1st Grade · 2nd Grade · 1.OA.C.6 · 2.OA.B.2

Addition facts in 1st and 2nd grade

Addition facts are the sums of two one-digit numbers, like $8 + 5 = 13$ , together with the subtraction facts that go with them. In 1st grade, your child works on addition and subtraction within 20 with strategies such as the making ten strategy. In 2nd grade, your child uses mental math strategies until every sum of two one-digit numbers is known from memory.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

What it means, in plain words

1st grade: strategies for addition and subtraction within 20 1.OA.C.6

Within 20 means that the numbers in the problem and the answer are 20 or less. In 1st grade, children should be quick and sure with facts within 10, such as $6 + 3$ or $8 - 5$ . For bigger facts, they use a strategy, a short way to the answer that does not count every one.

The making ten strategy is the most important one. To add $9 + 4$ , your child moves 1 from the 4 to the 9: $9 + 1 + 3 = 10 + 3 = 13$ . Adding to 10 is easy. Subtraction works the same way in reverse: $14 - 6 = 14 - 4 - 2 = 10 - 2 = 8$ .

Other strategies use facts your child already knows. A double such as $7 + 7 = 14$ gives the near double $7 + 8$ , which is one more, 15. Knowing $9 + 5 = 14$ also gives $14 - 9 = 5$ . Addition facts in 1st grade are still worked out this way, not yet known by heart.

Your child should be able to:

Add and subtract within 10 quickly and correctly
Use the making ten strategy, such as turning $9 + 4$ into $10 + 3$
Use a known double, such as $7 + 7$ , to find $7 + 8$
Use an addition fact to find the matching subtraction

Example

What is $8 + 7$ ? Use the making ten strategy.

8 needs 2 more to make 10.
Break the 7 into 2 and 5.
$8 + 2 = 10$ , then $10 + 5 = 15$ .
So $8 + 7 = 15$ . The answer is 15.

2nd grade: knowing the facts from memory 2.OA.B.2

Addition facts in 2nd grade move from working out to knowing. By the end of the year, your child should know every sum of two one-digit numbers from memory, from $0 + 0$ up to $9 + 9$ . Teachers often call these the math facts.

Fluent means fast, correct and without fingers. Children get there through mental math strategies, ways of solving a problem in the head. The strategies from 1st grade, such as making ten and near doubles, get used again and again until the answer comes without them. Subtraction within 20 is done in the head too, often by thinking of the matching addition.

This matters for the rest of 2nd grade. Adding bigger numbers, such as $36 + 27$ , uses a one-digit fact at every step.

Your child should be able to:

Say the sum of any two one-digit numbers from memory
Subtract within 20 without counting on fingers
Pick a mental math strategy that fits the numbers
Explain how a known fact helps with one that is not known yet

Example

What is $13 - 8$ ? Solve it without fingers.

Think of the addition: 8 and what number make 13?
8 and 2 make 10, and 10 and 3 make 13.
2 and 3 make 5, so $8 + 5 = 13$ .
So $13 - 8 = 5$ . The answer is 5.

Where children usually get stuck

In 2nd grade, your child still counts on fingers for $7 + 6$ , starting at 7 and counting six more.
Counting on gives the right answer, so the child has no reason to stop. Each fact is counted fresh instead of linked to a fact already known, such as $6 + 6 = 12$ .
What helps. Pick one small group of facts for the week, such as the doubles. Ask $6 + 6$ in the car and wait for the answer, then ask $6 + 7$ .
Making ten for $8 + 5$ , your child writes $8 + 2 = 10$ , then $10 + 5 = 15$ .
The 2 that made the ten came out of the 5, but the child forgot to take it away. Only 3 is left to add, so the answer is 13.
What helps. Draw a ten-frame, a box of 10 squares in two rows of 5. Put 8 coins in it and 5 coins beside it. Move coins in until the frame is full, then count what is left outside.
Your child knows $7 + 5 = 12$ but counts back to answer $12 - 7$ .
The facts were learned as a list of sums. The link to subtraction was never made.
What helps. Ask each subtraction right after its addition: first $7 + 5$ , then $12 - 7$ . Point out that the same three numbers are in both.

Try four practice questions

Real 1st grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Find the difference. Select the answer.
$\displaystyle 9 - 3 = ?$
A
6
B
7
C
5
D
12
Show the answer and how to solve it
The difference is $6$ because $9 - 3 = 6$ .
1. 1Look at the subtraction equation. We need to find $9 - 3$ .
2. 2Count back $3$ from $9$ : $8$ , $7$ , $6$ . The difference is $6$ .
3. 3The difference is $6$ .
Common mistake. A common mistake is adding instead of subtracting. The minus sign means take away.
2On level
What number makes the equation true?
$\displaystyle 5 + 6 = 5 + 5 + \underline{\phantom{00}}$
A
$\displaystyle 1$
B
$\displaystyle 0$
C
$\displaystyle 2$
D
$\displaystyle 6$
Show the answer and how to solve it
The missing number is $1$ , because $6$ is $1$ more than $5$ . The doubles fact $5 + 5 = 10$ , plus the extra $1$ , equals $11$ — which is the same as $5 + 6$ .
1. 1Look at the equation. It rewrites $5 + 6$ using the doubles fact $5 + 5$ , with one number missing.
2. 2 $6$ is just $1$ more than $5$ . So the doubles fact $5 + 5$ needs $1$ more added to it to equal $5 + 6$ .
3. 3The missing number is $1$ . Check:
Common mistake. A common mistake is writing $0$ (forgetting that $5 + 6$ is bigger than $5 + 5$ , so the doubles fact alone is too small) or writing $2$ (over-counting how much bigger $6$ is than $5$ when the difference is just $1$ ).
The idea underneath. Near-doubles work by doubling the smaller number and adding the difference. For $5 + 6$ , double $5$ to get $10$ , then add the $1$ extra (since $6$ is $1$ more than $5$ ).
3On level
Subtract.
$\displaystyle 10 - 1 = \underline{\phantom{00}}$
Show the answer and how to solve it
Answer. 9
The difference is $9$ because counting back $1$ from $10$ gives $9$ .
1. 1The equation says to take $1$ away from $10$ . Start at $10$ .
2. 2Count back $1$ number. Each step goes to the next-smaller number:
3. 3The last number you said is $9$ . So $10 - 1 = 9$ .
Common mistake. A common mistake is to type $10$ itself instead of counting back one step to $9$ .
The idea underneath. Counting back means each step makes the number $1$ smaller. Start at the bigger number and say the next-smaller number as your first step.
4Stretch
Find the sum.
$\displaystyle 8 + 9 =$
Show the answer and how to solve it
The sum is $17$ . Using the doubles fact $8 + 8 = 16$ , then adding $1$ more for the extra in $9$ , you get $17$ .
1. 1Look at the addition. The $8$ and $9$ are next to each other when you count — they are near doubles.
2. 2Start with a doubles fact you already know.
3. 3Since $9$ is $1$ more than $8$ , add $1$ more to the doubles fact.
4. 4So $8 + 9 = 17$ .
Common mistake. A common mistake is stopping at the doubles fact $8 + 8 = 16$ and writing $16$ as the answer. Since $9$ is $1$ more than $8$ , you need to add $1$ more: $16 + 1 = 17$ .
The idea underneath. Near-doubles like $8 + 9$ can be solved quickly by using a doubles fact you already know ( $8 + 8 = 16$ ) and adjusting by $1$ .