Grade 2 · Operations · MAT-02-OPS-011
Odd and Even Numbers
Classify numbers to 100 as odd or even.
Learning objectives
What you should be able to do
- Classify numbers to 100 as odd or even.
- Use pairing and groups of two to justify classifications.
- Recognize the repeating ones-digit pattern of odd and even numbers.
Prerequisite check
Make sure the foundation is ready.
Checks readiness for parity reasoning.
Learn
Build the idea from meaning, not memorization.
Even numbers can be paired with none left over
A whole number is even when its objects can be grouped into pairs of two with no leftover object. Examples include2,4,6,8,and10.
Odd numbers leave one unpaired
A whole number is odd when pairing by twos leaves exactly one object without a partner. Examples include1,3,5,7,and9.
The ones digit determines parity in base ten
Because ten is even, all complete tens can be paired. Only the ones place determines whether a base-ten whole number has a leftover. Ones digits0,2,4,6,8 are even;1,3,5,7,9 are odd.
Parity follows useful operation patterns
Even+even is even, odd+odd is even, and even+odd is odd. At Grade2, models can show why these patterns occur.
Interactive math lab
Change it. See what stays true.
Array Builder
Build equal rows and columns, then connect the grid to repeated addition.
- pair objects
- classify number
- ones digit pattern
- combine parities
Worked examples
Twenty different ways to see the concept work.
Pair6 objects.
3 pairs, none leftover6 is even.
Pair7 objects.
3 pairs +1 leftover7 is odd.
Classify12.
even6 pairs.
Classify15.
odd7 pairs+1.
Classify20.
even10 pairs.
Classify31.
oddones digit1.
Classify48.
evenones digit8.
Classify53.
oddones digit3.
Classify100.
evenones digit0.
Classify99.
oddones digit9.
2+4=6 parity.
even+even=evenPairing remains complete.
3+5=8 parity.
odd+odd=evenTwo leftovers pair together.
4+3=7 parity.
even+odd=oddOne leftover remains.
18−2=16.
evenRemoving one pair preserves evenness.
17−2=15.
oddRemoving one pair preserves oddness.
Which next even after26?
28Even numbers rise by2.
Which next odd after41?
43Odd numbers rise by2.
Is0 even?
YesZero objects can be paired with none leftover.
Why is62 even?
6 tens are even groups and2 ones form a pairNo leftover.
Why can ones digit decide?
Each ten is already evenOnly leftover ones affect parity.
Practice
Guided practice with hints
01Classify24.
Hint: Check ones digit.
Answer: even
02Classify37.
Hint: Check ones digit.
Answer: odd
03Pair9 objects.
Hint: How many pairs and leftover?
Answer: 4 pairs,1 leftover; odd
04Is50 even?
Hint: Ones digit0.
Answer: Yes
05What is next odd after29?
Hint: Add2.
Answer: 31
06Explain odd+odd.
Hint: Pair two leftovers.
Answer: Even
Practice
Independent practice
0114
Answer: even
0227
Answer: odd
0360
Answer: even
0481
Answer: odd
05Next even after38
Answer: 40
06Next odd after55
Answer: 57
070 odd/even?
Answer: even
08Why is73 odd?
Answer: Ones digit3 leaves one unpaired.
Common mistakes
Learn to catch the error, not just the answer.
Odd specifically means one object remains after pairing by twos.
Zero has no leftover, so it satisfies evenness.
Complete tens are even; inspect ones digit.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Pair students or objects to see whether one remains.
- Use parity to predict alternating patterns in turns or positions.
Challenge problems
Why is every number ending6 even?
The tens are pairable and6 ones form3 pairs.
What parity is odd+odd?
Even
Can an even number end in5?
No
Explain why adding1 flips parity.
It either creates or removes the single leftover object.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Pair It Up
Pair objects and classify numbers as odd or even.
Practice
Mastery check
0128
Answer: even
0243
Answer: odd
0390
Answer: even
0475
Answer: odd
05Why is0 even?
Answer: No objects remain unpaired.
06Next even after64
Answer: 66
07Odd+even parity
Answer: odd
08What determines parity in base ten?
Answer: The ones digit.
Terminology
Words to know
- even
- A whole number whose objects can be paired with none left over.
- odd
- A whole number whose objects leave one unpaired when grouped by twos.
- pair
- A group of two.
- parity
- Whether a whole number is odd or even.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.OA.C.3
Odd/even determination and pairing.