Checkpoint: squares, cubes and the first split

A square verandah is 9 m along each edge. A strip 2 m wide is lifted along two edges. How much floor is left?

• 49 m²
• 77 m², from 81 take away twice 2
• 45 m², from 81 take away 9 times 4

Two plots have edges 62 and 58 paces. What is 62² − 58², without squaring either number?

• 4, because the two sides differ by 4
• 480
• 16, because 62 − 58 is 4 and 4 squared is 16

A square's side is cut into three parts of different lengths. How many of the nine pieces are squares?

• 6, the crossings
• 3, on the diagonal
• 9, because every piece is cut from a square

A stack of bricks is 4 bricks along every edge. One brick's width is added in all three directions. How many bricks are new in exactly one direction?

• 16, because one slab is 4 bricks by 4
• 61, because that is every brick the stack gained
• 48, in three slabs of 16

A bed has area x² + 5x − 24. Which pair splits the middle term?

• 8 and −3
• 5 and −24, because those are the two numbers written down
• 4 and 6, because they multiply to 24