Problem
Divide 30 into 6 equal parts, then take 1 part, giving 5 m.
A fraction of a length means split into equal parts and take that many.
3.NF.A.1Identify SubproblemsDivide 30 into 15 equal parts, then take 4 parts, giving 8 m.
Same split-and-take rule with denominator 15 and numerator 4.
3.NF.A.1Identify SubproblemsDivide 30 into 10 equal parts, then take 3 parts, giving 9 m.
Same rule with denominator 10 and numerator 3.
3.NF.A.1Identify SubproblemsNoah's share, which is 3/10 of the 30 m ribbon, measures 9 m.
Taking 3/10 of the ribbon means cutting the 30 m into 10 equal parts and keeping 3 of them.
Each of the 10 equal parts is 3 m, because sharing 30 m fairly among 10 parts gives 3 m to each part.
The 10 parts are all equal and, with no gaps or overlaps, they add back up to the whole 30 m.
Finding the size of one part undoes the fact that 10 of those parts make 30, and 10 groups of 3 make 30.
Keeping 3 of those parts is 3 equal groups of 3 m, which is 9 m.
List them: Liam 5 m, Mia 8 m, Noah 9 m. The largest is 9 m, so Noah cut the longest piece.
Once all three are plain meter amounts, comparing is just ordering whole numbers.
3.OA.A.2Make A Systematic ListThis only needs Grade 3 fraction sense: split the 30 m, take your parts, then see whose pile is biggest!