Odd and Even Numbers: a week of ready-to-teach maths
Five days of lessons for Year 4 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out dot cards, number cards and sum cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the two card sheets once; they are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week is pairing. An even number splits into pairs with none left over; an odd number always has exactly one left over. Every rule this week, from the last digit to odd times odd, comes from following that one leftover.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Explain, then use
The descriptor asks children to explain and use the properties. So each day asks for a reason in pairs and leftovers, not just the rule: “odd plus odd is even because the two leftovers make a pair”. A rule children can explain is a rule they can use to check their own sums.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Pairs or one left over | Pair up counters and dots: an even number splits into pairs, an odd number has one left over, and zero is even | Pairing up |
| 2 | Odd plus odd | Join two numbers and follow the leftovers to explain odd plus odd, even plus even and even plus odd | Odd plus odd |
| 3 | Only the last digit | Tell whether any number is odd or even from its last digit, and explain why tens and hundreds always pair up | Spot the odd one; Only the last digit |
| 4 | Odd and even products | Predict whether a product is odd or even from its two factors, and check with arrays | Parity of a product |
| 5 | The parity rules | Collect the rules for adding and multiplying and use them to spot answers that cannot be right | The parity rules |
How the week builds
Day 1 gives odd and even their meaning through pairing; Day 2 follows the leftovers when two numbers are added; Day 3 shows why the last digit alone decides; Day 4 turns to products; and Day 5 gathers every rule and uses it to check answers. It builds on counting in twos and the two times table from Year 3, and it gives children a quick check on every sum and product they work out from here on.
Materials for the week (one trip)
- From the classroom: about 20 counters, buttons or blocks per pair, scissors, pencils, coloured pencils, this pack printed.
- Cut out once, use all week: the dot cards, the number cards and the sum cards in this pack. No maths equipment to buy.
Words for the word wall
odd, even, pair, left over, parity, last digit, ones digit, sum, product, factor, rule, predict
Dear families
This week in maths, Year 4 explores odd and even numbers. An even number of things can be shared into pairs with none left over; an odd number always has one left over. We use that idea to explain why odd plus odd is even and how the last digit tells you everything.
Try this at home
- Pair up socks, shoes or pegs. Is the number even or odd? Is there one left over?
- Look at house numbers on your street. Are the odd numbers all on one side?
- Pick two odd numbers, such as 7 and 9. Ask whether their sum will be odd or even before you add.
- Read a big number on a sign or a docket and decide if it is odd or even from the last digit.
My odd and even finds this week
Fill one row a day. Find a number, decide if it is odd or even, and say how you know.
| Day | My number | Odd or even | How I know |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Odd and Even Numbers teaching pack · seegongsik.com/au/y4/number/AC9M4N02/pack
Pairs or one left over
Children pair up counters and dots to sort numbers. An even number splits into pairs with none left over; an odd number always has exactly one left over. They find the pattern on a number strip and decide whether zero is even.
We are learning to
- explain that an even number splits into pairs with none left over,
- explain that an odd number has exactly one left over when it is paired,
- describe the odd-even pattern when counting, and say why zero is even.
Success criteria
- I can show with counters or dots whether a number is odd or even.
- I can explain my answer using pairs and left over.
You need
About 20 counters per pair. The dot cards (cut-out sheet 1), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Line up in pairs Ask eight children to stand and hold a partner’s hand. Add one more child, then another, and each time ask who has no partner. Ask: “Nine children: did everyone get a partner? What happens when one more joins?” |
| 30 min | Pair the dots Show the board picture (see the box). Pairs loop the dots on each dot card into twos and sort the cards into two piles: pairs up, and one left over. Then they do Parts A and B. Ask: “Can an odd number ever have two left over? Why not?” |
| 10 min | Is zero even? Hold up an empty hand. Zero counters make zero pairs, and nobody is left without a partner. Children finish Parts C and D. Ask: “Zero comes just before 1 on the strip. Does the pattern say odd or even?” |
Two half-sessions instead? Split after the dot cards; start Session B with the number strip.
Watch for these ideas
- Hearing “odd” as “strange”. In maths it means one left over when you pair up.
- Thinking zero is neither odd nor even. Zero pairs up with none left over, so zero is even.
- Thinking an odd number can have two left over. Two leftovers make another pair.
Answers
- Part A: 11 is 5 pairs and 1 left over, odd; 14 is 7 pairs and 0 left over, even; 9 is 4 pairs and 1 left over, odd; 16 is 8 pairs and 0 left over, even.
- Part B: colour 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20; odd and even take turns. Part C: 6 pairs and 1 left over, odd; 9 pairs and 0 left over, even. Part D: 40; 29.
Pair them up
A. Loop the dots in pairs
____ dots ____ pairs, ____ left over odd / even | ____ dots ____ pairs, ____ left over odd / even | ____ dots ____ pairs, ____ left over odd / even | ____ dots ____ pairs, ____ left over odd / even |
B. Colour the even numbers
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
What pattern do you see? _____________________________________________
C. Fill the gaps
13 is ______ pairs and ______ left over, so 13 is __________.
18 is ______ pairs and ______ left over, so 18 is __________.
D. Think it through
The next even number after 38 is ______. The odd number just before 30 is ______.
Tell your partner how pairs helped you.
Odd plus odd
Children join two numbers of dots and follow the leftovers. Two odd numbers each have one left over, and the two leftovers make a pair, so odd plus odd is even. Even plus even has no leftovers; even plus odd keeps its one.
We are learning to
- explain with pairs why odd plus odd is always even,
- explain even plus even and even plus odd the same way,
- say whether a sum will be odd or even before adding.
Success criteria
- I can show with dots why odd plus odd is even.
- I can predict if a sum is odd or even and say why.
You need
About 20 counters per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Two leftovers One partner lays out 3 counters in pairs, the other 5. Each has one left over. Push the two piles together and pair them again. Ask: “Where did the two leftovers go when we joined the piles?” |
| 30 min | Join the dots Show the board (see the box). Children do Part A: draw each total in pairs and say odd or even. Then they fill the rule table in Part B with a reason for each row. Ask: “Even plus odd: which number brings the leftover, and does it find a partner?” |
| 10 min | Will it be odd? Read the Part C sums aloud. Thumbs up for even, down for odd, before anyone adds. Then children check two of them. Ask: “You did not add 250 and 37. How did you know the answer is odd?” |
Two half-sessions instead? Split after Part A; start Session B with the rule table.
Watch for these ideas
- Thinking odd plus odd is odd because “odd stays odd”. Point to the two leftovers making a pair.
- Adding first and deciding odd or even after. Today the point is to predict from the leftovers.
- Mixing up adding with multiplying. Odd times odd is odd, which is Day 4.
Answers
- Part A: 5 + 7 = 12, even; 4 + 6 = 10, even; 3 + 8 = 11, odd. Part B: odd + odd = even (the leftovers pair up); even + even = even (no leftovers); even + odd = odd and odd + even = odd (one leftover stays).
- Part C: 21 + 35 is even; 40 + 16 is even; 13 + 28 is odd; 99 + 1 is even; 250 + 37 is odd.
Follow the leftovers
Each number is drawn in pairs. A dot on its own is a leftover.
A. Join them
| The two numbers | Draw the total in pairs | Odd or even? |
|---|---|---|
| + 5 + 7 = ______ | ||
| + 4 + 6 = ______ | ||
| + 3 + 8 = ______ |
B. The adding rules
| Sum | Result | Why, using leftovers |
|---|---|---|
| odd + odd | ||
| even + even | ||
| even + odd |
C. Odd or even? Decide before you add.
21 + 35: ________40 + 16: ________13 + 28: ________99 + 1: ________250 + 37: ________
Only the last digit
Children find that the last digit alone tells whether a number is odd or even, however big the number. Tens, hundreds and thousands always split into pairs, so only the ones can leave one over.
We are learning to
- decide whether a number is odd or even from its last digit (0, 2, 4, 6, 8 are even),
- explain why the other digits do not matter: every ten, hundred and thousand pairs up,
- use the rule to make odd and even numbers from digit cards.
Success criteria
- I can say if a big number is odd or even from its last digit.
- I can explain why the other digits do not change the answer.
You need
The number cards (cut-out sheet 2), one set per pair. Three digit cards, 4, 7 and 2, per pair (write them on scrap paper). The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Spot the odd one Show the first board picture (see the box). Children vote on the odd one before you press it, then explain how they knew. Ask: “You did not pair up 13 dots. What did you look at?” |
| 30 min | Why only the last digit? Write 374 = 300 + 70 + 4. Three hundred pairs up, seventy pairs up, so only the 4 decides. Show the second board picture, then pairs sort the number cards and do Parts A and B. Ask: “Every ten is five pairs. So can the tens digit ever leave one over?” |
| 10 min | Make it odd With the digit cards 4, 7 and 2, pairs make three-digit numbers and do Part C. Ask: “Which card has to go last to make an odd number? Why that one?” |
Two half-sessions instead? Split after the card sort; start Session B with 374 = 300 + 70 + 4.
Watch for these ideas
- Looking at the first digit. 471 starts with an even 4 but ends in 1, so it is odd.
- Thinking a number with lots of even digits is even. 2461 ends in 1: odd.
- Thinking 1000 is odd because it starts with 1. It ends in 0, so it is even.
Answers
- Part A even: 374, 1000, 52, 90, 7778, 2468. Odd: 947, 285, 4061, 305, 13 579, 8001.
- Part B: the 8 decides, so 4718 is even; 7 tens and 3 hundreds always pair up. Part C: largest odd 427, smallest odd 247, largest even 742, smallest even 274.
The last digit decides
A. Sort the number cards
Look at the last digit of each card. Write every number in the right column.
| Even (ends in 0, 2, 4, 6 or 8) | Odd (ends in 1, 3, 5, 7 or 9) |
|---|---|
B. Why only the last digit?
4718 = 4000 + 700 + 10 + 8
Which part decides if 4718 is odd or even? ______ Is 4718 odd or even? ______
Why do the 4000, the 700 and the 10 not change the answer?
C. Make it with the digit cards 4, 7 and 2
Use each card once to make a three-digit number.
Largest odd number: ________ Smallest odd number: ________
Largest even number: ________ Smallest even number: ________
Tell your partner which card had to go last each time, and why.
Odd and even products
Children predict whether a product is odd or even from its two factors. If either factor is even, everything pairs up and the product is even. Only odd times odd leaves a leftover: each odd group has one, and an odd number of leftovers cannot all pair up.
We are learning to
- explain that a product is even when at least one factor is even,
- explain with groups of dots why odd times odd is odd,
- predict whether a product is odd or even without multiplying.
Success criteria
- I can say if a product is odd or even from its factors.
- I can explain odd times odd with groups and leftovers.
You need
About 20 counters per pair. Coloured pencils. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Groups of pairs Pairs make 3 groups of 4 counters, then 3 groups of 5, each group laid out in pairs. Count the leftovers in each case. Children do Part A. Ask: “Three groups of 5 make three leftovers. Can three leftovers all find partners?” |
| 30 min | Predict, then check Show the board (see the box). Children do Part B: predict odd or even from the factors first, then multiply and tick if the prediction held. Ask: “4 times 7: four is even. Do you need to work out 28 to know it is even?” |
| 10 min | Colour the times square Children colour the even products in Part C and look for the white cells that are left. Ask: “Which rows and columns hold the white cells? What do their factors have in common?” |
Two half-sessions instead? Split after Part A; start Session B with the board picture.
Watch for these ideas
- Using the adding rule: even plus odd is odd, so even times odd must be odd. For products, one even factor makes it even.
- Thinking odd times odd is even because “two odds make an even”. That is adding, not multiplying.
- Thinking you must multiply to know. The factors decide before you start.
Answers
- Part A: 3 groups of 4 is 12, even; 3 groups of 5 is 15, odd (three leftovers make one pair and one more).
- Part B: 6 × 7 = 42, even; 5 × 9 = 45, odd; 8 × 3 = 24, even; 7 × 7 = 49, odd; 4 × 10 = 40, even; 9 × 11 = 99, odd. Part C: 9 white cells, all where both factors are odd (1, 3 and 5).
Odd and even products
A. Groups of dots
B. Predict, then check
| Product | I predict (odd or even) | Work it out | Was I right? |
|---|---|---|---|
| 6 × 7 | |||
| 5 × 9 | |||
| 8 × 3 | |||
| 7 × 7 | |||
| 4 × 10 | |||
| 9 × 11 |
C. Colour every even product
| × | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 |
Which products stay white? What do their factors have in common? ______________________
The parity rules
Children gather the rules for adding and multiplying odd and even numbers, explain each with leftovers, and use them to sort sums unworked and to catch impossible answers.
We are learning to
- state the parity rules for adding and for multiplying, and explain each with pairs,
- use the rules to tell if a sum or product is odd or even without calculating,
- use the rules to show that an answer must be wrong.
Success criteria
- I can fill in the parity rules and explain one of them.
- I can use parity to spot an answer that cannot be right.
You need
The sum cards (cut-out sheet 2), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Reveal the rules Show the board (see the box). Before each row is revealed, children call the result and give a reason with leftovers. They then fill Part A. Ask: “The table shows four rules. Which ones are missing?” |
| 30 min | Sort without solving Pairs sort the sum cards into even and odd piles using only the rules, record them in Part B, then check two cards by working them out. Then they do Part C. Ask: “Someone wrote 27 + 38 = 64. How can you tell it is wrong without adding?” |
| 10 min | Quiz game Run the unit’s self-check quiz as a class game: pairs hold up their answer before you reveal it. Children finish Part D. Ask: “Is 0 even? Which rule from this week proves it?” |
Two half-sessions instead? Split after the card sort; start Session B with Part C.
Watch for these ideas
- Using an adding rule for a product. Even times odd is even, though even plus odd is odd.
- Thinking the rules only work for small numbers. They work for any size, because only the leftovers matter.
- Thinking the right parity proves an answer right. Parity can show an answer is wrong; 8 × 9 = 70 is even too.
Answers
- Part A: even, even, odd, odd; even, odd, even, even. Part B even: 17 + 25, 12 × 5, 33 + 33, 8 × 8, 11 × 4, 20 + 30. Odd: 36 + 41, 9 × 7, 45 + 10, 3 × 5 × 7, 100 + 99, 1 + 3 + 5.
- Part C: 27 + 38 = 64 must be wrong (it should be odd; it is 65); 13 × 7 = 91 could be right (it is the right parity); 46 + 28 = 75 must be wrong (it should be even; it is 74); 8 × 9 = 72 could be right (it is the right parity); 15 + 16 + 17 = 49 must be wrong (it should be even; it is 48). Part D: no; odd + odd is even and one more odd makes it odd, so three odd numbers always make an odd number.
Use the parity rules
A. Fill in the rules
| even + even = ______ | odd + odd = ______ | even + odd = ______ | odd + even = ______ |
| even × even = ______ | odd × odd = ______ | even × odd = ______ | odd × even = ______ |
B. Sort the sum cards without working them out
| Even | Odd |
|---|---|
C. Could it be right, or must it be wrong?
27 + 38 = 64 could be right / must be wrong
13 × 7 = 91 could be right / must be wrong
46 + 28 = 75 could be right / must be wrong
8 × 9 = 72 could be right / must be wrong
15 + 16 + 17 = 49 could be right / must be wrong
D. Can three odd numbers add up to 20? Explain.
Dot cards
Cut out the twelve cards. Loop the dots on each card into pairs, then sort the cards into two piles: pairs up with none left over, and one left over (Day 1). One set per pair.
Teacher note: the dots are scattered on purpose, so children have to pair them rather than read a pattern. Six cards are odd and six are even.
Number cards and sum cards
Cut out the cards. Sort the number cards into odd and even by their last digit (Day 3). Sort the sum cards into odd and even using the parity rules, without working them out (Day 5).
Number cards (Day 3)
Sum cards (Day 5)
Teacher note: the number cards begin with the four numbers from “Only the last digit” on screen (374, 285, 1000, 947). Each set has six odd and six even cards.
What we know: Odd and Even Numbers
Work on your own. Show your thinking if you can.
- Circle the even numbers: 14, 27, 30, 41, 58, 0
- Draw 9 dots in pairs. Is 9 odd or even? How do the pairs show it? ______________________________
- Without adding: is 35 + 47 odd or even? ________ Why? ______________________________
- Without adding: is 246 + 31 odd or even? ________
- Without multiplying: is 7 × 9 odd or even? ________ Is 6 × 13 odd or even? ________
- Is 5068 odd or even? ________ How do you know? ______________________________
- Jo says 23 + 46 = 68. Use odd and even to show Jo must be wrong. ______________________________
- Can three odd numbers add up to 20? Explain. ______________________________________________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- 14, 30, 58, 0 (zero is even: zero pairs, none left over).
- Odd: four pairs and one dot left over.
- even: both are odd, and the two leftovers make a pair (35 + 47 = 82).
- odd: even plus odd keeps the one leftover (246 + 31 = 277).
- 7 × 9 is odd (odd times odd); 6 × 13 is even (6 is even).
- Even: it ends in 8, and the thousands, hundreds and tens always pair up.
- Odd plus even is odd, but 68 is even; the true sum is 69.
- No: odd + odd is even, and adding a third odd number makes it odd, so three odd numbers always make an odd number.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Pairs and leftovers (Q1, Q2) | sorts small numbers with counters | explains odd and even with pairs and one left over, including zero | explains why an odd number can never have two left over |
| Adding (Q3, Q4) | adds first, then decides odd or even | predicts the parity of a sum and gives the leftover reason | extends the rule to three or more numbers |
| Products and the last digit (Q5, Q6) | uses the last digit but mixes up the product rule | predicts products from their factors and uses the last digit for big numbers | explains odd times odd with groups and leftovers |
| Using the rules (Q7, Q8) | checks an answer by working it out again | uses parity to show an answer must be wrong | explains why the right parity does not prove an answer right |
Eight questions, four ideas. A child at standard answers most questions and gives a reason with pairs and leftovers, not just the rule.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Pairs up | Adds odd and even | Uses the last digit | Predicts products | Uses the rules |
|---|---|---|---|---|---|
The five columns are the five days: pairing, adding, the last digit, products and the rules.