Identify and Explain Patterns in Addition Tables

Students explore an addition table to find and describe patterns, such as the even/odd pattern in sums, the symmetry of the table, and diagonal patterns. They explain why these patterns occur using properties of operations.

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Grade 3 · Arithmetic Patterns · question 1 of 3

0 of 12

12 rungs. A star at the top.

Addition table, row 1. Which entry is odd?

1 + 5

1 + 2

1 + 3

1 + 7

How it is taught

0:00 of 3:58

An addition table follows a rule.

The diagonal is a number plus itself.

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 diagonal of doubles in a 1–4 addition table

Addition tables hide secret patterns. Let's find one together!

Here's a small addition table. The numbers across the top and down the side are what we add together.

Each cell shows the sum. For example, two plus three is five.

Now look at the diagonal — the cells where a number meets itself.

We get two, four, six, and eight.

Every single one is an even number!

That makes sense. When we add a number to itself, we make two equal groups — and two equal groups are always even.

Grade 3 · Spotting and explaining a hidden pattern

So all along the diagonal, the sums are even. Pattern found!

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.

Where this sits

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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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