TIPS4Math
Grade 8
Operations Involving Integers
Overall Expectations
Students will:
• Represent, compare, and order equivalent representations of numbers, including those involving positive exponents (8m8)
• Solve problems involving whole numbers, decimal numbers, fractions, and integers, using a variety of computational strategies
(8m9)
• 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, compare, and order rational numbers (i.e., positive and negative [integers] fractions and decimals to thousandths
(8m13)
• Use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to
help judge the reasonableness of a solution (8m18)
• Represent the multiplication and division of integers, using a variety of tools (8m21)
• Solve problems involving operations with integers, using a variety of tools (8m22)
• Evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations
(8m23)
• Evaluate algebraic expressions with up to three terms, by substituting fractions, decimals, and integers for the variables (8m62)
• Solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection guess
and check and a “balance” model (8m64)
Lesson
Addition and
Subtraction of
Integers Review
Multiplication of
Integers
Division of Integers
Learning Focus
•
Review addition and subtraction of integers using a variety of tools (e.g., two colour
counters, virtual manipulatives, number lines)
8m13
8m22
•
Represent the multiplication of integers using a variety of tools (e.g., two-colour
counters, virtual manipulatives, number lines)
Make connections to repeated addition and to patterns
Review the commutative property and apply it to multiplication of integers
Represent the division of integers using a variety of tools (e.g., two-colour counters,
virtual manipulatives, number lines)
Make connections to repeated subtraction and to patterns
Make connections to multiplication and to fact families
8m13
8m21
•
•
•
•
•
EduGAINS-Mathematics
Specific
Expectations
8m13
8m21
Page 1 of 18
TIPS4Math
Operations Involving Integers (continued)
Lesson
Multiplication and
Division Practice
Order of Operations
with Integers
Integer Problems
Learning Focus
•
Multiply and divide integers and reinforce the use of representations
•
Evaluate expressions that involve integers including expressions that contain
brackets and exponents
Reinforce addition, subtraction, multiplication and division of integers
Solve problems involving operations with integers in real-life contexts that require
choosing the appropriate operation or operations
Use estimation to judge for reasonableness of a solution
Evaluate algebraic expressions with up to three terms, by substituting integers for the
variables
•
•
•
•
Evaluate Algebraic
Expressions Involving
Integers
Solve Linear
• Solve and verify linear equations involving a one-variable term and having solutions
Equations Involving
that are integers, by using inspection, guess and check, and a balance model
Integers
Consolidation and Summative Tasks
EduGAINS-Mathematics
Grade 8
Specific
Expectations
8m21
8m22
8m21
8m23
8m18
8m21
8m22
8m62
8m64
Page 2 of 18
TIPS4Math
Grade 8
Addition and Subtraction of Integers Review
Specific Expectations: 8m13, 8m22
Learning Focus
Minds • Review representations of
integers
On
Action • Review addition and subtraction
of integers using a variety of
tools (e.g., two colour counters,
virtual manipulatives, number
lines)
Consolidation
Blended Learning
Other Resources
TIPS 4RM Grade 8 Unit 1: Integers and
Algebraic Expressions
• Day 1: A Positive Attitude Toward Negative Numbers
• Day 2: Living with Negatives
TIPS4RM Continuum & Connections; Integers (7-9)
Homework Help
• Integers- Adding and Subtracting
mathies
• Number Line
• Colour Tiles
• Diamond Drop - Sign of a Sum (Integers)
Gizmos
• Adding and Subtracting Integers with Chips
• Adding and Subtracting Integers
OERB
• Representing the Addition of Integers with Bingo
Chips
o OERB ID: ELO1414360
• Representing the Subtraction of Integers with Bingo
Chips
o OERB ID: ELO1414370
Geometer’s Sketchpad
• Addition with Integers- Integer Addition 2 Colour
Counters
• Subtraction with Integers – Integer Subtraction
Counters
EduGAINS-Mathematics
Page 3 of 18
TIPS4Math
Addition and Subtraction of Integers Review (Continued)
Specific Expectations: 8m37
Learning Focus
Consolidation
Blended Learning
Grade 8
Other Resources
GeoGebra
• Adding Integers
• Subtracting integers
NCTM Illuminations
• Game – Flipping for Integers
Dynamic Number
• Jump Along Games – Taking Trips on the Numberline
YouTube
• How to Add and Subtract Integers Using Integer Chips
Gap Closing I/S Student Book: Integers
pp 5 – 14
Gap Closing I/S Facilitators Guide: Integers
pp 9 – 20
EduGAINS-Mathematics
Page 4 of 18
TIPS4Math
Specific Expectations: 8m38
Learning Focus
Minds
On
•
Action •
•
•
Multiplication of Integers
Blended Learning
Teacher Guide
Unit 1, Activity 2: Multiplication and
Division of Integers
OERB ID: ELO1477240
Solve questions that
Unit 1 Activity 2: Minds On
involve repeated addition of OERB ID: ELO1476870
integers
• Check Your Understanding
o Multiplication, repeated addition,
commutative property, fact families
• Discussion
Represent the multiplication Unit 1 Activity 2: Action
of integers using a variety of • Multiplying Integers [5:17]
o zero principle, integer tiles, number
tools (e.g., two-colour
counters, virtual
line, patterning
manipulatives, number lines) • Assignment 1: Multiplying Integers
• Discussion
Make connections to
o possible rules for x Anchor Chart
repeated addition and to
patterns
Review the commutative
Note: supplementation required for
property and apply it to
multiplication of integers, repeated
multiplication of integers
addition, fact families and commutative
property
Consolidation
EduGAINS-Mathematics
Grade 8
Other Resources
TIPS 4RM Grade 8
Unit 1: Integers and Algebraic Expressions
• Day 3: Unfamiliar Territory
• Day 4: Getting Used to the Territory
TIPS 4RM Continuum & Connections;
Integers (7-9)
Homework Help
• Integers: Multiplying and Dividing
mathies
• Number Line
• Colour Tiles
GeoGebra
• Multiplying Integers
Gap Closing I/S Student Book: Integers
pp 15 – 20
Gap Closing I/S Facilitators Guide: Integers
pp 21 – 27
Page 5 of 18
TIPS4Math
Specific Expectations: 8m39
Learning Focus
Minds
On
•
Action •
•
•
Review connections
between multiplication and
division
Represent the division of
integers using a variety
of tools (e.g., two-colour
counters, virtual
manipulatives, number
lines)
Make connections to
repeated subtraction and
to patterns
Make connections to
multiplication and to fact
families
Consolidation
EduGAINS-Mathematics
Grade 8
Division of Integers
Blended Learning
Teacher Guide
Unit 1, Activity 2: Multiplication and
Division of Integers
OERB ID: ELO1477240
Other Resources
TIPS 4RM Grade 8 Unit 1: Integers and
Algebraic Expressions
• Day 6: It’s the Inverse
• Day 7: Dividing it Up
TIPS4RM Continuum & Connections;
Integers (7-9)
Unit 1 Activity 2: Action
OERB ID: ELO1476870
• Dividing Integers [4:47]
o integer tiles, number line,
patterning and relationship
between x and ÷
• Assignment 2: Dividing Integers
• Discussion
o possible rules for ÷; add to Anchor
Chart from previous lesson
Homework Help
• Integers: Multiplying and Dividing
mathies
• Number Line
• Colour Tiles
Gap Closing I/S Student Book: Integers
pp 15 – 20
Gap Closing I/S Facilitator’s Guide: Integers
Note: supplementation required for the
pp 21 – 27
division of integers, repeated
subtraction, fact families
Unit 1 Activity 2: Consolidation
• Identifying Patterns in the
Multiplication and Division of Integers
o patterning, explores rules, practice
Page 6 of 18
TIPS4Math
Multiplication and Division Practice
Specific Expectations: 8m21, 8m22
Learning Focus
Minds • Compare representations
of multiplication and
On
Action •
Grade 8
division
Multiply and divide
integers and reinforce the
use of representations
Consolidation
Blended Learning
Other Resources
TIPS 4RM Grade 8 Unit 1: Integers and
Algebraic Expressions
• Day 8: But Was It Useful?
mathies
• Number Line
• Colour Tiles
Math Playground
• Integer Wrap – Blast Through The Galaxy
Multiplying Integers As You Go!
Sheppard Software
• Fruit Shoot Integer Multiplication
Math-Play
• Integers Jeopardy Game
Gap Closing I/S Student Book: Integers
pp 15 – 20
Gap Closing I/S Facilitator’s Guide: Integers
pp 21 – 27
EduGAINS-Mathematics
Page 7 of 18
TIPS4Math
Order of Operations with Integers
Specific Expectations: 8m21, 8m23
Learning Focus
Blended Learning
Teacher Guide
Unit 1, Activity 3: Order of
Operations and Integer Problems
OERB ID: ELO1477240
Minds
On
•
Action •
•
Grade 8
Review the need for
and use of order of
operations
Evaluate expressions
that involve integers
including expressions
that contain brackets
and exponents
Reinforce addition,
subtraction, multiplication and division of
integers
Consolidation
EduGAINS-Mathematics
Other Resources
TIPS 4RM Grade 8 Unit 1: Integers and Algebraic
Expressions
• Day 9: Now, What Did BEDMAS Stand For?
• Day 11: Life’s Full of Numbers
Homework Help
• Order of Operations
OERB
• Order Matters
o OERB ID: ELO1414880
• Order of Operations, Part 2
o OERB ID: ELO1417920
Learn Alberta Interactives
• Exploring Order of Operations
Unit 1 Activity 3: Minds On
OERB ID: ELO1476880
• Order of Operations and
Integer Problems – Discussion
Gap Closing I/S Student Book: Integers
pp 21 – 24
Gap Closing I/S Facilitator’s Guide: Integers
pp 28 – 31
Page 8 of 18
TIPS4Math
Integer Problems
Specific Expectations: 8m18, 8m21, 8m22
Learning Focus
Blended Learning
Minds • Create addition,
subtraction, multiplication
On
Action •
•
Grade 8
Other Resources
and division problems
involving integers and
real-life contexts
Solve problems involving
operations with integers
in real-life contexts that
require choosing the
appropriate operation or
operations
Use estimation to judge
for reasonableness of a
solution
Consolidation
EduGAINS-Mathematics
Page 9 of 18
TIPS4Math
Grade 8
Evaluate Algebraic Expressions Involving Integers
Specific Expectations: 8m62
Learning Focus
Minds • Review evaluating expressions
that involve integers
On
Action • Evaluate algebraic expressions
with up to three terms, by
substituting integers for the
variables
Consolidation
Blended Learning
Other Resources
TIPS 4RM Grade 8 Unit 1: Integers and
Algebraic Expressions
• Day 5: Writing Letters in Math Class
• Day 9: Now, What Did BEDMAS Stand For?
• Day 10: Putting It Together
Gizmos
• Using Algebraic Expressions
Geometer’s Sketchpad
• Understanding Variables
OERB
• Code Breakers Part 3 – Cybercrypto’s Computer
o OERB ID: ELO1412450
Learn Alberta Interactives
• Exploring Algebra Video and Interactive
Gap Closing I/S Student Book:
Algebraic Expressions and Equations
pp 18 – 20
Gap Closing I/S Facilitator’s Guide:
Algebraic Expressions and Equations
pp 19 – 23
Gap Closing I/S Student Book: Solving Equations
pp 6 – 9
Gap Closing I/S Facilitator’s Guide: Solving Equations
pp 8 – 12
EduGAINS-Mathematics
Page 10 of 18
TIPS4Math
Solve Linear Equations Involving Integers
Specific Expectations: 8m64
Learning Focus
Minds • Verify solutions presented for a
linear equation
On
•
Action •
Grade 8
Blended Learning
Other Resources
Review what the task is when
asked to solve an equation
Solve and verify linear equations
involving a one-variable term and
having solutions that are
integers, by using inspection,
guess and check, and a balance
model
Consolidation
Consolidation and Summative Tasks
Specific Expectations:8m13, 8m18, 8m21, 8m22, 8m23, 8m62, 8m64
Blended Learning
EduGAINS-Mathematics
Other Resources
Page 11 of 18
TIPS4Math
Addition and Subtraction Review
Grade 8
Resource
URL
TIPS 4RM Grade 8 Unit 1:
Integers and Algebraic Expressions
TIPS4RM Continuum & Connections;
Integers (7-9)
mathies:
Number Line
mathies:
Colour Tiles
mathies:
Diamond Drop – Sign of a Sum
(Integers)
Homework Help:
Integers- Adding and Subtracting
Gizmos:
Adding and Subtracting Integers with
Chips
Gizmos:
Adding and Subtracting Integers
OERB:
Representing the Addition of Integers
with Bingo Chips
OERB:
Representing the Subtraction of Integers
with Bingo Chips
Geometer’s Sketchpad:
Addition with Integers- Integer Addition 2
Colour Counters
Subtraction with Integers –
Integer Subtraction Counters
GeoGebra:
Adding Integers
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit1_Integers_AlgebraicExpressions.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/ContiuumAndConnections/Integers_Grades7-9.pdf
http://mathies.ca/learningTools.php#Nn0
EduGAINS-Mathematics
http://mathies.ca/learningTools.php
http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=lib/CL007_IntegersAdditionSubtraction/
CL007_Games/CL007_DiamondDrop.swf
https://homeworkhelp.ilc.org/tools/listen_learn/details.php?t_id=302
https://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=599
https://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=291
https://download.elearningontario.ca/repository/14/1414360000/Pare_Gr7IntegersPart2.
html
https://download.elearningontario.ca/repository/14/1414370000/Pare_Gr7IntegersPart3.
html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/Integers/IntegerAddition2ColourCounters.gsp
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/Integers/IntegerSubtractionCounters.gsp
https://www.geogebra.org/material/simple/id/2930251
Page 12 of 18
TIPS4Math
Addition and Subtraction Review (continued)
Resource
URL
GeoGebra:
Subtracting integers
NCTM Illuminations:
Game – Flipping for Integers
Dynamic Number:
Jump Along Games – Taking Trips on the
Numberline
YouTube:
How to Add and Subtract Integers Using
Integer Chips
Gap Closing I/S Student Book: Integers
https://www.geogebra.org/material/simple/id/2930277
Gap Closing I/S Facilitators Guide:
Integers
EduGAINS-Mathematics
Grade 8
http://illuminations.nctm.org/Lesson.aspx?id=4086
http://www.dynamicnumber.org/jump_along_games__taking_trips_on_the_number_line
https://www.youtube.com/watch?v=UyWM_9oWPbw
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_SB_
IS.pdf
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_FG_
IS.pdf
Page 13 of 18
TIPS4Math
Multiplication of Integers
Grade 8
Resource
URL
Teacher Guide:
Unit 1, Activity 2: Multiplication and
Division of Integers
Unit 1 Activity 2: Minds On
https://download.elearningontario.ca/repository/14/1477240000/GRD8MTHEU06A02/
content_2.html
Multiplying Integers
Assignment 1: Multiplying Integers
Unit 1 Activity 2: Action
TIPS 4RM Grade 8
Unit 1: Integers and Algebraic Expressions
TIPS 4RM Continuum & Connections;
Integers (7-9)
Homework Help:
Integers: Multiplying and Dividing
mathies:
Number Line
mathies:
Colour Tiles
GeoGebra:
Multiplying Integers
Gap Closing I/S Student Book: Integers
https://download.elearningontario.ca/repository/14/1476870000/GRD8MTHEU01A02/
content.html
https://www.youtube.com/watch?v=IH0VLOMrFZk&feature=youtu.be
https://download.elearningontario.ca/repository/14/1476870000/GRD8MTHEU01A02/
assignment.html
https://download.elearningontario.ca/repository/14/1476870000/GRD8MTHEU01A02/
content_2.html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit1_Integers_AlgebraicExpressions.pdf
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/ContiuumAndConnections/Integers_Grades7-9.pdf
https://homeworkhelp.ilc.org/tools/listen_learn/details.php?t_id=325
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/learningTools.php
https://www.geogebra.org/m/te3Ze2Hx
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
SB_IS.pdf
Gap Closing I/S Facilitators Guide: Integers http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
FG_IS.pdf
EduGAINS-Mathematics
Page 14 of 18
TIPS4Math
Division of Integers
Grade 8
Resource
URL
Teacher Guide:
Unit 1, Activity 2:
Multiplication and Division of Integers
Dividing Integers
Assignment 2: Dividing Integers
https://download.elearningontario.ca/repository/14/1477240000/GRD8MTHEU06A02/
content_2.html
https://www.youtube.com/watch?v=3TcTWYPB5JA
https://download.elearningontario.ca/repository/14/1476870000/GRD8MTHEU01A02/
assignment.html
Unit 1 Activity 2: Action
https://download.elearningontario.ca/repository/14/1476870000/GRD8MTHEU01A02/
content_2.html
Identifying Patterns in the Multiplication and http://www.learnalberta.ca/content/mec/flash/index.html?url=Data/1/C/A1C2.swf
Division of Integers
TIPS 4RM Grade 8 Unit 1:
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Integers and Algebraic Expressions
Unit1_Integers_AlgebraicExpressions.pdf
TIPS4RM Continuum & Connections:
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/ContiuumAndIntegers (7-9)
Connections/Integers_Grades7-9.pdf
Homework Help:
https://homeworkhelp.ilc.org/tools/listen_learn/details.php?t_id=325
Integers: Multiplying and Dividing
mathies:
http://mathies.ca/learningTools.php#Nn0
Number Line
mathies:
http://mathies.ca/learningTools.php
Colour Tiles
Gap Closing I/S Student Book:
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
Integers
SB_IS.pdf
Gap Closing I/S Facilitator’s Guide:
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
Integers
FG_IS.pdf
EduGAINS-Mathematics
Page 15 of 18
TIPS4Math
Multiplication and Division Practice
Grade 8
Resource
URL
TIPS 4RM Grade 8 Unit 1:
Integers and Algebraic Expressions
mathies:
Number Line
mathies:
Colour Tiles
Math Playground:
Integer Wrap – Blast Through The Galaxy
Multiplying Integers As You Go!
Sheppard Software:
Fruit Shoot Integer Multiplication
Math-Play:
Integers Jeopardy Game
Gap Closing I/S Student Book:
Integers
Gap Closing I/S Facilitator’s Guide:
Integers
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit1_Integers_AlgebraicExpressions.pdf
http://mathies.ca/learningTools.php#Nn0
EduGAINS-Mathematics
http://mathies.ca/learningTools.php
http://www.mathplayground.com/ASB_IntegerWarp.html
http://www.sheppardsoftware.com/mathgames/integers/FS_Integer_multiplication.htm
http://www.math-play.com/Integers-Jeopardy/Integers-Jeopardy.html
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
SB_IS.pdf
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
FG_IS.pdf
Page 16 of 18
TIPS4Math
Order of Operations with Integers
Grade 8
Resource
URL
Teacher Guide:
Unit 1, Activity 3:
Order of Operations and Integer Problems
Unit 1 Activity 3: Minds On
https://download.elearningontario.ca/repository/14/1477240000/GRD8MTHEU06A02/
content_3.html
TIPS 4RM Grade 8 Unit 1:
Integers and Algebraic Expressions
Homework Help:
Order of Operations
OERB:
Order Matters
OERB:
Order of Operations, Part 2
Learn Alberta Interactives:
Exploring Order of Operations
Gap Closing I/S Student Book: Integers
Gap Closing I/S Facilitator’s Guide:
Integers
EduGAINS-Mathematics
https://download.elearningontario.ca/repository/14/1476880000/GRD8MTHEU01A03/
content.html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit1_Integers_AlgebraicExpressions.pdf
https://homeworkhelp.ilc.org/chat/chat.php?config=playback&question_id=1025999&type=bs#/question/1025999/type/bs
https://download.elearningontario.ca/repository/14/1414880000/Fiore_Gr8NumStoryboard10.html
https://download.elearningontario.ca/repository/14/1417920000/LO1136.html
http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/object_interactives/order_of_operations/
use_it.html
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
SB_IS.pdf
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/3-Integers_
FG_IS.pdf
Page 17 of 18
TIPS4Math
Evaluate Algebraic Expressions Involving Integers
Grade 8
Resource
URL
TIPS 4RM Grade 8 Unit 1:
Integers and Algebraic Expressions
Gizmos:
Using Algebraic Expressions
Geometer’s Sketchpad:
Understanding Variables
OERB:
Code Breakers Part 3 – Cybercrypto’s
Computer
Learn Alberta Interactives:
Exploring Algebra Video and Interactive
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade8English/
Unit1_Integers_AlgebraicExpressions.pdf
https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=257
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/ExpressionsAndEquations/AlgebraicExpressions_UnderstandingVariables.gsp
https://download.elearningontario.ca/repository/14/1412450000/LO1167.html
Gap Closing I/S Student Book:
Algebraic Expressions and Equations
Gap Closing I/S Facilitator’s Guide:
Algebraic Expressions and Equations
Gap Closing I/S Student Book:
Solving Equations
Gap Closing I/S Facilitator’s Guide:
Solving Equations
EduGAINS-Mathematics
http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.PATT&ID2=AB.MATH.JR.PATT.ALG&lesson=html/video_interactives/algebra/algebraInteractive.html
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/6-AlgebraicExp_SB_IS.pdf
http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/6-AlgebraicExp_FG_IS.pdf
http://www.edugains.ca/resources/LearningMaterials/GapClosing/
Grade9/7-SolvingEquations_SB_IS.pdf
http://www.edugains.ca/resources/LearningMaterials/GapClosing/
Grade9/7-SolvingEquations_FG_IS.pdf
Page 18 of 18