Let's break down the three questions from the image you uploaded:

7. How many rectangles are there in the 12 shapes below?

• Answer: C. 3 rectangles
  Looking at the shapes, we can identify three rectangles:

1. First shape in the second row (third position).
2. Last shape in the second row (fourth position).
3. Last shape in the third row (fourth position).

8. How many blocks are there in total?

The blocks form a pyramid-like structure, where the top layer has 1 block, the second layer has 3 blocks, and so on. This is a structure with layers, and the number of blocks in each layer forms a triangular number sequence:

• Top layer: 1 block
• Second layer: 3 blocks
• Third layer: 5 blocks
• Fourth layer: 7 blocks

The total number of blocks = $1 + 3 + 5 + 7 = 16$.

Answer: A. 16 blocks

9. How do you cut the cake into 8 equal pieces with only 3 straight-line cuts?

To divide a cake into 8 equal pieces with 3 cuts, the best strategy is:

1. First cut: Slice the cake vertically from top to bottom through the center, dividing it into two halves.
2. Second cut: Slice again vertically, but at a 90-degree angle to the first cut, dividing the cake into 4 pieces.
3. Third cut: Make a horizontal cut through the center of the cake, dividing the top and bottom layers, making 8 pieces.

Answer: B.

Do you need more details or have any questions?

Here are 5 related questions:

1. How can we generalize the formula for finding the number of blocks in similar pyramidal structures?
2. What is the formula for finding the number of rectangles in a set of shapes?
3. How would you divide a cake into 16 pieces using 4 cuts?
4. Can you derive a pattern for the total number of blocks in larger pyramid structures?
5. What other 2D shapes can be divided into equal parts with a similar cutting strategy?

Tip: When dealing with geometric figures, it helps to visualize the shapes and count systematically to avoid missing any possibilities.