For parents
Odd and even numbers: a pairing game
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Will every block find a partner? This question makes odd and even numbers visible before a child needs division notation. Gather ten blocks and a sheet of paper, then try a few relaxed rounds together.
What counts as a pair?
A pair contains exactly two objects. In this activity, colour and shape do not matter: two different blocks can still form a pair. A number is even when all its objects can be arranged in pairs. If one object remains after every possible pair has been made, the number is odd. We are describing the quantity, not the shape of its written numeral.
Compare six and seven step by step
Count out six blocks, touching each once. Make three rows of two and write 6 = 2 + 2 + 2. Every block has a partner, so six is even. Add one block: 7 = 2 + 2 + 2 + 1. Seven is odd. Move the unpaired block to the beginning of the arrangement. Its position changes, but the quantity and its oddness do not.
Play the two-seat bus game
Draw five rows of seats, with two spaces in each row. The blocks are passengers. A parent chooses a number from one to ten; the child seats that many passengers in pairs, starting at the front. Is the last occupied row full? Ask the child to explain, then swap roles. Empty rows do not count as incomplete pairs: only the passengers are being paired.
What happens when you add one or two?
Add one passenger to seven. The eighth passenger completes the final pair: adding one changes odd to even or even to odd. Now add two to eight. They make a new complete pair, so ten is still even. An empty bus has zero passengers and none left without a partner. Zero is even too; it can be split into two groups of zero.
Four questions with explanations
1. Is nine even? No: it makes four pairs with one block left over. 2. How many pairs can eight blocks make? Four; eight counts blocks, not pairs. 3. Add one passenger to five. Does everyone have a partner? Yes: six passengers make three pairs. 4. Remove two from ten. Is the result odd or even? Eight is even because you removed one complete pair.
Common mix-ups and a next step
Finding one pair is not enough: check the entire collection. Five contains two pairs but is still odd. If your child confuses the number of pairs with the number of objects, count each separately. Once pairing makes sense, introduce a shortcut: whole numbers ending in 0, 2, 4, 6 or 8 are even. Test twelve and thirteen with blocks before using the shortcut on paper.
Continue with Otto Math
Finish when your child can explain one answer in their own words. A parent can then choose a short addition or subtraction route in Otto Math and return to the question of what one extra block changes. The app is available for iPhone and iPad on the App Store. Five routes in each book are free; Otto Plus unlocks the remaining routes.