# Gallery Problems

## Overview

# Gallery Overview

Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.

# Gallery Description

## The Surveyor

Students will read and follow a land surveyor's instructions in order to draw property boundaries on a coordinate plane.

## The Ink Blot

Oops! Part of a land surveyor’s report is covered by an ink blot. Students will figure out what the missing instructions are in order to draw property boundaries on a coordinate plane.

## A Mistake in the Survey

The surveyor made a mistake! Students will correct the mistake in order to draw property boundaries on a coordinate plane.

## More Reflections

Students will reflect a figure located in two quadrants across the *x*-axis.

## Reflect Across the Origin

Students will reflect a figure across the origin and observe what happens to the coordinates of the figure.

## Reflect Letters

Students will reflect letters of the alphabet across the origin and observe what happens to the letters.

## Graphing a Coordinate Plane Video

Students will create a video about graphing on the coordinate plane.

## History

Students will create a report, poster, or video about the history of the coordinate plane.

# The Surveyor

# Answers

## Work Time

# The Surveyor

Surveyors mark the boundaries of property. To relay this information, they write instructions as if someone were walking on a piece of property. The instructions state where to start, which direction to walk in, and how far to walk before making a change in direction.

Use the surveyor’s instructions to draw the boundaries of the property on the coordinate plane. Adjust the graph so the axes range from –100 to 100.

The Surveyor’s Instructions

A. Start at (40, 30).

B. Go north 20 yards.

C. Go west 70 yards.

D. Go south 30 yards.

E. Go west 20 yards.

F. Go south 40 yards.

G. Go east 30 yards.

H. Go south 30 yards.

I. Go east 40 yards.

J. Go north 80 yards.

K. Go east 20 yards.

HANDOUT: The Surveyor

# The Ink Blot

# Answers

Last two directions:

J. Go east 110 yards.

K. Go north 50 yards.

**Work Time**

# The Ink Blot

Use the surveyor’s instructions to draw the boundaries of the property on the coordinate plane. The last two steps are covered by an ink blot. Figure out what the steps should be and complete the drawing of the boundaries. You can only walk north, south, east, or west—no walking on the diagonal. Adjust the graph so the axes range from –100 to 100.

The Surveyor’s Instructions

A. Start at (60, 10).

B. Go west 40 yards.

C. Go north 30 yards.

D. Go west 60 yards.

E. Go south 30 yards.

F. Go west 30 yards.

G. Go south 30 yards.

H. Go east 20 yards.

I. Go south 20 yards.

J. (ink blot)

K. (ink blot)

HANDOUT: The Ink Blot

# A Mistake in the Survey

# Answers

- Line 7 should state, “Go east 50 yards.”

**Work Time**

# A Mistake in the Survey

Use the surveyor’s instructions to draw the boundaries of the property on the coordinate plane. Adjust the graph so the axes range from –100 to 100.

What is wrong with this survey?

The head surveyor says the mistake is in line 7 of the report. Correct the report and fix your drawing of the boundaries.

The Surveyor’s Instructions

A. Start at (70, 20).

B. Go north 30$\frac{1}{2}$ yards.

C. Go west 40 yards.

D. Go south 30$\frac{1}{2}$ yards.

E. Go west 60 yards.

F. Go south 50 yards.

G. Go east 60 yards.

H. Go south 20$\frac{1}{2}$ yards.

I. Go east 50 yards.

J. Go north 70$\frac{1}{2}$ yards.

HANDOUT: A Mistake in the Survey

# More Reflections

# Answers

**Work Time**

# More Reflections

- Reflect the given triangle across the
*x*-axis. Label the vertices of the original triangle and the reflected triangle. HANDOUT: More Reflections

# Reflect Across the Origin

# Answers

- Graph
- Answers will vary.
- Possible answer: A reflection across the origin is a reflection across both the
*x*- and*y*-axes. So take the opposite of the coordinates given. The reflection of (*a*,*b*) across the origin is (−*a*,−*b*).

**Work Time**

# Reflect Across the Origin

You can reflect figures across the origin (0, 0).

For example, to reflect point *A* across the origin, draw a line from point *A* through the origin and mark a point on the other side of the origin that is the same distance from the origin.

- Reflect the given figure across the origin. Label the coordinates of vertices of the original triangle and the reflected triangle.
- Reflect other figures across the origin.
- What rule can you use to reflect any point (
*a*,*b*) across the origin?

HANDOUT: Reflect Across the Origin

# Reflect Letters

# Answers

- Graph:
- The letter E is rotated so that it is upside down and backwards.
- Answers will vary.
- The letters O and X are the same when reflected across the origin.

**Work Time**

# Reflect Letters

You can reflect figures across the origin (0, 0), too.

- Reflect the letter E across the origin. Label the vertices of the original letter and the reflected letter.
- What happens to the letter E when you reflect it across the origin?
- Reflect other letters across the origin.
- Are there any letters that look the same when they are reflected across the origin? Try to find some of these letters. HANDOUT: Reflect Letters

# Graphing a Coordinate Plane Video

# Answers

- Videos will vary. Have students present their videos to the class.

**Work Time**

# Graphing a Coordinate Plane Video

Create a video about graphing on the coordinate plane.

- Think about the key concepts about graphing on the coordinate plane.
- Develop a story line that encompasses those concepts.
- Film and edit the video.

# History

# Answers

- Reports, posters, and videos will vary.

**Work Time**

# History

- Create a report, poster, or video about the history of the coordinate plane.