Linear and Non-Linear Graphs

Linear and Non-Linear Graphs

eWORKBOOK SEQUENCE

  • Student learning matrix
  • WorkSHEET: Linear and non-linear graphs I
  • WorkSHEET: Linear and non-linear graphs II
  • Word search
  • Code puzzle
  • Project
  • Thinking about my learning

Student Learning Matrix

  • A matrix to monitor learning progress throughout the topic.
  • Uses a traffic light system:
    • Green = I understand
    • Yellow = I can do it with help
    • Red = I do not understand
  • Includes sections for:
    • learnON Pre-test
    • 6.2 Plotting linear graphs
    • 6.3 The equation of a straight line
    • 6.4 Sketching linear graphs
    • 6.5 Technology and linear graphs
    • 6.6 Determining linear rules
    • 6.7 Practical applications of linear graphs
    • 6.8 Midpoint of a line segment and distance between two points
    • 6.9 Non-linear relations (parabolas, hyperbolas, circles)
    • WorkSHEET: Linear and non-linear graphs I
    • WorkSHEET: Linear and non-linear graphs II
    • Word search
    • Code puzzle
    • Project
    • Topic test
  • Areas for improvement

WorkSHEET: Linear and Non-Linear Graphs I

  1. Plotting points from a table of values and joining them with a straight line.
    • Given table of values for x and y, plot the points and connect them to form a line.
  2. Completing a table of values for the rule y = 3x, plotting the points, and forming a linear graph.

Calculating Gradient

  • Calculating the gradient of lines shown on a graph.

Stating Gradient

  • Stating the gradient of lines shown.

Finding Gradient (m) Between Two Points

  • Finding the gradient (m) of the line joining the points (1, 4) and (5, 9).
  • Finding the gradient (m) of the line joining the points (-3, 4) and (5, -6).

Finding Gradient from a Rule

  • Finding the gradient of the rule y = 7x + 2.
  • Finding the gradient of the rule 3x - 5y = 10.

Finding y-intercept

  • Finding the y-intercept of the rule y = 4x – 3.

Finding Gradient and y-intercept

  • Finding the gradient and y-intercept for the rule 2x + 3y – 6 = 0.

WorkSHEET: Linear and Non-Linear Graphs II

  1. Completing a table of values for the rule y = 2x + 2, plotting the points, and forming a linear graph.
  2. Sketching the graph of y = –4x – 9 using the gradient–intercept method.
  3. Drawing the graph of y = −4x – 9, for x = −20 to +20, without completing a table of values.
  4. Sketching the graph of y = 5x – 10 using the x- and y-intercept method.
  5. Sketching the graph of y = 6.
  6. Sketching the graph of x = −1.
  7. Determining the rule for the straight line whose x-intercept = 10 and y-intercept = –5.
  8. Determining the rule for the straight line with a gradient = −1.7 and which passes through the point (0.2, −1.8).
  9. Determining the rule for the straight line passing through (-4, 10) and (10, 38).
  10. Determining the linear rule for the line passing through the origin and through the point (-5, 12).

Word Search

  • A word search puzzle containing terms related to linear and non-linear graphs.
  • Terms include: Circle, Straight line, Gradient, Intercept, Hyperbola, Linear graphs, Line segment, Midpoint, Non-linear relations, Parabola, Plotting, Sketching, Vertical lines, Horizontal lines.

Code Puzzle

  • A code puzzle activity related to straight lines.
  • Find the required information relating to each of the following straight lines. The letters for each part of the questions and numbers beside the answers combine to solve the code.

Project: Path of a Billiard Ball

  • Mapping the path of a billiard ball using mathematics.
  • The billiard table is represented by a rectangle, and the ball's path by line segments.
  • Investigating the trajectory of a single ball, unobstructed by other balls.
  • A billiard table has a pocket at each of its corners and one in the middle of each of its long sides.
  • Consider the path of a ball that is hit on its side, from the lower left-hand corner of the table, so that it travels at a 45°angle from the corner of the table.
  • Assume that the ball continues to move, rebounding from the sides and stopping only when it comes to a pocket.
    1. How many times does the ball rebound off the sides before going into a pocket?
    2. For each table, determine the trajectory of a ball hit at 45° on its side, from the lower left-hand corner of the table. Draw the path each ball travels until it reaches a pocket.
    3. Which tables show the ball travelling through the simplest path? What is special about the shape of the tables?
    4. Which table shows the ball travelling through the most complicated path? What is special about the path? Draw another table (and path of the ball) with the same feature.
    5. Which tables show the ball travelling through a path that does not cross itself? Draw another table (and path of the ball) with the same feature.
    6. Will a ball hit on its side from the lower left-hand corner of a table at 45° always end up in a pocket (assuming it does not run out of energy)? Simplify matters a little and consider a billiard table with no pockets in the middle of the long sides. Look, in a systematic way, for patterns for tables whose dimensions are related in a special way.
    7. On paper, draw a series of billiard tables of length 3 m. Increase the width from an initial value of 0.25 m in increments of 0.25 m. Investigate the destination pocket of a ball hit from the lower left-hand corner. Complete the table below.
    8. How can you predict (without drawing a diagram) the destination pocket of a ball hit from the lower left- hand corner of a table that is 3 m long? Provide an illustration with your answer to verify your prediction.

Thinking About My Learning

  • Reflection questions about the learning process.
  • Includes questions like:
    • What new things did you learn?
    • What and/or who helped you with your learning?
    • What things did you already know about the topic before you started?
    • What made your learning difficult?
    • How could those difficulties be overcome next time?
    • What learning routines were the most helpful?