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⭐ Connecting Geometric Reasoning to Essential Key Concepts ⭐
Exploring Geometric Reasoning offers authentic opportunities to revisit the Essential Key Concepts of Decimal Reasoning and Fractional Reasoning and Operations:
B1.5 → Round decimal numbers
When students estimate angle sums (e.g., complementary and supplementary angles), they might round angle measures to simplify calculations while maintaining mathematical accuracy.
B1.6 → Show equivalence among fractions and decimal numbers
Exploring fractional turns helps students link those to decimals, reinforcing proportional reasoning within rotational symmetry tasks.
B2.9 → Multiply whole numbers by proper fractions
When scaling models or construction 3-D shapes from views, students might multiply side lengths or angles by fractional factors (e.g., half-size), reinforcing proportional scaling in spatial reasoning.
Expectation Cluster
Expectation Cluster
E1.1 create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry
E1.2 construct three-dimensional objects when given their top, front, and side views
E2 compare, estimate, and determine measurements in various contexts
E2.2 use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise
E2.3 use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures
Organize your observations of student learning related to the key concepts and skills for this topic:
Explore a menu of possible MathUP lessons, Building Fluency lessons, problems, explorations and games.
During this topic, pay attention to the students' ability to build relationships and communicate effectively.
How do students respond to feedback, questions or prompts from the teacher and their peers?
Do students build on each others’ thinking?
Do students use supportive ‘math talk’ language?
Models and Tools
Models and Tools
Concrete Learning Resources Tools:
rulers
protractors
miras
tracing paper
linking cubes
grid paper
Virtual Learning Resources and Tools:
Building Using Three Views (interactive activity)
Rotational Symmetry in Quadrilaterals (interactive activity)
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