Vectors

Autor:: Christoph Painer, GeoGebra Team

Authors

Lukas Kurt Schenk, Christoph Painer

Lesson Information

Topic: Vectors
5th Grade Level, Mathematics
Duration: 50 min.
Student activities: "Vectors Book"

This applets gives students a first approach with the topic of vectors. It can be used in different ways:

The students get the task to go through the applets in its entirety in the lesson.
The students get this applets as homwork assigned.
The teacher can choose the applets which he/she wants to use in the lesson.

Previous Knowledge

coordinate systems
phytagorean theorem
trigonometric functions

Learning Outcomes and Learning Goals

Students...

know that a vector is an arrow with specific properties (length, direction).
are able to identify x- and y-components of a given drawn vector in a coordinate system.
are able to calculate the the components of a vector between two points without a drawn vector.
are able to add two vectors together (analytically and graphically).
recognize that the length of a vector is calculated by the pythagorean theorem.
know that vector calculation is also applied in physics.

Description of Lesson Activities

In the first few minutes of the lesson the teacher should repeat coordinate systems, pythagorean theorem and trigonometric functions, so that everyone in class is at the same level. After that the students work on the applets by their own in their individual speed and write also the given explanations in each applet in their notebooks.

Activity 1 (5-10 min)

The first applet ("Explanation: What is a vector?")shows a vector in a coordinate system. By moving the slidebar the students get an step-by-step-explanation of how to identify the components of the shown vector. If the students already know how to solve this task, they can also fill in the correct solution an the slider jumps to the final position and the students can read the complete explanation. If the vector is incorrect the slider jumps one step further and the students get another hint.

Activity 2 (5-10 min)

In this applet ("A->B") the focus lies on the mathematical computation of vectors with two points given. By moving the slidebar a step-by-step explanation is shown.

Activity 3 (5-10 min)

This applet ("Game: Setting up vectors")is a game in which the students can check their gained knowledge from the two applets before. They have to "help" the figure to find the correct vector to the house, so that the figure is able to go inside the house. The game is completed when 5 points are achieved.

Activity 4 (5-10 min)

This applet ("Magnitude") introduces the magnitude of a vector. Like in activity 1 and 2 the students get an step-by-step-explanation and can also finish early. The applet shows how to calculate the magnitude of the vector by a formula the students should be able to recognize (pythagorean theorem)

Activity 5 (5-10 min)

The topic of this applet ("Direction") is the direction of vectors. At first the definition of the tangent is repeated/given. By moving the slidebar the calculation is shown for the given vector. As in all simulations before, the option to finish early exists.

Activity 6 (5-10 min)

In this applet ("Graphical and analytical addition")the students learn how two vectors can be add together. By moving the slider the explanation graphically and analytically is given.

Activity 7 (5-10 min)

The last applet ("Game: Resulting force")of this lesson is another game in which combines a little bit of physics with vector calculation. The applet shows two boats which are pulling on another boat, which in physics are called "forcevectors" and are very common in this subject. The goal of the game is to add two vectors (graphically or analytically) and collect 5 points.

Lesson Assessment

Self control: with the games and the option in the applets to fill out early, the students see for them selves what they have done well and what they have to repeat again.