We have learned what the coordinates are in this blog post, and about the quadrants in which coordinates are divided. But with the exercises in Smartick, we also work with movement within the same quadrant and between them.

The placement of Cartesian coordinates has three elements:

- The
**initial position**: the coordinate in which it starts. - The
**movement**: the movements carried out. - The
**final position**: the final coordinate after the movement.

##### Known Initial Coordinates and Simple Movement with Visual Help in the First Quadrant

In these exercises, the initial position and movements are given, and they only contain one movement. We only use the first quadrant and ask for the final position after seeing the movement. In addition, we offer a visual aid for the first few tries. The axes are different colors and the coordinates assigned to these axes maintain the same color code.

In this example, Zoe **begins at the coordinates (2,1)** and moves** one space to the right**. Since she only moves along the X axis, only the X coordinate changes. Her **final position will be (3,1)**.

##### Known Initial Coordinates and Various Movements with Visual Help in the First Quadrant

It is the same as the previous example with one difference: the number of movements is increasing.

Max had started at the coordinates** (4,5)**. He’s moved** once to the left and down two times**. If we follow his movement along the grid we see that the** final position is (3,3)**.

##### Known Final Coordinates with Visual Help in the First Quadrant

Now, in place of the final position, we’re looking for the starting position. Knowing where they finish and the movements they have made, we can calculate their path in reverse.

Here, Amy has moved **once to the right** and **has finished at the coordinates (4,4)**. Following her movements in reverse (one space to the left) we can verify that the **origin position was (3,4).**

The difficulty will increase as the number of movements increases.

##### Numerical Help in the First Quadrant

We also ask for the final or starting position, but no longer offer help by using colors to identify each one. Additionally, the coordinates become points on the plane instead of squares.

Here Eva **begins at the position, (4,3).** She moves **once to the right and down two times**. If we follow her movements we can see** Eva’s final position is (5,1)**.

##### All the Quadrants

The dynamic is the same as the previous activities but the rest of the quadrants have been added.

Otto has moved **once to the right and up two times**. He’s **ended at the point (-3,4).** If we follow his path in reverse (once to the left and down two times) we see that his **origin coordinates are (-4,2).**

And finally, we made the grid where you can move the avatar bigger.

If Leo **begins at the position (3,-6)** and **he moves once to the right and down once**…..where will he end?

That’s it! **He will end at (4,-7).**

If you want to practice and learn **more about elementary math**, log in to Smartick and try it for free.

Learn More:

- Cartesian Coordinates: The Quadrants
- Coordinates: What They Are Used for and Some Examples with Smartick
- Teaching Novelties at Smartick: Tables, Coordinates, and Fraction Problems
- What Do Double and Half Mean?
- Angles Explained with Clockhands