[FREE] End of Year Math Assessments

Looking to assess math progress or prepare for state assessments? Try our free mixed-topic assessments aligned to state standards and created by US math experts!

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Adding and subtracting Integers Multiplying and dividing Integers Integers Coordinate Plane

Here you will learn about plotting points on a graph, including how to identify the quadrant or axis the points are on. You will also learn how to find the distance between points on the coordinate plane.

Students first learn how to plot points in the 6th grade with their work in the number system and expand that knowledge through middle school and high school when graphing linear equations.

To plot points on a graph means to graph points on the coordinate plane where the point, also called an ordered pair, is in the form of (x,y).

When plotting a point on a graph, always start from the center, which is called the origin and has coordinates (0, 0).

Then move horizontally the amount of units represented by the x -coordinate, and move vertically the amount of units represented by the y -coordinate. The x -coordinate and the y -coordinate are represented by rational numbers.

For example, let’s plot the points (0, 2) and (4, 0) on the coordinate plane.

(0, 2) → 0 represents the x -coordinate and 2 represents the y -coordinate.

This means you do not move left or right on the x -axis, you just move up 2 places on the y -axis. This point is on the y -axis.

(4, 0) → 4 represents the x -coordinate and 0 represents the y -coordinate.

This means that you move four units right on the x -axis and 0 units up on the y -axis. This point is on the x -axis.

On this graph, each unit or tick mark represents 1 unit.

For example, the table represents coordinates. Let’s plot them on the coordinate plane.

Notice how each of the points lands in one of the four quadrants on the coordinate plane. Each unit on this coordinate plane represents 1 unit.

We can find the distance between two points on a graph by counting the number of units between the points.

For example,

Plot the point A \, (-4, 4) and the point B \, (3, 4). Find the distance between the points.

To find the distance from point A to point B , count the number of units. The distance from point A to point B is 7 units.

For example,

Let’s plot the polygon on the coordinate plane with vertices at A \, (4, 2), B \, (4,-3), C \, (-2, -3) , and D \, (-2, 2) .

Let’s find the side lengths of the plotted rectangle. To do this, count the number of units from one point to the next.

The distance from point A to point B is 5 units.

The distance from point A to point D is 6 units.

The distance from point D to point C is 5 units.

The distance from point C to point B is 6 units.

The distance between points is always positive because distance is a positive measurement.

Now that you know the side lengths, you can find the perimeter of the rectangle ABCD.

To find the perimeter of a rectangle, add up each of the side lengths or use the formula, P=2l + 2w

The perimeter of rectangle ABCD is 5 + 5 + 6 + 6 = 22 units OR 2 \, (6) + 2 \, (5) = 22 units

How does this relate to 6th grade math?

In order to plot points on a graph:

In order to find the distance between points on a graph:

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

Plot the point (6, 0) .

The x -coordinate is 6 which means to move right 6 spaces.

The y -coordinate is 0 which means there is no movement up or down.

2Follow the gridlines until the two values meet and draw a point.

3Identify which axis or quadrant the point(s) is in.

(6, 0) is on the x -axis.

Plot the point (-2, 5).

Identify the horizontal ( \textbf{x} -value) and vertical position ( \textbf{y} -value) of the ordered pair.

The x -coordinate is -2 which means to move 2 spaces left.

The y -coordinate is 5 which means to move 5 spaces up.

Follow the gridlines until the two values meet and draw a point.

Identify which axis or quadrant the point(s) is in.

(-2, 5) is in Quadrant II.

Plot the point (1, -2).

Identify the horizontal ( \textbf{x} -value) and vertical position ( \textbf{y} -value) of the ordered pair.

The x -coordinate is 1 which means to move one space right.

The y -coordinate is -2 which means to move two spaces down.

Follow the gridlines until the two values meet and draw a point.

Identify which axis or quadrant the point(s) is in.

(1, -2) is in Quadrant IV.

Plot the points (0, 3) and (7, 3) and find the distance between them.

Identify the horizontal ( \textbf{x} -value) and vertical position ( \textbf{y} -value) of the ordered pair.

(0, 3)

The x -coordinate is 0 which means there is no movement right or left.

The y -coordinate is 3 which means to move up 3 spaces.

(7, 3)

The x -coordinate is 7 which means to move right 7 spaces.

The y -coordinate is 3 which means to move up 3 spaces.

Follow the gridlines until the two values meet and draw a point.

Connect the points.

Count the units between the points.

There are 7 spaces (units) between (0,3) and (7, 3) so the distance between them is 7 units.

On a map of an amusement park, the roller coaster is at coordinate (-1, 5) and the water slide is at coordinate (-1, 3).

On the map, how many units is the roller coaster for the water slide?

Identify the horizontal ( \textbf{x} -value) and vertical position ( \textbf{y} -value) of the ordered pair.

(-1, 5)

The x -coordinate is -1 which means to move left 1 space.

The y -coordinate is 5 which means to move up 5 spaces.

(-1, -3)

The x -coordinate is -1 which means to move left 1 space.

The y -coordinate is -3 which means to move down 3 spaces.

Follow the gridlines until the two values meet and draw a point.

Connect the points.

Count the units between the points.

There are 8 spaces (units) between (-1, -3) and (-1, 5). The distance between the points is 8 units.

So the distance between the roller coaster and the water slide on the map is 8 units.

Plot the points A \, (-3, 2), B \, (2, 2), C \, (2, -3), D \, (-3, -3). Find the perimeter of the rectangle.

Identify the horizontal ( \textbf{x} -value) and vertical position ( \textbf{y} -value) of the ordered pair.

A \, (-3, 2)

The x -coordinate is -3 which means to move left 3 spaces.

The y -coordinate is 2 which means to move up 2 spaces.

B \, (2, 2)

The x -coordinate is 2 which means to move right 2 spaces.

The y -coordinate is 2 which means to move up 2 spaces.

C \, (2, -3)

The x -coordinate is 2 which means to move right 2 spaces.

The y -coordinate is -3 which means to move down 3 spaces.

D \, (-3, -3)

The x -coordinate is -3 which means to move left 3 spaces.

The y -coordinate is -3 which means to move down 3 spaces.

Follow the gridlines until the two values meet and draw a point.

Connect the points.

Count the units between the points.

There are 5 spaces between each of the points which means the distance from point to point is 5 units.

To find the perimeter, add up the lengths.

5+5+5+5 = 20.

1. Which graph shows the plotted point (0, 4)?

(0, 4)

The x -coordinate is 0 , which means there is no movement right or left.

The y -coordinate is 4 , which means move 4 spaces up.

Place a point where the gridlines meet.

2. Which graph shows the plotted point (-6, 1)?

(-6, 1)

The x -coordinate is -6 , which means to move 6 spaces left.

The y -coordinate is 1 , which means to move 1 space up.

Place a point where the gridlines meet.

3. Which quadrant is (3, -6) in?

The x -coordinate is 3 , which means move 3 spaces right.

The y -coordinate is -6 , which means move 6 spaces down.

Where the gridlines meet, place the point.

The x -coordinate is positive and the y -coordinate is negative, which is in Quadrant IV.

4. On map of city, the train station is at the coordinate (-4, 2) and the park is at the coordinate (1, 2) . If each unit on the map is a city block, how many city blocks are there between the train station and the park?

6 city blocks between the train station and the park

5 city blocks between the train station and the park

1 city block between the train station and the park

7 city blocks between the train station and the park

Plot the points, connect the points, and count the spaces between the points.

(-4, 2)

The x -coordinate is -4 , which is 4 spaces left.

The y -coordinate is 2 , which is 2 spaces up.

(1, 2)

The x -coordinate is 1 , which is 1 space right.

The y -coordinate is 2 , which is 2 spaces up.

Counting the spaces, there is 5 spaces between the two points, which means there is 5 units or 5 city blocks between the train station and the park.

5. What is the distance between the points (-2, 5) and (-2, -4)?

9 units

8 units

6 units

7 units

Plot the points, connect the points, and count the spaces between the points.

(-2, 5)

The x -coordinate is -2 , which is 2 spaces left.

The y -coordinate is 5 , which is 5 spaces up.

(-2, -4)

The x -coordinate is -2 , which is 2 spaces left.

The y -coordinate is -4 , which is 4 spaces down.

Counting the spaces, there are 9 spaces or 9 units between the points.

6. What is the perimeter of the rectangle with the following points?

A \, (1, 1), B \, (1, 6), C \, (-1, 6), D \, (-1, 1)?

10 units

7 units

12 units

14 units

Plot the points.

A \, (1, 1)

The x -coordinate is 1 , which is 1 space right.

The y -coordinate is 1 , which is 1 space up.

B \, (1, 6)

The x -coordinate is 1 , which is 1 space right.

The y -coordinate is 6 , which is 6 spaces up.

C \, (-1, 6)

The x -coordinate is -1 , which is 1 space left.

The y -coordinate is 6 , which is 6 spaces up.

D \, (-1, 1)

The x -coordinate is -1 , which is 1 space left.

The y -coordinate is 1 , which is 1 space up.

Connect the points and count the spaces from point to point. Count the spaces or units between each of the points.

Add the units from point to point to find the perimeter.

2 + 2 + 5 + 5 = 14 units.

The perimeter is 14 units.

This is the same as a coordinate plane. This name refers to the French mathematician Rene Descartes who is credited with incorporating the use of the coordinate plane into mathematics.

Coordinate planes have many uses in the real world and come up extensively in upper level math topics like coordinate geometry, algebra, trigonometry, and statistics.

Yes, an ordered pair can be any rational number.

Linear equations are equations that form straight lines on the coordinate plane, and quadratic equations form curves called parabolas on the coordinate plane. You will begin to graph linear equations in the 7th grade.

The coordinate grid is another name for the coordinate plane.

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