TIPS4Math
Grade 8
Linear Relationships
Overall Expectation
Students will:
• Represent linear growing patterns (where the terms are whole numbers) using graphs, algebraic expressions, and equations
(8m54)
• Model linear relationships graphically and algebraically, and solve and verify algebraic equations, using a variety of strategies,
including inspection, guess and check, and using a “balance” model (8m55)
Specific Expectations
Students will:
• Represent, through investigation with concrete materials, the general term of a linear pattern, using one or more algebraic
expressions (8m56)
• Represent linear patterns graphically (i.e., make a table of values that shows the term number and the term, and plot the
coordinates on a graph), using a variety of tools (8m57)
• Determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation (8m58)
• Model linear relationships using tables of values, graphs, and equations, through investigation using a variety of tools (8m60)
• Make connections between solving equations and determining the term number in a pattern, using the general term (8m63)
Lesson
Explore Patterns
Represent Linear
Patterns Graphically
Determine Terms from a
Graph
Determine Terms from an
Algebraic Equation
General Term of a Linear
Pattern
Determine a Term Number
Learning Focus
•
•
•
•
•
•
•
•
•
•
•
EduGAINS-Mathematics
Explore, identify and create growing, shrinking, and repeating numeric patterns
Make predictions related to growing, shrinking, and repeating numeric patterns
Identify characteristics of a linear relationship
Work with input and output tables for linear relationships
Make a table of values, and plot ordered pairs on a graph
Determine a term given its term number in a linear pattern that is represented by
a graph
Determine a term given its term number in a linear pattern that is represented by
an algebraic equation
Through investigation, with concrete materials, develop algebraic expression(s)
for the general term of a linear relationship
Aware that an algebraic expression for the general term allows for predictions of
any particular term of a linear relationship
Given a graph, an algebraic equation or a pattern determine the term number if
the term is known
Make connections to solving algebraic equations
Specific
Expectations
8m56
8m60
8m57
8m60
8m58
8m58
8m56
8m63
Page 1 of 15
TIPS4Math
Linear Relationships (continued)
Lesson
Model Linear Relationships
Part 1
Model Linear Relationships
Part 2
Grade 8
Learning Focus
Model linear relationships that involve real-life contexts
8m60
Use the models to develop equations and solve for a term given a term number
Model linear relationships that involve real-life contexts
8m60
Use the models to develop equations and solve for the term number given a term
number in a linear pattern
• Create and solve problems related to linear patterns
Consolidation and Summative Tasks
EduGAINS-Mathematics
•
•
•
•
Specific
Expectations
Page 2 of 15
TIPS4Math
Specific Expectations: 8m56, 8m60
Learning Focus
Minds
On
•
Explore Patterns
Blended Learning
Teacher Guide
Unit 4, Activity 2: Linear Equations
OERB ID: ELO1477280
Extend growing, shrinking, Unit 4 Activity 2: Minds On
and repeating numeric
OERB ID: ELO1477110
patterns
• Making Sense of Our World video
[10 scenes]
• Discussion
o describe a linear relationship
Note: supplementation required for
extending growing, shrinking, and
repeating numeric patterns
Action • Explore, identify and
•
create growing, shrinking,
and repeating numeric
patterns
Make predictions related
to growing, shrinking, and
repeating numeric
patterns
Consolidation
EduGAINS-Mathematics
Grade 8
Other
Resources
TIPS4RM Grade 8 Unit 2: Representing Patterns
in Multiple Ways
• Day 1: What do Patterns Tell Us?
TIPS4RM Continuum and Connections
• Patterning and Algebraic Modelling
(Grades 6-10)
Homework Help
• Patterns - Find the Next 3 Terms
mathies
• Robot Rule Game
Gizmos
• Finding Patterns
Learn Alberta Interactives
• Exploring Patterns
Desmos
• The O Pattern
Page 3 of 15
TIPS4Math
Represent Linear Patterns Graphically
Specific Expectations: 8m57, 8m60
Learning Focus
Minds
On
•
Action •
•
•
Grade 8
Blended Learning
Teacher Guide
OERB ID: ELO1477280
• Unit 4, Activity 1: Input/Output tables
• Unit 4, Activity 2: Linear Equations
Represent the term numbers Unit 4 Activity 1: Minds On
and term values of a linear
• Robot Transformer
pattern as ordered pairs then
plot them on a grid
Identify characteristics of a
Unit 4 Activity 1: Action
linear relationship
OERB ID: ELO1477100
Work with input and output
• Required Reading
tables for linear relationships
o representing patterns in multiple ways
Make a table of values, and • Assignment 1: Input/Output Tables
plot ordered pairs on a graph
o program machines, creating input/output
tables
• Assignment 2: Strategies
o Discussion
o strategies to determine functions
Consolidation
EduGAINS-Mathematics
Other
Resources
TIPS4RM Grade 8 Unit 2:
Representing Patterns in
Multiple Ways
• Day 2: Different Representations
of the Same Patterns
CLIPS
• Creating a Graphical Representation
Geometer’s Sketchpad
• Building and Using Scatterplots
Unit 4 Activity 2: Action
• Invasion Force Part 2: Mars Guard
OERB ID: ELO1412490
o graphs, table of values, linear or
non-linear
• Practice Graphing
Unit 4 Activity 2: Consolidation
OERB ID: ELO1477110
• Group Work
o create a table of values, make a set of
ordered pairs, graph the ordered pairs,
explain if this is a linear growing pattern
Page 4 of 15
TIPS4Math
Specific Expectations: 8m58
Determine Terms from a Graph
Learning Focus
Minds
On
•
Action •
Represent linear patterns graphically
and extend these representations to
predict the next term
Determine a term given its term
number in a linear pattern that is
represented by a graph
Consolidation
Grade 8
Blended Learning
Other
Resources
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
• Day 5: Space Race: Graphic
Representations
OERB
• Invasion Force Part 3: Space Guard
o OERB ID: ELO1412500
mathies
• Exploring Different Representations
Desmos
• Visual Patterns + Desmos = Amazing
• Match My Pattern
EduGAINS-Mathematics
Page 5 of 15
TIPS4Math
Determine Terms from an Algebraic Equation
Specific Expectations: 8m58
Learning Focus
Minds
On
•
Action •
Grade 8
Review substituting whole numbers
into algebraic expressions and
evaluating
Determine a term given its term
number in a linear pattern that is
represented by an algebraic
equation
Consolidation
EduGAINS-Mathematics
Blended Learning
Other
Resources
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
• Day 3: Finding the nth Term
• Day 4: Exploring Patterns
CLIPS
• Position 0 and Beyond
mathies
• Representation Match (Linear Growing
Patterns)
Page 6 of 15
TIPS4Math
Specific Expectations: 8m56
General Term of a Linear Pattern
Learning Focus
Blended Learning
Teacher Guide
• Unit 4, Activity 1: Input/Output tables
OERB ID: ELO1477280
• Unit 4, Activity 3: Finding the nth term
Minds
On
•
Action •
•
Grade 8
Make predictions about future
terms in a linear growing pattern
by extending a graph or
applying a pattern
Through investigation, with
concrete materials, develop
algebraic expression(s) for the
general term of a linear
relationship
Aware that an algebraic
expression for the general term
allows for predictions of any
particular term of a linear
relationship
Other
Resources
Unit 4 Activity 1: Action
• Invasion Force – Part 1: Home Guard
OERB ID: ELO1412480
o extending linear patterns
o best expression for general term
Unit 4 Activity 1: Consolidation
OERB ID: ELO1477100
• Practice Exercise: Exploring Patterns
complete three of six stations
Unit 4 Activity 3: Minds On
OERB ID: ELO1477120
• Group Work
o representations of patterns using cards
o sort deck
o represent data in a model, table of values,
graph, and pattern rule
EduGAINS-Mathematics
Page 7 of 15
TIPS4Math
Grade 8
General Term of a Linear Pattern (Continued)
Specific Expectations: 8m56
Learning Focus
Action
Blended Learning
•
Assignment 1: Reflection on Different
Representations of Growing Patterns
o for each representation what
information is easily revealed
o strategy used to extend the pattern
Other
Resources
Note: supplementation required for
making predictions
Consolidation
Specific Expectations: 8m63
Determine a Term Number
Learning Focus
Minds • Identify the term number for a term in a
graphical representation of a linear pattern
On
Action • Given a graph, an algebraic equation or a
•
Blended Learning
Other
Resources
TIPS4RM Grade 8 Unit 2:
Representing Patterns in Multiple Ways
• Day 7: Determining the Term
pattern determine the term number if the
term is known
Make connections to solving algebraic
equations
Consolidation
EduGAINS-Mathematics
Page 8 of 15
TIPS4Math
Specific Expectations: 8m60
Model Linear Relationships Part 1
Learning Focus
Blended Learning
Teacher Guide
Unit 4, Activity 3: Finding the nth term
OERB ID: ELO1477280
Minds • Explore examples of linear
relationships in real life
On
Action • Model linear relationships that Unit 4 Activity 3: Action
•
Grade 8
involve real-life contexts
•
Use the models to develop
equations and solve for a term
given a term number
•
Other
Resources
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
• Day 6: When Can I Buy This Bike?
CLIPS
• Comparing Families of Linear
Growing Patterns
• Linear Growing Patterns: Check
Your Understanding
Rocket Rules
o build linear patterns
o see effect of changing constant and
multiplier
mathies
Assignment 2: Check Your Understanding • Exploring Different Representations
o create a table of values and graph the • Representation Match
values
(Linear Growing Patterns)
Unit 4 Activity 3: Consolidation
OERB ID: ELO1477120
• Assignment 3: Finding the nth Term
o represent story pattern on the pattern
maker
o build up to 8th term
o identify variable, constant and nth term
Tap Into Teen Minds
• Placing Toothpicks
Desmos
• Some Constant Rate Problems
Consolidation
EduGAINS-Mathematics
Page 9 of 15
TIPS4Math
Specific Expectations: 8m60
Grade 8
Model Linear Relationships Part 2
Learning Focus
Other
Resources
Blended Learning
Minds
On
Action • Model linear relationships that involve
•
•
real-life contexts
Use the models to develop equations and
solve for the term number given a term
number in a linear pattern
Create and solve problems related to
linear patterns
Consolidation
Consolidation and Summative Tasks
Specific Expectations:8m56, 8m57, 8m58, 8m60, 8m63
Blended Learning
EduGAINS-Mathematics
Other
Resources
Page 10 of 15
TIPS4Math
Explore Patterns
Grade 8
Resource
URL
Teacher Guide:
Unit 4, Activity 2: Linear Equations
Unit 4 Activity 2: Minds On
https://download.elearningontario.ca/repository/14/1477280000/GRD8MTHEU06A05/content_2.html
https://download.elearningontario.ca/repository/14/1477110000/GRD8MTHEU04A02/content.html
http://mathclips.ca/?cluster=4
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit2_RepresentingPatternsInMultipleWays.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/ContiuumAndConnections/PatterningAndAlgebraicModelling_Grades6-10.pdf
Making Sense of Our World
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
TIPS4RM Continuum and Connections
Patterning and Algebraic Modelling
(Grades 6-10)
Homework Help:
Patterns - Find the Next 3 Terms
mathies:
Robot Rule Game
Gizmos:
Finding Patterns
Learn Alberta Interactives:
Exploring Patterns
Desmos:
The O Pattern
EduGAINS-Mathematics
https://homeworkhelp.ilc.org/tools/best_sessions/best_sessions_details.php?q_id=559300
http://mathies.ca/games.php
https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=219
http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.PATT&ID2=AB.MATH.JR.PATT.PATT&lesson=html/object_interactives/patterns/use_it.html
https://teacher.desmos.com/activitybuilder/custom/56426649b3a715b11abbc726
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TIPS4Math
Represent Linear Patterns Graphically
Grade 8
Resource
URL
Teacher Guide:
Unit 4, Activity 1: Input/Output tables
Teacher Guide:
Unit 4, Activity 2: Linear Equations
Robot Transformer
Unit 4 Activity 1: Action
https://download.elearningontario.ca/repository/14/1477280000/GRD8MTHEU06A05/content.html
https://download.elearningontario.ca/repository/14/1477280000/GRD8MTHEU06A05/content_2.html
http://mathclips.ca/?cluster=4&clip=1&activity=1
https://download.elearningontario.ca/repository/14/1477100000/GRD8MTHEU04A01/content_2.html
https://download.elearningontario.ca/repository/14/1477100000/GRD8MTHEU04A01/assignment.html
https://download.elearningontario.ca/repository/14/1477100000/GRD8MTHEU04A01/assignment.html
https://download.elearningontario.ca/repository/14/1412490000/LO1163-InvasionForcePart2Mars.html
http://mathclips.ca/?cluster=4&clip=2&activity=4
https://download.elearningontario.ca/repository/14/1477110000/GRD8MTHEU04A02/content_3.html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit2_RepresentingPatternsInMultipleWays.pdf
http://mathclips.ca/?cluster=4&clip=1&activity=2
Assignment 1: Input/Output Tables
Assignment 2: Strategies
Invasion Force Part 2: Mars Guard
Practice Graphing
Unit 4 Activity 2: Consolidation
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
CLIPS:
Creating a Graphical Representation
Geometer’s Sketchpad:
Building and Using Scatterplots
EduGAINS-Mathematics
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/GraphingPoints/BuildingAndUsingScatterPlots.gsp
Page 12 of 15
TIPS4Math
Determine Terms from a Graph
Grade 8
Resource
URL
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
OERB:
Invasion Force Part 3: Space Guard
mathies:
Exploring Different Representations
Desmos:
Visual Patterns + Desmos = Amazing
Desmos:
Match My Pattern
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit2_RepresentingPatternsInMultipleWays.pdf
https://download.elearningontario.ca/repository/14/1412500000/LO1164.html
http://mathies.ca/learningTools.php#Ee0
http://reasonandwonder.com/visual-patterns-desmos-amazing/
https://teacher.desmos.com/activitybuilder/custom/55d0a1afe63779855e492364
Determine Terms from an Algebraic Equation
Resource
URL
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
CLIPS :
Position 0 and Beyond
mathies:
Representation Match
(Linear Growing Patterns)
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit2_RepresentingPatternsInMultipleWays.pdf
http://mathclips.ca/?cluster=4&clip=2&activity=2
EduGAINS-Mathematics
http://mathies.ca/games.php#Rr0-2
Page 13 of 15
TIPS4Math
General Term of a Linear Pattern
Grade 8
Resource
URL
Teacher Guide:
Unit 4, Activity 1: Input/Output tables
Teacher Guide:
Unit 4, Activity 3: Finding the nth term
Invasion Force – Part 1: Home Guard
https://download.elearningontario.ca/repository/14/1477280000/GRD8MTHEU06A05/content.html
https://download.elearningontario.ca/repository/14/1477280000/GRD8MTHEU06A05/content_3.html
https://download.elearningontario.ca/repository/14/1412480000/LO1143-InvasionForcePart1.html
https://download.elearningontario.ca/repository/14/1477100000/GRD8MTHEU04A01/content_3.html
https://download.elearningontario.ca/repository/14/1477120000/GRD8MTHEU04A03/content.html
https://download.elearningontario.ca/repository/14/1477120000/GRD8MTHEU04A03/assignment.html
Unit 4 Activity 1: Consolidation
Unit 4 Activity 3: Minds On
Assignment 1: Reflection on Different
Representations of Growing Patterns
Determine a Term Number
Resource
URL
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit2_RepresentingPatternsInMultipleWays.pdf
EduGAINS-Mathematics
Page 14 of 15
TIPS4Math
Model Linear Relationships Part 1
Grade 8
Resource
URL
Teacher Guide:
Unit 4, Activity 3: Finding the nth term
Rocket Rules
Assignment 2: Check Your
Understanding
Assignment 3: Finding the nth Term
https://download.elearningontario.ca/repository/14/1477280000/GRD8MTHEU06A05/content_3.html
http://mathclips.ca/?cluster=4&clip=2&activity=1
http://mathclips.ca/?cluster=4&clip=2&activity=3
TIPS4RM Grade 8 Unit 2: Representing
Patterns in Multiple Ways
CLIPS:
Comparing Families of Linear Growing
Patterns
Linear Growing Patterns: Check Your
Understanding
mathies:
Exploring Different Representations
mathies:
Representation Match
(Linear Growing Patterns)
Tap Into Teen Minds:
Placing Toothpicks
Desmos:
Some Constant Rate Problems
EduGAINS-Mathematics
https://download.elearningontario.ca/repository/14/1477120000/GRD8MTHEU04A03/assignment.html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit2_RepresentingPatternsInMultipleWays.pdf
http://mathclips.ca/index.html?cluster=4&clip=3
http://mathclips.ca/index.html?cluster=4&clip=4
http://mathies.ca/learningTools.php#Ee0
http://mathies.ca/games.php#Rr0-2
https://tapintoteenminds.com/3act-math/placing-toothpicks/
https://teacher.desmos.com/activitybuilder/custom/56266e04a463e7ea075a3d5a
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