Students connect algebra to geometric concepts with polygons as they explore the distance formula, slope criteria for parallel and perpendicular lines, and learn to calculate and justify the area and perimeter of polygons.
Math
Unit 5
10th Grade
In Unit 5, Polygons & Algebraic Relationships, students connect algebra to geometric concepts with polygons through distance on the coordinate plane, partitioning line segments, slope criteria for perpendicular and parallel lines, area (with composition and decomposition), and perimeter. Students then use this knowledge, in part, to describe properties and prove theorems of triangles and parallelograms.
In this unit, students will draw on previous understanding of elementary geometry standards as well as many middle school standards. The primary foundational content students will need to have prior to beginning this unit are application of the Pythagorean Theorem from eighth grade; areas of polygons from sixth grade; and algebraic skills with square roots and factoring from eighth grade, Algebra 1, and Unit 4.
The Unit begins with Topic A, Distance on the Coordinate Plane. Students develop the distance formula using the Pythagorean Theorem to partition line segments proportionally. In Topic B, Classify Polygons using Slope Criteria and Proportional Line Segments, students describe and apply the slope criteria for parallel and perpendicular lines in order to algebraically identify characteristics of triangles and quadrilaterals, with a particular focus on midsegments, medians, and diagonals. Extending these skills, Topic C, Area and Perimeter On and Off the Coordinate Plane, focuses on calculating and justifying the area and perimeter of polygons. In addition, students identify scale factors of dilated polygons and use quadratic equations and systems of inequalities to describe polygons on and off the coordinate plane.
The material from this unit is foundational to the next unit, Three-Dimensional Measurement and Application, where students will need to use the composite area concepts and the Pythagorean Theorem, and focus on measurement units to solve application problems.
Pacing: 17 instructional days (15 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Distance formula | Pythagorean Theorem |
Polygon | Partition proportionally |
Ratio | Directed line segment |
Slope | Perpendicular line |
Parallel line | Parallelogram |
Rectangle | Rhombus |
Square | Midsegment |
Median | Point of concurrency |
Diagonal | Trapezoid |
Area | Perimeter |
Composite shape | Irregular shape |
Scale factor | Quadratic equation |
System of inequalities |
Topic A: Distance on the Coordinate Plane
Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments
Topic C: Area and Perimeter On and Off the Coordinate Plane
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 4
Right Triangles and Trigonometry
Unit 6
Three-Dimensional Measurement and Application