Algebra 1 Mrs. Blake B256 Mini-Golf Course Description Guidelines for your creation: 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. 2. On the graph paper itself, label the coordinates of the corner points (intersections of walls). 3. The goal is to get a hole-in-one. Show the route on the graph paper (label those points, too). Make sure the route is clear. (We re assuming that there is no friction and that the ball will travel until it reaches the hole.) 4. Curves in the courses are allowed but, the ball must always hit a flat segment of the course. 5. You may add any extra structures as long as you first meet the basic design criteria below. 6. Once you have drawn your plans, and they have been OK d by me, you may commence construction. We will create each hole using green felt, poster board, glue, etc. A marble will serve as the ball. Course Design Criteria: 1. The course must have at least 8 sides, but not more than 20 segments. 2. Have at least 8, but not more than 13 checkpoints where the ball bounces off a side wall or blocker. The tee and the hole also are checkpoints. (This is the theoretical route of the ball!) 3. Have at least 1 but no more than 3 blockers that deflect the ball at the same angle that it hit it. Blockers should have a minimum width of one square on the graph paper. (A blocker is like a structure built in the middle of a course.) 4. Have at least 1 but no more than 3 obstacles (tunnels, ramps, sand traps, water hazards). 5. When you create your plans, be sure to label a scale (1 inch on graph paper = inches on poster board model). Also be sure to use color coding for the special structures (blockers & obstacles). 6. The more variety in slopes and angles, the higher your grade! 7. The ball must always hit the side, blocker, obstacle, or ramp at the intersection of grid lines on the graph paper.
Dotty Blake PDP s Request The Tufts Pre-College Engineering for Teachers (PCET) Workshop that I participated in last summer was a two-week, 80-hour course designed to help teachers infuse engineering into classroom activities and meet the new Massachusetts State Engineering/Technology frameworks. This aligns with district goals and my individual professional development plan to improve student learning and align class work with MA curriculum frameworks. Attached are the course goals and syllabus for the two-week workshop and my project packet with evaluation rubric. Outside course work involved designing a project to incorporate into the curriculum that involved the engineering design process identify the problem, research the problem, develop possible solutions, select a solution, construct a prototype, test/evaluate solution, share the solution, redesign. I developed a mini-golf hole project for my Algebra 1 Level 3 sections. I gave each student a packet with design criteria, a sample design, notes on how to do calculations for slope and linear equations, a table to fill out for the line segments of the theoretical hole-inone path of the ball, and a grading rubric for the entire project. Each student received a 22 x 28 poster board, an 18 x 24 piece of green felt, and toilet paper or paper towel tubes, if needed for tunnels. This project involves a substantial amount of design and redesign for the students as they try to meet design criteria and simplify the linear equations for the path of the ball. Each student must design his/her mini-golf hole on graph paper, complete with blockers, tunnels and other obstacles, and create the theoretical hole-in-one path of the ball such that each angle of incidence equals the angle of reflection. On the graph paper design, the student must label the x- and y-axes, and all coordinates at course corners, blockers and obstacles, and endpoints of each segment ball s path. They must label the scale ratio of the graph paper design to the poster board model. After the students finished building their models, they paired up and played a round of mini-golf on fellow classmates mini-golf holes using a large wooden popsicle stick and a small marble for a golf club and ball. Each student was required to turn in their packet complete with score sheet, the hole design on graph paper, the spreadsheet of segment angles, slopes, and linear equations, and a short journal entry of their experience with the project. Grading was based on the evaluation rubric given to each student in the mini-golf design packet. I incorporated this project right after mid-year exams, at the conclusion of chapters 4 and 5 in the Algebra 1 text that covers graphing and writing equations of lines. I believe this is a tough but doable project for level 3 Algebra 1 students, and that they are forced to learn how to determine slope of a line and write the equation for that line. It also teaches them how to use a protractor, how to scale a design, and how important keeping things simple is when the imagination wants to run away with them! Many students modified their initial sketches of their course design when they realized they could not meet the design criteria for the theoretical hole-in-one path of the ball. They also learned how to adjust the angle of the blocker or obstacle to force the path of the ball to go where they wanted it to go. This aided in making sure that segment endpoints of the ball s path were integers and thus easier to calculate the slope and equation of the line. I think this project is a valuable lesson in how engineering design and math relate in the real world. It applies a substantial amount of the Algebra 1math concepts and the students were very motivated when working on their own, given specific guidelines and criteria to follow. Many stated in their journal entries that they learned a lot about designing and keeping things simple, how to write equations of lines, and had a lot of fun with the building and playing of the models.
Algebra 1 Mrs. Blake B256 Mini-Golf Course Description Guidelines for your creation: 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. 2. On the graph paper itself, label the coordinates of the corner points (intersections of walls). 3. The goal is to get a hole-in-one. Show the route on the graph paper (label those points, too). Make sure the route is clear. (We re assuming that there is no friction and that the ball will travel until it reaches the hole.) 4. Curves in the courses are allowed but, the ball must always hit a flat segment of the course. 5. You may add any extra structures as long as you first meet the basic design criteria below. 6. Once you have drawn your plans, and they have been OK d by me, you may commence construction. We will create each hole using green felt, poster board, glue, etc. A marble will serve as the ball. Course Design Criteria: 1. The course must have at least 8 sides, but not more than 20 segments. 2. Have at least 8, but not more than 13 checkpoints where the ball bounces off a side wall or blocker. The tee and the hole also are checkpoints. (This is the theoretical route of the ball!) 3. Have at least 1 but no more than 3 blockers that deflect the ball at the same angle that it hit it. Blockers should have a minimum width of one square on the graph paper. (A blocker is like a structure built in the middle of a course.) 4. Have at least 1 but no more than 3 obstacles (tunnels, ramps, sand traps, water hazards). 5. When you create your plans, be sure to label a scale (1 inch on graph paper = inches on poster board model). Also be sure to use color coding for the special structures (blockers & obstacles). 6. The more variety in slopes and angles, the higher your grade! 7. The ball must always hit the side, blocker, obstacle, or ramp at the intersection of grid lines on the graph paper.
Math Work: 1. Label on the graph paper, using ordered pairs, showing the path of the ball and the corners of the walls on the course design. Also, label the ball s path with letters starting with A at the tee. Using a protractor, label all of the angles of incidence on the ball s route and be sure it equals the angle of reflection. We will learn how to use a protractor correctly. 2. Fill in the spread sheet showing the legs of the path of the ball in order to theoretically get a hole-in-one. This would be the same as the checkpoints the 7 12 different segments of the ball s route ( AB, BC, CD,... ). 3. The spreadsheet asks for angles, slopes, and equations of lines. We will fill this in over the course of the project. You will find the slope m (rise/run) for each segment of the ball s route, and calculate b (y-intercept) for each segment to write the equation of the line in y = mx + b form. Evaluation: 1. The spreadsheet (accuracy, neatness, thoroughness). 2. The graph paper plan (covers all four quadrants, corners labeled with coordinates, route of ball clearly marked with letters and coordinates, extras coded, a scale for the model, correctness of angles, variety of the angles, neatness, and creativity). 3. The constructed course model (true to plan, neatness, creativity, and workability). 4. The score sheet filled in completely with name of players, scores tallied for each, and over or under par calculated based on par for holes played. 5. The reflection journal entry (Self-assessment: What did you learn or discover? What were your frustrations and successes? Any suggestions for another year?). Accurate spelling, grammar, thoroughness, and neatness will be assessed. 6. Certainly, the more math and science/engineering you employ and explain, the more impressive the project! Conclusion: Yes, we will test all of the courses by playing a tourney!
Tunnel y-axis Blocker (-8. 13) B (2, 13) (10,13) (-6, 10) Tee (-1, 10) (4, 9) (6, 9) C (-6, 9) A (10, 9) (6, 7) D E (-8, 5) (0, 5) (4, 5) (6, 5) (10, 5) F (4, 0) (6, 0) (0, 0) x- axis (4, -2) G H (0, -4) (4, -4) (6, -4) (-8, -8) (0, -8) Ho le K (-6,-11) (2, -12) (7, -12) I (10,-9) (-8, -14) J (0, -14) (10,-14) Mini-Golf Course Incidence = Reflection Scale: 1:2 Inches
Slope and Equation of Lines Notes 1) Plot the points on a piece of graph paper. 2) Create a right triangle using the grid of the graph paper. 3) Count the blocks that create each leg. 4) Remember rise over run, and positive and negative correlations if the line falls from left to right it s a negative slope, if it rises from left to right it s a positive slope. 5) The slope is a fraction made by the difference of the y-coordinates over the difference of the x-coordinates at the end points of each line segment. Remember, no decimals in fractions and reduce to simplest form. 6) Find the y-intercept of the line by using the slope and the x- and y- values from one of the endpoints of the line segment and plugging them into the equation y = mx + b and solving for b (or solve for b in terms of y, x, and m by transforming y = mx + b into b = y mx).
Spreadsheet to Record Ball s Hole-In-One Course Criteria 1. Name the legs of the ball s route by letters ( AB, BC, CD, DE, EF, FG, GH,... ). 2. Find the angle of incidence at the end of each leg in degrees (using a protractor). 3. Write the slope as a reduced fraction of rise over run (No decimals in fractions!). 4. Calculate the equation of the line for each leg of the ball s route in y = mx + b (slopeintercept) form. A B C D Angle created with Slope of leg (relative wall or obstacle to coordinate plane) Leg of ball s route (letters of endpts.) Equation of line y = mx + b AB m = y = x + BC
Mini-golf Evaluation Spread Sheet (15 Points) Point Value Leg segments labeled correctly (sequential letters with bar on top) 2 Angles (angle of incidence at the end of each leg segment) 3 Slopes (as reduced fractions or whole # s - positive or negative!) 3 Equations of lines ( y = mx + b ) 3 Accuracy 2 Thoroughness 1 Neatness 1 Graph (15 Points) Course corners labeled as ordered pairs (x,y) 2 Theoretical path of the ball clearly marked with letters and coordinates 2 Angle of Incidence = Angle of Reflection, labeled correctly 3 Variety of Angles ( >3 = 3 pts.; 3 = 2 pts.; 2 = 1 pt.; 1 = 0 pts.) 3 Extras blockers, tunnels, obstacles clearly marked 1 Quadrants drawn and x- and y- axes labeled 1 Scale noted in relation to constructed model (Ex: 1 in.(4 squares) = 2 in.) 1 Neatness 2 Constructed Model (10 Points) Accuracy to plans for course and obstacle dimensions & placement 3 Tee marked and labeled 1 Hole marked, cut out, and labeled 1 Variety of Extras blockers, tunnels, obstacles 3 Neatness 2 Score Sheet (5 Points) Filled in completely (as possible) with names of players 2 Scores tallied in both columns 2 Over par or under par score calculated 1 Journal Entry reflecting upon the unit your accomplishments, frustrations, what you learned, what you are more curious about, etc. (5 Pts.) Completed 2 Complete sentences (grammar, punctuation, spelling) 1 Thoroughness 1 Neatness 1 Points Earned Comments Final Grade:
Blake s Putt-Putt Hole Par Player #1 Player #2 Hole Designer Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total: Pts. Over/Under Par
Math Work: 1. Label on the graph paper, using ordered pairs, showing the path of the ball and the corners of the walls on the course design. Also, label the ball s path with letters starting with A at the tee. Using a protractor, label all of the angles of incidence on the ball s route and be sure it equals the angle of reflection. We will learn how to use a protractor correctly. 2. Fill in the spread sheet showing the legs of the path of the ball in order to theoretically get a hole-in-one. This would be the same as the checkpoints the 7 12 different segments of the ball s route ( AB, BC, CD,... ). 3. The spreadsheet asks for angles, slopes, and equations of lines. We will fill this in over the course of the project. You will find the slope m (rise/run) for each segment of the ball s route, and calculate b (y-intercept) for each segment to write the equation of the line in y = mx + b form. Evaluation: 1. The spreadsheet (accuracy, neatness, thoroughness). 2. The graph paper plan (covers all four quadrants, corners labeled with coordinates, route of ball clearly marked with letters and coordinates, extras coded, a scale for the model, correctness of angles, variety of the angles, neatness, and creativity). 3. The constructed course model (true to plan, neatness, creativity, and workability). 4. The score sheet filled in completely with name of players, scores tallied for each, and over or under par calculated based on par for holes played. 5. The reflection journal entry (Self-assessment: What did you learn or discover? What were your frustrations and successes? Any suggestions for another year?). Accurate spelling, grammar, thoroughness, and neatness will be assessed. 6. Certainly, the more math and science/engineering you employ and explain, the more impressive the project! Conclusion: Yes, we will test all of the courses by playing a tourney!
Tunnel y-axis Blocker (-8. 13) B (2, 13) (10,13) (-6, 10) Tee (-1, 10) (4, 9) (6, 9) C (-6, 9) A (10, 9) (6, 7) D E (-8, 5) (0, 5) (4, 5) (6, 5) (10, 5) F (4, 0) (6, 0) (0, 0) x- axis (4, -2) G H (0, -4) (4, -4) (6, -4) (-8, -8) (0, -8) Ho le K (-6,-11) (2, -12) (7, -12) I (10,-9) (-8, -14) J (0, -14) (10,-14) Mini-Golf Course Incidence = Reflection Scale: 1:2 Inches
Slope and Equation of Lines Notes 1) Plot the points on a piece of graph paper. 2) Create a right triangle using the grid of the graph paper. 3) Count the blocks that create each leg. 4) Remember rise over run, and positive and negative correlations if the line falls from left to right it s a negative slope, if it rises from left to right it s a positive slope. 5) The slope is a fraction made by the difference of the y-coordinates over the difference of the x-coordinates at the end points of each line segment. Remember, no decimals in fractions and reduce to simplest form. 6) Find the y-intercept of the line by using the slope and the x- and y- values from one of the endpoints of the line segment and plugging them into the equation y = mx + b and solving for b (or solve for b in terms of y, x, and m by transforming y = mx + b into b = y mx).
Spreadsheet to Record Ball s Hole-In-One Course Criteria 1. Name the legs of the ball s route by letters ( AB, BC, CD, DE, EF, FG, GH,... ). 2. Find the angle of incidence at the end of each leg in degrees (using a protractor). 3. Write the slope as a reduced fraction of rise over run (No decimals in fractions!). 4. Calculate the equation of the line for each leg of the ball s route in y = mx + b (slopeintercept) form. A B C D Angle created with Slope of leg (relative wall or obstacle to coordinate plane) Leg of ball s route (letters of endpts.) Equation of line y = mx + b AB m = y = x + BC
Mini-golf Evaluation Spread Sheet (15 Points) Point Value Leg segments labeled correctly (sequential letters with bar on top) 2 Angles (angle of incidence at the end of each leg segment) 3 Slopes (as reduced fractions or whole # s - positive or negative!) 3 Equations of lines ( y = mx + b ) 3 Accuracy 2 Thoroughness 1 Neatness 1 Graph (15 Points) Course corners labeled as ordered pairs (x,y) 2 Theoretical path of the ball clearly marked with letters and coordinates 2 Angle of Incidence = Angle of Reflection, labeled correctly 3 Variety of Angles ( >3 = 3 pts.; 3 = 2 pts.; 2 = 1 pt.; 1 = 0 pts.) 3 Extras blockers, tunnels, obstacles clearly marked 1 Quadrants drawn and x- and y- axes labeled 1 Scale noted in relation to constructed model (Ex: 1 in.(4 squares) = 2 in.) 1 Neatness 2 Constructed Model (10 Points) Accuracy to plans for course and obstacle dimensions & placement 3 Tee marked and labeled 1 Hole marked, cut out, and labeled 1 Variety of Extras blockers, tunnels, obstacles 3 Neatness 2 Score Sheet (5 Points) Filled in completely (as possible) with names of players 2 Scores tallied in both columns 2 Over par or under par score calculated 1 Journal Entry reflecting upon the unit your accomplishments, frustrations, what you learned, what you are more curious about, etc. (5 Pts.) Completed 2 Complete sentences (grammar, punctuation, spelling) 1 Thoroughness 1 Neatness 1 Points Earned Comments Final Grade:
Blake s Putt-Putt Hole Par Player #1 Player #2 Hole Designer Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total: Pts. Over/Under Par