2nd Grade · 2.OA.C.3

Odd and even numbers in 2nd grade

Odd and even numbers are two kinds of whole numbers: an even number of things splits into pairs with nothing left over, but an odd number always has one left over. In 2nd grade, your child decides whether a group of up to 20 objects is odd or even and writes an even number as two equal numbers added together, such as $6 + 6 = 12$ .

What the standard says

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

2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

What it means, in plain words

Children start with things they can move. Put 13 buttons on the table and match them in pairs. You get 6 pairs and 1 button with no partner, so 13 is odd. With 14 buttons, every button has a partner, so 14 is even.

Counting by 2s gives the same answer. The numbers you say when you count by 2s from 2 (2, 4, 6, 8, 10 and so on) are the even numbers. The numbers in between are odd. There is also a shortcut: a number is even when its last digit is 0, 2, 4, 6 or 8.

Your child also writes an even number as two equal parts added together, called a doubles fact. 18 is even because it splits into two equal groups of 9: $9 + 9 = 18$ . An odd number cannot be split this way. 17 splits into 8 and 9, and the two groups are not equal.

Your child should be able to:

Pair up a group of up to 20 objects and say whether it is odd or even
Count by 2s and name the even numbers up to 20
Write an even number as a doubles fact, such as $5 + 5 = 10$
Sort numbers up to 20 into even and odd numbers

Example

Is 15 odd or even?

Draw 15 dots and circle them in pairs.
That makes 7 pairs, with 1 dot left over.
One dot has no partner, so 15 is odd.

Example

Is 20 odd or even? Write a doubles fact to show it.

Split 20 into two equal groups.
Each group has 10, because $10 + 10 = 20$ .
The groups are equal with nothing left over, so 20 is even.

Where children usually get stuck

Your child says 12 is odd because it starts with a 1.
The child looks at the first digit instead of the last one. Only the ones digit tells whether a number is odd or even.
What helps. Count out 12 spoons and pair them up together. Then point to the 2 in 12 and agree that this is the digit to check.
Asked for a doubles fact for 15, your child writes $7 + 8 = 15$ .
The child knows the answer is two numbers that add up to 15 and picks two that are close. A doubles fact needs two equal numbers, and an odd number does not have one.
What helps. Share 15 crackers between two plates, one at a time. One cracker is always left over, which shows why 15 has no doubles fact.
Your child pairs up a pile of toys, counts some twice and gets a different answer each time.
The toys stay in a heap, so it is hard to see which ones already have a partner. Pairing is the right method, but the messy pile hides the pairs.
What helps. Line the toys up in two rows, side by side, like children walking in pairs. If one row is longer by one toy, the number is odd.

Try four practice questions

Real 2nd 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
Drag frogs into the pond to make an even group. Use between 2 and 6 frogs.
Tap or click a picture, then tap the grid to place it. Tap a placed picture to remove it.
Show the answer and how to solve it
Drag 2, 4, or 6 frogs into the pond. Each of these makes an even group, because the frogs can be paired with none left over.
1. 1The prompt asks for an even group between 2 and 6 frogs. An even group can be split into pairs of 2 with none left over.
2. 2Even numbers between 2 and 6 are: 2, 4, and 6. Any one of these is a correct answer.
3. 3Pick one even number, like 4, and drag that many frogs into the pond. Four frogs make exactly 2 pairs with none left over, so 4 is even.
Common mistake. A common mistake is dragging 3 or 5 frogs. Those are odd numbers — when you try to pair them, one frog is left over. The prompt asked for an even group, so the count must be 2, 4, or 6.
The idea underneath. Even means the group can be split into pairs of 2 with nothing left over. Odd means there is exactly one extra after pairing.
2On level
Which equation shows doubles for 10?
A
$\displaystyle 4 + {}$
$\displaystyle 4 = {}$
$\displaystyle 8$
B
$\displaystyle 3 + {}$
$\displaystyle 6 = {}$
$\displaystyle 9$
C
$\displaystyle 4 + {}$
$\displaystyle 6 = {}$
$\displaystyle 10$
D
$\displaystyle 5 + {}$
$\displaystyle 5 = {}$
$\displaystyle 10$
Show the answer and how to solve it
The doubles equation for $10$ is $5 + 5 = 10$ , because adding $5$ to itself gives $10$ .
1. 1Doubles means two of the same number added together. We need two equal numbers that add to $10$ .
2. 2Split $10$ into two equal parts. Each part is $5$ .
3. 3Check the equation:
4. 4 $5 + 5 = 10$ has two equal addends and the correct sum, so this is the doubles equation for $10$ .
Common mistake. A common mistake is picking $4 + 6 = 10$ because the sum is correct, but $4$ and $6$ are not equal — doubles needs two of the same number.
The idea underneath. A doubles equation always has two of the same number. To find it for any even number, split that number into two equal parts.
3On level
Choose the missing number to make the equation true.
$\displaystyle + 6 = 12$
A
12
B
6
C
7
D
3
Show the answer and how to solve it
The missing number is $6$ because $6+6=12$ — the equation is a doubles fact with two equal addends.
1. 1Look at the equation. What number plus $6$ equals $12$ ?
2. 2This is a doubles fact. Two equal numbers add together to make $12$ .
3. 3The missing number is $6$ .
Common mistake. A common mistake is picking $12$ — the total — instead of the equal addend. The missing number matches the visible $6$ , not the sum.
The idea underneath. A doubles equation has two equal addends. If you know one addend, the other is exactly the same.
4Stretch
Maya was practicing doubles. Look at her work below.
$\displaystyle 10 = 5 + 5$
Choose the sentence that is true.
A
The equation is correct.
B
The addends are not the same.
C
The addends do not add to the sum.
D
The operation is wrong.
Show the answer and how to solve it
The answer is 'The equation is correct.' Maya's equation shows $5 + 5 = 10$ , which is a correct doubles equation because both addends are equal and they add to the sum.
1. 1Look at Maya's work.
2. 2A doubles equation needs the two addends to be the same. The addends 5 and 5 are the same number. Adding them: $5 + 5 = 10$ . The sum matches.
3. 3So Maya's equation is a correct doubles equation. The answer is: The equation is correct.
Common mistake. A common mistake is assuming there must be an error somewhere. Always check both that the addends are equal AND that they add to the sum before deciding.
The idea underneath. A doubles equation has the form n + n: both addends must be the same number, like $6 + 6$ or $8 + 8$ . To check it: (1) are the two addends the same number? (2) do they add to the sum? Both must be true.