P2 odd and even numbers: pair them up

Every detective needs a case. This one opens on a bedroom desk in soft warm daylight, as the lid of a round biscuit tin lifts with a creak. Inside are a few crumbs and a folded note. The Mastermind, a folded-paper detective cap perched on his red beanie, raises a toy magnifying glass to his eye: "Magnifying glass: out." The case has a name, The Case of the Hidden Biscuit, and the detective has a method: "Five questions a day." The Partner, standing in the doorway with his juice box, is not convinced. "...Five?"

That is The Detective Method, the eighth episode of our comedy series, The Mastermind. Watch it first (it is under a minute), then read on. The detective's last clue is a Primary 2 idea: odd and even numbers.

The Detective Method: five questions a day. Case closed. It was practice.

The case looks like a whodunit, but it is really a where-is-it. Nobody took anything and nobody is blamed: the biscuit was simply put away. After a case board strung with red wool and four clue cards, clue five is the note from the tin: "The biscuit is on the only even shelf." The bookcase has four shelves, tagged 3, 5, 8 and 9. Under each tag is a row of dots, and a felt-tip loop goes round the dots two at a time. The answer is Shelf 8. The Partner sums it up flatly: "Case closed. It was practice."

The detective's method is one your child can use too.

What odd and even really mean

Many children first meet odd and even numbers as a list to remember: 2, 4, 6 and 8 are even; 1, 3, 5, 7 and 9 are odd. A list works for small numbers, but it does not say why, and it gives a child nothing to fall back on when the number is 47 or 358.

The P2 way starts with objects. Here is the whole idea in two sentences:

A number is even when its objects can all be put into pairs with none left over. It is odd when one is left over.

Six buttons make three pairs with none left over, so 6 is even. Seven buttons make three pairs with one button on its own, so 7 is odd. A number never leaves two over, because two left-over objects would simply make one more pair.

This follows the Singapore math order: objects first, then a drawing, then the numbers. Real buttons come first, dots on paper next, and only then a rule about digits.

Worked example: the only even shelf

Here is the detective's puzzle, worked the way the episode shows it. The note says the biscuit is on the only even shelf. Which shelf is it: 3, 5, 8 or 9?

Step 1: Draw the dots. Under each shelf number, draw that many dots in a row: 3 dots, 5 dots, 8 dots and 9 dots.

Step 2: Loop the dots in pairs. Starting from the left, draw a loop round every two dots. Keep going until there are no longer two dots without a loop.

Step 3: Look at what is left over.

Shelf	Pairs	Left over	Odd or even?
3	1 pair	1	odd
5	2 pairs	1	odd
8	4 pairs	0	even
9	4 pairs	1	odd

Step 4: Answer the question. Shelves 3, 5 and 9 each leave one dot over, so they are odd. Shelf 8 makes four pairs with none left over, so 8 is even. It is the only even number of the four. The biscuit is on Shelf 8.

Step 5: Check the pairs. Four pairs is 4 × 2 = 8, so all 8 dots are used. For 9, the same four pairs use 8 dots, and 8 + 1 = 9, so one dot is left over.

Notice that 8 and 9 both make four pairs. The single dot left over is the whole difference between even and odd.

The ones-digit shortcut

Once pairing feels solid, your child can use a shortcut: 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, the number is odd.

The shortcut works because of pairing. Every ten makes five pairs with none left over, and every hundred makes fifty pairs. The tens and hundreds never leave anything over, so only the ones can.

36: 3 tens make 15 pairs, and 6 ones make 3 pairs. Nothing is left over, so 36 is even. The ones digit, 6, says the same.
47: 4 tens make 20 pairs, and 7 ones make 3 pairs with 1 left over. So 47 is odd, and the ones digit, 7, agrees.
358: the hundreds and tens all pair up, and 8 ones make 4 pairs. So 358 is even.

A ones digit of 0 counts as even too: 10 is five pairs and 20 is ten pairs, with none left over.

We suggest saving the shortcut until pairing is comfortable. A child who knows why the ones digit matters can always check it with a quick drawing.

Common slips

Looking at the wrong digit. A child may see the 8 in 81 and call it even. Ask, "Which digit tells us the ones?" 81 has 1 one, so it is odd.
Loose pairing. When dots are scattered, it is easy to loop one dot twice or miss one. Lining the dots up in a row, as the episode does, makes the pairs easy to see.
Unsure about 0. Zero objects leave nothing over, so 0 is even, and so is every number that ends in 0.

Five ways to practise at home

Sock detective. Tip a pile of clean socks onto the bed. Count them, then pair them up. A lone sock at the end means the number was odd.
Share it between two. Share some crackers or biscuits between two people, one each at a time. If both people get the same number with none left over, the number was even. The episode's end card has a small note of its own: the biscuit was shared.
The shelf game. Tape number tags to three or four shelves, hide a small toy behind the only even one, and leave a note like the detective's. Your child pairs dots on paper to find it, then hides it for you.
Count in twos. Clap or hop while counting 2, 4, 6, 8, 10, then 1, 3, 5, 7, 9. Ask what your child notices about the last digit each time.
Number spotting. On a walk, look at block numbers, bus numbers or lift buttons. Your child calls out odd or even and says how they know.

Keep each session short and stop while your child still wants to play. When your child is unsure, ask "Can you put them into pairs?" before giving the answer, and praise the method rather than the speed.

If you would like more Primary 2 examples, our guide to Primary 2 sample questions explained works through three more P2 questions step by step.

Five calm questions a day

In the episode, the Detective Method is five questions a day. Each clue card gets a careful look through the magnifying glass and a tick in the notebook, while the day counter goes Day 1, Day 7, Day 30. It only ever goes up. Odd and even numbers settle in the same way: one clear idea, met often and checked with a drawing whenever there is doubt.

That is the idea we built Singapore Math Drills around:

Daily Five drills: five hand-picked drill cards are waiting each day, so your child never has to decide what to practise.
Streaks and mastery stars: steady progress markers that reward turning up and getting things right, never speed.
Calm by design: no guilt-tripping over a missed streak and no dark patterns. Your child's progress is only ever measured against their own.

Whole Numbers, Fractions and Money, the three cards on the episode's case board, are all Primary 2 topics in our collection.

The case is closed, but the detective is already looking ahead. He snaps his notebook shut and whispers: "Shh. New case tomorrow."

Try it free

Try a free interactive Primary 2 worksheet and see how calm practice feels, with no signup or credit card required.

Try the free Primary 2 sample worksheet