6th Grade Math: Unit 8

Unit 8 – Item 1
At a middle school, a group of students are participating in a video game design challenge.
They are tasked with creating a game character that moves across different zones on the
screen, which is represented by a coordinate plane.

The game screen is divided into four quadrants, and the origin point (0,0) is the center of the
screen. The character starts at the origin and needs to collect items placed at the vertices of a polygon. The coordinates for the vertices are as follows: 

(4, 5), (-4, 5), (-4, -5), and (4, -5).

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PART A: Draw the polygon on the coordinate plane.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

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PART B: Calculate the length of the side where both points have the same first coordinate.

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PART C: Determine the total distance the character needs to travel to collect all items and return to the origin.

Unit 8 – Item 2
Shyla is planting various trees in her backyard. The locations of each tree are marked on the
map below. Each unit represents one foot.

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Select all the pairs of trees that are separated by a distance of exactly 4 feet in a straight line, either horizontally or vertically.

Unit 8 – Item 3
Hadia and Thomas are creating a map using a coordinate plane that shows the locations of a
school and a library in their town. Their instructions are to place the following places using the given coordinates:

Library (-4, -1)
School (3, -1)
Post Office (3, -5)

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Each unit on the map represents 1 mile. They are trying to determine which places are the closest to each other.

Who is correct? Justify your reasoning.

Unit 8 – Item 4
On a map, the school is located at A(-4, 4), the library is located at B(0, 4) and the post office is located at C(0,0).

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PART A
Represent the locations as points on the coordinate grid with a unit of 1 mile.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

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PART B
What shape is formed by connecting the three locations?

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PART A: Draw the polygon on the coordinate plane.

PART B: Calculate the length of the side where both points have the same first coordinate.

PART C: Determine the total distance the character needs to travel to collect all items and return to the origin.

Select all the pairs of trees that are separated by a distance of exactly 4 feet in a straight line, either horizontally or vertically.

Each unit on the map represents 1 mile. They are trying to determine which places are the closest to each other.Who is correct? Justify your reasoning.

PART ARepresent the locations as points on the coordinate grid with a unit of 1 mile.

PART BWhat shape is formed by connecting the three locations?

PART CThe city council is planning to place a city park in this area. How large is the area of the planned park?

Each unit on the map represents 1 mile. They are trying to determine which places are the closest to each other.

Who is correct? Justify your reasoning.

PART A
Represent the locations as points on the coordinate grid with a unit of 1 mile.

PART B
What shape is formed by connecting the three locations?

PART C
The city council is planning to place a city park in this area. How large is the area of the planned park?