Uvero — STEM Learning

Divisibility Tests

Digit tests quickly decide whether a number has factors 2, 3, 5, 9 or 10. A number is divisible by 3 when its digit sum is divisible by 3. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

A multiple of 5 ends in 0 or 5.
The digit sum of 135 is 9, so it is also divisible by 3.

Which number is divisible by both 3 and 5?

135

142

203

224

Which statement best captures the central mathematical idea in Divisibility Tests?

A number is divisible by 3 when its digit sum is divisible by 3.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Divisibility Tests, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for divisibility tests.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Divisibility Tests?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A number is divisible by 3 when its digit sum is divisible by 3.

Represent the given information clearly and identify the operation or relationship required for divisibility tests.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.