Greatest Common Factor and Distributive Property - Scoffolded Practice

List all factors of a whole number up to 40

Identify the common factors of two numbers and pick out the greatest

Rewrite a sum as its greatest common factor times a sum of two numbers, as in 8 + 12 becoming 4(2 + 3)

Recognise when two numbers share no common factor above 1 and cannot be factored this way

Carry out the whole procedure without prompts once the sub-steps stop being supplied

The support fades on purpose — five sub-steps, then three, then two, then none — so the sheet can be cut at whichever point a group is ready to work unaided

Items 1 and 2 print the answer blanks as ___ ( ___ + ___ ), which fixes the shape of the expression before students have to produce it themselves

Item 9 is 8 + 40, where the reduced sum is 1 + 5; students who expect both bracket terms to be greater than one will need that case discussed

Item 11 pairs 14 and 25, which share no factor above 1 — decide beforehand how you want students to write that result

The standard code 6.NS.04 is printed in the header of both student pages, which makes the sheet easy to file against a unit plan

Listing factors — students write out every factor of numbers such as 12, 18, 24 and 32 before doing anything else with them.

Finding the greatest common factor — items work from the full common-factor list (1, 2, 4 for 8 and 12) down to the single greatest value.

Applying the distributive property in reverse — each sum is rewritten as a factor outside a bracket and a reduced sum inside, as in 24 + 32 becoming 8(3 + 4).

Working without prompts — the last five items give only a sum, so students must run all four steps from memory.

Testing whether a factorisation exists — one item pairs numbers with no shared factor above 1, which stops the procedure being applied automatically.