Problem
The ball drops the full starting height of 150 m.
The first leg is simply the height it is released from.
3.NF.A.1Draw A DiagramIt rebounds to 2/5 of the 150 m fall — divide by 5, then multiply by 2, to get 60 m.
A fraction of a number means split into equal parts, then take that many parts.
3.NF.A.1Identify SubproblemsThe first rebound rises to 60 m, which is 2/5 of the 150 m the ball just fell.
Finding 2/5 of 150 m means splitting 150 m into 5 equal parts and then taking 2 of those parts.
Splitting 150 m into 5 equal parts makes each part 30 m, because 5 equal parts of 30 m and nothing else make up the whole 150 m.
The 5 equal parts, laid together with no gaps or overlaps, have to add back to the original 150 m.
Five equal groups of 30 m come to 150 m, since five groups of 30 is just 30 added five times.
Taking 2 of the 30 m parts gives 60 m, since two equal groups of 30 m is 30 m added twice.
The ball falls back down from its first bounce height, so it drops the same 60 m it rose.
Whatever height it reaches, it falls that same distance straight back down.
3.OA.A.2Draw A DiagramIt rebounds to 2/5 of the 60 m it just fell — divide by 5, then multiply by 2, to get 24 m.
Same fraction rule applied to the new, smaller fall height.
3.NF.A.1Identify SubproblemsAdd the first fall, first rise, second fall, and second rise: 150 + 60 + 60 + 24 = 294 m.
Total path length is just every up-and-down leg summed.
3.OA.A.2Identify SubproblemsThis only needs Grade 3 fraction sense: split by 5, take 2 parts, and add up each up-and-down trip!