Kindergarten · K.CC.B.4

Number sense in kindergarten

Number sense is the understanding that a number stands for an amount: 5 means five things, and 6 is one more than 5. In kindergarten, your child builds number sense by counting objects carefully and learning what the last number in a count means.

What the standard says

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

K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
K.CC.B.4.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
K.CC.B.4.b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
K.CC.B.4.c Understand that each successive number name refers to a quantity that is one larger.

What it means, in plain words

One-to-one correspondence means matching each object with exactly one number word. Your child touches one block and says one, touches the next block and says two. No block gets skipped and no block gets counted twice. This is the first part of counting objects, and it is harder than it looks when the objects are not in a line.

The second part has a long name, cardinality, for a simple idea: the last number you say tells how many there are. When your child counts four toy cars, the answer is 4, not "1, 2, 3, 4". The amount also stays the same however the cars are arranged and whichever car is counted first. Four cars in a row and four cars in a pile are both 4.

The third part is that each number in the count is one more than the number before it. Counting adds one each time. Number sense in kindergarten grows from these three ideas. A child who has them can tell that 7 blocks are more than 6 blocks without counting both groups.

Your child should be able to:

Touch or move each object once while counting, saying one number for each
Answer "How many?" with the last number said
Explain that moving the objects around does not change how many there are
Say that the next number in a count is one more

Example

Six spoons are counted on the table. Then they are spread out. How many spoons are there now?

The spoons were counted once: 1, 2, 3, 4, 5, 6.
Spreading them out does not add a spoon or take one away.
There are still 6 spoons.

Example

A tower has 8 blocks. One more block goes on top. How many blocks are in the tower now?

Each number in a count is one more than the number before it.
The number after 8 is 9, so $8 + 1 = 9$ .
The tower now has 9 blocks.

Where children usually get stuck

Your child counts faster than pointing, so the words run ahead of the finger and 6 cookies come out as 8.
Saying the numbers is a song your child knows well, and touching objects is slower. The voice runs ahead of the hand.
What helps. Count by moving each object from one side of the table to the other as you say its number. Moving is slower than pointing, so voice and hand stay together.
After counting 7 cars, your child is asked how many and counts them all again.
Your child can count but does not yet know that the last number is the answer. Counting feels like the whole job, and the question "how many" sounds like a new job.
What helps. After every count, ask "So how many?" and say the last number together, a little louder than the others.
Your child counts 7 books in a row, then counts them again after you spread them out, expecting a different number.
Your child is not yet sure that the amount stays the same when the arrangement changes. A long, spread-out row looks like more than a tight pile.
What helps. Count a few toys, spread them out and ask whether there are more now. Count again together and talk about why the answer stayed the same.

Try four practice questions

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

1Warm-up
Liam is counting apples. Match each number to one apple, in order, starting with 1.
Connect each item on the left to its match on the right.
Numbers
Apples
1
2
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
Each number 1 and 2 is matched to one apple, in order. The last number is 2, so Liam counted 2 apples.
1. 1Liam has apples on the right and the numbers 1, 2 on the left. To count, give one apple the number 1, and the next apple the number 2.
2. 2Start at the top. Match the number 1 to the first apple. Then match the number 2 to the next apple. Each number is used one time, in order.
3. 3Now two apples each have one number. The last number you said is 2, so Liam counted 2 apples.
Common mistake. A common mistake is matching two numbers to the same apple, or skipping the order. Each number 1 and 2 should be used one time, in order: 1, then 2.
The idea underneath. When you count, each object gets exactly one number, said in order. The last number you say tells you how many objects there are.
2On level
Liam looked at the apples and said there are 5 apples. Is Liam correct?
A
Yes, Liam is correct.
B
No, Liam is wrong.
Show the answer and how to solve it
The answer is 'No, Liam is wrong.' There are 6 apples, not 5.
1. 1Look at the apples below.
2. 2Count each apple one time. Touch each one as you count: 1, 2, 3, 4, 5, 6.
3. 3There are 6 apples in all. Liam said there are 5. So Liam's count is one too few.
Common mistake. A common mistake is to trust Liam's number without checking. Always count each apple one at a time before deciding.
The idea underneath. When you count, touch each thing one time. The last number you say tells how many.
3On level
Carlos and Zara counted the fish below.
Carlos said there are 4 fish. Zara said there are 6 fish. Who is right?
A
Carlos is right
B
Zara is right
C
Neither one is right
Show the answer and how to solve it
Neither one is right. There are 5 fish in the picture. Carlos said 4 (too few), and Zara said 6 (too many). When both numbers are wrong, the answer is 'Neither one is right.'
1. 1Look at the fish in the picture. Touch each fish one time as you count.
2. 2Count: 1, 2, 3, 4, 5. There are 5 fish in all.
3. 3Carlos said 4, but there are 5 fish. Carlos is not right — he said one too few.
4. 4Zara said 6, but there are 5 fish. Zara is not right either — she said one too many.
5. 5Both Carlos and Zara said the wrong number, so neither one is right.
Common mistake. A common mistake is picking one of the named students without counting the fish first. Some students also pick the larger number (Zara's 6) because bigger feels like more, without checking the actual count of 5.
The idea underneath. To check who is right, count the objects yourself one at a time. If a stated number does not match your count, that person is not right.
4Stretch
These are some apples. Which student counted them correctly?
A
Carlos: 1, 2, 3, 4, 6
B
Devontae: 1, 2, 4, 3, 5
C
Maria: 1, 2, 3, 4, 5
D
Aiyana: 1, 2, 3, 3, 4
Show the answer and how to solve it
Maria counted correctly. They said 1, 2, 3, 4, 5 — one number for each apple, with the numbers in order.
1. 1First, count the apples. Touch each apple one time and say a number.
2. 2There are 5 apples. The right way to count 5 apples is to say 1, 2, 3, 4, 5 — one number for each apple, with the numbers in order.
3. 3Now look at what each student said. Maria said 1, 2, 3, 4, 5. Maria said each number one time, in order. Carlos said 1, 2, 3, 4, 6. Carlos skipped the number 5. Aiyana said 1, 2, 3, 3, 4. Aiyana said the number 3 two times. Devontae said 1, 2, 4, 3, 5. Devontae said 4 before 3.
4. 4Maria counted correctly.
Common mistake. A common mistake is only checking the last number. Devontae's last number is 5, but the numbers must also be said in order: 1, 2, 3, 4, 5 — not 1, 2, 4, 3, 5.
The idea underneath. When you count, you say one number for each thing, and the numbers go in order: 1, 2, 3, 4, 5.