TIPS4Math
Modelling Linear Relationships
Grade 9 Applied
Overall Expectations
Students will:
• demonstrate an understanding of constant rate of change and its connection to linear relations (LRV.03)
• connect various representations of a linear relation, and solve problems using the representations (LRV.04)
Specific Expectations
Students will:
• determine, through investigation, that the rate of change of a linear relation can be found by choosing any two points on the line
that represents the relation, finding the vertical change between the points (i.e., the rise) and the horizontal change between the
points (i.e., the run), and writing the ratio rise/run (i.e. rate of change = rise/run) (LR3.01)
• determine, through investigation, connections among the representations of a constant rate of change of a linear relation (LR3.02)
• compare the properties of direct variation and partial variation in applications, and identify the initial value (LR3.03)
• express a linear relation as an equation in two variables, using the rate of change and the initial value (LR3.04)
• describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation (LR3.05)
• describe a situation that would explain the events illustrated by a given graph of a relationship between two variables (LR4.02)
• describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the
situation they represent are varied (LR4.05)
Lessons:
•
•
•
•
Graphs Tell Stories
Rate of Change
Linear Growing Patterns
Direct and Partial Variation
EduGAINS-Mathematics
Page 1 of 9
TIPS4Math
Specific Expectations: LR4.02, LR4.05
Learning Focus
•
•
•
•
•
Make connections between the
steepness of a line segment and the
speed of an object described in a story
Make connections between the
direction an object is travelling and
information shown on a two-variable
graph
Make connections between the
starting position of an object and
information shown on a two variable
graph
Create a two variable graph including
titles, labels and scales from a story
that represents a real life situation
over a period of time
Write a story representing a real life
situation over a period of time that
relates to the various linear and
non-linear parts of a graph
EduGAINS-Mathematics
Graphs Tell Stories
Blended Learning
Unit 5 Activity 1: Graphs Tell Stories
o OERB Resource ID: ELO1465900
Investigation
• Mellow Yellow Interpreting Graphs.gsp
Videos
• Texas Instruments CBR 2 Motion Detector
• Movie Theatre Graph
• Movie Theatre Graph 2
• Movie Theatre Graph 3
• Features of a Good Two-Variable Graph
Grade 9 Applied
Other Resources
TIPS4RM
• Unit 5 Day 1: Match Me!
• Unit 5 Day 2: Story Graphs
Desmos
• Polygraph: Distance-Time
Homework Help
• Cartesian Grid
OERB
• Battleship Game
o ELO1241280
Gap Closing I/S
• Module 4 Proportional
Reasoning: Facilitator’s Guide
o Diagnostic questions 3, 8, 10,
11
• Module 4 Proportional
Reasoning: Student Book
o Pages 6-17
Page 2 of 9
Specific Expectations: LR 3.01, LR 3.02
Learning Focus
•
•
•
Calculate the rate of change of a linear
relationship
Make connections between the rate of
change and the steepness of a ramp
or hill
Represent the rate of change as a
fraction, percent or decimal
Rate of Change
Blended Learning
Unit 5 Activity 2: Rate of Change
o OERB Resource ID: ELO1465910
Presentation
• Rate of Change
Investigation
• Distance-Time Graph Gizmo
Video
•
Zak the Tiny Skateboarder
EduGAINS-Mathematics
Other Resources
TIPS4RM
• Unit 5 Day 3: Ramps, Roofs, and
Roads
• Unit 5 Day 4: Models of
Movement
• Unit 5 Day 5: Story Graphs
Gap Closing I/S
• Module 4 Proportional
Reasoning: Facilitator’s Guide
o Diagnostic questions 7 - 9
• Module 4 Proportional
Reasoning: Student Book
o Pages 12 - 17
Page 3 of 9
Linear Growing Patterns
Specific Expectations: LR2.02, LR3.04
Learning Focus
•
•
•
•
Identify a linear growing pattern
Determine the initial value and
growing part of a linear growing
pattern
Represent a linear growing pattern
using a graph
Represent a linear growing pattern
using an equation
Blended Learning
Other Resources
Unit 5 Activity 3: Linear Growing Patterns
o OERB Resource ID: ELO1465920
TIPS4RM
• Unit 5 Day 7: Walk the Line
Explore
• CLIPS Activity 3.1: Comparing Pattern Rules
Homework Help
• Characteristics of Linear
Relations Interactive (Section 4)
Investigation
• CLIPS Activity 3.2: Same Constant, Different
Multiplier
• CLIPS Activity 3.3: Different Constant, Same
Multiplier
Gizmos
• Finding Patterns
Annenberg Learner
• Guess My Rule
Practice
• CLIPS Activity 3.4: Check Your Understanding Gap Closing I/S
• Module 4 Proportional
Reasoning: Facilitator’s Guide
o Diagnostic 7 - 9
• Module 4 Proportional
Reasoning: Student Book
o Pages 12 - 17
EduGAINS-Mathematics
Page 4 of 9
Direct and Partial Variation
Specific Expectations: LR3.03, LR3.04, LR3.05
Learning Focus
Blended Learning
•
•
•
•
Identify a linear relationship as either a
direct or partial variation
Connect the rate of change to the
variable part in an equation
Connect the initial value of a partial
variation to the constant in an equation
Represent a linear relationship as an
equation using the rate of change and
initial value
EduGAINS-Mathematics
Unit 5 Activity 4: Direct and Partial Variation
o OERB Resource ID: ELO1465930
Explore
• CLIPS 4.2: Building Patterns from Graphs
Investigation
• CLIPS 4.3: Telling Stories
Practice
• CLIPS 4.4: Check Your Understanding
Other Resources
TIPS4RM
• Unit 5 Day 6: Tables of Values,
Equations, Graphs
• Unit 5 Day 8: Modelling Linear
Relations with Equations
• Unit 5 Day 9: Graphing Linear
Relations in Context
Homework Help
• Rate of Change
• Making Equations from Real-Life
Problems
Page 5 of 9
TIPS4Math
Graphs Tell Stories Shapes
Resource
Grade 9 Applied
URL
Blended Learning:
https://download.elearningontario.ca/repository/14/1465900000/MFM1PPU05A01/overview.html
Unit 5 Activity 1: Graphs Tell
Stories
Mellow Yellow Interpreting Graphs http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/LinearRelationships/MellowYellow.gsp
Texas Instruments CBR 2 Motion https://www.youtube.com/watch?v=eMRr9qUpshw
Detector
Movie Theatre Graph
https://www.youtube.com/watch?v=761I4GW3AVg,
Movie Theatre Graph 2
https://www.youtube.com/watch?v=97laVMqZMQw
Movie Theatre Graph 3
https://youtu.be/U_w38sTgN9I
Features of a Good Two-Variable https://download.elearningontario.ca/repository/14/1465900000/MFM1PPU05A01/content_4.html
Graph
TIPS4RM:
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/Unit5_
Unit 5 Day 1: Match Me!
LinearRelationships.pdf
TIPS4RM:
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/Unit5_
Unit 5 Day 2: Story Graphs
LinearRelationships.pdf
Desmos:
https://teacher.desmos.com/polygraph/custom/560ad68f7701c303063305f5
Polygraph: Distance-Time
Homework Help:
https://homeworkhelp.ilc.org/tools/listen_learn/details.php?t_id=262
Cartesian Grid
OERB:
https://download.elearningontario.ca/repository/1241280000/Battleship_V09.html
Battleship Game
Gap Closing: I/S
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GapClosing/NumberSense_Int-SeModule 4 Proportional Reasoning: nior/4-PropReasoning_FG_IS.pdf
Facilitator’s Guide
Gap Closing: I/S
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GapClosing/NumberSense_Int-SeModule 4 Proportional Reasoning: nior/4-PropReasoning_SB_IS.pdf
Student Book
EduGAINS-Mathematics
Page 6 of 9
TIPS4Math
Rate of Change
Resource
Blended Learning:
Unit 5 Activity 2: Rate of Change
Rate of Change
Distance-Time Graph Gizmo
Grade 9 Applied
URL
https://download.elearningontario.ca/repository/14/1465910000/MFM1PPU05A02/overview.html
hhttp://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_RatesOfChange.ppt
https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=625
https://www.youtube.com/watch?v=ji0a5BDMdNI
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GapClosing/NumberSense_
Int-Senior/4-PropReasoning_FG_IS.pdf
Zak the Tiny Skateboarder
TIPS4RM:
Unit 5 Day 3: Ramps, Roofs, and Roads
TIPS4RM:
Unit 5 Day 4: Models of Movement
TIPS4RM:
Unit 5 Day 5: Story Graphs
Gap Closing: I/S
Module 4 Proportional Reasoning:
Facilitator’s Guide
Gap Closing: I/S
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GapClosing/NumberSense_
Module 4 Proportional Reasoning: Student Int-Senior/4-PropReasoning_SB_IS.pdf
Book
EduGAINS-Mathematics
Page 7 of 9
TIPS4Math
Linear Growing Patterns
Resource
Blended Learning:
Unit 5 Activity 3: Linear Growing Patterns
CLIPS Activity 3.1: Comparing Pattern
Rules
CLIPS Activity 3.2: Same Constant,
Different Multiplier
CLIPS Activity 3.3: Different Constant,
Same Multiplier
CLIPS Activity 3.4: Check Your
Understanding
TIPS4RM
Unit 5 Day 7: Walk the Line
Homework Help:
Characteristics of Linear Relations
Interactive (Section 4)
Gizmos:
Finding Patterns
Annenberg Learner:
Guess My Rule
Gap Closing: I/S
Module 4 Proportional Reasoning:
Facilitator’s Guide
Gap Closing: I/S
Module 4 Proportional Reasoning: Student
Book
EduGAINS-Mathematics
Grade 9 Applied
URL
https://download.elearningontario.ca/repository/14/1465920000/MFM1PPU05A03/overview.html
http://oame.on.ca/CLIPS/?cluster=4&clip=3&activity=1
http://oame.on.ca/clips/index.html?cluster=4&clip=3&activity=2,
http://oame.on.ca/clips/index.html?cluster=4&clip=3&activity=3
http://oame.on.ca/clips/index.html?cluster=4&clip=3&activity=4
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
https://homeworkhelp.ilc.org/tutorials/html5/index.php?object_id=491#/tutorial/38/section/3/page/9
https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=219
https://www.learner.org/courses/learningmath/algebra/session9/part_b/index.html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GapClosing/NumberSense_
Int-Senior/4-PropReasoning_FG_IS.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GapClosing/NumberSense_
Int-Senior/4-PropReasoning_SB_IS.pdf
Page 8 of 9
TIPS4Math
Direct and Partial Variation
Resource
Blended Learning:
Unit 5 Activity 4: Direct and Partial
Variation
CLIPS 4.2: Building Patterns from Graphs
CLIPS 4.3: Telling Stories
CLIPS 4.4: Check Your Understanding
TIPS4RM:
Unit 5 Day 6: Tables of Values, Equations,
Graphs
TIPS4RM:
Unit 5 Day 8: Modelling Linear Relations
with Equations
TIPS4RM:
Unit 5 Day 9: Graphing Linear Relations in
Context
Homework Help:
Rate of Change
Homework Help:
Making Equations from Real-Life
Problems
EduGAINS-Mathematics
Grade 9 Applied
URL
https://download.elearningontario.ca/repository/14/1465930000/MFM1PPU05A04/overview.html
http://oame.on.ca/clips/index.html?cluster=4&clip=4&activity=2
http://oame.on.ca/clips/index.html?cluster=4&clip=4&activity=3
http://oame.on.ca/clips/index.html?cluster=4&clip=4&activity=4
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade9Applied/
Unit5_LinearRelationships.pdf
https://homeworkhelp.ilc.org/tools/listen_learn/details.php?t_id=301
https://homeworkhelp.ilc.org/tools/listen_learn/details.php?t_id=241
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