Sure, let's break this down step by step and ensure everything is clear. To follow the Fibonacci sequence in constructing the squares, we start with smaller squares and incrementally build larger ones based on the sum of the previous two squares' dimensions.

Here's a step-by-step guide to creating the Fibonacci sequence squares:

1. Draw the First Two Squares (0.5 cm each):

   • Draw two squares, each with sides of 0.5 cm, side by side.

2. Draw the 1 cm Square (Next in Sequence):

   • Above the first two squares, draw a square with sides of 1 cm.

3. Draw the 1.5 cm Square:

   • Draw a square with sides of 1.5 cm adjacent to the 1 cm square and the two 0.5 cm squares.

4. Draw the 2.5 cm Square:

   • Draw a square with sides of 2.5 cm adjacent to the 1.5 cm square.

5. Continue with the Pattern:

   • Keep adding squares according to the Fibonacci sequence, with each new square's side length being the sum of the sides of the previous two squares.

6. Draw the 4 cm Square:

   • Draw a square with sides of 4 cm adjacent to the previous squares.

7. Draw the 6.5 cm Square:

   • Draw a square with sides of 6.5 cm.

8. Draw the 10.5 cm Square:

   • Draw a square with sides of 10.5 cm.

This should complete the sequence up to the 21x21 square with sides of 10.5 cm.

Visual Representation

Let's represent this sequence step-by-step in a visual format:

1. Two 0.5 cm squares side by side.
2. A 1 cm square on top of the first two 0.5 cm squares.
3. A 1.5 cm square to the right of the initial three squares.
4. A 2.5 cm square below the initial squares.
5. A 4 cm square to the left of the combined previous squares.
6. A 6.5 cm square above the combined previous squares.
7. A 10.5 cm square to the right of the combined previous squares.

Diagram

I can't draw directly here, but the arrangement can be visualized as follows:

|  0.5  |  0.5  |
|-------|-------|
|       1       |
|---------------|
|   1.5  |       |
|--------|       |
|       2.5      |
|----------------|
|       |  4     |
|       |--------|
|       | 6.5    |
|----------------|
| 10.5            |
|-----------------|

Placement of Squares:

• The placement should ensure that each new square touches at least two previous squares, forming a continuous pattern.

Additional Details:

If you'd like, I can create an image to illustrate this more clearly. Would you like that? If you have any questions or need further details, please let me know.

Questions to Expand Understanding:

1. What is the formula for the Fibonacci sequence?
2. How do you calculate the side length of the next square in the sequence?
3. What are the first ten numbers in the Fibonacci sequence?
4. How does the Fibonacci sequence relate to the golden ratio?
5. Can you explain the importance of the Fibonacci sequence in nature?
6. What are some real-life applications of the Fibonacci sequence?
7. How would the pattern change if you started with squares of different sizes?
8. Can you find a pattern or formula for the area of the squares as they increase in size?

Tip:

The Fibonacci sequence is widely used in computer algorithms, art, architecture, and even in predicting stock market movements. Familiarity with this sequence can provide insights into various fields beyond mathematics.