Identify and Explain Patterns in Multiplication Tables

Students explore a multiplication table to identify patterns such as the symmetry created by the commutative property, the patterns in the 9s column (digit sums equal 9), the doubling pattern in the 2s row, and how every product in the 5s row ends in 0 or 5. They use properties of operations to explain why these patterns exist.

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Grade 3 · Arithmetic Patterns · question 1 of 3

0 of 12

12 rungs. A star at the top.

In the table, row 3 runs 6, 9, 12, … What sits next?

How it is taught

0:00 of 3:59

A multiplication table follows a rule.

6 times 4 is the same as 4 times 6.

Read it: Up by the same jump

A row grows 3, 6, 9, 12. Each jump is 3 more. It is also the 3 times table: 1 × 3, 2 × 3, 3 × 3, 4 × 3.

Compare two neighbors: 6 after 3.
Name the jump: up by 3.
Do that jump again: after 12 comes 15.

Adding one after twelve is how you count, and that habit is strong, but this row is not the counting numbers.

Six is three more than three, nine is three more than six, twelve is three more than nine — the jump never changes.

You can add three to twelve in one move instead of stacking a whole new pile of cubes from one.

Find the jump from one number to the next, then use that jump again.

Writing the next counting number after twelve, as if the row went up by one.

Measure the jump: three to six is three. Keep adding three after twelve.

4, 8, 12, 16, ___ — 20. Measure the jump from one to the next — it is 4 every time — and take it once more from 16.

The 5s row

Let's hunt for a pattern in the five times table. We'll list a few rows and look for something that repeats.

Five times one is five.

Five times two is ten.

Five times three is fifteen.

Five times four is twenty.

Five times five is twenty-five.

Now zoom in on the ones digits — the last digit of each answer.

Five, zero, five, zero, five! The ones digit flips between five and zero.

Each row we add five more. Two fives make ten, so the ones digit lands back on zero, then jumps up to five again.

Grade 3 · Why every multiple of 5 ends in 0 or 5

Let's test it. Five times six is thirty — and look, it ends in zero. The pattern keeps going.

Any number times five ends in zero or five. That's the pattern of the fives!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Standard

CCSS.3.OA.D.9

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations

Grade 3

Quoted from the Common Core State Standards.

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What a star here means

A star here is the top of a twelve-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 3

This is one rung of 104 in Grade 3 mathematics, in the order they build on each other.

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