Kindergarten · K.OA.A.3

Number bonds in kindergarten

Number bonds show how a number splits into two parts, like 4 splitting into 3 and 1. In kindergarten, your child finds different ways to break up the numbers up to 10 and writes each way as an equation, such as $4 = 3 + 1$ .

What the standard says

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

K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

What it means, in plain words

Decomposing numbers means breaking a number into smaller parts. In kindergarten, the number is 10 or less and it breaks into two parts. The parts can change, but together they always make the same whole. The number 4 can be 3 and 1, 2 and 2, or 4 and 0.

A number bond is a small drawing of this idea. The whole number sits in one circle, and two lines join it to two smaller circles that hold the parts. Number bonds in kindergarten are often drawn with the whole on top and the parts below.

Finding the ways to make a number builds the facts your child needs for adding and subtracting. A child who knows that 8 is 5 and 3 has an easier time with $5 + 3 = 8$ and $8 - 5 = 3$ later.

Your child should be able to:

Break a number up to 10 into two parts in more than one way
Show each way with objects or a drawing
Write each way as an equation, like $8 = 6 + 2$
Fill in a number bond drawing with the whole and both parts

Example

Your child has 8 buttons and two cups. What are the different ways to share the buttons between the two cups?

Put 7 buttons in one cup and 1 in the other: $8 = 7 + 1$ .
Move one button across each time: $8 = 6 + 2$ , then $8 = 5 + 3$ , then $8 = 4 + 4$ .
All the buttons can also go in one cup: $8 = 8 + 0$ .
So 8 splits into two parts in 5 ways. The parts change each time, but the whole is always 8.

Where children usually get stuck

Your child finds one way to make 8 and says there are no more.
The child treats the first split as the answer. The idea that one number has many right splits is new.
What helps. Play the two-cup game: after each split, move one button to the other cup and ask whether there are still 8.
Your child writes the numbers in the order they were found, like $8 + 5 = 3$ .
The equals sign is new. The child copies the numbers without knowing that the whole stands alone on one side.
What helps. Draw a number bond first, with the whole in the top circle and the parts below. Then write the equation from the drawing: the whole, the equals sign, then the two parts with a plus sign between them.
Your child never lists 8 and 0 as a way to make 8.
Zero does not feel like an amount to a young child. A cup with nothing in it does not seem to count as a part.
What helps. Put all the buttons in one cup and hold up the empty one. Ask how many are in it, and say "zero" together.

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
Maya looked at this picture.
$\displaystyle \text{Maya wrote: } 2 + 1 = 3$
Which sentence best describes Maya's equation?
A
Maya counted the first group in the picture wrong.
B
Maya counted both groups in the picture correctly.
C
Maya counted both groups in the picture wrong.
D
Maya counted the second group in the picture wrong.
Show the answer and how to solve it
Maya counted both groups correctly. The picture shows 2 stars and 1 heart, and Maya wrote $2 + 1 = 3$ .
1. 1Look at the picture. The first group has 2 stars and the second group has 1 heart.
2. 2Now look at Maya's equation. The first number is 2 and the second number is 1.
3. 3Compare each number to its group. Maya's first number 2 matches the 2 stars. Maya's second number 1 matches the 1 heart. So Maya counted both groups correctly.
Common mistake. A common mistake is to assume Maya must have made an error and pick 'both groups wrong.' But checking each group one at a time shows both numbers match: 2 stars matches 2, and 1 heart matches 1.
The idea underneath. An equation tells the count for each group. To check if it matches a picture, compare each number in the equation to its matching group, one at a time.
2On level
Which picture shows the addition?
$\displaystyle 2 + 4 = 6$
A
B
C
D
Show the answer and how to solve it
The picture with $2$ bananas and $4$ cherries matches the equation $2 + 4 = 6$ .
1. 1Read the addition. We need a picture with two groups — one with $2$ and one with $4$ .
2. 2Count each group in the choices. Look for a picture that has $2$ bananas and $4$ cherries.
3. 3The picture with $2$ bananas and $4$ cherries matches. $2$ bananas plus $4$ cherries makes $6$ pieces of fruit in all.
Common mistake. A common mistake is picking a picture by the total only. The picture with $5$ bananas and $1$ cherry also adds to $6$ , but it does not show the numbers $2$ and $4$ from the equation.
The idea underneath. An addition picture must show each number in its own group, not just the total. Count each group separately to match both numbers in the equation.
3On level
Maya saw one way to make 7. She tried to make 7 a different way.
First way:
Maya's way:
Select the statement that best describes Maya's picture.
A
The new picture has different numbers but the same total.
B
The new picture has too many counters.
C
The new picture has too few counters.
D
The new picture has the same numbers, just in different colors.
Show the answer and how to solve it
Maya used different numbers ( $6$ and $1$ ) but the same total. $6 + 1 = 7$ , just like $4 + 3 = 7$ .
1. 1Count the first picture. It has $4$ apples and $3$ bananas. The total is $4 + 3 = 7$ .
2. 2Now count Maya's picture. It has $6$ apples and $1$ banana. The total is $6 + 1 = 7$ .
3. 3Both pictures show $7$ . But the numbers are different. The first picture used $4$ and $3$ . Maya's picture used $6$ and $1$ .
4. 4Maya made $7$ a different way. She used different numbers but kept the same total of $7$ .
Common mistake. A common mistake is thinking the total changed. But $6 + 1 = 7$ , the same total as $4 + 3 = 7$ .
The idea underneath. To show a number a different way, you use different numbers that still add up to the same total.
4Stretch
Maya made 9 this way:
$\displaystyle 1 + 8 = 9$
Make 9 a different way. Drag two number tiles into the boxes.
Tap or click a tile to drop it into the highlighted blank, or tap an empty blank first to choose a different one. Tap a filled blank to send its tile back.
+
=
9
0
1
2
3
4
5
6
7
8
9
Tap an item to place it in the next empty slot, or drag it to a specific slot. With a keyboard: select an item with Enter or Space, then select a slot to place it. Press Delete or Backspace on a slot to remove an item.
Show the answer and how to solve it
$4 + 5 = 9$ is one correct answer. You could also drag $5 + 4$ , $0 + 9$ , $9 + 0$ , $2 + 7$ , $7 + 2$ , $3 + 6$ , or $6 + 3$ into the boxes.
1. 1Look at Maya's equation. She added 1 and 8 to make 9.
2. 2Find two different numbers that add to 9. Here are other pairs that make 9:
3. 3Pick one pair Maya did not use. For example, drag 4 into the first box and 5 into the second box.
Common mistake. A common mistake is using the same numbers Maya used (1 and 8), just in a different order. Switching $1 + 8$ to $8 + 1$ uses the same two numbers, so it is not a different way.
The idea underneath. There are many ways to make 9. Each different pair of numbers that adds to 9 is a different way.