1) 8 The length, width, and height are all half the size and the volume of a cube is the length times height times width so the new volume is the same as the old volume multiplied by 1/2 x 1/2 x 1/2 = 1/8. 64/8 = 8 You can also find the original length of a side length of a cube by taking the cube root of 64, which is 4. Therefore the new cube has side lengths of 4/2 = 2. 2^3 = 8 2) 12 The four shaded areas are 1/2 the total area because each of the four triangles splits up a rectangle into 2 equal parts. This is because the area of a triangle is 1/2 the area of a rectangle with the same height and base. 6/x = 0.5 x = 12 3) 10:50 She wakes every third time the clock makes a noise and it makes a noise every 15 minutes so it takes 15 x 3 = 45 minutes for her to wake up each time. By the time she woke up for the fourth time, 45 x 4 = 180 minutes passed which is equal to 3 hours since 180/60 = 3. The last time the alarm made a noise before she went to sleep was 7:50 so she woke up the last time 3 hours after that, at 10:50. 4) 3, Circle The only shape that has an infinite amount of lines of symmetry is a circle, because there is an infinite number of lines that can pass through a circle’s center and split it into two equal halves. An equilateral triangle has 3 lines of symmetry, the height of each side. The line of symmetry shown in the picture can be replicated for each side of the triangle since the three sides are identical. 5) Nosy Neighbor It can't be the housekeeper since she has a footprint size of women’s 8 and not men’s 12. It can’t be the mailman because her dogs are still out at 10:50 and she would have heard them barking at the mailman. It must be the neighbor as he is the only choice left. The circle shapes next to the footprints were caused by the neighbor’s cane.