Even & Odd Numbers | Grade 2 Math

Grade 2 Math ›  Equal Groups & Number Patterns  ›  Lesson 20

Grade 2 Math — Equal Groups & Number Patterns

Even & Odd Numbers

What makes a number even or odd? Discover the answer by making pairs of counters, counting by twos, and splitting sets into two equal groups. Learn why an even number leaves no object unpaired and an odd number leaves exactly one object unpaired.

Explore even and odd numbers from 0 to 20, explain doubles such as 8 = 4 + 4, and solve puzzles, stories, and mistake-checking problems. Includes 25 step-by-step worked examples, 30 independent practice problems, and a 15-question lesson test, with separate hidden answer keys.

Even & odd numbersPair objectsCount by twosTwo equal addendsNumbers 0–20Explain your thinking

🎯 What You Will Learn

Make pairs

Put objects into groups of two and see whether anything is left without a partner.

Count by twos

Use 2, 4, 6, 8, ... to count complete pairs instead of counting each object separately.

Build two equal groups

Explain an even total with two equal addends, such as 14 = 7 + 7.

Prove and explain

Decide whether a number is even or odd and justify your answer with pairs, a drawing, or an equation.

For parents & teachers — standards alignment: The primary standard is CCSS 2.OA.C.3: determine whether a group of up to 20 objects is even or odd by pairing or counting by twos, and express an even number as the sum of two equal addends. Counting and finding small totals also support earlier fluency work in CCSS 2.OA.B.2. This lesson builds a concrete foundation for equal groups; formal multiplication and rectangular arrays are deliberately left for later lessons. Number patterns are explored within 0–20, not presented as a separate required rounding or multiplication skill.

🧠 Key Vocabulary

even number

A number that can be made into complete pairs of two with nothing left over.

odd number

A number with exactly one object left over after making as many pairs as possible. For 1, there are zero complete pairs and one left over.

pair

A group of exactly two objects.

unpaired / left over

An object that has no partner after you make all possible pairs.

count by twos

Say 2, 4, 6, 8, ... to count complete pairs, then check for any extra object.

equal groups

Groups with the same number of objects in each.

equal addends / double

Two matching numbers added together, such as 5 + 5 = 10.

equation

A number sentence showing that two amounts are equal, such as 12 = 6 + 6.

🟦 Start with Objects: Complete Pairs or One Left Over?

Think of a pair of shoes or two mittens worn together. Make pairs of two objects. If every object has a partner, the number is even. If one is left without a partner, the number is odd.

EVEN — 8 counters

4 complete pairs, 0 left over. 8 is even.

ODD — 9 counters

4 complete pairs, 1 left over. 9 is odd.

Big idea: A pair means two. You must pair every object, not just find one pair somewhere in the group. An odd number can make many complete pairs, but exactly one object remains unpaired at the end.

👣 Count by Twos to Find Complete Pairs

Every time you count another pair, add two. The counting-by-twos sequence goes through the positive even numbers up to 20:

2468101214161820

For 10 objects, you can count five pairs: 2, 4, 6, 8, 10. No object is left, so 10 is even. For 11 objects, count the same five pairs to 10, then notice the one extra object: 11 is odd.

Be careful: Counting by twos tells you how many objects are in the complete pairs. To name an odd total, you still count the one extra object. For example, 5 complete pairs and 1 extra object make 10 + 1 = 11 objects, not 10.

🟢 Two Equal Groups: Write a Double

There are two useful ways to show an even set. Pairs are groups of two; two equal groups are two groups with the same number of objects. They are different arrangements of the same total.

12 counters divided into TWO EQUAL GROUPS

6 counters

6 counters

12 = 6 + 6

Two groups of 6 make 12. You could also arrange the same 12 counters into 6 pairs.

Even total: 14

14 counters can split into two equal groups of 7.

14 = 7 + 7

Odd total: 7

7 counters make two groups of 3 and one extra.

7 = 3 + 3 + 1

Don't confuse these statements: “6 pairs” means six groups of two, so there are 12 objects. “2 equal groups of 6” also means 12 objects. Both show an even total, but they organize the objects differently. 6 + 6 = 12 is the requested two-equal-addends equation.

🔢 See the Even–Odd Pattern from 0 to 20

The colored tiles show every whole number from 0 to 20. Green tiles are even; pink tiles are odd. Each step of +1 changes the kind of number.

01234567891011121314151617181920

Green = even. Pink = odd. Color helps show the pattern, and every tile also has its number so the pattern does not rely on color alone.

Even numbers, 0–20

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

Odd numbers, 1–19

1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

Is zero even? Yes. Zero counters leave none unpaired, and 0 = 0 + 0 is a sum of two equal addends. Zero is even, not odd.

🔄 What Changes When We Add or Take Away Objects?

Add 1 object10 is even; 10 + 1 = 11 is odd. One new object has no partner.

Add 2 objects11 is odd; 11 + 2 = 13 is still odd. The two new objects make another pair.

Take away 1 object16 is even; 16 − 1 = 15 is odd. One partner is left alone.

Adding or removing one object changes even to odd or odd to even. Adding two objects makes one more complete pair, so the even-or-odd kind stays the same.

🧭 How to Explain Your Answer

1. Show the objectsDraw or count a group of no more than 20 objects.

2. Pair or share equallyMake complete pairs, or split them into two groups with the same number in each.

3. Write a reasonSay “even” or “odd,” name any leftover object, and write a helpful equation.

Example explanation for 13

“I made six pairs of counters. That uses 12 counters, and one counter is left without a partner. So 13 is odd. I can write 13 = 6 + 6 + 1.”

Looking ahead: This lesson uses pairs and two equal groups to explain even and odd. Lesson 21 will explore more kinds of equal groups and repeated addition. Lesson 22 will introduce rectangular arrays. You do not need multiplication facts to succeed here.

🌟 25 Worked Examples

Try each question using counters, dots on paper, or a quick sketch. Then open Show solution to compare your reasoning with the step-by-step explanation. Pairs and equal groups are shown in different ways, so read the question carefully.

1Make pairs with 4 counters

You have 4 counters. Make pairs. Is the number even or odd? Write a double.

Show solutionHide solution

Put the counters into pairs: (● ●) and (● ●). There are 2 complete pairs and no extra counter.

That means 4 is even. To write a double, divide the four counters into two equal groups of 2: 4 = 2 + 2.

2Find the one extra counter

Make pairs with 5 counters. Explain whether 5 is even or odd.

Show solutionHide solution

First make two complete pairs: 2 + 2 = 4 counters. One of the five counters has no partner.

So 5 is odd. We can show two equal groups plus the leftover counter: 5 = 2 + 2 + 1. The extra 1 is why the number is odd.

3Count complete pairs to 8

How many complete pairs can you make from 8 buttons? Is 8 even or odd?

Show solutionHide solution

Pair the buttons two by two. Count the groups: first pair (2), second pair (4), third pair (6), fourth pair (8).

There are 4 pairs and no button remains. Therefore 8 is even. In two equal groups, we can write 8 = 4 + 4.

4Show why 9 is odd

Arrange 9 beads into pairs. How many are left without a partner?

Show solutionHide solution

Count four pairs of two beads: 2, 4, 6, 8. That uses eight beads.

The ninth bead has no partner, so there are 4 complete pairs and 1 left over. Thus 9 is odd and 9 = 4 + 4 + 1.

5Understand zero

There are 0 counters in a box. Is zero even or odd? Explain.

Show solutionHide solution

There are no counters to pair, and none is left unpaired. We do not need to invent an extra counter.

Zero is even. It can be written using two equal addends: 0 = 0 + 0.

6One counter cannot make a pair

You have just 1 marble. Is 1 even or odd?

Show solutionHide solution

A complete pair needs two marbles, but there is only one. We can make 0 complete pairs, with 1 marble left over.

So 1 is odd. One can be described as 0 + 0 + 1 = 1: no pairs and one extra marble.

7Use pairs to recognize 12

Arrange 12 counters into pairs. Is 12 even or odd? Write an equation with two equal addends.

Show solutionHide solution

Count by twos as you pair: 2, 4, 6, 8, 10, 12. The count ends after 6 complete pairs, with nothing left over.

Therefore 12 is even. To split the set into two equal groups, put six counters in each: 12 = 6 + 6.

8Find the unpaired object in 15

Arrange 15 craft sticks into pairs. Explain your answer using a number sentence.

Show solutionHide solution

Make groups of two until you have used 14 craft sticks. Fourteen sticks make 7 complete pairs.

One stick remains, so 15 is odd. The equal groups plus the extra stick give 15 = 7 + 7 + 1.

9Skip-count the complete pairs of 18

Count 18 paper clips by twos. How many pairs are there? Is 18 even?

Show solutionHide solution

Count one pair at a time: 2, 4, 6, 8, 10, 12, 14, 16, 18. You said nine numbers because you counted nine pairs.

There are 9 pairs and no extra paper clip, so 18 is even. Dividing into two equal groups also gives 18 = 9 + 9.

10Spot the extra one after 18

There are 19 counters. Count by twos to explain why 19 is odd.

Show solutionHide solution

Make nine complete pairs. They contain 2, 4, 6, 8, 10, 12, 14, 16, 18 counters in all.

We started with 19, so one counter remains. That proves 19 is odd: 19 = 9 + 9 + 1.

11Show two equal groups for 10

Split 10 stickers equally between two students. Is 10 even? Write an equation.

Show solutionHide solution

Give one sticker to each student until all ten are shared. Each student receives 5 stickers; the groups have equal size.

There is nothing left. We can write 10 = 5 + 5, so 10 is even. We could also pair the stickers into five groups of two.

12Why 13 does not share equally

Could 13 buttons be put into two equal whole-number groups with no button left over? Explain.

Show solutionHide solution

Place one button into each group, back and forth, until both groups have 6. Those equal groups use 6 + 6 = 12 buttons.

One of the 13 buttons remains. Therefore there cannot be two equal groups containing all the buttons, and 13 is odd. We can write 13 = 6 + 6 + 1.

13Pair to 16, then make two groups

Use 16 counters. Find the number of pairs and show two equal addends.

Show solutionHide solution

Counting by twos reaches 16 after 8 complete pairs. There is no extra counter, so 16 is even.

Now reorganize the same 16 counters into two equal groups of 8. This gives the double 16 = 8 + 8. Remember: eight pairs and two groups of eight are different arrangements of sixteen.

14Count the leftover after five pairs

A tray has 11 blocks. You pair 10 of them. What does that tell you about 11?

Show solutionHide solution

Ten blocks make five complete pairs, since 2, 4, 6, 8, 10 counts five pairs.

We have 11 blocks altogether, so 1 block is left over. The total is odd: 11 = 5 + 5 + 1.

15Sort numbers by pairing

Which numbers are even in 2, 7, 14, 19? Explain your choices.

Show solutionHide solution

Two makes one pair, so 2 is even. Fourteen makes seven pairs, so 14 is even.

Seven makes three pairs and one extra; nineteen makes nine pairs and one extra. Those are odd. Thus the even numbers are 2 and 14, and the odd numbers are 7 and 19.

16Find matching addends

Complete 6 = □ + □, using the same whole number in both boxes.

Show solutionHide solution

Divide six counters into two equal groups. Put one counter into each group until there are three in each.

Both boxes contain 3, because 6 = 3 + 3. This equal-addends equation shows that 6 is even.

17Explain why 20 is even

Show that 20 is even by pairing and by writing a double.

Show solutionHide solution

Count by twos to 20: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. That is 10 complete pairs and no extras.

Split the set into two equal groups of ten: 20 = 10 + 10. Both models show that 20 is even.

18Compare neighboring numbers

Why is 3 odd but 4 even? Explain with pairs.

Show solutionHide solution

Three counters make one complete pair and leave one counter without a partner. So 3 is odd: 3 = 1 + 1 + 1.

When we add one counter, the unpaired counter finds a partner. Four counters make two complete pairs, so 4 is even: 4 = 2 + 2.

19Add one to an even group

A collection has 10 crayons. One crayon is added. Is the new number even or odd?

Show solutionHide solution

Before the change, ten crayons make five complete pairs. Adding one crayon gives 10 + 1 = 11 crayons.

The five pairs are still there, but the new crayon has no partner. The new number, 11, is odd.

20Take one away from an even group

There are 16 game pieces, with every piece paired. One is removed. Is the new total even or odd?

Show solutionHide solution

Sixteen pieces make eight complete pairs. Remove one piece from one of those pairs.

The new total is 16 − 1 = 15. One of the remaining pieces has lost its partner, so 15 is odd.

21Add an entire pair to an odd group

Start with 7 stones, an odd number. Add 2 stones. What is the new total? Is it even or odd? Explain.

Show solutionHide solution

Seven stones make three complete pairs and one unpaired stone. The two new stones can pair with each other, adding one complete pair.

Now there are 7 + 2 = 9 stones, four complete pairs and the same single extra stone. So 9 is still odd.

22Remove two counters and regroup

Begin with 18 counters, an even number. Remove exactly 2 counters. Is the result odd or even?

Show solutionHide solution

Eighteen counters can make nine complete pairs. After removing any two counters, 18 − 2 = 16 counters remain.

Rearrange those sixteen counters into 8 complete pairs. No counter is left unpaired, so 16 is even. This reasoning works even if the removed counters came from different original pairs.

23Make one more pair in a story

A jar contains 17 counting beads. Arrange as many complete pairs as possible. How many pairs and unpaired beads are there? How many more beads would make the total even?

Show solutionHide solution

Seventeen counting beads make 8 complete pairs and 1 unpaired bead, since 8 + 8 + 1 = 17. That means 17 is odd.

Add one more bead to partner the leftover bead. Then 17 + 1 = 18 beads, making nine complete pairs and an even total.

24Share items into two equal groups

There are 14 paper flowers. Two identical gift bags should contain the same number. How many flowers go in each bag? What does this prove?

Show solutionHide solution

Place one flower into each bag, alternating until all 14 flowers are used. Seven go into the first bag and seven into the second.

The equal groups give 14 = 7 + 7. Because every flower belongs to one of two equal groups, 14 is even.

25Correct a confusing equation

A student makes 6 pairs from 12 counters and writes 12 = 2 + 2. Explain the mistake and write a correct two-equal-addends equation.

Show solutionHide solution

Each pair contains 2 counters, but the student has six pairs, not two. The equation 2 + 2 = 4 counts only two of the six pairs and cannot equal 12.

To show the requested two equal groups, rearrange all 12 counters as one group of 6 and another group of 6. Then 12 = 6 + 6. Twelve is even because every counter can be paired without a leftover counter.

🎮 Independent Practice — 30 Problems

Directions: Solve each question on paper or with counters. When asked to explain, describe the pairs, equal groups, extra objects, or number pattern that supports your answer. For a double, the two addends must be equal. Keep the answer key closed until you are finished.

1. Make pairs with 2 cubes. Is 2 even or odd? How many complete pairs are there?
2. Pair 7 toy cars. How many pairs and unpaired cars are there? Is 7 odd or even?
3. There are 10 paper clips. How many complete pairs can you make? Classify the total.
4. There are 15 shells. One shell is taken away. What is the new total, and can it be paired completely?
5. There are 18 pennies. Six pairs have already been made. How many more pairs can you make from the pennies that remain?
6. Can you pair 13 pencils without leftovers? How many pairs can you form?
7. A page has 0 stickers. Is zero even or odd? Write an equal-addends equation.
8. Make pairs with 17 leaves. Explain the number left unpaired.
9. Use 6 marbles to make pairs. How many pairs? Is 6 even or odd?
10. A child has 19 blocks. After putting one block away, can all the remaining blocks be paired? Explain.
11. Continue counting by twos: 2, 4, 6, 8, 10, __, __. Are your two missing numbers even?
12. Continue the odd-number pattern: 1, 3, 5, 7, __, __. Explain the pattern.
13. A child makes 7 complete pairs of socks. Is that 7 socks or 14 socks? Write an equal-addends equation for the total.
14. Use 18 counters. Write an equation expressing 18 as two equal addends.
15. A student says 9 = 4 + 5 shows that 9 is even. Explain why this conclusion is wrong, and write an equation with two equal addends and one extra 1.
16. Complete 16 = □ + □ with equal addends. What number belongs in each box?
17. A student says 7 = 3 + 4 proves 7 is even. Is the student correct? Explain.
18. Complete 8 = 4 + □. Does the completed equation show two equal addends?
19. You have 9 tickets. How many tickets must be added to reach the next even number? Name that number.
20. A box holds 12 markers. One marker is taken away. Is the new total even or odd?
21. Start with 5 counters (odd) and add 2 counters. What is the new total? Is it even or odd?
22. Start with 8 counters (even) and add 2 counters. What is the new total? Is it even or odd?
23. Sort 4, 11, 16, 19 into even and odd numbers.
24. A classmate says, “14 is odd because 7 + 7 = 14.” Is the conclusion correct? Explain.
25. Split 5 counters into two equal groups as far as possible. What is left over? Write a number sentence.
26. A baker puts 18 cookies into bags holding 2 cookies each. How many full bags are needed? Is 18 even?
27. A student has 15 stickers and shares them as equally as possible between two friends without cutting any. How many does each friend get, and how many remain?
28. At a game, 12 children make pairs. How many pairs? If one more child joins, is the new total even or odd?
29. Choose the only odd number from 14, 15, 16. Prove it with two equal groups and one extra.
30. A student draws five complete pairs but writes 10 = 5 + 4. Correct the two-equal-addends equation and say whether 10 is even.

🏆 Lesson Test — 15 Questions

Directions: Complete the test independently. For each explanation problem, show why the number is even or odd by making pairs, using two equal groups, or writing a correct equation. Reveal the test key only after you finish.

1. A box holds 8 counters: 5 blue and 3 red. If any two counters may form a pair, how many complete pairs can you make? Is the total even or odd? Explain why the colors do not matter.
2. Share 11 bottle caps between two children as equally as possible. How many does each receive, and what remains?
3. A child has 16 counters in two groups: 7 in one group and 9 in the other. Move exactly one counter to make the groups equal. How many are in each group now? Write a two-equal-addends equation and decide whether 16 is even.
4. A jar has 3 pencils. Make pairs. How many are left unpaired? Is 3 odd or even?
5. A child has 14 cards and has put 12 of them into 6 pairs. How many cards have not yet been paired? Can those remaining cards make one more pair?
6. There are 5 pairs of objects. Three more complete pairs are added. How many objects are there now? Is the number even or odd?
7. A collection has 4 complete pairs and 1 unpaired counter. One more counter is added. What is the new total? Is it even or odd? Write a two-equal-addends equation for the new total.
8. Two equal groups have 4 counters each. Add 5 counters to each group. How many counters are there now? Write the new two-equal-addends equation and explain why the total is even.
9. A classmate writes 12 = 5 + 7 and says this shows two equal groups. Is that explanation correct? Write a proper equation.
10. There are 15 game tokens. Two tokens, making one complete pair, are put away. How many tokens remain, and is the number odd or even?
11. A tray has 3 complete pairs of counters and 5 more loose counters. Rearrange all the counters into pairs. How many complete pairs can you make? How many counters are left unpaired? Is the total even or odd?
12. One bag holds 5 counters and another holds 7 counters. Each bag has an odd number. When you combine both bags, is the total even or odd? Explain what happens to the two previously unpaired counters.
13. Complete the pattern 10, 11, 12, __, __, 15. Which missing number is even? Prove it with a two-equal-addends equation.
14. At a party there are 13 balloons. Lila says 7 complete pairs account for all the balloons. Noah says 6 complete pairs and 1 extra balloon account for them. Who is correct? Count both suggestions and tell whether 13 is even or odd.
15. A student claims, “If I take 13 counters away from 19, the number left is still odd because 19 was odd.” Check the claim. How many counters remain? Show with pairs and a two-equal-addends equation whether the new total is even or odd.

🔐 Complete Answer Key

Show practice answer keyHide practice answer key

Practice Answers

Teacher note: Accept correct drawings, counter arrangements, and equivalent explanations. The number of pairs, the size of two equal groups, and any extra object must match the problem. For optional explanations, accept other mathematically correct ways of showing the same idea.

1. 2 is even. The two cubes make 1 complete pair, with 0 left over.

2. 3 pairs, 1 extra — odd. Three pairs use 6 cars and leave 1; 7 = 3 + 3 + 1.

3. 5 pairs — even. Five groups of two use all ten paper clips.

4. 14 shells — even. 15 − 1 = 14. Seven pairs use all fourteen shells with none left over.

5. 3 more pairs. The first 6 pairs use 12 pennies. Six are left, and they make 3 additional pairs; all 18 pennies form 9 pairs in total.

6. 6 pairs, 1 extra — odd. Twelve pencils form six pairs and the thirteenth is unpaired.

7. even; 0 = 0 + 0. No sticker is unpaired; both equal groups can contain zero.

8. 8 pairs, 1 extra — odd. Eight complete pairs use 16 leaves; 1 remains.

9. 3 pairs — even. All six marbles fit into three complete pairs.

10. 18 blocks — even. 19 − 1 = 18. The remaining blocks make nine complete pairs without a leftover.

11. 12, 14; both even. Each step adds a complete pair; neither missing number leaves an extra object.

12. 9, 11. The pattern adds 2 each time. Adding a complete pair leaves the original one unpaired.

13. 14 socks; 14 = 7 + 7. Seven complete pairs each contain two socks. Fourteen is even; in a different arrangement, make two equal groups of seven.

14. 18 = 9 + 9. Each group contains 9 counters, with no leftovers; 18 is even.

15. No; 9 = 4 + 4 + 1 — odd. The addends 4 and 5 are not equal. Two equal groups of 4 leave one extra object, proving nine is odd.

16. 8 and 8. Eight objects in each group give 16 = 8 + 8, so 16 is even.

17. No; 7 is odd. 3 and 4 are not equal groups. Seven makes 3 pairs and 1 extra: 7 = 3 + 3 + 1.

18. 4; yes — 8 is even. Both groups contain 4 and use all eight counters.

19. +1 ticket; 10. Nine has one extra after four pairs; the added ticket completes a fifth pair.

20. 11 — odd. Twelve was even; taking away one leaves a partner without a match.

21. 7 — odd. The new two counters make another pair; the original one extra remains.

22. 10 — even. Adding one complete pair to four existing pairs leaves no extra counter.

23. Even: 4, 16; odd: 11, 19. 4 and 16 can pair without leftovers; 11 and 19 each leave one.

24. No; 14 is even. The equal addends 7 and 7 prove 14 can split into two equal groups.

25. 1 extra; 5 = 2 + 2 + 1. Two groups of 2 use four counters; one remains, so five is odd.

26. 9 bags; yes, even. Nine bags each hold one pair of cookies, with none left over.

27. 7 each, 1 left over. 7 + 7 + 1 = 15, so 15 is odd.

28. 6 pairs; 13 is odd. Six pairs use twelve children, and the thirteenth has no partner.

29. 15; 15 = 7 + 7 + 1. Seven in each equal group uses fourteen; the last counter is unpaired.

30. 10 = 5 + 5; even. Five pairs make 10 counters. Two equal groups must hold five counters each; 5 + 4 is only 9.

Show test answer keyHide test answer key

Test Answers

Teacher note: Give credit for correct mathematical evidence: complete pairs with no extra means even; one extra means odd; for an even total an equation with two genuinely equal addends is required when requested.

1. 4 pairs — even. Eight counters make four complete pairs, with none left over. Their colors do not matter because any two counters can be paired: 2 + 2 + 2 + 2 = 8.

2. 5 each, 1 extra — odd. Five in each group uses ten caps; one of the eleven is left. 11 = 5 + 5 + 1.

3. 8 in each group; 16 = 8 + 8; even. Move one counter from the group of 9 into the group of 7. Each group now has 8 counters. Both groups are equal and use all 16 counters, so 16 is even.

4. 1 unpaired — odd. One pair uses 2 pencils; one is left.

5. 2 cards have not yet been paired; yes — 14 is even. Six pairs use 12 cards. The other two form a seventh pair, so no card remains unpaired.

6. 16 objects — even. Five pairs use 10 objects and three pairs use 6 more. The total is 16, with eight complete pairs and none left over.

7. 10 — even; 10 = 5 + 5. Four complete pairs make 8 counters, and the extra counter makes 9. Adding one more counter completes a fifth pair: 9 + 1 = 10. The 10 counters also form two equal groups of 5.

8. 18 counters; 18 = 9 + 9; even. Each group starts with 4 counters. Adding 5 counters to each group gives 4 + 5 = 9 counters in each. The new total is 9 + 9 = 18 counters. Both groups are equal, and the 18 counters could also form 9 complete pairs with none left over, so 18 is even.

9. No; 12 = 6 + 6. 5 and 7 are unequal addends, although their sum is 12. Six in each group proves 12 is even.

10. 13 tokens — odd. 15 − 2 = 13. Removing two tokens leaves thirteen. We can make six complete pairs with one token left over, so 13 is odd.

11. 11 counters — 5 complete pairs, 1 unpaired; odd. The first 3 pairs contain 6 counters. Of the 5 loose counters, 4 make 2 more pairs and 1 remains without a partner. So 6 + 5 = 11 counters make 5 complete pairs with 1 extra, and 11 is odd.

12. 12 — even; 12 = 6 + 6. Five counters make 2 pairs and 1 extra; seven make 3 pairs and 1 extra. The two extras pair with each other when combined. The total is 5 + 7 = 12 counters, forming six complete pairs. Hence 12 is even and 12 = 6 + 6.

13. 13, 14; 14 is even. Count forward by ones: 10, 11, 12, 13, 14, 15. Fourteen is even because it makes 7 complete pairs, and 14 = 7 + 7. Thirteen leaves one extra after six pairs.

14. Noah; 13 is odd. Seven pairs would require 14 balloons, which is one too many. Six pairs use 12 balloons and leave 1 extra, so 13 = 6 + 6 + 1. Noah is correct, and 13 is odd.

15. 6 counters; 6 = 3 + 3; even. Nineteen counters minus thirteen leave 19 − 13 = 6 counters. Pair those six counters to make 3 complete pairs, with none left over. You can also split them into two equal groups of 3: 6 = 3 + 3. The claim is incorrect: removing thirteen counters changes the odd total of 19 into the even total of 6.

💡 Common Mistakes to Watch For

Counting one pair and stopping

An odd number can contain several complete pairs. Pair all the objects; then look for the one extra.

Mixing up pairs and equal groups

Six pairs make 12 objects, but the requested equation using two equal addends is 12 = 6 + 6, not 12 = 2 + 2.

Calling zero odd

Zero leaves no object without a partner. The equation 0 = 0 + 0 proves that 0 is even.

Thinking the objects must line up

Move or draw the objects into pairs. Their color, arrangement, or size does not change whether the number is even or odd.

Writing two unequal addends

9 = 4 + 5 is true, but it does not show two equal groups. Two equal groups and one extra object can be shown by 9 = 4 + 4 + 1.

Leaving out the extra object

If 13 counters make six pairs, all six pairs contain only 12 counters. The thirteenth counter still needs to be counted.

Family practice idea: Use socks, buttons, or coins. Ask your student to arrange 1–20 objects in pairs and complete: “I made ___ complete pairs. ___ object(s) are left. The number is ___ because ___.” For an even total, ask for a matching double.

🔗 Related Lessons

Grade 2 Lesson 5 — Skip Count by 2s, 5s, 10s & 100sPractice counting pairs by twos to recognize even numbers. Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20Use familiar addition facts and doubles to explain equal groups. Grade 2 Lesson 2 — Compose & Decompose Three-Digit NumbersRemember that rearranging objects does not change the total. Grade 2 Lesson 13 — Mental Addition & Subtraction StrategiesConnect doubles and near doubles to mental math. Grade 2 Lesson 19 — Explain, Estimate & Check StrategiesBuild on explanations and mathematical justifications. Grade 2 Math Hub — Full Lesson LibraryExplore more free lessons and practice resources.

🖨️ Printable Companion

A future Even & Odd Numbers Practice Pack can include pair-the-counters mats, skip-counting strips, odd-or-even sorting cards, two-equal-addends puzzles, and story-problem practice with answer keys.

← Lesson 19: Explain, Estimate & Check Grade 2 Math Hub Next → Lesson 21: Equal Groups & Repeated Addition