Go about half way down this page and you will see the two quilt blocks.
http://blog.missouriquiltco.com/4x4-quilt-tutorial/
In one, you use all different colors and make a 16 patch block that sews up to 8.5 inches; 8 inches after you sew all of them together as in the quilt. In the other, you use two white squares, cut at 4.5 inches square and make 2 - 4 patches with white on one corner. Then sew a 4 patch to a white square, making sure the white is positioned as you see in the block. Do the same thing again, then sew them together across the middle, making sure the small whites stay in the center.
When you mention that she sews some together, then cuts them....she is probably making stratas.... 4 fabrics sewn together for the 16 patch block. She does 4 of the stratas from different fabrics, then cuts them into 2.5 inch wide strips. Then you take all the four strips cut from the stratas and sew them together to make a 16 patch. Change placement of the stratas....turn them upside down, move from position 1 to position 4 in the blocks...makes the pattern seem more scrappy.
For the block with the larger white squares, she may have made a 2 fabric strata, then subcut into 2.5 inch strips, then sew them together to make the 4 patch corners of the primary block.