Learning Coding and Math with RoboBlockly...operating system. It is important to know that every browser functions differently. We encourage you to test RoboBlockly on the computers

Copyright © 2015, UC Davis C-STEM Center DRAFT Version 1 Released October 2015

Learning Coding and Math with RoboBlockly Teaching Resource for Integrated Mathematics 1/Algebra I

Harry H. Cheng

UC Davis Center for Integrated Computing and STEM Education (C-STEM)

http://c-stem.ucdavis.edu

http://roboblockly.ucdavis.edu

http://c-stem.ucdavis.edu/

http://roboblockly.ucdavis.edu/

Integrated Mathematics I/Algebra I Activities with RoboBlockly

Copyright © 2015, UC Davis C-STEM Center DRAFT Version 1 Released October 2015 1

Learning Coding and Math with RoboBlockly Teaching Resource for Integrated Mathematics 1/ Algebra I

Harry H. Cheng UC Davis Center for Integrated Computing and STEM Education (C-STEM)

University of California-Davis

Copyright © 2015, UC Davis C-STEM Center, All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of the author, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Acknowledgements: This work was supported in part by the National Science Foundation under grant numbers CNS-1132709, IIS-1208690, IIS-1256780, and by the CaMSP Program of the California Department of Education.

Additional Contributor(s): Kayce Mastrup



How to Use RoboBlockly Activities in your Classroom

What is the purpose of RoboBlockly? In RoboBlockly, students program a robot using a user-friendly drag-and-drop method. Students will complete basic problem solving to move a robot or multiple robots. RoboBlockly is built to allow students to work at their own pace, but in general each problem should take approximately 5 minutes to complete each activity. We encourage you to give students additional time if needed or make it clear that they don’t need to finish the entire set of activities during one class session.

General Computer Usage Requirements Technology Requirements: Any modern browser on computers, laptops, tables, or smartphones with any type of operating system. It is important to know that every browser functions differently. We encourage you to test RoboBlockly on the computers you will have students using before implementation. Please test out the following: audio and video streaming quality, default browser specific mechanisms for saving blocks and saving Ch code, etc. all so you are better able to support your students. Make sure that pop ups have been enabled on all computers. You may wish to provide headphones or ask students to bring headphones to allow students to independently watch tutorial videos.

Prepare yourself Go through the activities yourself so that you are familiar with what your students will be experiencing. The Teacher Resource Packet contains all the activities and solutions for the pathway. Please note that the activities build on previous activities in each pathways such that students may need to complete some or all activities prior to the activity selected. 1) Determine the purpose for students using RoboBlockly:

To support student learning in Math,

To support student learning in Computer Programming,

To support student learning in Robotics.

2) Based on your purpose, determine what additional resources your students will need for instruction. We do not recommend using RoboBlockly to introduce a mathematical concept but to rather use it for skill building or as a culminating performance task. Use as skill building: We recommend that you provide your students with a worksheet that includes important related definitions, work space, leading questions, etc. and encourage your students to refer to their class notes which cover these topics. Use as a culminating performance task: Carefully select which activity directly relates to the content you have taught, making note that the previous activities may be necessary to complete to build prior knowledge.

Prepare your students Help students get excited about RoboBlockly by inspiring students and discussing how computer science impacts every part of our lives. As a class, list things that use code in everyday life, or discuss different ways technology impacts our lives etc. When using RoboBlockly in class, first demonstrate to students how to navigate and use the RoboBlockly website. There are five Video Tutorials, along with a self-guided interactive non-video tutorial which should be used to help familiarize your students with the different functionalities of RoboBlockly. Helping students understand the functionality of RoboBlockly and which elements can be manipulated in which manners is very important to ensuring your students have full access to the content.



Pre-Requisite Skills Math We are currently developing a comprehensive wiring guide to assist you with your planning. Please refer to the Table of Contents Standard Mapping for a complete list of Common Core Algebra Math Standards addressed in the RoboBlockly activities. Computer

Basic computer skills: o Drag and drop using a mouse o Key boarding o Navigating a web browser o Zoom In/Out in a browser o Disabling or enabling pop-up windows o Adjusting volume for videos

Extension Using hardwired robots, Linkbot Controller, RoboSim or Robot Controller to execute programs built in RoboBlockly. All can be downloaded from the UC Davis C-STEM Center’s webpage: http://c-stem.ucdavis.edu/downloads/

http://c-stem.ucdavis.edu/downloads/



Learning Coding and Math with RoboBlockly Teaching Resource for Integrated Mathematics I/ Algebra I

Table of Contents Activity CCSSM Blocks Used

1. Modeling Linear Relationship of Velocity and Time A.CED.4 driveTime setSpeed

2. Modeling Linear Relations in the Coordinate Plane A.CED.4 driveDistance setSpeed driveTime

3. Modeling Linear Relations in the Coordinate Plane A.CED.4 setSpeed driveDistance

4. Graphing Linear Equations with Robots: Key Features - Intercepts

A.REI.10 trace drivexyTo

5. Graphing Linear Equations with Robots: Using Slope & y-intercept

A.REI.10 trace drivexyTo

6. Graphing Systems of Linear Equations with Robots A.REI.3 A.REI.6

turn driveDistace

7. Graphing Systems of Linear Inequalities with Robots A.REI.3 A.REI.12

turn driveDistance

8. Geometry: Area of Basic Shapes in Coordinate Plane A.REI.3 turn driveDistance

9. Geometry: Area of Basic Shapes in Coordinate Plane A.REI.3 drivexyTo

10. Model & Calculate the Average Speed of a Robot in the Coordinate Plane

A.REI.3 setSpeed driveDistance

11. Graphing Functions in the Coordinate Plane Given a Relation

F.IF.1 trace drivexyTo

12. Equations – Solving for Missing Values and Modeling their Solutions

A.REI.3 setSpeed driveTimeNB driveTime moveWait driveDistance



Activity CCSSM Blocks Used

13. Initial Position – Modeling in the Coordinate Plane A.REI.3 setSpeed driveDistanceNB driveDistance moveWait

14. Initial Position and Initial Angle – Modeling in the Coordinate Plane

A.REI.3 setSpeed driveDistanceNB driveDistance moveWait



Learning Coding and Math with RoboBlockly Teaching Resource for Integrated Mathematics I/ Algebra I

Standard Mapping Common Core State Standards for Mathematics – IMI/Alg I Activities

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law VIR to highlight resistance R.

1, 2, 3

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

6, 7, 8, 9, 10, 12, 13, 14

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. *for this standard this activity introduces the concept using a system of inequalities that form a horizontal and vertical line – students are asked to identify a solution that would fall into the solution set, without graphing the lines.

6

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line)

4, 5

A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. *for this standard this activity introduces the concept using a system of inequalities that form a horizontal and vertical line – students are asked to identify a solution that would fall into the solution set, without graphing the lines.

7

F.IF.1 Understand that a function from one set (called domain) to another set (called range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

11



Table of Contents: Textbook to Activity Alignment

Learning Robot Programming with Linkbot for the Absolute Beginner 5th Edition

Activities

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Section 5.4 Move a Distance for a Two-Wheel Robot X X X X X X

Section 5.6 Turn Left and Turn Right

X X X

Section 9.1 Move a Two-Wheel Robot with the Specified Distance X X X X X X X

Section 9.2 Move a Two-Wheel Robot with the Specified Time

X X

Section 10.1 Move a Linkbot-I in a Coordinate System

X X X X

Section 10.3 Trace the Position of a Linkbot-I X X X

Section 12.5 Move Multiple Linkbots with Specified Distances or Joint Angle X X X

Section 12.7 Move Multiple Linkbots with Specific Time X X



Activity #1 Modeling Linear Relationship of Velocity and Time

Common Core State Standards - Mathematics: A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law VIR to highlight resistance R.

Objective: Students apply their understanding of solving equations to a real world situation involving distance, velocity and time. They will need to determine the appropriate velocity needed to move a robot a given distance with regards to velocity and time.

RoboBlockly Student Activity:

Initial Student Prompt Linear Relations

We will be modeling a linear relation of distance with regards to velocity and time.

Pre-Placed Blocks None.

Problem Statement Move the robot a total distance of 20 units in 2 seconds using driveTime() block.

Wrong Prompt You did not move the robot the correct distance in the given time. Please try again.

Hint Remember, distance = velocity * time.

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.setSpeed(2, radius); robot.driveTime(10);



Activity #1 Modeling Linear Relationship of Velocity and Time Picture of solution in RoboBlockly

Location of solution for “Load Blocks” tab in RoboBlockly C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m1.xml

Student Mathematical Calculations Students will need to use the equation Distance = velocity*time. They will need to substitute the given values for distance and time into the equation in order to solve for the driveTime function (velocity). D = vt where, d = 20 and t = 2 sec. 20 = v*2 10 = v students now plug time in the setSpeed block and velocity in the driveTime block

C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition

a) Section 9.1 Move a Two-Wheel Robot with the Specified Distance 9.1.1. (setSpeed block) b) Section 9.2 Move a Two-Wheel Robot with the Specified Time (driveTime block) c) Section 2.2 Connect Linkbots from a Computer – have students move a hardwired robot by

generating the Ch code using “Save Ch” on RoboBlockly.



Activity #2 Modeling Linear Relations in the Coordinate Plane



RoboBlockly Activity:




Problem Statement Move the robot backwards 10 units using driveDistance() block, then move the robot forward 32 units in 8 seconds using driveTime() block.



Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.driveDistance(-10, radius); robot.setSpeed(4, radius); robot.driveTime(8);



Activity #2 Modeling Linear Relations in the Coordinate Plane Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m2.xml

Student Mathematical Calculations Students will need to do two tasks:

1. Move the robot backwards by plugging a negative value into the driveDistance block. 2. Students will then need to use the equation Distance = velocity*time. They will need to

substitute the given values for distance and time into the equation in order to solve for the driveTime function (velocity).

D = vt where, d = 32 and t = 8 sec. 32 = v*8 4 = v students now plug time in the setSpeed block and velocity in the driveTime block C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition

a) Section 5.4 Move a Distance for a Two-Wheel Robot. (driveDistance block) b) Section 9.1 Move a Two-Wheel Robot with the Specified Distance 9.1.1. (setSpeed block) c) Section 9.2 Move a Two-Wheel Robot with the Specified Time (driveTime block) d) Section 2.2 Connect Linkbots from a Computer – have students move a hardwired robot by

generating the Ch code using “Save Ch” on RoboBlockly.



Activity #3 Modeling Linear Relations in the Coordinate Plane







Problem Statement Change the initial position of the robot using the command window in the lower left hand side (under the Coordinate Plane). Change the initial position of the robot so it starts 8 units to the left and 4 units down. Set the robot’s speed to 3 units per second and then drive the robot to y = 12.



Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.setSpeed(3, radius); robot.driveDistance(16, radius);



Activity #3 Modeling Linear Relations in the Coordinate Plane Picture of solution in RoboBlockly


Student Mathematical Calculations Students will need to do two things:

1. Students will first need to change the initial position of the robot. This is done in the set-up section, below the coordinate plane.

2. Students will then need to calculate the driveDistance from their initial position of (-8, -4) to end at (-8, 12). To calculate they calculate the change in y-values: 12—(-4) = 16.


a) Section 5.4 Move a Distance for a Two-Wheel Robot. (driveDistance block) b) Section 9.1 Move a Two-Wheel Robot with the Specified Distance 9.1.1. (setSpeed block) c) Section 2.2 Connect Linkbots from a Computer – have students move a hardwired robot by

generating the Ch code using “Save Ch” on RoboBlockly. OR if your students are ready

d) Chapter 4: Robot Simulation with RoboSim, all section. If you have already introduced hardwired robots, introduce RoboSim and have students generate the Ch code using “Save Ch” on RoboBlockly and run in RoboSim.



Activity #4 Graphing Linear Equations with Robots: Key Features - Intercepts

Common Core State Standards - Mathematics: A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Objective: Students will demonstrate their knowledge of graphing linear equations in the coordinate plane by using a robot to graph a given linear function, by first solving for the x-&y-intercepts, and then having the robot draw the function through those points.


Initial Student Prompt Graphing Linear Equations

Identifying and using key features of a graph to graph a linear function.

Pre-Placed Blocks

Problem Statement Find the x-&y-intercepts of the linear equation 3x – 6y = 24. Then use the

drivexyTo() and trace blocks to have the robot graph the linear function, making sure to go through the intercepts.

Wrong Prompt I did not get to my destination. Please try again.

Hint The x-intercept is always when y = 0, and the y-intercept is always when x = 0.

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69;

robot.traceOff(); robot.drivexyTo(8, 0, radius, trackwidth); robot.traceOn(); robot.drivexyTo(0, -4, radius, trackwidth);



Activity #4 Graphing Linear Equations with Robots: Key Features - Intercepts Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m4.xml Student Mathematical Calculations Students need first solve for the x-&y-intercepts of the equation 3x—6y=24.

x-intercept is when y = 0 y-intercept is when x = 0 substitute y = 0 substitute x = 0 3x – 6(0) = 24 3(0) – 6y = 24 3x = 24 -6y = 24 x = 8 y = -4


a) Section 10.1 Move a Linkbot-I in a Coordinate System (drivexyTo block) b) Section 10.3 Trace the Positions of a Linkbot-I. (trace block)

Extension: Have students use a hardwired robot or RoboSim to practice running their “Save Ch” blocks.



Activity #5 Graphing Linear Equations with Robots: Using Slope & y-intercept

Common Core State Standards - Mathematics: A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Objective: Students will demonstrate their knowledge of graphing linear equations in the coordinate plane by using a robot to graph a given linear function, by identifying the slope and y-intercept of the given equation and using that information to find three additional points (solutions) on the line. They will then have the robot draw the function through those points.


Initial Student Prompt Graphing Linear Equations Graphing a line using slope & y-intercept

Pre-Placed Blocks

Problem Statement Given y = -2/3x + 6. Have the robot draw the line of the graph by

plotting a point and using the slope to find additional points. Your graph must go through the y-intercept and contain three additional points not including the y-intercept. The points should lie on both sides of the y-intercept (in Quadrant II and I)

Wrong Prompt You did not go through the y-intercept, and three additional points. Please try again.

Hint Remember when an equation is in slope-intercept form y = mx + b, m is the slope and b is the y-intercept. Slope is rise/run, and can be used to plot additional points

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.traceOff();

robot.drivexyTo(-3, 8, radius, trackwidth);

robot.traceOn();

robot.drivexyTo(0, 6, radius, trackwidth);





Activity #5 Graphing Linear Equations with Robots: Using Slope & y-intercept Picture of solution in RoboBlockly


Student Mathematical Calculations Students will need to use the slope and y-intercept to graph the linear equation y = -2/3x + 6. They need to know that when an equation is in slope-intercept form y = mx + b, m is the slope and b is the y-intercept. For y = -2/3x + 6 slope = -2/3 y-intercept = 6 To graph: Plot the y-intercept (0, 6)

From their use the slope to plot three additional points. They can either rise 2 and move left 3 OR fall 2 and move right 3.

Possible points: (3, 4) (-3, 8) and (6, 2) C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition





Activity #6 Graphing Systems of Linear Equations with Robots

Common Core State Standards - Mathematics: A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

*for this standard this activity introduces the concept using a system of inequalities that form a horizontal and vertical line – students are asked to identify a solution that would fall into the solution set, without graphing the lines.

Objective: Students will demonstrate their knowledge of solving & graphing linear equations in the coordinate plane by using a robot to graph the solution (point of intersection) of a given system.


Initial Student Prompt Modeling System of Linear Equations in a Coordinate Plane

This problem with involve solving systems of linear equations.

Pre-Placed Blocks

Problem Statement Drive the robot to the point (x, y) where x and y can be determined by

solving this system of linear equations 5x – 25 = 10 and 90x - 3y = 45.

Wrong Prompt I did not get to those two places. Please try again.

Hint Solve each equation by isolating the variable

Possible Solution in Ch in Ch

#include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.turnRight(90, radius, trackwidth); robot.driveDistance(7, radius); robot.turnLeft(90, radius, trackwidth); robot.driveDistance(15, radius);



Activity #6 Graphing Systems of Linear Equations with Robots Picture of solution in RoboBlockly


Student Mathematical Calculations

Students will need to solve each equation to find the point of intersection for {5𝑥 − 25 = 1090 − 3𝑦 = 45

5𝑥 − 25 = 10 → 5𝑥 = 35 → 𝑥 = 7 90 − 3𝑦 = 45 → −3𝑦 = −75 → 𝑦 = 15

The lines would intersect at the ordered pair (7, 15) students will drive the robot to that location. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition

a) Section 5.4 Move a Distance for a Two-Wheel Robot. (driveDistance block) b) Section 5.6 Turn Left and Turn Right. (turn block)




Activity #7 Graphing Systems of Linear Inequalities with Robots


A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.*

*for this standard this activity introduces the concept using a system of inequalities that form a horizontal and vertical line – students are asked to identify a solution that would fall into the solution set, without graphing the lines.

Objective: Students will demonstrate their knowledge of solving & graphing linear inequalities in the coordinate plane by using a robot to graph the solution (point of intersection) of a given system.


Initial Student Prompt Modeling Systems of Linear Inequalities in a Coordinate Plane

This problem will involve solving systems of linear inequalities. A linear inequality is like a linear equation except the ‘=’ is replaced by ‘<’, ‘>’, ‘<’, ‘>’ or ‘≠’.

Pre-Placed Blocks

Problem Statement Drive the robot to any coordinate pair (x, y) where x and y are restricted by

the inequalities -12x + 30 < -60 and 7y +30 ≤ 2y

Wrong Prompt I did not to a point (x, y) that is a solution for the given system of inequalities. Please try again.

Hint Use the same method as solving systems of linear equations. In systems of linear inequalities, a solution lies in the overlapping shaded region bound by the two linear inequalities. Note: Remember that dividing/multiplying by negatives inverts the inequality sign.

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.turnRight(90, radius, trackwidth); robot.driveDistance(8, radius); robot.turnLeft(90, radius, trackwidth); robot.driveDistance(6, radius);



Activity #7 Graphing Systems of Linear Inequalities with Robots Picture of solution in RoboBlockly


Student Mathematical Calculations

Students will need to solve each inequality to find the solution set bounded by {−12𝑥 + 30 < −60

7𝑦 + 30 ≤ 2𝑦

−12𝑥 + 30 < −60 → −12𝑥 < −90 → 𝑥 > 7.5 7𝑦 + 30 ≤ 2𝑦 → 30 ≤ −5𝑦 → −6 ≥ 𝑦

The solutions for the line x > 7.5 are any x-values larger than 7.5 The solutions for the line -6 > y are any y-values smaller or equal to -6. One possible solution (8, -6) C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition





Activity #8 Geometry: Area of Basic Shapes in Coordinate Plane


Objective: Students will apply their understanding of solving equations to Area formulas in order to solve for missing dimensions of a rectangle. They will then have a robot graph the rectangle in the coordinate plane using either specified distances or indicated ordered pairs that represent the vertices of the rectangle.


Initial Student Prompt Area of Rectangles Use your understanding of solving equations to solve for the length of the rectangle, and graph the shape.

Pre-Placed Blocks

Problem Statement Draw the rectangle whose area is 91 square units with a height of 7 units.

The bottom left vertex of the rectangle is at (0,0).

Wrong Prompt You did not draw the rectangle with those properties. Please try again.

Hint The formula for calculating the area of the rectangle is Area = Base * Height (or Area = Length * Width)

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.driveDistance(7, radius); robot.turnRight(90, radius, trackwidth); robot.driveDistance(13, radius); robot.turnLeft(90, radius, trackwidth); robot.driveDistance(7, radius); robot.turnRight(90, radius, trackwidth); robot.driveDistance(13, radius);



Activity #8 Geometry: Area of Basic Shapes in Coordinate Plane Picture of solution in RoboBlockly


Student Mathematical Calculations Area of a rectangle is A = b*h Students are given the area is 91 units and a height of 7 units. They will need to substitute in the given values and solve for the unknown base to draw the rectangle. A = b*h 91 = b*7 b = 13 units Now that students know they are drawing a rectangle with height of 7 and base length 13 they begin a the origin and either drive the robot forward those distances, turning right at each vertex OR they can find out the coordinates of the vertices and use the drivexyTo() to plot points. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition





Activity #9 Geometry: Area of Basic Shapes in Coordinate Plane


Objective: Students will apply their understanding of solving equations to Area formulas in order to solve for missing dimensions of a triangle. They will then have a robot graph the triangle in the coordinate plane using either specified distances or indicated ordered pairs that represent the vertices of the triangle.


Initial Student Prompt Area of Triangles

Use your understanding of solving equations to solve for the missing coordinates and graph the triangle.


Problem Statement Draw a right triangle with an area of 24 square units, with a hypotenuse equal to 10 units and one leg measuring 8 units. The legs of your triangle must remain on the x and y axes and the triangle must be graphing in Quadrant I.

Wrong Prompt I did not get the correct triangle. Please try again.

Hint The area of a triangle is Area = 1/2 (Base * Height). Solve for the missing values to determine the distance your robot needs to travel for each leg.

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.drivexyTo(0, 6, radius, trackwidth); robot.drivexyTo(8, 0, radius, trackwidth); robot.drivexyTo(0, 0, radius, trackwidth);



Activity #9 Geometry: Area of Basic Shapes in Coordinate Plane Picture of solution in RoboBlockly


Student Mathematical Calculations Area of a triangle can be calculated by A = bh/2. Students are given the area of 24, length of hypotenuse and one of the legs. Students will need to know which information to substitute appropriately into the area formula.

A = bh 24 = 8h/2 (since it’s a right triangle it doesn’t matter if 8 is the base or height) 48 = 8h 6 = h The height of the triangle is 6 units, the base is 8 units and the hypotenuse is 10 units. Students can now find the ordered pairs of the vertices to have the robot draw the triangle.


a) Section 10.1 Move a Linkbot-I in a Coordinate System (drivexyTo block)




Activity #10 Model & Calculate the Average Speed of a Robot in the Coordinate Plane


Objective: Students will apply their knowledge of solving equations to a real-world problem involving average speed of a robot over a set of specified intervals.


Initial Student Prompt Averages

Calculating the average speed of a robot to drive a total distance.


Problem Statement Drive Robot 1: 6 units in 3 seconds, then 4 units in 5 seconds, and finally 5 units in 2 seconds.

Instead of using those steps, make Robot 1 drive to the same destination using the average speed.

Wrong Prompt You did not calculate the average correctly. Please try again.

Hint Average speed = Total distance / Total time

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.setSpeed(1.5, radius); robot.driveDistance(15, radius);



Activity #10 Model & Calculate the Average Speed of a Robot in the Coordinate Plane

Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m10.xml Student Mathematical Calculations Students will need to use the formula Average Speed = total distance / total time. Calculate total distance and time traveled: Total distance = 6 units + 4 units + 5 units = 15 units Total time = 3 sec + 5 sec + 2 sec = 10 seconds Average Speed = 15 units / 10 seconds = 1.5 units per second Students now have all the information they need to plug their solution into RoboBlockly C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition

a) Section 9.1 Move a Two-Wheel Robot with the Specified Distance 9.1.1. (setSpeed block) b) Section 5.4 Move a Distance for a Two-Wheel Robot. (driveDistance block)

Extension:

a) Have students use a hardwired robot or RoboSim to practice running their “Save Ch” blocks. b) You can also use C-STEM Studio to access Ch Linkbot Controller with Single Vehicles Control to

display distance versus time graph with one robots.



Activity #11 Graphing Functions in the Coordinate Plane Given a Relation

Common Core State Standards - Mathematics: F.IF.1 Understand that a function from one set (called domain) to another set (called range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.The graph of f is the graph of the equation y = f(x).

Objective: Students will use a robot to model a given relation in the coordinate plane. They will plot the last point of the relation and use the robot to travel the path of the relation. Students can then determine if the relation is a function.


Initial Student Prompt Functions Graph a function from a given relation.

Pre-Placed Blocks

Problem Statement

Given: (

2356

) (

−36

−17

) of a function. Use the robot to draw the last point in

the relation and then connect the points of the function.

Wrong Prompt You did not draw the last relation of the function and connect all the points in the relation. Please try again.

Hint Use the robot to plot the last point (6, 7), tracing the distance from the x-axis to the ordered pair. The connect all the points of the relation using drivexyTo() blocks.



Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.traceOff(); robot.drivexyTo(2, 0, radius, trackwidth); robot.traceOn(); robot.drivexyTo(2, -3, radius, trackwidth); robot.traceOff(); robot.drivexyTo(3, 0, radius, trackwidth); robot.traceOn(); robot.drivexyTo(3, -1, radius, trackwidth); robot.traceOff(); robot.drivexyTo(5, 0, radius, trackwidth); robot.traceOn(); robot.drivexyTo(5, 6, radius, trackwidth); robot.traceOff(); robot.drivexyTo(6, 0, radius, trackwidth); robot.traceOn(); robot.drivexyTo(6, 7, radius, trackwidth); robot.drivexyTo(5, 6, radius, trackwidth); robot.drivexyTo(3, -1, radius, trackwidth); robot.drivexyTo(2, -3, radius, trackwidth);



Activity #11 Graphing Functions in the Coordinate Plane Given a Relation Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m11.xml Student Mathematical Calculations The students need to plot the remaining point of the relation show: (6, 7) Then they need to connect all the ordered pairs of the function: (6, 7) to (5, 6) to (3, -1) to (2, -3) C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition





Activity #12 Equations – Solving for Missing Values and Modeling their Solution


Objective: Students will apply their knowledge of solving equations to determine the distances two different robots need to travel, provided a rate in./sec. and then represent the paths traveled in the coordinate plane.


Initial Student Prompt Driving two robot to the same destination using different speeds for each robot. You will need to add a second robot for this problem. Each robot will have a different color set of blocks.


Problem Statement Drive the two robots forward to the line y = 5. Robot 1 will travel at a rate of 5 in/sec. Robot 2 will travel at a rate of 7 in/sec. Both robots need to finish at the line y = 15 and start at the same time.

Wrong Prompt You did not get the robots to the correct destination OR you did not start the robots at the same time. Please try again.

Hint Remember to use a non-blocking with post-fix NB for one of two robots. You will need to determine the distance from robot’s initial position and the line y = 5 to set the distance the robot needs to travel.

Possible Solution in Ch 1 #include <linkbot.h> CLinkbotI robot1; double radius1 = 1.75; CLinkbotI robot2; double radius2 = 1.75;

robot1.setSpeed(5, radius1); robot2.setSpeed(6, radius2); robot1.driveTimeNB(3); robot2.driveTime(2.5); robot1.moveWait();

Possible Solution in Ch 2 #include <linkbot.h> CLinkbotI robot1; double radius1 = 1.75; CLinkbotI robot2; double radius2 = 1.75; robot1.setSpeed(5, radius1); robot2.setSpeed(6, radius2);



robot1.driveDistanceNB(15, radius1); robot2.driveDistance(15, radius2); robot1.moveWait();



Activity #12 Equations – Solving for Missing Values and Modeling their Solution

Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m12.xml Student Mathematical Calculations Students need to determine the total distance both of the robots need to travel. They then need to calculate the velocity (driveTime) for each robot to ensure they start at the same time, and travel the same total distance. Since they are both starting when y = 0 (x-axis) they will travel 15 units. Robot 1: d = v*t 15 = v*5 v = 3 Robot 2: d = v*t 15 = v*6 v = 2.5 Students will need to remember to use a driveTimeNB() and moveWait() for the same robot to ensure they start at the same time.


a) Section 9.1 Move a Two-Wheel Robot with the Specified Distance 9.1.1. (setSpeed block) b) Section 12.5 Move Multiple Linkbots with Specified Distances or Joint Angles (driveDistance,

driveDistanceNB blocks and moveWait blocks) c) Section 12.7 Move Multiple Linkbots with Specifie Time (driveTime, driveTimeNB blocks and

moveWait blocks)

Extension: a) Have students use a hardwired robot or RoboSim to practice running their “Save Ch” blocks. b) You can also use C-STEM Studio to access Ch Linkbot Controller with Two Vehicles Control to

display distance versus time graph with two robots.



Activity #13 Initial Position – Modeling in the Coordinate Plane Common Core State Standards - Mathematics: A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Objective: Students will apply their knowledge of solving equations to determine the speeds for two different robots that must reach the same destination point. They will model the robot’s path traveled in the coordinate plane.


Initial Student Prompt Initial Position

Driving two robot to the same destination using different speeds, and a different initial position for each robot.

You will need two robots for this problem, and you will need to change the initial starting position of one of you robots.


Problem Statement Robot 1 will start at the origin and drive 18 units at a rate of 6 units/sec. Robot 2 will start at (6, -6) and travel at a rate of 6 units/sec. Both robots need to start at the same time, and robot 2 needs to end at the same place as robot 1.

Wrong Prompt You did not start the robots at the same time OR you did not get both robots to end at the same place. Please try again.

Hint Distance = speed * time. Use the control panel on the lower left to change the robot’s initial position.

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot1.setSpeed(6, radius1); robot2.setSpeed(6, radius2); robot1.driveDistanceNB(18, radius1); robot2.driveDistance(24, radius2); robot1.moveWait();



Activity #13 Initial Position – Modeling in the Coordinate Plane Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m13.xml Student Mathematical Calculations First students will need to change the initial position of robot 2, this can be done in the set-up section below the coordinate plane. Students will also have to change the degree of Robot 1 to 270 – this is likely something they will overlook so remind them to read the directions and think about how to move the robot from y = 18 to y = -3 without using a negative input for the driveDistance. For robot 1 students know the total distance and time – no calculations are needed for robot 1. For robot 2, students need to calculate the distance from y = -6 to y = 18 to ensure it ends at the same place as robot 1. Distance for robot 2 is |-6| + 18 = 24. They now can plug all the information in to solve the problem. Students will need to remember to use a driveDistanceNB() and moveWait() for the same robot to ensure they start at the same time. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5th edition


driveDistanceNB blocks and moveWait blocks) c) Section 12.7 Move Multiple Linkbots with Specifie Time (driveTime, driveTimeNB blocks and

moveWait blocks)





Activity #14 Initial Position and Initial Angle – Modeling in the Coordinate Plane


Objective: Students will apply their knowledge of solving equations to determine the speed and or distance needed for two different robots that must reach the same destination point. They will model the robot’s path traveled in the coordinate plane.


Initial Student Prompt Initial Position and Initial Angle

You will place two robots at different starting positions, and drive them towards each other, having them arrive to a destination at the same time.


Problem Statement Robot 1 will start at (0, 18) and is traveling at 7 units/sec. Robot 2 will start at (6, -9) and travel 6 units. Have the robots arrive at the line y = -3 at the same time.

Wrong Prompt Your robots did not arrive at the same time. Please try again.

Hint Distance = speed * time. Remember robots need to drive towards each other, make sure to turn Robot 1 the correct amount at its initial position.

Possible Solution in Ch #include <linkbot.h> CLinkbotI robot1; double radius1 = 1.75; CLinkbotI robot2; double radius2 = 1.75; robot1.setSpeed(7, radius1); robot2.setSpeed(2, radius2); robot1.driveDistanceNB(21, radius1); robot2.driveDistance(6, radius2); robot1.moveWait();



Activity #14 Initial Position and Initial Angle – Modeling in the Coordinate Plane Picture of solution in RoboBlockly

Location of Solution for “Load Blocks” C-STEM Studio -> Teaching Resources ->TeachIm1Alg1->RoboBlocklySolution->m14.xml Student Mathematical Calculations First students will need to change the initial position of both robots, this can be done in the set-up section below the coordinate plane. Robot 1 Calculate the total distance

Starting at y = 18 and ending at y = -3 |-3|+18 = 21 Total distance 21 units

Robot 2 Calculate the speed robot 2 needs to travel. Students will need to find the velocity of robot 1 to set robot 2 at the appropriate speed. Robot 1 -> d = vt, 20 = 7v, v = 3 Since robot 1 is traveling at v = 3 use that with the distance robot 2 is going to travel to find the appropriate speed for robot 2. d = vt, 6 = 3t, t = 2. Robot 2 needs to travel at a speed of 2 in/sec

They now can plug all the information in to solve the problem. Students will need to remember to use a driveDistanceNB() and moveWait() for the same robot to ensure they start at the same time.



driveDistanceNB blocks and moveWait blocks)



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