Make a table with a process column to represent each pattern. Write an expression for the number of circles in the Nth figure.
The first figure is 5 circles long and 2 circles wide, the second 5 circles long and 3 circles wide.
How do I complete this problem? I just need some guidance not the answer, thank you :)
Well, I'd be happy to help guide you in solving this problem! Let's break it down step by step.
First, let's start by creating a table with a process column to represent each pattern. We'll also label the figures as Figure 1, Figure 2, and so on.
| Figure | Process | Number of Circles |
|--------|---------|------------------|
| Figure 1 | | |
| Figure 2 | | |
| Figure 3 | | |
| Figure 4 | | |
| Figure 5 | | |
| Figure 6 | | |
Now let's fill in the process column. We know the first figure is 5 circles long and 2 circles wide. So, the process for Figure 1 could be written as "5 circles x 2 circles."
| Figure | Process | Number of Circles |
|--------|---------------|------------------|
| Figure 1 | 5 circles x 2 circles | |
| Figure 2 | | |
| Figure 3 | | |
| Figure 4 | | |
| Figure 5 | | |
| Figure 6 | | |
Next, let's think about how the pattern changes from one figure to the next. We can see that the width of the pattern increases by 1 circle each time. So, for Figure 2, we can write the process as "5 circles x 3 circles."
| Figure | Process | Number of Circles |
|--------|---------------|------------------|
| Figure 1 | 5 circles x 2 circles | |
| Figure 2 | 5 circles x 3 circles | |
| Figure 3 | | |
| Figure 4 | | |
| Figure 5 | | |
| Figure 6 | | |
Now it's your turn to fill in the remaining process and number of circles. See if you can determine the pattern and complete the table!
Remember, the key is to look for patterns and think logically about how the number of circles changes as the figures progress. Good luck, and let me know if you have any more questions!
To represent each pattern in a table with a process column, you can note the changes in the number of circles as the pattern progresses. Let's start by noting the given information:
Pattern 1: 5 circles long and 2 circles wide
Pattern 2: 5 circles long and 3 circles wide
Now, let's determine the expression for the number of circles in the Nth figure. We'll start by observing the changes in the width and length of the patterns as N increases.
Pattern 1:
Length: 5, Width: 2
Length remains constant at 5, while the width increases by 1 for each successive figure.
Pattern 2:
Length: 5, Width: 3
Length remains constant at 5, while the width also increases by 1 for each successive figure.
From these observations, we can conclude that the number of circles in each figure can be expressed as follows:
Pattern 1: 5 (length) * (2 + (N-1)) (width)
Pattern 2: 5 (length) * (3 + (N-1)) (width)
Now, you can use these expressions to fill in the process column of the table, indicating the changes in the number of circles for each pattern as N increases.
To complete this problem, you need to first observe the pattern and identify a process that can be applied to determine the number of circles in the Nth figure. Let's break it down step by step:
1. Start by creating a table with two columns: N (representing the figure number) and process. We will fill in the process column later.
| N | Process |
|---|---------|
2. Look at the given figures and observe how the number of circles changes as the figure number increases. In this case, the number of circles increases by 1 each time a wider figure is constructed.
3. Write down the number of circles for the given figures in the process column.
| N | Process |
|---|---------|
| 1 | 5 |
| 2 | 5 |
4. Now, let's find an expression for the number of circles in the Nth figure. Since we know that the first figure is 5 circles wide and the number of circles increases by 1 each time the width increases, we can use the formula:
Number of circles = Width + (N - 1)
5. Fill in the process column with the expressions for the number of circles in each figure.
| N | Process |
|---|-------------------|
| 1 | 5 |
| 2 | 5 + (2 - 1) = 6|
6. Continue this process for additional figures, where you increase the width and calculate the number of circles using the formula:
Number of circles = Width + (N - 1)
As you fill in more rows in the table, you should start seeing a pattern emerge and the expression for the number of circles become more clear.
Remember, this guidance is meant to help you understand the process of solving the problem. Try to apply these steps and think critically about the pattern as you complete the table.