Subtraction for Kids

Subtraction is taking an amount away, or finding how many more one number is than another, as in 5 − 2 = 3. The answer is the difference, the number you start with is the minuend, and the number taken away is the subtrahend. Children subtract within 20 with four strategies, learned in order: count back, count up, think addition, and down over ten.

For subtraction, the most useful move is to count up from the smaller number. For 13 − 9, say “nine” and count up to 13: ten, eleven, twelve, thirteen. That is four counts, so 13 − 9 = 4. The Common Core Standards Writing Team calls counting down “difficult and error-prone” and says counting on “makes subtraction as easy as addition”. Each strategy, with an example, is in the subtraction strategies, and where subtraction sits beside addition, step by step, is in the addition and subtraction strategy order.

What is subtraction?

Subtraction takes an amount away, or finds the difference between two amounts. The Common Core’s kindergarten standards ask children to “understand subtraction as taking apart and taking from”, in the same line that defines addition as “putting together and adding to”.

Subtraction has two meanings, and a child meets both. The first is taking away: 5 − 2 means five, take away two, which leaves 3. The second is comparing: how many more is 5 than 3? The gap between them, 2, is the difference, which is why the answer to every subtraction is called the difference. Everyday subtraction is five crackers with two eaten, or seven children with four in hats and three without.

Subtraction is also a missing addend. 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”. Addition and subtraction are one relationship seen from two sides: 8 + 2 = 10 and 10 − 8 = 2 use the same three numbers, which is what a fact family shows.

Subtraction story problems use the same five situations as addition. The first-grade standard 1.OA.A.1 names them: “adding to, taking from, putting together, taking apart, and comparing”. A one-line story for each, with its number sentence, is in the five situations on our addition and subtraction page.

What are the parts of a subtraction problem?

A subtraction problem has three parts: the minuend, the subtrahend, and the difference. In 9 − 4 = 5, 9 is the minuend, the number you start with; 4 is the subtrahend, the number taken away; and 5 is the difference. The Common Core’s progression document says these two names are “not needed for Kindergarten, Grade 1, and Grade 2” and “may inhibit students seeing and discussing relationships between addition and subtraction”. It says “total” and “addend” are enough for those grades, which is why homework may use those words instead.

Part	In 9 − 4 = 5	What it is	The word K–2 homework may use
Minuend	9	The number you start with	Total
Subtrahend	4	The number taken away	Addend
Difference	5	The answer	Addend

Subtraction strategies: count back, count up, and think addition

Counting up is easier than counting back for most subtraction, and counting back is best kept for taking away 1, 2, or 3. Children use four subtraction strategies within 20, in this order:

1. Count back, to take away 1, 2, or 3. For 9 − 2, say “nine” and count back two: eight, seven. Many children start here, and Texas asks kindergartners to “count forward and backward to at least 20 with and without objects” (TEKS K.2(A)).
2. Count up, for everything else. For 13 − 9, start at 9 and count up to 13: ten, eleven, twelve, thirteen. That is four counts, so the answer is 4.
3. Think addition. For 12 − 8, ask “8 plus what makes 12?” It is the Common Core’s own example in 1.OA.C.6: “knowing that 8 + 4 = 12, one knows 12 − 8 = 4”.
4. Down over ten, for teen numbers. For 13 − 4, take away 3 to reach 10, then 1 more: 13 − 3 − 1 = 10 − 1 = 9. That is the standard’s example again, and Texas first-grade standard 1.3(D) calls it “decomposing a number leading to a 10”.

Counting up beats counting back because of what a child has to keep track of. Counting back 9 from 13 means saying nine numbers backward and counting the counts at the same time. Counting up from 9 to 13 is four numbers forward. The appendix to the progression document by the Common Core Standards Writing Team says: “Many children attempt to count down for subtraction, but counting down is difficult and error-prone. Children are much more successful with counting on; it makes subtraction as easy as addition.” It notes that 9 + 4 and 13 − 9 sound the same when a child works them out: “Niiiiine, ten, eleven, twelve, thirteen”. Counting back is not wrong. It is the early method, and it stays the quick one for taking away 1, 2, or 3.

Think addition is why the facts come in families. A child who knows 8 + 4 = 12 has 12 − 8 = 4 as well, and learning fact families turns every known sum into two subtractions. Down over ten is the subtraction half of making ten, and the Take From Ten sheet on doubles and make ten practices it. Drawn as jumps on a number line, counting up is one jump from 9 to 13, and the length of the jump is the answer.

Past 20, subtraction works in tens and ones. Second graders subtract within 100 by place value (2.NBT.B.5), and regroup to subtract when there are too few ones. The standard algorithm, the borrowing method, arrives by name in fourth grade, as our guide to new math explains.

What grade do kids learn subtraction?

Children subtract with objects in kindergarten, learn the strategies above in first grade, and know the facts within 20 by the end of second grade. The Common Core asks kindergartners to add and subtract within 5 fluently (K.OA.A.5). First graders subtract within 20 with strategies such as counting on and making ten, and fluently within 10 (1.OA.C.6). Second graders subtract within 20 fluently (2.OA.B.2), and third graders within 1,000 (3.NBT.A.2). Every grade’s goal for addition and subtraction together, with the Texas standards beside the Common Core, is on the grade-by-grade table.

How to practice subtraction at home, with games

Practice subtraction as a missing part, a few minutes at a time, with things you already have. 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. Six short routines for addition and subtraction together are in how to help your child at home.

Each of these two games practices counting up, with dice or counters.

• Count-up race. On a 1–10 number path, each player counts up from their square to 10 before rolling and says how many are left: from 6, seven, eight, nine, ten, so four to go. Then they roll and move, and the first to land on 10 wins. A free board is in math board games.
• Cup and counters. Put out 8 counters and hide some under a cup while your child looks away. If 5 are showing, ask how many are hiding: 5 plus what makes 8?

For a page of plain subtraction, the Subtraction Within 10 and Subtraction Within 20 sheets are on the worksheets by range. Once your child is accurate, the subtraction flash cards print each answer on the back of its card.

When subtraction is hard for your child

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

• Losing track counting back. For 15 − 9, your child counts back nine and lands on 5 or 7. Switch to counting up: from 9 to 15 is six.
• Turning a subtraction around. Your child writes 5 − 8 for a story that starts with 8 birds and has 5 fly away. Act the story out and write the number you start with first.
• Adding when the story means subtract. “Sam has 8 stickers, which is 3 more than Mia has. How many does Mia have?” The word “more” invites adding, but the answer is 8 − 3 = 5. Ask who has more before choosing.

When subtraction is hard in general, go back one step for a few days. Go back to objects, or from counting up to counting back for small numbers, then climb again. The signs that addition and subtraction together are hard, and when to talk to your child’s teacher, are on when addition and subtraction are hard.