Problem
The tick marks split the rectangle into an 8-by-4 array of equal cells, so the whole is 32 equal parts and each cell is .
Equal partitioning is what lets us name the shaded amount with a single fraction.
3.G.A.2Draw A DiagramBecause the rectangle is cut into 32 same-size cells, each single cell is of the whole rectangle.
The tick marks slice the rectangle into an 8-by-4 array, and eight columns of four cells each is 32 cells in all.
Eight columns that each hold four cells is eight equal groups of four, which is exactly the amount multiplication counts.
All 32 cells are the same size and together they fill the rectangle with no gaps or overlaps, so the whole is 32 equal copies of one cell and one cell is of it.
Pieces that cover a thing with no gaps or overlaps add back up to the whole, so the 32 equal cells rebuild the whole rectangle and one of them is one part out of the 32.
The orange region spans 7 of the 8 columns and the top 3 of the 4 rows, so it covers 7 times 3 = 21 cells out of 32.
Counting full rows of equal cells is faster than counting one cell at a time.
3.NF.A.1Identify SubproblemsShaded over total is . Since 21 and 32 share no common factor greater than 1, the fraction is already in simplest form.
The shaded part as a fraction of the whole is just shaded cells over all cells.
3.NF.A.1Draw A DiagramWhen the whole is split into equal cells, the shaded fraction is just shaded cells over all cells!