1st Grade · 1.OA.C.5

The counting on strategy in 1st grade

The counting on strategy is a way to add by starting at one number and counting up, instead of counting everything from 1. In 1st grade, your child learns counting on to add and counting back to subtract. Your child also sees that each count of one is the same as adding 1 or taking away 1.

What the standard says

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

1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

What it means, in plain words

Many young children add by counting all. For $6 + 3$ , they count out 6 blocks, then 3 more blocks, then count the whole pile from 1 to 9. Counting on skips the first count. Your child keeps 6 in mind and counts three more: 7, 8, 9. The last number said is the answer.

Counting back works the same way for subtraction. For $12 - 3$ , your child starts at 12 and counts back three: 11, 10, 9. So $12 - 3 = 9$ . Children also learn to start with the bigger number when adding. $2 + 8$ is quicker as 8, then 9, 10.

The hard part is keeping track of how many counts were made. Fingers help, and so does a number line, a line with the numbers in order where each jump of one space is one count. The counting on strategy in 1st grade works best for adding or taking away small numbers like 1, 2 or 3. For bigger numbers, children move on to other strategies, such as making a ten.

Your child should be able to:

Add a small number by starting at the bigger number and counting on
Subtract a small number by counting back from the starting number
Keep track of the counts with fingers or jumps on a number line
Explain that counting on 1 is the same as adding 1

Example

What is $9 + 3$ ? Use counting on.

Start at the bigger number, 9. Do not count it again.
Count on three, holding up one finger for each count: 10, 11, 12.
Three fingers are up, so stop. $9 + 3 = 12$ . The answer is 12.

Example

What is $14 - 2$ ? Use counting back.

Start at 14.
Count back two: 13, 12.
The last number said is 12, so $14 - 2 = 12$ . The answer is 12.

Where children usually get stuck

For $6 + 3$ , your child says "6, 7, 8" and answers 8. Counting back, the same slip gives $10 - 2 = 9$ .
The child counts the starting number as the first count. The first count should be the number after 6, or the number before 10.
What helps. Write the numbers 1 to 20 on a strip of paper. Put a finger on 6, then make three hops, saying a number only when the finger lands: 7, 8, 9.
Your child counts all, even for $8 + 1$ , and starts again at 1 every time.
The child does not yet trust that the first group still holds 8 without counting it again. Counting on depends on that trust.
What helps. Drop 8 pennies into a cup while counting them, and say "there are 8 in here". Add pennies one at a time and ask how many there are now, without tipping the cup out.
For $2 + 9$ , your child starts at 2, counts on nine and often loses track.
The child always starts with the first number written. Starting with the bigger number gives the same answer with far fewer counts.
What helps. Before adding, ask which number is bigger. Show with blocks that a pile of 2 and 9 is the same size as a pile of 9 and 2.

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
Match each count back to the subtraction sentence that shows it.
Connect each item on the left to its match on the right.
Count Back
Subtraction Sentence
8,7,6,5
6,5,4
$\displaystyle 8 - 3 = 5$
$\displaystyle 8 - 4 = 4$
$\displaystyle 6 - 2 = 4$
Use Tab to navigate between items. Click or tap a card to select it, then click or tap a card on the opposite side to create a match. You can also drag a card or its connector dot to a card on the opposite side.
Show the answer and how to solve it
The first count back matches $8 - 3 = 5$ , and the second count back matches $6 - 2 = 4$ .
1. 1Look at the first count back: 8, 7, 6, 5. Start at 8 and count the jumps: 8 to 7, 7 to 6, 6 to 5. That is 3 jumps. So this count back shows 8 minus 3.
2. 2Look at the second count back: 6, 5, 4. Start at 6 and count the jumps: 6 to 5, 5 to 4. That is 2 jumps. So this count back shows 6 minus 2.
3. 3The remaining subtraction sentence does not match either count back. Counting back 4 from 8 would end at 4, but the count back 8, 7, 6, 5 only has 3 jumps and ends at 5.
Common mistake. A common mistake is matching by the first number alone. Two subtraction sentences both start with 8, so you need to count the jumps in the sequence to find the right one.
The idea underneath. In a count back, the number of jumps tells you how much you subtract. The number of values in the list is one more than the number of jumps.
2On level
Lily used the number line below to find $6 + 4$ by counting on. She said her answer is $9$ .
Select the statement that best describes Lily's answer.
A
Lily made one too many counts.
B
Lily counted backward by mistake.
C
Lily counted her starting place by mistake.
D
Lily got the right sum.
Show the answer and how to solve it
Lily counted her starting place by mistake. The number line lands on $10$ , which is the correct sum, but Lily said $9$ — one less than the right answer.
1. 1Look at the number line. Lily's path starts at $6$ and shows $4$ forward jumps, landing on $10$ .
2. 2Counting on from $6$ by $4$ jumps gives the correct sum:
3. 3Lily said her answer is $9$ . But the jumps land on $10$ . So Lily's answer is one less than the correct sum.
4. 4When counting on, the first count should be the NEXT number, not the starting number. To count on from $6$ , the correct count is the next $4$ numbers ending at $10$ . Lily probably said $6$ as the first count instead, which counts the starting place by mistake and gives one less.
Common mistake. When counting on, students often say the starting number as the first count. Saying " $6$ , ..." instead of " $7$ , ..." counts the starting place and gives one less than the correct sum.
The idea underneath. When you count on, the first count is the NEXT number, not the starting number itself. To add $4$ to $6$ , say the next $4$ numbers in order, ending at the sum.
3On level
Maya was given this count-on: "Start at 5, count on 4." Maya wrote: $5 + 5 = 10$ . Choose the best description of Maya's work.
A
Maya wrote a correct addition.
B
Maya wrote the wrong second number.
C
Maya wrote the wrong first number.
D
Maya wrote the wrong total.
Show the answer and how to solve it
Maya's second number is 5, but the prompt "count on 4" means the second number should be 4. So Maya wrote the wrong second number.
1. 1Look at the count-on prompt: "Start at 5, count on 4." The first number should be 5. The second number should be 4.
2. 2Now look at Maya's addition:
3. 3Maya's first number is 5. That matches "Start at 5" from the prompt. The first number is right.
4. 4Maya's second number is 5. But the prompt said "count on 4." So 5 should be 4. The second number is wrong.
5. 5Maya's addition has the wrong second number.
Common mistake. A common mistake is checking only that the addends and total agree. Here, $5 + 5 = 10$ is correct addition, but the prompt was "count on $4$ " — so $5$ doesn't match. Always check that the first AND second numbers match the prompt.
The idea underneath. A count-on like "Start at 5, count on 4" gives two numbers: the start (first number) and the count (second number). Both must match the prompt, and the total must equal start plus count.
4Stretch
Read the count-on below. Choose the addition sentence that matches.
Prompt: Start at 8, count on 4.
A
$\displaystyle 8 + {}$
$\displaystyle 4 = {}$
$\displaystyle 12$
B
$\displaystyle 7 + {}$
$\displaystyle 4 = {}$
$\displaystyle 11$
C
$\displaystyle 8 + {}$
$\displaystyle 5 = {}$
$\displaystyle 13$
D
$\displaystyle 8 + {}$
$\displaystyle 4 = {}$
$\displaystyle 13$
Show the answer and how to solve it
The matching addition sentence is $8 + 4 = 12$ . Counting on $4$ from $8$ moves through $9$ , $10$ , $11$ , and $12$ .
1. 1The prompt says 'Start at 8, count on 4.' Begin at 8.
2. 2Count on 4 numbers. Each step moves to the next number after 8.
3. 3Starting at 8 and counting on 4 lands on 12. The matching addition sentence is shown below.
Common mistake. A common mistake is counting the start number as the first step, going 8, 9, 10, 11 and landing on 11 instead of 12. In count on, the start is not counted — the next number is the first step.
The idea underneath. Counting on means moving past the start number to the next one. To count on 4 from 8, say '9, 10, 11, 12' — four numbers after 8 — not '8, 9, 10, 11'.