por Amanda Hinz 4 anos atrás
261
Mais informações
Division
Addition/multiplication
Script: The students knew that we could get -1/3 for the slope
"we know that the slope will be: - 1/3"
Perpendicular Lines (how to): Youtube Video. Retrieved January 28, 2020 from: (https://www.youtube.com/watch?v=0671cRNjeKI)
"demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);" http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
"developandapplyreasoningskills(e.g.,recognitionofrelationships,generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;" http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
Connecting
"makeconnectionsamongmathematicalconceptsandprocedures,andrelatemathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);" http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
Students used prior knowledge of slopes/negative and positive numbers in order to reflect on "how" they knew what next steps to take.
"Students used prior knowledge of slopes/negative and positive numbers in order to reflect on "how" they knew what next steps to take."
Communicating
"inductive reasoning. The process of reach- ing a conclusion or making a generalization on the basis of specific cases or examples." http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
Problem solving
"develop,select,apply,andcompareavarietyofproblem-solvingstrategiesastheyposeand solve problems and conduct investigations, to help deepen their mathematical under- standing;"http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
"slope. A measure of the steepness of a line, calculated as the ratio of the rise (vertical change between two points) to the run (hori- zontal change between the same two points)."http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
"Figure 1. Example of positive and negative slops on a graph. Plotting the points on the x and y axis to display the slopes intersecting. January 28, 2020 Retrieved from: (https://www.google.com/search?q=intersecting+slopes+in+math&source=lnms&tbm=isch&sa=X&ved=2ahUKEwij8OmwsKfnAhWrhOAKHTZ-BYMQ_AUoAXoECA0QAw&biw=1280&bih=698#imgrc=vF0PmoszlJStYM)"
"Figure 2. Example of graph to plot the points on the x and y axis. Retrieved January 28, 2020 from: (https://www.algebra.com/algebra/homework/Linear-equations/Linear- equations.faq.question.102253.html)"
"Figure 3. Example of positive slope on a graph plotted on the x and y axis. Retrieved January 28, 2020 from: https://www.google.com/search?q=slope+in+math&source=lnms&tbm=isch&sa=X&ved=2ahU KEwjugYLGu6znAhXHPM0KHVX6AJoQ_AUoAXoECA4QAw&biw=1280&bih=698#imgrc =IIZqz04OEHgVPM"
"Figure 4. Example of the final graph of the equation y= -1⁄3 x + 4.33."
Graph
"mathematical modelling. The process of describing a situation in a mathematical form. See also mathematical model."http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
"coordinate plane. A plane that contains an x-axis (horizontal) and a y-axis (vertical), which are used to describe the location of a point. Also called Cartesian coordinate grid or Cartesian plane."http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
"I started by putting in the known coordinates for “m” and multiply by the “x” number."
planningskills (e.g.,understandingtheproblem,makingaplanforsolvingtheproblem) processingskills (e.g.,carryingoutaplan,lookingbackatthesolution) critical/creativethinkingprocesses (e.g.,inquiry,problemsolving) http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
Students were asked to think about their prior knowledge about slopes, etc prior to solving the problem.
"S2: I think that two lines intersect to make two right angles. Is that right?"
"T: First, it is important that we consider what we already know. Can we come up with some prior knowledge that we all might have regarding perpendicular lines and slopes?"
"Location and Movement By the end of Grade 8, students will: – graph the image of a point, or set of points, on the Cartesian coordinate plane after applying a transformation to the original point(s) (i.e., translation; reflec- tion in the x-axis, the y-axis, or the angle bisector of the axes that passes through the first and third quadrants; rotation of 90°, 180°, or 270° about the origin); – identify, through investigation, real-world movements that are translations, reflec- tions, and rotations." http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
"S1: I learned that a positive slope is y=mx + b and a negative slope is y= 1/m x + b."
Slope
