### Home > CC1MN > Chapter 8 CC1: Unit 8 > Lesson CC1: 8.3.2 > Problem8-105

8-105.

Copy the dot pattern below and draw Figures $0$, $4$, and $5$. Explain how you could know the number of dots in any figure if you knew the figure number.

 $\begin{array}{c c c} \newcommand{blank}{\ } & \bullet\\ \bullet & \bullet & \bullet\\ \newcommand{blank}{\ } & \bullet\\ \end{array}\\ \text{Figure 1}$ $\begin{array}{c c c c c} \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \bullet & \bullet & \bullet & \bullet & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet \end{array}\\ \quad \;\,\text{Figure 2}$ $\array{ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet}\\ \qquad \quad \text{Figure 2}$

Could you write an expression to find the number of dots in a figure?

Look at Figure 2 to the right where $4$ groups of $2$ dots (the figure number) are circled and and the middle dot is left over.
An expression representing the number of dots in this figure would be $1 + 4x$, where $x$ is the figure number.