Complete the multiplication table and explain the methods you used.

Here is the completed multiplication table:

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \times & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline 2 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\ \hline 3 & 3 & 6 & 9 & 12 & 15 & 18 & \textbf{21} & 24 & \textbf{27} & \textbf{30} \\ \hline 4 & 4 & 8 & 12 & 16 & 20 & \textbf{24} & 28 & \textbf{32} & \textbf{36} & 40 \\ \hline \end{array}$$

1.2 Which methods did you use to complete the table? Discuss.

To complete the table, I used two primary methods:

• Direct Multiplication: For each empty cell, I multiplied the number in the corresponding row header by the number in the corresponding column header. For example, to find the value for row 3, column 7, I calculated $3 \times 7 = 21$.
• Pattern Recognition (Counting by Multiples): I also observed the patterns in the rows and columns. For instance, in row 3, after 18 (for $3 \times 6$), I added 3 to get 21 (for $3 \times 7$), then added 3 again to get 24 (for $3 \times 8$), and so on. This method involves recognizing that each number in a row or column is a multiple of the row or column header, respectively.