#### – Modeling Steering Differential with Fractions and Percentages –

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

#### Task Description

After Parts 1 and 2, students will understand how the <Move> steering setting varies the left and right wheel rotations to change the radius and direction of the robot’s turns.

The learning goal of Part 3 is to understand that the number entered in the <Move> steering determines a **steering differential**. The steering differential is the difference in power that is delivered to each wheel.

When the differential is at its maximum, each wheel is going in different directions for the same amount of rotations. For example, as found in Part 1, when the <Move> steering is set to 100, the left wheel moves forward and the right wheel moves equally backward. From Part 2 we know that the robot turns around a circle of radius 6 cm. This is the tightest turn the robot can make, and it essentially pivots on the spot.

#### Materials Needed

- Basic EV 3
**robot** **Recording Sheet**for Part 3, available at http://stem-education.ca/files/SteeringRecordingsheet_2020Part3.pdf

#### Note for Teachers

One of the teachers we have worked with demonstrated the concept of a steering differential using the YouTube video *Around the Corner – How Steering Differential Works*. A student noted that an excavator uses the same differential when moving. There could be a natural transition into a science inquiry of gears at this point. However, our focus is on the mathematics.

The Recording Sheet provides detailed instructions. Students measure the rotation of the wheels, record direction along with positive and negative numbers, and representing data.

#### 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 steering on the <Move> Programming Block set to 100 means 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 to represent how much each wheel rotates (when the steering block is set to 1-wheel rotation) for 75, 50, 25, and 0.

Color in the bars to indicate the amount of power going to the wheel. Describe the robot’s turn.

###### Student Tasks 2

Draw bars to represent how much each wheel rotates for -75, -50, -25, and -100.

Color in the bars to indicate the amount of power going to the wheel.

###### 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? — 3/4
- Express the fraction as a percentage. — 75%
- What do you notice about the relationship between the percentage you found and the number on the block?

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

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

#### Mathematics Learning

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

Students measure the rotation of the wheels (geometric measurement of circles), record direction along with positive and negative numbers (spatial understanding of number), order fractions and whole numbers (extend understanding of fraction equivalence and ordering), represent data, and find patterns and structures for interpretation.

To reinforce and scaffold spatial understandings of numbers, it would be useful to refer back to the vertical and horizontal number line representation of the fractions that was provided in Part 2.

#### Go To

- Move Steering Main Page
- Part 1 – Determining how the Wheels Rotate According to the Steering Setting
- Part 2 – Describing and Modeling the Robots’ Turns According to the Steering Setting

© 2020 Dr. Krista Francis & Stefan Rothschuh

## Recent Comments