Depth 2 · 36 s
Every number at once
Checking a few sums can't cover every number. Draw any even number as two rows of dots, and any odd number with one dot sticking out, and the picture shows why odd plus odd is always even.
About this video
Is odd plus odd always even? You could check 3 + 5, 7 + 9 and 11 + 13, and every check works. But there are always more numbers than you have checked, so examples alone can never make you sure. This short animation shows a way to see it for every number at once.
Draw an even number as a rectangle of dots two rows high, with a gap in the middle of each row that means "as long as you like". That one picture is not 8 or 12 or a thousand: it is every even number. An odd number is the same shape with one extra dot sticking out at the end. Now push two odd shapes together. The two extra dots meet and make a pair of their own, and the result is two full rows - an even number, however long the rows are.
Multiplying works the same way. Three rows of five dots: each row has one dot left over, two of those pair up, and one is still alone. An odd number of rows, each with one dot over, always leaves one over, so odd times odd is odd. This video goes with the Even and Odd, Again lesson of Number Theory Level 1 on Knaph.
This video shows depth 2 of Even and odd numbers.
Learn Even and odd numbersTranscript
- 0:00Odd plus odd. Three checks, and each time it's even.
- 0:05But there are always more numbers to check.
- 0:09Any even number: two rows of dots.
- 0:12An odd number has one dot sticking out.
- 0:15Push two odd numbers together. The extra dots make a pair. Even.
- 0:21Three rows of five. Each row has one dot over.
- 0:26Two pair up, and one stays alone. Odd.
- 0:29One picture shows every number at once.