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# 3.6: Stars and Moons

Difficulty Level: At Grade Created by: CK-12

Can you continue the pattern shown below? In this concept, we will practice figuring out patterns and then extending them.

### Guidance

In order to continue patterns like the one with stars and moons shown above, we can use the problem solving steps to help.

• First, describe what you see.
• Second, figure out what your job is. In these problems, your job will be to continue the pattern and fill in the empty cards.
• Third, make a plan. Decide how you will figure out and then continue the pattern.
• Fourth, solve. Fill in the empty cards with the correct number of stars and moons.
• Fifth, check. State the pattern you found and verify that it worked for all of the cards.

#### Example A

Solution:

We can use the problem solving steps to help us extend this pattern.

\begin{align*}& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\ &&& \text{Card} \ 1:1 \ \text{star and} \ 1 \ \text{moon}\\ &&& \text{Card} \ 2:1 \ \text{star and} \ 2 \ \text{moons}\\ &&& \text{Card} \ 3:1 \ \text{star and} \ 3 \ \text{moons}\\ &&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\ & \mathbf{My \ Job:} && \text{Figure out the pattern.}\\ &&& \text{Make drawings on the empty cards.}\\ & \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\ &&& \text{Look at the card numbers. Figure out the pattern of moons.}\\ &&& \text{Make the drawings.}\\ & \mathbf{Solve:}\end{align*}

\begin{align*}& \mathbf{Check:} && \text{The number of moons is the same as the card number.}\\ &&& \text{The number of stars is always one.}\end{align*}

#### Example B

Solution:

We can use the problem solving steps to help us extend this pattern.

\begin{align*}& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\ &&& \text{Card} \ 1:1 \ \text{star and} \ 1 \ \text{moon}\\ &&& \text{Card} \ 2:2 \ \text{stars and} \ 2 \ \text{moons}\\ &&& \text{Card} \ 3:3 \ \text{stars and} \ 3 \ \text{moons}\\ &&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\ & \mathbf{My \ Job:} && \text{Figure out the pattern.}\\ &&& \text{Make drawings on the empty cards.}\\ & \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\ &&& \text{Look at the card numbers. Figure out the pattern of moons.}\\ &&& \text{Make the drawings.}\\ & \mathbf{Solve:}\end{align*}

\begin{align*}& \mathbf{Check:} && \text{The number of moons is the same as the card number.}\\ &&& \text{The number of stars is the same as the number of moons.}\end{align*}

#### Example C

Solution:

We can use the problem solving steps to help us extend this pattern.

\begin{align*}& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\ &&& \text{Card} \ 1:2 \ \text{stars and} \ 1 \ \text{moon}\\ &&& \text{Card} \ 2:4 \ \text{stars and} \ 1 \ \text{moon}\\ &&& \text{Card} \ 3:6 \ \text{stars and} \ 1 \ \text{moon}\\ &&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\ & \mathbf{My \ Job:} && \text{Figure out the pattern.}\\ &&& \text{Make drawings on the empty cards.}\\ & \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\ &&& \text{Look at the card numbers. Figure out the pattern of moons.}\\ &&& \text{Make the drawings.}\\ & \mathbf{Solve:}\end{align*}

\begin{align*}& \mathbf{Check:} && \text{The number of moons is always one.}\\ &&& \text{The number of stars is twice as many as the card number.}\end{align*}

#### Concept Problem Revisited

We can use the problem solving steps to help us extend this pattern.

\begin{align*}& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\ &&& \text{Card} \ 1:2 \ \text{stars and} \ 1 \ \text{moon}\\ &&& \text{Card} \ 2:3 \ \text{stars and} \ 2 \ \text{moons}\\ &&& \text{Card} \ 3:4 \ \text{stars and} \ 3 \ \text{moons}\\ &&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\ & \mathbf{My \ Job:} && \text{Figure out the pattern.}\\ &&& \text{Make drawings on the empty cards.}\\ & \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\ &&& \text{Look at the card numbers. Figure out the pattern of moons.}\\ &&& \text{Make the drawings.}\\ & \mathbf{Solve:}\end{align*}

\begin{align*}& \mathbf{Check:} && \text{The number of moons is always the same as the card number.}\\ &&& \text{The number of stars is one more than the number of moons.}\end{align*}

### Vocabulary

One type of pattern is when the number of a certain object increases, decreases, or stays the same in a consistent way. In this concept, we saw patterns of stars and moons. With any pattern you should be able to describe the pattern and how to get from one step of the pattern to the next.

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Date Created:
Jan 18, 2013