#### – The Steering Differential –

**Please find a printable version of this page HERE.**

#### Considerations for Robotics Task

###### Learning Goal

Students understand that a **steering differential** is determined by the number entered in the <Move> Programming Block.

###### Mathematical Engagement

The **steering differential describes the different power that is delivered to each wheel**. When the differential is zero, each wheel gets the same power and they go in the same direction, whereas at its maximum the wheels are going in different directions at their maximum power. For example, when -100 is entered in the <Move> Programming Block, the left wheel moves backwards and the right wheel moves equally forward. Students learned in Part 2 that at -100 steering setting the robot turns around a circle of radius 6 cm. For Part 3, we adapted the convention of **expressing the steering differential as a percentage** ranging from -100% to 100%, or as a fraction between -1 and 1.

###### Teaching Suggestions

A partner teacher has used the video *Around the Corner – How Steering Differential Works* to illustrate the steering differential to their students.

(click on image to go to video)

We also found that it may be helpful to refer back to the vertical and horizontal number line representation of Part 2 to further scaffold spatial understanding of number.

#### Materials Needed

- Basic EV 3
**robot** **Recording Sheet**for Part 3, available HERE

#### Instructions, Steps and Programming for Part 3

**Please find a printable version of the Recording Sheet HERE.**

###### Introduction

The **power differential** is the different power that is delivered to each wheel. When the power differential is at its maximum, each wheel is going in different directions. When the slider is set to 100 the power is going to both wheels for a maximum or tight turn.

In the image below

a) shows how the steering is programmed – the setting on the <Move> Programming Block as 100 meaning 100%,

b) shows how the direction the wheels rotate, and

c) shows the movement of the robot.

Note: The right wheel turns one wheel rotation backward and the left wheel turns one wheel rotation forward. This can be represented as equal sized bars or rectangles (see image a) above).

###### Student Tasks 1

- Draw bars left and right of the robot to represent how much each wheel rotates (when the <Move> Block is set to 1 wheel rotation) for 75, 50, 25, and 0.
- Color in the bars under the <Move> Block to indicate the amount of power going to the wheel.
- Describe the robot’s turn.

###### Student Tasks 2

Draw bars left and right of the robot to represent how much each wheel rotates for -75, -50, -25, and -100.

Color in the bars under the <Move> Block to indicate the amount of power going to the wheel. Describe the robot’s turn.

###### Extension

Differential means difference. What is the difference between each wheel’s rotation? For example: with 75% steering, the left wheel rotates 1 rotation forward and the right wheel rotates 1/2 a rotation backwards.

- What is the fraction (proportion) of the total power differential?
- Express the fraction as a percentage.
- What do you notice about the relationship between the percentage you found and the number on the <Move> Block?

Answer: 3/4

Answer: 75%

Answer: They are both 75.

Identify the difference between the right and left wheels for 50, 25, and 0. Fill in the table below.

What do you notice about the relationship between the percentage you found and the steering number on the <Move> Block?

#### Assessment of Student Understanding

###### Indicators of Student Understanding

The illustrations of the steering differential on the Recording Sheet are useful for spatially representing proportional relationships (Grades 4-6), and spatially scaffolding algebraic ideas about opposite quantities with distance from a center in Grade 7.

When engaging with Part 3, students measure wheel rotations (geometric measurement of circles), record positive and negative numbers to indicate direction (spatial understanding of number), order fractions and whole numbers (fraction equivalence and ordering), represent data, and determine patterns and structures.

###### Assessment of Student Understanding

Students can **articulate/explain how the percentage of the steering differential relates to** the number and direction of **left and right wheel rotations**.

The fourth column of our summary table includes an overview of steering settings and the steering differential represented as a fraction.

#### Go To

A printable version of this page can be found HERE.

Please find other parts of the task, instructions, and more on the following pages:

- Move Steering Main Page
- Part 1 – How the Steering Setting Determines Wheel Rotations
- Part 2 – Mathematically Modeling the Robot’s Turns
- Summary

© 2022 Dr. Krista Francis & Stefan Rothschuh

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