**Grade 9 Math**

**David Weiss, Ontario, Canada**

**CHAPTER FIVE EXPECTATIONS**

- construct tables of values, graphs, and formulas to represent linear relations derived from descriptions of realistic situations (e.g., the cost of holding a banquet in a rented hall is $25 per person plus $975 for the hall);

- construct tables of values and scatter plots for linearly related data collected from experiments (e.g., the rebound height of a ball versus the height from which it was dropped) or from secondary sources (e.g., the number of calories in fast food versus the number of grams of fat);

- determine the equation of a line of best fit for a scatter plot, using an informal process (e.g., a process of trial and error on a graphing calculator; calculation of the equation of the line joining two carefully chosen points on the scatter plot);

- construct tables of values and graphs to represent non-linear relations derived from descriptions
of realistic situations (*Sample problem*: A triangular prism has a height of 20 cm and a square
base. Represent the relationship between the volume of the prism and the side length of its base,
as the side length varies);

- construct tables of values and scatter plots for non-linearly related data collected from experiments (e.g., the relationship between height and age) or from secondary sources (e.g., the population of Canada over time); sketch a curve of best fit;

- demonstrate an understanding that straight lines represent linear relations and curves represent non-linear relations.

- determine values of a linear relation by using the formula of the relation and by interpolating or extrapolating from the graph of the relation (e.g., if a student earns $5/h caring for children, determine how long he or she must work to earn $143);

- describe, in written form, a situation that would explain the events illustrated by a given graph of a relationship between two variables (e.g., write a story that matches the events shown in the graph);

- identify, by calculating finite differences in its table of values, whether a relation is linear or non-linear;

- describe the effect on the graph and the formula of a relation of varying the conditions of a
situation they represent (e.g., if a graph showing partial variation represents the cost of producing
a yearbook, describe how the appearance of the graph c changes if the cost per book is altered;
describe how it changes if the fixed costs are altered).

CHAPTER FIVE

LINEAR & NON-LINEAR RELATIONS

Section | Title | Homework |

5.1 | Relations as Ordered Pairs | pp. 243-245 #2-5 (all) #10-13 (all), |

5.2 | Graphing Ordered Pairs | pp. 248-249 #1-29 (odd), #32-35 |

5.3 | Graphing Linear Relations | pp. 252-253 #1-6 (all), #8-10 (all) |

5.4 | Graphing Linear Equations | pp. 257-258 #1-15 (odd), #22, 24, 26 |

5.5 | Direct and Partial Variation | pp. 265-267 #1-11 (odd), #18, 20, 23, 26, 28 |

Technology | Finding the Equation of a Line | p. 268 (all) |

5.6 | Equations of Lines of Best Fit | pp. 271-274 #2 (all), 5 (all), 7 (all), 8 (all), 9 (all) |

5.7 | Non-Linear Relations | pp. 277-279 #1-2, #7-9 (all) |

Investigating Math | Finite Differences | p. 281 (all) |

5.8 | General Relations | pp. 283-285 #1-4 (all), #6 (all), #8 (all) |

Review | pp. 290-292 |

**Name: _________________________________**

**CHAPTER FIVE: LINEAR & NON-LINEAR RELATIONS**

Level |
What |
How
Many
Points |
My Score |

C
Maximum
# points: 65 |
Listen to the lecture and take notes | 5 /day | |

Read 5.1 and 5.2 and do assigned questions | 10 | ||

Read 5.3 and 5.4 and do assigned questions | 10 | ||

Read 5.5, p. 268, and 5.6 and do assigned questions | 10 | ||

Read 5.7, pp. 280 - 281, and 5.8 and do assigned questions | 10 | ||

Mental Math p. 237 |
5 | ||

Pattern Power p. 267 |
5 | ||

Sample Quiz | 10 | ||

Flash Cards | 10 | ||

Study Notes | 10 | ||

Journalling (Choose one of three topics from website) | 5 | ||

Mind Map | 10 | ||

B |
Investigating Math pp. 238 - 239 | 15 | |

5.9 Modelling Math - Sports pp. 288 - 289 | |||

Website Review | |||

A
CHOOSE
ONE |
Exploring Math p. 291 | 20 | |

Challenge Problems (download from website) | |||

Research Paper: The Invention of the Cartesian Coordinate System |

TOTAL NUMBER OF POINTS |