# 3.7: Function Machines

**At Grade**Created by: CK-12

**GEO Patterns – Extend Patterns**

Students identify patterns of circles, triangles and rectangles on three cards, extend the patterns to complete the next two cards in the pattern, and answer questions about the \begin{align*}10^{th}\end{align*}

**Solutions**

GEO Pattern 1

1. Card 5: 1 circle, 1 triangle, 5 rectangles

Card 6: 1 circle, 1 triangle, 6 rectangles

2. Card 10: 1 circle, 1 triangle, 10 rectangles

GEO Pattern 2

1. Card 5: 1 circle, 6 triangles, 6 rectangles

Card 6: 1 circle, 7 triangles, 7 rectangles

2. Card 10: 1 circle, 11 triangles, 11 rectangles

GEO Pattern 3

1. Card 5: 4 circles, 2 triangles, 10 rectangles

Card 6: 5 circles, 2 triangles, 12 rectangles

2. Card 10: 9 circles, 2 triangles, 20 rectangles

GEO Pattern 4

1. Card 5: 4 circles, 4 triangles, 10 rectangles

Card 6: 5 circles, 5 triangles, 12 rectangles

2. Card 10: 9 circles, 9 triangles, 20 rectangles

1. Continue the pattern of circles, triangles and rectangles.

Draw the shapes on Cards 5 and 6.

**Think about it.**

2. On card 10,

\begin{align*}& \mathbf{Describe:} && \text{There \ are \ 6 \ cards. \ Cards \ 1-4 \ have \ circles, \ triangles \ and \ rectangles.}\\ &&& \text{Cards \ 5 \ and \ 6 \ are \ empty.}\\ & \mathbf{My \ Job:} && \text{Figure \ out \ the \ patterns \ of \ circles, \ triangles \ and \ rectangles.}\\ &&& \text{Draw \ shapes \ on \ cards \ 5 \ and \ 6. \ Answer \ questions \ about \ Card \ 10.}\\ & \mathbf{Plan:} && \text{Count \ the \ number \ of \ circles \ on \ each \ card. \ Look \ for \ a \ pattern. \ Draw}\\ &&& \text{circles \ on \ Cards \ 5 \ and \ 6.}\\ &&& \text{Count \ the \ number \ of \ triangles \ on \ each \ card. \ Look \ for \ a \ pattern. \ Draw}\\ &&& \text{triangles \ on \ Cards \ 5 \ and \ 6.}\\ &&& \text{Count \ the \ number \ of \ rectangles \ on \ each \ card. \ Look \ for \ a \ pattern.}\\ &&& \text{Draw \ rectangles \ on \ Cards \ 5 \ and \ 6.}\\ &&& \text{Extend \ the \ patterns. \ Answer \ questions \ about \ Card \ 10.}\\ & \mathbf{Solve:} && \text{ART: \ Show \ cards \ 5 \ and \ 6. \ Card \ 5 \ has \ one \ red \ circle \ next \ to \ a \ stack \ of}\\ &&& \text{5 \ green \ triangles, \ next \ to \ a \ stack \ of \ 6 \ blue \ rectangles. \ Card \ 6 \ has \ one}\\ &&& \text{red \ circle \ next \ to \ a \ stack \ of \ 6 \ green \ triangles, \ next \ to \ a \ stack \ of \ 7 \ blue}\\ &&& \text{rectangles.}\\ &&& \text{Card \ 10 \ has \ one \ red \ circle, \ 10 \ green \ triangles, \ and \ 11 \ blue \ rectangles.}\\ & \mathbf{Check:} && \text{There \ is \ always \ one \ red \ circle.}\\ &&& \text{The \ number \ of \ green \ triangles \ is \ the \ same \ as \ the \ card \ number.}\\ &&& \text{The \ number \ of \ blue \ rectangles \ is \ always \ one \ more \ than \ the \ card \ number.}\end{align*}

**GEO Pattern 1**

1. Continue the pattern of circles, triangles and squares.

Draw the shapes on Cards 5 and 6.

**Think about it.**

2. On card 10,

**GEO Pattern 2**

1. Continue the pattern of circles, triangles and squares..

Draw the shapes on Cards 5 and 6.

**Think about it.**

2. On card 10,

**GEO Pattern 3**

1. Continue the pattern of circles, triangles and squares.

Draw the shapes in Cards 5 and 6.

**Think about it.**

2. On card 10,

**GEO Pattern 4**

1. Continue the pattern of circles, triangles and squares.

Draw the shapes on Cards 5 and 6.

**Think about it.**

2. On card 10,

**Extra for Experts: GEO Patterns – Extend Patterns**

**GEO Pattern 1**

1. Continue the pattern of circles, triangles and rectangles.

Draw the shapes in Cards 5 and 6.

**Think about it.**

2. On card 10,

**GEO Pattern 2**

1. Continue the pattern of circles, triangles and rectangles.

Draw the shapes on Cards 5 and 6.

**Think about it.**

2. On card 10,

**Solutions**

**GEO Pattern 1**

1. Card 5: 7 circles, 6 triangles, 5 rectangles

Card 6: 8 circles, 7 triangles, 6 rectangles,

2. Card 10: 12 circles, 11 triangles, 10 rectangles

**GEO Pattern 2**

1. Card 5: 1 circle, 5 triangles, 16 rectangles

Card 6: 1 circle, 6 triangles, 18 rectangles

2. Card 10: 1 circle, 10 triangles, 26 rectangles

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