Critical Learning Instructional Pathway
MATHEMATICS
Glen Street Public School
Teachers: A. Jaglall, R. Lekkas
Concept Foci/Big Idea:
Geometry – Focus on 2D shapes and angles. We want students to see the relationship between properties of shapes
and how to identify shapes.
Grade 5
distinguish among polygons, regular
polygons, and other two-dimensional
shapes
Identify and classify acute, right,
obtuse, and straight angles;
identify triangles (i.e., acute, right,
obtuse, scalene, isosceles, equilateral),
and classify them according to angle
and side properties;
construct triangles, using a variety of
tools (e.g., protractor, compass,
dynamic geometry software), given
acute or right angles and side
measurements
Grade 6
sort and classify quadrilaterals by
geometric properties related to symmetry,
angles, and sides, through investigation
using a variety of tools
sort polygons according to the number of
lines of symmetry and the order of
rotational symmetry, through investigation
using a variety of tools
measure and construct angles up to 180°
using a protractor, and classify them as
acute, right, obtuse, or straight angles
construct polygons using a variety of
tools, given angle and side measurements
Grade 7
construct related lines (i.e., parallel;
perpendicular; intersecting at 30º, 45º, and
60º), using angle properties and a variety of
tools
sort and classify triangles and quadrilaterals
by geometric properties related to symmetry,
angles, and sides, through investigation
using a variety of tools
construct angle bisectors and perpendicular
bisectors, using a variety of tools (e.g., Mira,
dynamic geometry software, compass) and
strategies (e.g., paper folding), and represent
equal angles and equal lengths using
mathematical notation;
identify, through investigation, the minimum
side and angle information (i.e., side-sideside; side-angle-side; angle-side angle)
needed to describe a unique triangle
determine, through investigation using a
variety of tools (e.g., dynamic geometry
software, concrete materials, geoboard),
relationships among area, perimeter,
corresponding side lengths, and
corresponding angles of congruent shapes
distinguish between and compare similar
shapes and congruent shapes, using a
variety of tools
Diagnostic Assessment:
Students completed a 2D Geometry Leaps and Bounds with an angle focused Leaps and Bounds.
General Misconceptions were:
-
Students were unfamiliar with proper geometric terms of polygons, students struggled with symmetry for
irregular or multi-line of symmetry shapes, students struggled with constructing and measuring with a
protractor.
AREAS OF NEED/Focused Lessons
Big Ideas, Strategies,
Social Skills, Computational Fluency,
Reasoning/Groupings/Lesson Topic
Students need review of
proper identification and
investigation with angles
Whole Group (W)
Small Group (SM)
Individual/Independent (I)
Ideas for Next Steps
(i.e., Resources, Strategies,
Mini-Lessons, Games, Centres)
Minds on:
- Use body to go through angles (arms to represent angles)
- Modeled measuring angles with protractor under ELMO
Working on it:
-
Each student measured various angles and adults circulated to ensure
proper protractor use. Asked questions, “How could you find reflex
angle?”, “What if you changed by measuring on the other line? Would
it change your measurement? Why, or why not?” Clarifying any
misconceptions around protractor us.
Consolidation:
- Some students shared their angles and discussions that you wanted to
highlight
- Played angle bingo – tied in classification angles within the game
Students require more work with
lines of symmetry
Minds on:
Show photos of real world items, and find lines of symmetry. Talk about where
they are.
Working on it:
-pre-cut shapes find lines of symmetry by folding. Talk about what we noticed.
Create anchor chart of different polygons with lines of symmetry.
-Then show a mira, and have them find lines of symmetry of different shapes.
Consolidating:
-Ticket out the door: Identify the lines of symmetry
Students will work on classifying
and sorting polygons
Minds On: On SMART notebook, have shapes and then identify. Talk about
why. Think Pair Share. Parallelogram, rhombus, rectangle, pentagon, hexagon,
heptagon, octagon, scalene, isosceles, equilateral
Working On It: Sort various shapes. How can you sort? Sort the shapes in a
different way? Glue them on and explain their thinking. Sort in partners.
Consolidation: Bansho – Organizing the methods of sorting by similarities.
Discuss the different methods that were sorted, and share and discuss. Are
there more ways we could sort?
Irregular Vs. Regular – Properties
of polygons
Minds on: What makes these two pentagons similar? What makes them
different?
Working on it: Students will investigate different shapes and determine if they
are regular or irregular based on their properties
Consolidate with a ticket out the door.
** Midpoint assessment ** - EQAO question + word problems. Regular VS.
Irregular, properties of triangles, and sorting based on lines of symmetry
Students will work on measuring
angles
Minds on: Put an angle under the ELMO. Think-pair-share – What kind of angle
is it? (acute, obtuse, right, half a right) – Discuss as a pair
Model how to measure using a protractor
Students will work in pairs trying questions and checking each other’s work.
Circulate to ensure each student can model how to use a protractor accurately.
Push for further understanding: “If I start measuring from the other base line,
will my angle be the same? Why or why not?”
Consolidate with math bingo and Ticket out the door to check for student
understanding.
Constructing Triangles with given
side lengths and angles
Minds on: Quick group brainstorm of the different types of triangles and their
particular properties.
Working on it: Shared construction of a triangle based on given properties. –
Students will then construct a triangle with given properties and then check
each other’s shape to make sure they meet the requirements.
Consolidate: Final shape construction with given properties to be handed in.
Constructing Pentagons (6’s) and
heptagons (6/7’s) with given
requirements
Minds on: Recap of the different types of pentagons and heptagons that we
have seen
Working on it: Shared working on construction of a pentagon on Smart
Notebook.
Students will then be given a pentagon/heptagon to construct that must
contain certain properties.
Students who finish early will research shapes with number of sides greater
than 10 and then try to build it with given requirements.
Consolidation: Check each other’s shape for the required properties by
comparing in groups– What do we notice?
Summative Assessment: EQAO style question – Constructing a pentagon that has certain angle and side length
requirements. Students who finish this accurately will then be pushed to try more challenging shapes through next
steps.