# 4.8: GEO Patterns

**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*} card. Shape patterns may differ. For example, the number of circles may remain constant while the number of triangles increases by 1 and the number of rectangles increases by 2. In lieu of drawing the figures, you may want to have students identify the number of shapes of each type on each of the empty cards.

**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