Grade 5 › G5U03 Divisibility

Grade 5 › G5U03 Divisibility › L2
GRADE 5 · ALBERTAOUTCOME AB-G5-5N3

L2 · Divisibility tests for 3 (and patterns for 4, 6, 8, 9)

Learning goal

“I can decide whether a number is divisible by 3 by adding its digits - and I can use the patterns we noticed for 9, 6 and 4 while investigating, without mixing up which tests are rules.”

Digit sum — the sum of all the digits of a number. The digit sum of 4,215 is 4 + 2 + 1 + 5 = 12.
Multiple — a number you land on when counting by another number. 12 is a multiple of 3.
Divisibility test — a quick check that tells whether a number is divisible by another, without doing the division.
Pattern — something we notice happening again and again while investigating. A pattern is a clue; a generalized test is a rule we are sure of.
Worked example

Is 2,718 divisible by 3? Step 1: Here is why the trick works. 100 = 99 + 1 and 10 = 9 + 1: every hundred and every ten splits into a multiple of 3 plus 1 left over. So each digit leaves that many 1s over, and the leftovers add up to the digit sum. Step 2: Digit sum of 2,718: 2 + 7 + 1 + 8 = 18. Step 3: 18 is a multiple of 3, so 2,718 is divisible by 3. (Check: 2,718 / 3 = 906.) Say it plainly: for the 3-test, ignore the size of the number - add its digits. If the digit sum is a multiple of 3, the number is a multiple of 3.

Check yourself — explain it

Why does the 3-test use the digit sum instead of the last digit?

Paired problem — example still visible

Is 5,431 divisible by 3? -> No - digit sum 5 + 4 + 3 + 1 = 13, and 13 is not a multiple of 3.

Faded completion — last step is yours

"6,204: digit sum is 6 + 2 + 0 + 4 = ___, which ___ a multiple of 3, so 6,204 ___ divisible by 3" -> 12; is; is

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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