You will learn
- Say what even and odd mean.
- Tell odd from even by the ones digit.
- Sort numbers into odd and even.
- Explain with pairs.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Even numbers make pairs with none left over.
- Odd numbers have one left over.
- Look at the ones digit.
- Even ends in 0, 2, 4, 6 or 8.
Words to know
Can be put in pairs with none left over.
Has one left over when put in pairs.
A group of two.
The last digit of a number.
1. Discover: pairs of shoes
You have 8 shoes and your friend has 7. Whose shoes can all be made into pairs?
2. Understand: odd and even numbers
A number is even if it can be put into pairs with none left over: 2, 4, 6, 8, 10. A number is odd if one is left over: 1, 3, 5, 7, 9.
Look at the ones digit. If it is 0, 2, 4, 6 or 8, the number is even. If it is 1, 3, 5, 7 or 9, it is odd. So 346 is even and 347 is odd.
Idea 1: Pairs
A number is even if it can be put in pairs with none left over. 8 makes 4 pairs. A number is odd if one is left over. 7 makes 3 pairs and 1 left.
Idea 2: The ones digit
Look at the ones digit, the last digit. If it is 0, 2, 4, 6 or 8 the number is even. If it is 1, 3, 5, 7 or 9 it is odd. So 346 is even and 347 is odd.
Idea 3: Adding
Even + even = even (4 + 4 = 8). Odd + odd = even (3 + 3 = 6). Odd + even = odd (5 + 4 = 9).
Why the ones digit? Tens, hundreds and so on are always made of pairs, so only the ones decide.
3. Worked examples
Example 1 (I show you): Even or odd
Is 28 odd or even?
- The ones digit is 8.
- 8 is even.
Answer: Even
Example 2 (We do it together): Odd
Is 95 odd or even?
- The ones digit is 5.
Answer: Odd
Example 3 (You try): Add doubles
Is 4 + 4 + 4 even or odd?
Show the steps and answer
- 4 + 4 = 8.
- 8 + 4 = 12.
Answer: Even, because 12 ends in 2.
Did you know?
Houses on one side of many streets have even numbers. Houses on the other side have odd numbers.
Why this matters
Odd and even help us share things fairly in pairs and check our answers.
4. Explore: pairs
You need 20 counters.
- Take 7 counters and make pairs.
- Take 8 counters and make pairs.
- Write odd or even for each.
- Test 12, 15 and 20 with pairs.
Think about it: what did you notice?
7 is odd (1 left over). 8 is even. 12 and 20 are even; 15 is odd.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ is even because ___.
- ___ is odd because ___.
- The ones digit of ___ is ___.
- Pairs left over: ___.
Guided practice
Question 1. Is 346 odd or even?
Even (ends in 6).
Question 2. Is 347 odd or even?
Odd (ends in 7).
Question 3. Which ones digits make a number even?
0, 2, 4, 6, 8.
Independent practice
Level 1: Start
- Is 28 odd or even?
- Is 95 odd or even?
- Is 600 odd or even?
- Write three odd numbers.
- Is 4 + 4 even or odd?
Level 2: Grow
- Is 71 odd or even?
- Is 130 odd or even?
- Write three even numbers.
Level 3: Stretch
- Is 7 + 7 even or odd?
- Is 6 + 3 even or odd?
- Ana says 36 is odd because 3 is odd. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
There are 15 children. Can they all work in pairs?
Show a sample answer
No, 15 is odd so one child is left over.
Another one. 17 children line up in pairs. How many are left without a partner?
Show a sample answer
1 (17 is odd)
7. Common mistakes
Fix: Look at the ones digit (the last digit).
Fix: Look at the ones digit, the last one.
Fix: 0 is even. 10, 20 and 100 are even.
8. Lesson summary and revision card
- I can say what even and odd mean.
- I can tell odd from even by the ones digit.
- I can sort numbers into odd and even.
- I can explain with pairs.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Even makes pairs; odd leaves one.
- Check the last digit.
- Sort numbers as odd or even.
11. Next lesson
Next lesson: Mental addition strategies. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Is 64 odd or even? [1 mark]
- Is 87 odd or even? [1 mark]
- Write three odd numbers between 10 and 20. [2 marks]
- Is 6 + 6 + 6 even or odd? [2 marks]
- Kofi says 50 is odd because it has a 5. Is he right? Explain. [2 marks]
Total: 8 marks.
Marking guide and model answers
- Even [1]
- Odd [1]
- Any three of 11, 13, 15, 17, 19 [2]. Give 1 mark for two.
- 18 [1]; even [1]
- No [1]. The ones digit is 0, so it is even [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- 28 odd or even?
- 95 odd or even?
- 600 odd or even?
- Write three odd numbers.
- 4 + 4 even or odd?
- Is 42 odd or even?
- Is 109 odd or even?
- What ones digits do even numbers have?
- Is 5 + 5 even or odd?
- Write an odd number bigger than 90.
Homework
Look at house numbers on your street. Sort 6 as odd or even.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 28 odd or even? | even | 2 |
| 95 odd or even? | odd | 2 |
| 600 odd or even? | even | 2 |
| Write three odd numbers. | any three ending in 1,3,5,7,9 | 2 |
| 4 + 4 even or odd? | even | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 even; 2 odd; 3 even; 4 any three ending in 1,3,5,7,9; 5 even.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 even; 7 odd; 8 0, 2, 4, 6 or 8; 9 even; 10 For example 91.
Independent practice answers. Level 1: 1 even; 2 odd; 3 even; 4 for example 3, 7 and 21; 5 even (8). Level 2: 1 odd; 2 even; 3 For example 2, 4 and 6. Level 3: 1 even (14); 2 odd (9); 3 Look at the ones digit. 6 is even, so 36 is even..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what even and odd mean | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Tell odd from even by the ones digit | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Sort numbers into odd and even | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Explain with pairs | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Looking at the first digit. Look at the ones digit (the last digit).
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters in pairs to test small numbers.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child learns what odd and even numbers are and how to tell them apart. You do not need to be good at mathematics to help.
- Put sweets or beans in pairs to see if there is one left.
- Look at house numbers on your street.
- Ask: is 36 odd or even? How do you know?
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: say what even and odd mean; tell odd from even by the ones digit; sort numbers into odd and even; explain with pairs.
Prerequisite knowledge. Lessons 1 to 8.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need 20 counters. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. Can it be put in pairs? What is the ones digit? Is it odd or even?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Looking at the first digit. Look at the ones digit (the last digit).
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Use counters in pairs to test small numbers. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 2 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 2.OA.C.3 (odd and even numbers); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.