract within 1,000 “using concrete models or drawings” (2.NBT.B.7).

Each model on homework serves a different step:

Model	What it shows	The step it serves
Dot cards	Small amounts seen at a glance	Count all, then seeing 5 without counting
Ten frame	Any number to 10 as fives and tens, with the empty boxes as the partner of 10	Partners of 10, make ten
Number bond	A number and two parts that make it	Splitting numbers, think addition
Rekenrek	Beads in fives and tens on two rods	Doubles, near doubles, make ten
Number line	Jumps from one number to another	Count on, count up
Base ten blocks	Ones, tens, and hundreds as blocks, from 1st grade	Adding and subtracting past 20, regrouping

Everyday things make good counters: snacks to share, socks to pair, and stairs to count up. Homemade math manipulatives has more. To move toward numbers, take the objects away one step at a time. Cover the counters and ask again, then draw instead of building, then say the number sentence with neither. If the answers go wrong without the objects, bring them back for a few days.

Why do schools teach strategies instead of just memorizing facts?

Schools teach strategies as the road to memorized facts, not instead of them. The same Common Core standards that teach counting on and making ten ask second graders to “know from memory all sums of two one-digit numbers” (2.OA.B.2). The Common Core’s progression document describes that memory as “an outcome of a multi-year process” and “not a matter of instilling facts divorced from their meanings”.

A strategy is what a child uses on the day a fact will not come. A child who forgets 7 + 8 can work it out as 7 + 7 + 1 = 15, instead of guessing or counting from 1. Each fact a child works out this way, again and again, is a fact on its way to memory.

Speed or understanding: both, in that order. “Fluent” in the standards means “fast and accurate”, in the progression document’s words, so timed practice belongs after a child is accurate, not before. Why homework looks so different from the way most parents learned is the subject of why math is taught differently now.

How to help your child with addition and subtraction at home, with games

Practice at home in the order the strategies come, a few minutes at a time, with things you already have. Each routine takes about 5 minutes, and the first one works from the age of 4.

1. 1

   Act out stories with real things

   Line up 3 toy cars, drive 2 more in, and ask how many there are now. Then say the number sentence together: 3 and 2 more is 5. Snacks, socks, and blocks work as well as cars, because your child can move and count them.

2. 2

   Count on together

   Say "Put 8 in your head and count on 3," and hold up three fingers one at a time while you both say nine, ten, eleven. Start from the bigger number even when it comes second, so 3 + 8 is counted on from 8.

3. 3

   Practice doubles and the partners of ten

   Show doubles on fingers, from 1 + 1 to 5 + 5. Then find the pairs that make 10 on a ten frame, or on a dozen egg carton with one pair of cups cut off: 7 counters and 3 empty cups, 6 and 4.

4. 4

   Ask subtraction as a missing part

   Ask "I had 12 grapes, and now I have 8. How many did I eat?" Count up from 8 to 12 together, nine, ten, eleven, twelve, and count the four steps. Your child has subtracted 12 − 8 without counting back.

5. 5

   Ask how your child worked it out

   After each answer, ask "How did you work it out?" and accept any strategy that gives the right answer. Second graders are expected to explain why their addition and subtraction strategies work, and saying it aloud at home is the same skill.

6. 6

   Keep it short and often

   Keep sessions to 5–10 minutes on most days, and stop while it is still going well. Once your child is accurate, flash cards fit here: print them double-sided and flip on the long edge, so each answer lands on the back of its card.

Each of these three games practices one of the steps, with cards or dice. Take the face cards out of a deck and count an ace as 1.

• Make ten Go Fish (step 3). A pair is two cards that make 10, such as 7 and 3. The make-ten practice goes further.
• Double it (step 3). Roll one die and say its double: roll a 4, say 8. Then roll two dice, and when they land one apart, such as 4 and 5, use the double: 4 + 4 + 1 = 9.
• Card war (step 6). Each player turns over two cards and adds them, and the bigger total takes all four. For subtraction, take the smaller card from the bigger one, and the bigger difference wins.

Two games for counting up, a count-up race and cup and counters, are on practicing subtraction at home.

When addition and subtraction are hard for your child

Each of these is something a parent can see at the table, and each has one thing to change.

• Counting from 1 every time. For 8 + 3, your child counts out all eleven. That is the count-all step, and the next one is counting on, so practice counting forward from a number.
• Fingers for every fact in second grade. Fingers are normal in kindergarten and first grade. In second grade, practice doubles and make ten so the facts start to come without them, and see when children stop counting on their fingers.

Three subtraction mistakes, losing track counting back, turning a subtraction around, and adding when the story means subtract, each with its fix, are in when subtraction is hard.

When it is hard in general, go back one step for a few days. Go back one row of the strategy order, and back to objects, then climb again. Three habits make addition and subtraction harder: pushing for speed before your child is accurate, showing a shortcut before the strategy it shortens, and correcting a method that works because it is not the one you learned.

If adding and subtracting within 10 is still hard at the end of first grade, talk to your child’s teacher. Within 10 is first grade’s fluency line, and the teacher can say what the class has covered and what to practice next.

Addition and subtraction worksheets for each step

Every addition and subtraction worksheet on this site lives on the page that teaches its step, so each sheet comes with its explanation. For a page of plain sums, start with the practice sheets by range, within 10, 20, and 100.

Step	Worksheets	Where to find them
Seeing amounts without counting	Dot Cards	Subitizing dot cards
Partners and number bonds	Number Bonds; Ways to Make a Number; Blank Number Bond and Part-Part-Whole Mat	Number bond worksheets
Partners of 10 and making ten on a frame	Ten Frame Mats; Ten Frame Cards; Double Ten Frame Cards	Free ten frames
Fives and tens on beads	How Many Beads?	Rekenrek cards
Doubles, near doubles, make ten, and take from ten	Doubles Facts; Near Doubles Facts; Make Ten Facts; Take From Ten	Doubles and make ten sheets
Think addition	Fact Family Houses; Fact Family Triangle Cards	Fact family sheets
Count on and count up on a line	Adding and Subtracting on a Number Line; Open Number Line	Number line sheets
Practice by range	Addition Within 10; Subtraction Within 10; Addition Within 20; Subtraction Within 20; Mixed Addition and Subtraction; Adding and Subtracting Within 100	Worksheets by range
Knowing the facts	Addition Flash Cards; Subtraction Flash Cards	Addition and subtraction flash cards
Seeing every fact at once	Addition Chart; Blank Addition Chart	Free addition chart
Regrouping with blocks	Base Ten Blocks: Regrouping	Base ten block sheets
Addition with regrouping	Addition with Regrouping	Addition with regrouping worksheets
Subtraction with regrouping	Subtraction with Regrouping	Subtraction with regrouping worksheets

Going further: number bonds first, mental calculation, and number talks

Some programs add steps to the standards’ order, and each of these four gives a child who finds the sequence easy something new to try.

• Number bonds before addition. Singapore Math’s Dimensions Math teaches number bonds in kindergarten (KB, Chapter 8) before its first addition chapter (Chapter 9), and opens first grade the same way (1A, Chapters 2 and 3). A child who can split 7 into 5 and 2 is ready to make ten, and splitting numbers with number bonds shows how.
• Subtract from ten. Dimensions Math teaches “Subtract from 10” for teen numbers in 1A, Chapter 7. For 13 − 9, take the 9 from the 10 to leave 1, then add the 3, so 1 + 3 = 4. It is a cousin of down over ten, and the Take From Ten sheet on the make-ten page practices it.
• Mental calculation. Dimensions Math gives it a second-grade chapter of its own (2B, Chapter 8), with lessons such as “Making 100” and “Adding 97, 98, or 99”. For 46 + 99, add 100 and take 1 away: 146 − 1 = 145.
• Number talks. A number talk is a short classroom routine in which children solve a sum in their heads and then explain how they did it.