Patterns in addition and multiplication tables
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations
What a learner can do afterwards
- Notice that all products of 5 end in 0 or 5 and explain why
- Observe that the sum of two even numbers is always even
- Identify a pattern in the multiplication table and explain it using commutativity or the distributive property
1 · Read
Times tables are full of patterns. Once you notice one, you can explain why it happens using rules you already know, like commutativity and the distributive property.
Look at the multiplication table: 4 x 7 gives 28, and 7 x 4 also gives 28. That's the commutative property. You can swap the order of the two numbers and the answer stays the same. It's why every row and its matching column hold the same numbers.
Even numbers always pair up evenly, with nothing left over. That's why two even numbers added together always make another even number, like 6 + 8 = 14.
Spot the pattern, then explain it with what you know: commutativity, the distributive property, or how evens combine.
More to read
2.1: The Multiplication Table
The multiplication table is a map of all small facts. Rows and columns meet at products, and the patterns jump out at you. Fives always end in 0 or 5, and nines hide a digit sum trick.
Do not just read the table. Cover answers, quiz yourself, and watch your recall get faster every week.
Count by units of 9 to multiply
Nines have rhythms. Count 9, 18, 27, 36 and watch the tens climb while the ones fall. Your fingers can even do the 9 times table with a simple folding trick.
Patterns like these make the multiples easier to remember. Chant the multiples until you know them by heart.
Factors, multiples, and patterns: FAQ
Factors are numbers that divide evenly with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12. Pairs that multiply to the number, like 3 and 4, are factor pairs.
Multiples run the other way: they are what you get when you multiply. The multiples of 4 are 4, 8, 12, 16 and so on.
Explore more
2 · Watch
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Where it sits
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.