TIPS4Math
Grade 6
Area of Parallelograms and Triangles
Overall Expectations
Students will:
• Estimate, measure, and record quantities, using the metric measurement system (6m29)
• Determine the relationships among units and measurable attributes, including the area of a parallelogram, the area of a triangle,
and the volume of a triangular prism (6m30)
• Use variables in simple algebraic expressions and equations to describe relationships (6m56)
Specific Expectations
Students will:
• Estimate, measure, and record length, area, mass, capacity, and volume, using the metric measurement system (6m32)
• Construct a rectangle, a square, a triangle, and a parallelogram, using a variety of tools, given the area and/or perimeter (6m35)
• Determine, through investigation using a variety of tools and strategies, the relationship between the area of a rectangle and the
areas of parallelograms and triangles, by decomposing and composing (6m36)
• Develop the formulas for the area of a parallelogram (i.e., Area of parallelogram = base x height) and the area of a triangle [i.e.,
Area of triangle = (base x height) ÷ 2], using the area relationships among rectangles, parallelograms, and triangles (6m37)
• Solve problems involving the estimation and calculation of the areas of triangles and the areas of parallelograms (6m38)
• Determine, using concrete materials, the relationship between units used to measure area (i.e., square centimetre, square metre),
and apply the relationship to solve problems that involve conversions from square metres to square centimetres (6m39)
• Demonstrate an understanding of different ways in which variables are used (6m63)
• Identify, through investigation, the quantities in an equation that vary and those that remain constant (6m64)
• Solve problems that use two or three symbols or letters as variables to represent different unknown quantities (6m65)
• Determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies (6m66)
Lesson
Learning Focus
Area Relationships Between
•
Rectangles and Parallelograms
Area Relationships Between
Parallelograms and Triangles
•
•
•
EduGAINS-Mathematics
Through investigation using a variety of tools and strategies, determine the
relationship between the area of a rectangle and the area of a
parallelogram
Through investigation using a variety of tools and strategies, determine the
relationship between the area of a parallelogram and the area of a triangle
Develop the formula for area of a parallelogram and the formula for area of
a triangle
Identify the quantities in an equation that vary and those that remain
constant (e.g., A = (b x h)/2)
Specific
Expectations
6m32
6m36
6m32
6m36
6m37
6m63
6m64
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TIPS4Math
Grade 6
Area of Parallelograms and Triangles (continued)
Lesson
Area of Parallelograms and
Triangles Problem Solving
Learning Focus
•
•
Unit Conversions
•
Construct Parallelograms and
Triangles with a Given Area
•
Solve problems involving the estimation and calculation of the areas of
triangles and parallelograms
Solve problems that use two or three letters as variables
Specific
Expectations
6m32
6m38
6m65
6m66
Solve area problems that involve conversions from square metres to square 6m32
centimetres
6m39
Use a variety of tools (concrete materials, geoboard, dynamic geometry
6m32
software, grid paper, ruler) to construct triangles and parallelograms with a 6m35
given area
Consolidation and Summative Tasks
EduGAINS-Mathematics
Page 2 of 8
TIPS4Math
Area Relationships Between Rectangles and Parallelograms
Specific Expectations: 6m32, 6m36
Learning Focus
Minds
On
•
Action
•
•
Review the formula for area of a
rectangle using square units
Understands how variables are
used in formulas
Through investigation using a
variety of tools and strategies,
determine the relationship
between the area of a rectangle
and the area of a parallelogram
Blended Learning
Teacher Guide
Unit 2 Activity 2: Area of Parallelograms and
Triangles
OERB ID: ELO1474960
Grade 6
Other Resources
Guide to Effective Instruction:
Measurement Grades 4 – 6
• pp 31 – 34
NCTM Illuminations
• Area of a Parallelogram
• Finding the Area of
Parallelograms
Unit 2 Activity 2: Action
OERB ID: ELO1474920
• Virtual Geoboard
o investigate relationships between the
area of rectangles and parallelograms
• Area of a Parallelogram Video
Note: supplementation required for using
concrete materials
Consolidation
EduGAINS-Mathematics
Page 3 of 8
TIPS4Math
Area Relationships Between Parallelograms and Triangles
Specific Expectations: 6m32, 6m36, 6m37, 6m63, 6m64
Learning Focus
Blended Learning
Minds
On
•
Review the formula for area of a
parallelogram
Action
•
Through investigation using a
variety of tools and strategies,
determine the relationship
between the area of a
parallelogram and the area of a
triangle
Develop the formula for area of a
parallelogram and the formula for
area of a triangle
Identify the quantities in an
equation that vary and those that
remain constant
(e.g., A = (b x h)/2)
•
•
•
Consolidation
EduGAINS-Mathematics
Teacher Guide
Unit 2 Activity 2:
Area of Parallelograms and Triangles
OERB ID: ELO1474960
Unit 2 Activity 2: Action
• Rectangle Ricky’s Parallelogram Identity
Crisis
OERB ID: ELO1414660
o explores the relationship of the areas
of rectangles, parallelograms and
triangles (develops area formulas for
parallelogram and triangle)
Unit 2 Activity 2: Action
OERB ID: ELO1474920
• Area of a Triangle video
• Geometer’s Sketchpad Area activity
Grade 6
Other Resources
Guide to Effective Instruction:
Measurement Grades 4 – 6
• pp 31 – 34
NCTM Illuminations
• Area Tool
• Discovering the Area Formula
for Triangles
Note: supplementation required for estimation
Unit 2 Activity 2: Consolidation
• Discussion
o area of triangle and parallelogram
relationship
o Toolbox to illustrate thinking
Page 4 of 8
TIPS4Math
Area of Parallelograms and Triangles Problem Solving
Specific Expectations: 6m32, 6m38, 6m65, 6m66
Learning Focus
Blended Learning
Teacher Guide
Unit 2 Activity 2:
Area of Parallelograms and Triangles
OERB ID: ELO1474960
Minds
On
•
Action
•
•
Grade 6
Understand different ways
variables are used and
measurement formulas
Solve problems involving the
estimation and calculation of the
areas of triangles and
parallelograms
Solve problems that use two or
three letters as variables
Other Resources
Guide to Effective Instruction:
Measurement Grades 4 – 6
• pp 31 – 34
Unit 2 Activity 2: Action
OERB ID: ELO1414920
• Assignment 1: Area of Parallelograms
• Assignment 2: Area of Triangles
Note: supplementation required for solving
problems that use two or three letters as
variables
Consolidation
Specific Expectations: 6m32, 6m39
Learning Focus
Minds
On
•
Action
•
Use concrete materials to
determine the relationship
between units used to measure
area (square centimetre, square
metre)
Solve area problems that involve
conversions from square metres
to square centimetres
Unit Conversions
Blended Learning
Other
Resources
Consolidation
EduGAINS-Mathematics
Page 5 of 8
TIPS4Math
Construct Triangles and Parallelograms with a Given Area
Specific Expectations: 6m32, 6m35
Learning Focus
Minds • Review that base and height are
factors of double the area of a
On
•
Action
•
•
Blended Learning
Grade 6
Other Resources
triangle
Review formulas for the area of
triangles and parallelograms
Review that base and height are
factors of double the area of a
triangle
Review formulas for the area of
triangles and parallelograms
Consolidation
Consolidation & Summative Tasks
Specific Expectations: 6m32, 6m35, 6m36, 6m37, 6m38, 6m39, 6m63, 6m64, 6m65, 6m66
Other
Blended Learning
Resources
EduGAINS-Mathematics
Page 6 of 8
TIPS4Math
Area Relationships Between Rectangles and Parallelograms
Resource
URL
Teacher Guide:
Unit 2 Activity 2: Area of
Parallelograms and Triangles
Unit 2 Activity 2: Action
Virtual Geoboard
Area of a Parallelogram Video
Guide to Effective Instruction:
Measurement Grades 4 – 6
NCTM Illuminations:
Area of a Parallelogram
NCTM Illuminations:
Finding the Area of
Parallelograms
EduGAINS-Mathematics
Grade 6
https://download.elearningontario.ca/repository/14/1474960000/Combined%20Teacher%20
Notes%20for%20Activities%201%20-%203/content_2.html
https://download.elearningontario.ca/repository/14/1474940000/GRD6MTHEU02/GRD6MTHEU02A02/content_2.html
http://www.mathplayground.com/geoboard.html
https://download.elearningontario.ca/repository/14/1474940000/GRD6MTHEU02/GRD6MTHEU02A02/content_3.html
http://oame.on.ca/eduproject/ontariomathedresources/files/Measurement%204-6.pdf
https://illuminations.nctm.org/Activity.aspx?id=4158
https://illuminations.nctm.org/Lesson.aspx?id=1882
Page 7 of 8
TIPS4Math
Area Relationships Between Triangles and Parallelograms
Resource
URL
Teacher Guide:
Unit 2 Activity 2: Area of
Parallelograms and Triangles
Rectangle Ricky’s Parallelogram
Identity Crisis
Unit 2 Activity 2: Action
Geometer’s Sketchpad Area
Activity
Unit 2 Activity 2: Consolidation
Grade 6
https://download.elearningontario.ca/repository/14/1474960000/Combined%20Teacher%20
Notes%20for%20Activities%201%20-%203/content_2.html
https://download.elearningontario.ca/repository/14/1414660000/Brandon_Gr6_MeaStoryboard10.
html
https://download.elearningontario.ca/repository/14/1474940000/GRD6MTHEU02/GRD6MTHEU02A02/content_3.html
http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/AreaAndPermieter/AreaParallelogramTriangle_TimeToGetInShape.gsp
https://download.elearningontario.ca/repository/14/1474940000/GRD6MTHEU02/GRD6MTHEU02A02/content_4.html
http://oame.on.ca/eduproject/ontariomathedresources/files/Measurement%204-6.pdf
Guide to Effective Instruction:
Measurement Grades 4 – 6
NCTM Illuminations:
https://illuminations.nctm.org/Activity.aspx?id=3567
Area Tool
NCTM Illuminations:
https://illuminations.nctm.org/Lesson.aspx?id=1874
Discovering the Area Formula for
Triangles
Area of Parallelograms and Triangles Problem Solving
Resource
URL
Teacher Guide:
Unit 2 Activity 2: Area of
Parallelograms and Triangles
Assignment 1:
Area of Parallelograms
Assignment 2: Area of Triangles
Guide to Effective Instruction:
Measurement Grades 4 – 6
EduGAINS-Mathematics
https://download.elearningontario.ca/repository/14/1474960000/Combined%20Teacher%20
Notes%20for%20Activities%201%20-%203/content_2.html
https://download.elearningontario.ca/repository/14/1474940000/GRD6MTHEU02/GRD6MTHEU02A02/assignment.html
https://download.elearningontario.ca/repository/14/1474940000/GRD6MTHEU02/GRD6MTHEU02A02/assignment.html
http://oame.on.ca/eduproject/ontariomathedresources/files/Measurement%204-6.pdf
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