Learning Coding and Math with RoboBlockly Teaching Resource for Grade 7 Math

Transcription

1 Learning Coding and Math with RoboBlockly Teaching Resource for Grade 7 Math Harry H. Cheng UC Davis Center for Integrated Computing and STEM Education (C-STEM) Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October 2015

2 Learning Coding and Math with RoboBlockly Teaching Resource for Grade 7 Math 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 , IIS , IIS , and by the CaMSP Program of the California Department of Education. Additional Contributor(s): Kayce Mastrup Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

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

4 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 Grade 7 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: Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

5 Learning Coding and Math with RoboBlockly Teaching Resource for Grade 7 Math Table of Contents: Activity Description Activity CCSSM Blocks Used 1. Rational Numbers on a Coordinate Plane 7.NS1d 7.NS.2c 7.NS.2d drivedistance 2. Solving Equations: Modeling Ratios & Proportions Using Distance 7.EE.3 7.RP.2c drivedistance turn 3. Algebraic Expressions: Writing and Simplifying 7.NS.1 drivedistance 4. Algebraic Expressions: Modeling Solution in the Coordinate Plane 7.EE.3 7.RP.2c drivedistance turn 5. Graphing in the Coordinate Plane: Slope of a Line 7.RP.2a trace drivexyto drivedistance slope 6. Complementary and Supplementary Angles in the Coordinate Plane 7.G.5 drivedistance 7. Area in the Coordinate Plane 7.G.6 trace drivexyto area 8. Area in the Coordinate Plane 7.G.6 turn drivedistance 9. Geometry in the Coordinate Plane: Perimeter & Area 7.G.2 7.EE.2 turn drivedistance perimeter 10. Geometry in the Coordinate Plane 7.G.4 while loop drivedistance turn circumference area Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

6 Learning Coding and Math with RoboBlockly Teaching Resource for Grade 7 Math Standard Mapping Common Core State Standards for Mathematics Grade 7 7.NS.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Activities 3 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 1 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.2d Covert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.RP.2a Decide whether tow quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line thought the origin , RP.2c Represent proportional relationships by equations. 2, 4 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 7.G.6 Solve real-world and mathematical problems involving area, volume, surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms , 8 Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

7 Table of Contents: Textbook to Activity Alignment Learning Robot Programming with Linkbot for the Absolute Beginner 5 th Edition Section 5.4 Move a Distance for a Two-Wheel Robot Activities X X X X X X X X Section 5.5 Number Line for Distance Section 5.6 Turn Left and Turn Right X X X X X X X X X Section 10.1 Move a Linkbot-I in a Coordinate System X X Section 10.3 Trace the Positions of a Linkbot-I Appendix A.2 Use a While loop for Repeated Motions X X X X Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

8 Activity #1 Rational Numbers on a Coordinate Plane Common Core State Standards - Mathematics: 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.2d Covert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Objective: Students apply their understanding of operations with rational numbers to simplify an expression and model the solution with a robot in the coordinate plane. RoboBlockly Student Activity: Initial Student Prompt Rational Numbers on a Coordinate Plane. Rational numbers are numbers that can be expressed as a fraction of two integers. Pre-Placed Blocks Problem Statement Wrong Prompt Hint Possible Solution in Ch Drive the robot to y = (11/4 + 5)/(½). You did not drive the robot to the correct destination. Please try again. It is easier to work with numbers in the same form. Either change all numbers into fractions or all into decimals. #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.drivedistance (15.5, radius); Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

9 Activity #1 Rational Numbers on a Coordinate Plane Picture of solution in RoboBlockly Location of solution for Load Blocks tab in RoboBlockly C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m1.xml Student Mathematical Calculations Students will need to perform basic arithmetic to solve this problem using their understanding of working with rational numbers. It is best to convert numbers to either fraction with the same denominator or decimals. Decimal Method: y = (11/4 + 5) (1/2) 11 Convert fractions to decimals using division: = 2.75 and 1 = Simplify the expression using Order of Ops: y = ( ) 0.5 y = (7.75) 0.5 y = 15.5 Fractional Method: y = (11/4 + 5) (1/2) 5 = Convert decimals to fractions: and 0.5 = 1 = Simplify the expression using Order of Ops: y = (11/4 + 20/4) 2/4 y = (31/4) 2/4 y = *must convert for RoboBlockly y = 31 = C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition a) Section 5.4 Move a Distance for a Two-Wheel Robot. (drivedistance block) b) Section 5.5 Number Line for Distance (drivedistance block) Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

10 Activity #2 Solving Equations: Modeling Ratios & Proportions using Distances Common Core State Standards - Mathematics: 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.RP.2c Represent proportional relationships by equations. Objective: Students will translate a verbal equation involving rational numbers into mathematics and solve for the unknown value. They will then use RoboBlockly to model the solution in the coordinate plane. RoboBlockly Activity: Initial Student Prompt Ratios and Proportions. In this problem, we will be modeling ratios and proportions using distances. Pre-Placed Blocks None. Problem Statement In the previous activity, the robot drove a total of 15.5 units. This time, drive the robot 80% of the total distance up (along the y-axis). Then 20% of the total distance right (along the x-axis). Wrong Prompt You did not drive the robot correctly. Please try again. Hint You just need to calculate the distance the robot travels up and right according to the proportions. Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.drivedistance(12.4, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(3.1, radius); Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

11 Activity #2 Solving Equations: Modeling Ratios & Proportions using Distances Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m2.xml Student Mathematical Calculations Students will need to write and solve an equation given a proportional relationship. Total distance traveled = d = 15.5 units First move = a = 80% of d so, a/0.8 = 15.5, 15.5*0.8 = 12.4 Second move = b = 20% of 15.5 so, b/0.2 = 15.5, 15.5*0.2 = 3.1 Once students have solve for the two distances, they then need to determine which direction to drive the robot. By default the robot will move up first so the student will need to add a turn right block after the first distance traveled. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition a) Section 5.4 Move a Distance for a Two-Wheel Robot. (drivedistance block) b) Section 5.5 Number Line for Distance (drivedistance block) c) Section 5.6 Turn Left and Turn Right (turn 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. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

12 Activity #3 Algebraic Expressions: Writing and Simplifying Common Core State Standards - Mathematics: 7.NS.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Objective: Students will simplify an algebraic expression involving rational numbers and model the solution as a distance in the coordinate plane using RoboBlockly. RoboBlockly Activity: Initial Student Prompt Algebraic Expressions In this problem, you will simply algebraic expressions, Pre-Placed Blocks None. Problem Statement Drive the robot forward (4.5)^2 units and then backwards 225 units Wrong Prompt You did not drive the robot correctly. Please try again. Hint 4.5^2 is equivalent to 4.5 * 4.5. sqrt(225) is equivalent to solving x^2 = 225. Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.drivedistance(20.25, radius); robot.drivedistance(-15, radius); Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

13 Activity #3 Algebraic Expressions: Writing and Simplifying Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m3.xml Student Mathematical Calculations Students will need complete multiplication with decimal values. (4.5)^2 = 4.5*4.5 = Students will need to compute a square root of a three-digit number. To find the sqrt(225) students need to think what number times itself equals 225? they can begin by estimating: 10*10 = 100 and 20*20 = 400 so the number lies between 10 and 20. Most students know that 12*12 = 144 so the number must be larger than 12. Using other math facts they would assume to try 15*15 since 225 ends in a 5. 15*15 = 225 so the sqrt(225)=15. Students will also have to know that backwards on the y-axis means they need to use a -15. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition a) Section 5.4 Move a Distance for a Two-Wheel Robot. (drivedistance block) b) Section 5.5 Number Line for Distance (drivedistance block) Extension: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

14 Activity #4 Algebraic Equations: Modeling Solution in the Coordinate Plane Common Core State Standards - Mathematics: 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.RP.2c Represent proportional relationships by equations. Objective: Students will translate a real-world situation to a mathematical equation in order to solve for the total distance to have the robot travel in the coordinate plane. RoboBlockly Activity: Initial Student Prompt Algebraic Equations In this problem, we will model and solve algebraic equations Pre-Placed Blocks None. Problem Statement The robot drove forward 1/2 of the total distance, then turned right and travelled 25% of the total distance, and then moved an additional 7 units down. Write an equation for to solve for the total distance traveled in order to have the robot travel the path described above. Wrong Prompt You did not move the robot according to the problem statement. Please try again. Hint You can rewrite the problem as (½)*x + 25% of x + 7 = x. This can be further rewritten as.5x +.25x + 7 = x. Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.drivedistance(14, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(7, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(7, radius); Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

15 Activity #4 Algebraic Equations: Modeling Solution in the Coordinate Plane Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m4.xml Student Mathematical Calculations Students will gather the following information: Total distance = d First move is 1/2d Second move is 25%d Third move +7 units They would then write the problem as (½)*d + 25% of d + 7 = d 0.5d d + 7 = d 7 = 0.25d d = 28 After substitution they would get: Total distance = 28 units First move = (1/2)28 = 14 units Second move = 0.25*28 = 7 Third move = 7 Once students have solved for the distance of each move they then need to determine which direction to have the robot move (right/left). C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition a) Section 5.4 Move a Distance for a Two-Wheel Robot. (drivedistance block) b) Section 5.5 Number Line for Distance (drivedistance block) c) Section 5.6 Turn Left and Turn Right (turn block) Extension: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

16 Activity #5 Graphing in the Coordinate Plane: Slope of a Line Common Core State Standards - Mathematics: 7.RP.2a Decide whether tow quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line thought the origin. Objective: Given two ordered pairs, students will use the robot to graph the line that connects these points, then students will test for equivalent ratios between points to determine whether the graph is a straight line, they will substitute this ratio in as the value of the slope. RoboBlockly Activity: Initial Student Prompt Pre-Placed Blocks Slope of a Line In this problem, you will calculate the slope of a line from two points on the line. Problem Statement Wrong Prompt Hint Possible Solution in Ch Drive the robot from (-5, 10) to (9, 3). Enter the slope of the line created in the appropriate variable. You did not calculate the slope correctly. Please try again. Slope = (y2 - y1) / (x2 - x1), or Using the Slope triangle = Rise / Run #include <linkbot.h> double slope; CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.traceoff(); robot.drivexyto(-5, 10, radius, trackwidth); robot.traceon(); robot.drivedistance(7, radius); robot.drivexyto(9, 3, radius, trackwidth); slope = -0.5; Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

17 Activity #5 Graphing in the Coordinate Plane: Slope of a Line Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m5.xml Student Mathematical Calculations Students must use the appropriate blocks to drive the robot to the given points (-5, 10) and (9, 3). Students will then check for proportionality by comparing the slope. Student will physically count out the rise/run of the line. Starting at (-5,10) they count down 7 to get to y = 3, then the count to the right 14 to get to (9, 3). Therefore the slope is -7/14 which simplifies to -1/2 and in decimal form is -0.5 They should repeat this process for (-5, 10) and (-3, 9) proportional relationship graphically. (-5, 10) and (-1, 8) to show a C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition 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: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

18 Activity #6 Complementary and Supplementary Angles in the Coordinate Plane Common Core State Standards - Mathematics: 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. Objective: Students will apply their knowledge of solving equations to geometry in the coordinate plane, find the measurements of two supplementary angles and then one of them in the coordinate plane with a robot. RoboBlockly Activity: Initial Student Prompt Complementary and Supplementary Angles Complementary angles are a two angles that have a sum of 90 degrees. Supplementary angles are two angles that have a sum of 180 degrees. Pre-Placed Blocks None. Problem Statement Angle 1 and angle 2 are supplementary angles. Angle 1 measures 7x +35 degrees and Angle 2 measures 4x -72 degrees. Solve for each angle. Change the initial angle of the robot to graph angle 1, the positive x-axis will be one side of your angle, the robot will draw the other side of you angle, make it a distance of 12 units. Wrong Prompt You did not draw the angle according to the directions. Please try again. Hint Supplementary angles add up to 180 degrees. Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.drivedistance(12, radius); Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

19 Activity #6 Complementary and Supplementary Angles in the Coordinate Plane Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m6.xml Student Mathematical Calculations Given: Angle 1 = 3x + 35 and Angle 2 = 4x 72 Angle 1 & Angle 2 are supplementary angles Angle 1 + Angle 2 = 180 (3x + 35) + (4x 72) = 180 7x 37 = 180 7x = 217 x = 31 so, Angle 1 = 3(31) + 35 = 128 and Angle 2 = 4(31) 72 = 52 Students now need to change the initial angle of the robot to 128 degrees and use the drivedistance block to move the robot 12 units. The positive x-axis represents one side of the angle and the robot s path represents the other. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition a) Section 5.4 Move a Distance for a Two-Wheel Robot. (drivedistance block) Extension: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

20 Activity #7 Area in the Coordinate Plane Common Core State Standards - Mathematics: 7.G.6 Solve real-world and mathematical problems involving area, volume, surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Objective: Students will draw a trapezoid with a robot in the coordinate plane and then calculate the area by decomposing the shape right triangles and rectangles. RoboBlockly Activity: Initial Student Prompt Area of a Trapezoid Pre-Placed Blocks In this problem, you will draw a trapezoid and calculate its area. Problem Statement Connect the points (4,8), (10,8), (10,3) and (1,3) to form a trapezoid. Enter the area of the trapezoid in the appropriate variable. Wrong Prompt You did not follow instructions correctly. Please try again. Hint To find the area of the trapezoid decompose the shape into: right triangles and rectangles. Then find the sum of those areas. Area of a triangle is bh/2 and Area of a rectangle is lw. Possible Solution in Ch #include <linkbot.h> CLinkbotI robot; double radius = 1.75; robot.traceoff(); robot.drivexyto(4, 8, radius, trackwidth); robot.traceon(); robot.drivexyto(10, 8, radius, trackwidth); robot.drivexyto(10, 3, radius, trackwidth); robot.drivexyto(1, 3, radius, trackwidth); robot.drivexyto(4, 8, radius, trackwidth); area = 37.5; Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

21 Activity #7 Area in the Coordinate Plane Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m7.xml Student Mathematical Calculations Students will likely graph the trapezoid first. They will then break the trapezoid into two shapes: Right Triangle and a Rectangle. They will calculate the Area of each shape after the find count the dimensions using the coordinate grid, and the find the sum for their final solution. Right Triangle Rectangle Height = 5 units Length = 6 units Base = 3 units Width = 5 units Area = bb/2 = (5*3)/2 Area = l*w = 6*5 Area = 7.5 square units Area = 30 square units Total Area = = 37.5 square units. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition 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: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

22 Activity #8 Area in the Coordinate Plane Common Core State Standards - Mathematics: 7.G.6 Solve real-world and mathematical problems involving area, volume, surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Objective: Students will draw a trapezoid with a robot in the coordinate plane and then calculate the area by decomposing the shape right triangles and rectangles. RoboBlockly Activity: Initial Student Prompt Area of a Rectangle In this problem, you will use the area of the rectangle to draw the shape. Pre-Placed Blocks Problem Statement Wrong Prompt Hint Possible Solution in Ch A rectangle s area is 48 square units. The preplaced blocks draw one of its sides. Draw the rest of the rectangle. You did not draw the rectangle according to the specifications in the problem statement. Please try again. You need to solve the length of the rectangle because you are given the area and its width. A = l*w. #include <linkbot.h> CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.traceoff(); robot.drivedistance(5, radius); robot.traceon(); robot.drivedistance(12, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(4, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(12, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(4, radius); Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

23 Activity #8 Area in the Coordinate Plane Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m8.xml Student Mathematical Calculations Given rectangle Area = lw = 48 square units, and length = 12. Find the length of all the sides to draw the rectangle. Area = lw 48 = 12*w 4 = w Students will likely assume the first block of 5 units is the one of the dimensions for the rectangle. Have them run the code first to see that they traceoff block moved the rectangle up 5 units. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th edition a) Section 5.4 Move a Distance for a Two-Wheel Robot. (drivedistance block) c) Section 5.6 Turn Left and Turn Right (turn block). d) Section 10.3 Trace the Positions of a Linkbot-I. (trace block) Extension: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

24 Activity #9 Geometry in the Coordinate Plane: Perimeter & Area Common Core State Standards - Mathematics: 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed ling on the problem and how the quantities in it are related. Objective: Students will use the given area of a rectangle to solve for the dimensions and calculate the perimeter. RoboBlockly Activity: Initial Student Prompt Perimeter and Area of a Rectangle In this problem, you will use the area of the rectangle to find out the perimeter by setting up an equation to solve for unknown values. Pre-Placed Blocks Problem Statement Wrong Prompt Hint Possible Solution in Ch A rectangle s area is 108 square units. Its length is 3 times the width. Draw the rectangle when its bottom left corner is at (0,0) and enter its perimeter in the appropriate variable. You did not draw the rectangle and solve the perimeter. Please try again. You need to solve A = LW by substituting L = 3W. Then you can solve for the perimeter. #include <linkbot.h> double perimeter; CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; robot.drivedistance(6, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(18, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(6, radius); robot.turnright(90, radius, trackwidth); robot.drivedistance(18, radius); perimeter = 48; Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

25 Activity #9 Geometry in the Coordinate Plane Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m9.xml Student Mathematical Calculations Students will need to understand what it means to turn right or left in the coordinate plane considering the initial position of the robot. Students are given: Area = 108 square units Length = 3w Width = w Set up an equation to solve for w: A = w*l 108 = (3w)(w) 108 = 3w 2 36 = w 2 w = 6 so l = 18 Now calculate the perimeter: P = 2l + 2w = 2(18) + 2(6) = 48 units Student will then plug all the information into RoboBlockly to have the robot travel the perimeter of the rectangle. C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th 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) Extension: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

26 Activity #10 Geometry in the Coordinate Plane Common Core State Standards - Mathematics: 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Objective: Given the diameter of a circle, students will calculate the area and circumference and have the robot draw the image in the coordinate plane. RoboBlockly Activity: Initial Student Prompt Area and Circumference of a Circle Pre-Placed Blocks Problem Statement The preplaced blocks create a circle with a diameter of 10 units. Enter the circumference and area in the appropriate variables. Wrong Prompt You did not evaluate the circumference and area of the circle. Hint Circumference = 2 * PI * radius Area = PI * radius * radius You may use 3.14 for PI for your calculation. Possible Solution in Ch #include <linkbot.h> double circumference; double area; CLinkbotI robot; double radius = 1.75; double trackwidth = 3.69; int count; count = 0; while(count < 36) { robot.drivedistance(0.4358, radius); robot.turnright(10, radius, trackwidth); robot.drivedistance(0.4358, radius); count = count + 1; } circumference = 10 * M_PI; area = 25 * M_PI; Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October

27 Activity #10 Geometry in the Coordinate Plane Picture of solution in RoboBlockly Location of Solution for Load Blocks C-STEM Studio -> Teaching Resources ->TeachGrade7->RoboBlocklySolution->m10.xml Student Mathematical Calculations Students will use the area and circumference formula to calculate the total area and circumference of a circle with a diameter of 10 units. They will then need to plug this information into RoboBlockly to check their solution. Area of a Circle = πr 2 Area of a Circle = π(5) 2 Area of a Circle = 25π Circumference of a Circle = 2πr OR πd Circumference of a Circle = π10 C-STEM text alignment: Robot Programming with Linkbot for the Absolute Beginner, 5 th 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) Extension: Connect Linkbots from a Computer have students move a hardwired robot by generating the Ch code using Save Ch on RoboBlockly. Copyright 2015, UC Davis C-STEM Center DRAFT Version 1 Released October