Quang drew a 9x9 grid. Vanessa drew a 12x12 grid. They each shaded 1/3 of their grid squares. Who shaded more squares? Why did Quang and Vanessa each shaded a different number of squares?
9 * 9 * (1/3) = ______ squares
12 * 12 * (1/3) = _______ squares
If this is for fourth grade they can draw the grids, then put the squares into 3 groups evenly and shade in 1 of the groups.
To determine who shaded more squares, we first need to find the number of shaded squares in each grid.
For Quang's 9x9 grid, we can calculate the number of shaded squares by multiplying the total number of squares in the grid by 1/3.
Total number of squares in Quang's grid = 9 x 9 = 81 squares
Number of shaded squares in Quang's grid = 81 x 1/3 = 27 squares
Similarly, for Vanessa's 12x12 grid, we can apply the same procedure.
Total number of squares in Vanessa's grid = 12 x 12 = 144 squares
Number of shaded squares in Vanessa's grid = 144 x 1/3 = 48 squares
Therefore, Vanessa shaded more squares than Quang because 48 squares is greater than 27 squares.
Quang and Vanessa each shaded a different number of squares because they have grids of different sizes. Quang's grid has 9x9 squares while Vanessa's has 12x12 squares. Even though they shaded the same fraction (1/3) of their respective grids, the total number of squares differs due to the difference in grid sizes.