# 3.6: Stars and Moons

**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

**you should be able to describe the**

*pattern***and how to get from one step of the**

*pattern***to the next.**

*pattern*### Guided Practice

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3.

**Answers:**

1.

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3.

### Practice

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### Image Attributions

Students are given a pattern of stars and moons and asked to extend the pattern. Students will use the problem solving steps to help.