– Mathematically Modeling the Robots’ Turns –
Part 2 contains an unplugged activity and a plugged activity.
Unplugged Task Considerations
Beginning this task with an unplugged embodied activity will help students understand that the outer wheel of the robot requires more rotations to travel around a circle.
Student Mathematical Engagement
Groups of students should link arms, walk around a circle, and count their steps (see Figure above). Please see a video of students engaging in this unplugged task here https://vimeo.com/392986435.
In the video, some students are taking the same number of steps. The teacher is reminding the group to stay in a straight line. When asked how many steps they took, students respond 13, 10, 13, and 17. Note that the innermost student took more steps than the second, an indication for the group’s misunderstanding. It may not be intuitive to learners that more steps are needed for the outer part of the circle.
We suggest summarizing this lesson by having students explain their observations. It might be useful for a group with good understanding to demonstrate to the class that an increasing number of steps is needed when being further removed from the center of the circle. In other words, the outside person needs to travel further than the inside person. The robot moves similarly around a circle because the outside wheel needs to travel further than the inside wheel. Moreover, larger circles require more wheel rotations for the robot to travel around.
Plugged Robotics Task Considerations
Students understand how higher numbers in the steering setting result in tighter robot turns (or turns with smaller radii).
Students vary the steering setting of the <Move> Programming Block by plugging in -100, -75, -50, -25, 0, 25, 50, 75, and 100. They observe and record the direction and distance the robot travels, and identify which blue circle of the steering mat (or circles drawn on the floor) the outer wheel of the robot travels along.
We find that printouts of the Steering Mat on smooth vinyl hold up well in classroom use. Each printout costs about $50 CDN. Alternatively, you can prepare four concentric circles for each group with diameters 48 cm, 24 cm, 16 cm, and 12 cm. We suggest drawing circles on poster board, or on the floor with chalk or washable marker.
It may be necessary to introduce some terminology first for this part. Part 2 uses circumference of a circle, diameter and radius in context. The following figure below is an example of the terminology in context and may help students understand. Note: Steering on the <Move> Programming Block set to 25.
- EV3 robot
- Rulers for measuring radii
- Steering Mat, available at https://stem-education.ca/files/SteeringMat.pdf (cost for printing on smooth vinyl: approx. $50 CDN)
- Alternatively: 4 concentric circles drawn on poster boards or the floor (diameters: 48 cm, 24 cm, 16 cm, and 12 cm)
- Recording Sheet for Part 2, available at https://stem-education.ca/files/SteeringRecordingsheet_2020Part2.pdf
Instructions, Steps and Programming for Part 2
- Drag and drop a <Move> block onto the programming chain.
- Drag the arrow for the steering until 25 is entered.
- Which blue circle on the steering mat does the outer robot wheel follow?
- Measure the radius of the blue circle. Record the radius in the table.
- How many wheel rotations does it take for the robot to make one full circumference of the blue outer circle? Record the number of wheel rotations in the table.
- Record which robot wheel follows the outer circle.
- Repeat all the steps for 100, 75, 50, 25, 0, -25, -50, -75, and -100.
Evidence and Assessment of Student Understanding
Indicators of Student Understanding
Part 2 incorporates many geometric elements. Recall that the goal was to understand how higher numbers in the steering setting result in tighter robot turns, or turns with smaller radii. Students note which wheel of the robot is on the outer circle. Recall in the unplugged activity, students learned that the outer wheel travels further around a circle. Noting which wheel travels furthest can help student predict the direction of turn.
Students are also measuring and recording data using decimal numbers, and identifying patterns and structures for interpretation. Specifically, students use decimals numbers to the tenth (or hundredths) to express the circumference of different circles as a multiple of wheel rotations. Students also record radii of these circles in cm.
Assessment of Student Understanding
Student should be able to interpret and explain (i) how positive and negative steering settings impact the direction of the robot’s turn, (ii) how the steering input impacts the radius the robot travels around, and (iii) how the number of wheel rotations changes when the robot travels around circles of different radii (smaller and larger circumferences).
Please see the third column of our summary table for an overview of steering settings and associated circles that the robot travels around.
An extension for Grade 6 students and above is to calculate the circumference (c) of the circle mathematically, using the formula:
For example, when students record a circumference of 8.6 wheel rotations, it is close to the actual circumference, assuming they identified the circle with radius of 24 cm the robot travels around:
c = 2πr = 2π∙24 cm = 150.8 cm.
There are 17.6 cm per wheel rotation. So,
150.8 cm ÷ 17.6 cm/wheel rotation = 8.57 wheel rotations
Students can use the second table in the Recording Sheet for Part 2 for this extension:
With the extension, students can convert the measured circumference of wheel rotations into cm and compare the answers to explain similarities and differences. They should notice their answers are close, though slight variations may occur due to rounding or measurement errors, as well as mechanical friction when the robot moves.
An additional task that is not included in the Recordings Sheet but would scaffold learning about angles, is for students to measure the angle of the arc that the robot travels with one wheel rotation for each of the circles of radius 6 cm, 8 cm, 12 cm, and 24 cm.
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 3 – The Steering Differential
© 2020 Dr. Krista Francis & Stefan Rothschuh