Classroom Resource

Vector Scalar Product: Boat Race

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This interactive game will test students' knowledge of vector-scalar multiplication with the following scenario:

An orange motorboat and a blue sailboat are racing. The sailboat can go faster but must move diagonally with the wind. The motorboat isn't as fast, but it can race straight from start to finish.

In this race, each vector represents how far the boat travels in one hour of racing. 

    • To see how far the boat will travel in multiple hours, drag the red points to move the blue and orange vectors from the box in the corner and put them end to end starting with the vector attached to the boat.
    • To change the speeds of the boats, drag the red points of the vectors attached to the boats.
Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.13

Multiply a vector by a scalar.

Unpacked Content

UP:MA19.PRE.13

Vocabulary

  • Scalar Multiple
  • Scalar Multiplication
  • Scaling Vectors

Knowledge

Students know:
  • The representation of vectors graphically on the xy-plane.

Skills

Students are able to:
  • Find the components of a vector.
  • Find the magnitude and direction of a vector.

Understanding

Students understand that:
  • Scalar multiplication results in a dilation of the original vector where a scalar greater than 1 would increase the magnitude and a scalar from 0 to 1 would decrease the magnitude.
  • A negative scalar would reverse the direction of the vector.
  • The absolute value of the scalar has the resulting effect on the magnitude.
Link to Resource
https://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=MAT.CAL.802.0…

Resource Provider

Other

Resource Provider other

CK-12
Accessibility
License

License Type

CUSTOM

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Comments or Notes

It is recommended that students view the introductory video and solve practice problems prior to challenging their knowledge with this interactive game. These can be found by clicking the Learn More link on the resource page.

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