You have 9 blocks and try to split them into two equal groups. What happens, and what does it tell you about 9?
AYou get two groups of 4 with 1 leftover — so 9 is odd
BYou get two groups of 4 and one group of 1 — so 9 is even
CYou can make two groups of 4.5, so 9 is even
DYou cannot tell whether 9 is even or odd without counting to 10 first
Even numbers split perfectly into two equal groups with nothing left over. Nine cannot do this — you get 4 and 4 with 1 block left without a partner. That leftover is the defining mark of an odd number. Option B describes the same result but misclassifies it; options C and D reflect confusion about what 'splitting into equal groups' means.
Question 2 Multiple Choice
Sarah says: 'When I add two odd numbers, I should get an odd answer — because odd plus odd feels like it should stay odd.' Is she right?
AYes — odd + odd = odd, because odd numbers never become even
BNo — odd + odd = even, because each odd number's one leftover pairs up with the other's leftover
CIt depends on which odd numbers you pick
DIt alternates — sometimes odd, sometimes even
Every odd number has exactly one 'leftover' object that can't find a pair. When you add two odd numbers, their two leftovers pair with each other, leaving nothing unpaired — so the result is even. For example: 3 + 5 = 8 (even), 7 + 1 = 8 (even). The counterintuitive result follows directly from the 'leftover' definition.
Question 3 True / False
The number 100 is even because when you split 100 objects into two groups, each group gets exactly 50 with none left over.
TTrue
FFalse
Answer: True
This is exactly the definition of even. The 'ends in 0' shortcut also tells us 100 is even, but the underlying reason is the equal-pairing property. Any number that forms two perfectly equal groups with zero leftovers is even — and 50 + 50 = 100 with nothing remaining.
Question 4 True / False
Zero is an odd number because there are no objects to pair up.
TTrue
FFalse
Answer: False
Zero is even. The test is: can you split the objects into two equal groups with no leftovers? Zero objects split into two groups of zero — that's 0 + 0 = 0, with nothing left over. Zero fits the 'no leftovers' definition perfectly, so it is even. It also fits the last-digit rule: 0 ends in 0, which is on the even list.
Question 5 Short Answer
Why is the sum of two odd numbers always even? Use the 'leftover' idea in your explanation.
Think about your answer, then reveal below.
Model answer: Every odd number has exactly one object that cannot find a partner when you try to split the group into pairs. When you add two odd numbers, each brings one 'lonely' leftover. Those two leftovers pair with each other, so the combined total has no unpaired objects remaining — making the sum even.
The leftover framework makes the result feel inevitable rather than arbitrary. A student who only memorized 'odd + odd = even' without understanding why will forget it or misapply it; a student who understands the pairing logic can reconstruct the rule from scratch.