Unit 1Plan – Shapes and Designs (Two Dimensional Geometry)

Title of Unit / Shapes and Designs: / Grade Level / 7th7
Curriculum Area / Connected Mathematics Projects3-CMP3( Two Dimensional Geometry) / Time Frame / 56weeks- (August 14– September22)
Developed By / George Pringle
Content Standards and Benchmarks
Common Core Content Standards - Mathematics
  • 7. EE.A.2:Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
  • 7. EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
  • 7. G.A.2: Draw (freehand, with ruler and protractor, and technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
  • 7. G.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Overview (Describe and Contextualize the Unit)
The objective of this introductory unit is to develop students’ ability to recognize, display, analyze, measure, and reason about the shapes and visual patterns that are important features of the world. The unit focuses on polygons and on the edge and angle relationships of regular and irregular polygons. Students will use the skills learned to help them construct/draw figures with given constraints. The goal of Shapes and Designs is to have students discover and analyze many of the key properties of polygonal shapes that make them useful and attractive.
Learning Goals
Properties of Polygons: Understand the properties of polygons that affect their shape
Explore the ways that polygons are sorted into families according to the number and length of their sides and the size of their angles
Explore the patterns among interior and exterior angles of a polygon
Explore the patterns among side lengths in a polygon
Investigate the symmetries of a shape—rotation or reflection
Determine which polygons fit together to cover a flat surface and why
Reason about and solve problems involving various polygons
Relationships Among Angles: Understand special relationships among angles
Investigate techniques for estimating and measuring angles
Use tools to sketch angles
Reason about the properties of angles formed by parallel lines and transversals
Use information about supplementary, complementary, vertical, and adjacent angles in a shape to solve for an unknown angle in a multi-step problem
Constructing Polygons: Understand the properties needed to construct polygons
Draw or sketch polygons with given conditions by using various tools and techniques such as freehand, use of a ruler and protractor, and use of technology
Determine what conditions will produce a unique polygon, more than one polygon, or no polygon, particularly triangles and quadrilaterals
Recognize the special properties of polygons, such as angle sum, side-length relationships, and symmetry, that make them useful in building, design, and nature
Solve problems that involve properties of shapes
Focus Questions (if applicable)
Investigation 1
  • Problem (1.1):What properties do all polygons share? What properties do some sub-groups of polygons share?
  • Problem (1.2): What are some common benchmark angles? What part of a full turn is each angle equal to?
  • Problem (1.3): When a drawing shows two rays with a common endpoint, how many rotation angles are there? How would you estimate the measure of each angle?
  • Problem (1.4):How do you measure an angle with an angle ruler and a protractor?
  • Problem (1.5):In a triangle, what measures of sides and angles give just enough information to draw a figure that is uniquely determined?
Investigation 2
  • Problem (2.1):What is the size of each angle and the sum of all angles in a regular polygon with n sides?
  • Problem (2.2): What is the angle sum of any polygon with n sides? How do you know that your formula is correct?
  • Problem (2.3): Which regular polygons can be used to tile a surface without overlaps or gaps, and how do you know that your answer is correct?
  • Problem (2.4):What is an exterior angle of a polygon, and what do you know about the measures of exterior angles?
Investigation 3
  • Problem (3.1):What combinations of three side lengths can be used to make a triangle? How many different shapes are possible for such a combination of side lengths?
  • Problem (3.2): What is the angle sum of any polygon with n sides? How do you know that your formula is correct?
  • Problem (3.3):What combinations of side lengths can be used to make a quadrilateral? How many different shapes are possible for any such combination of side lengths?
  • Problem (3.4):When two parallel lines are cut by a transversal, what can be said about the eight angles that are formed?
  • Problem (3.5):How are squares, rhombuses, rectangles, and trapezoids similar? How are they different?

Knowledge (Content Understanding)
Students will know… / Skills (Essential Literacy Standards, Common Core, Content Area)
Students will be able to…
1)How to analyze, measure and reason about the shapes and visual patterns that are important features of the world.
2)Know definitions for (Key vocabulary):
  • angle ruler
  • complementary angles
  • Concave polygons
  • convex polygons
  • degree
  • exterior angles
  • interior angles
  • irregular polygon
  • parallel lines
  • polygon
  • protractor
  • quadrants rectangle
  • reflection symmetry
  • regular polygon
  • right angle
  • rotation
  • rotation symmetry
  • supplementary angles
  • symmetry
  • tessellation
  • tiling
  • transversal
  • vertical angles
/ Define vocabulary words and apply them in contextual situations.
Sort polygons into families according to the number and length of their sides and the size of their angles
Identify patterns among interior and exterior angles of a polygon
Identify patterns among side lengths in a polygon
Determine the symmetries of a shape as rotation or reflection
Determine which polygons fit together to cover a flat surface and why
Solve problems involving various polygons
Identify and apply special relationships among angles
Use techniques for estimating and measuring angles
Use angle ruler and protractor to sketch and measure angles
Use properties of angles formed by parallel lines and transversals to solve for unknown angle measures in a diagram
Use information about supplementary, complementary, vertical, and adjacent angles in a shape to solve for an unknown angle in a multi-step problem
Draw or sketch polygons with given conditions by using various tools and techniques such as freehand, use of a ruler and protractor, and use of technology
Determine what conditions will produce a unique polygon, more than one polygon, or no polygon, particularly triangles and quadrilaterals
Recognize the special properties of polygons, such as angle sum, side-length relationships, and symmetry, that make them useful in building, design, and nature
Solve problems that involve properties of shapes
Plans for Adjusting Core to Meet the Needs of All Students
Support / Challenge
Students who lack support for schooling will receive the following support:
Lesson material in printed form as needed
Chunking content in digestible bits
Assistance with reading and understanding text by underlining or highlighting key words to make sense of what a problem is asking
Formative assessment, using iPad showme and educreation app
When possible start homework in class and complete in help session
Additional guidance with lesson/investigation reflections – “what learned; what struggling with; steps to improve learning”
The use of manipulatives and materials from class set to assist with homework or review at home
Along with other grade 7 core teachers implement and maintain a "mentor program" for target students
Organizational support-keeping track of when assignments are due; completing and turning in assignments on time
Paired with a “class buddy” that is a positive role model
Encourage attendance to help sessions / Students that need a push or challenge will be able to extend their knowledge by doing the following activities:
Encouraged and challenged to complete “enrichment problems” from the in class lesson activity sections
Given additional extension problems that are more content rich and challenging
Assigned relevant component of MathXl (Online extension to math curriculum) for enrichment
Make video clips of problem solving strategies
Complete assigned math projects, and present to class
Assessment Evidence
Self-Assessment / Formative / Summative
Tracking progress sheets
Collaborative in-class problemsolving work group
ACE Homework Problems
Lesson/Investigation/Unit reflections / Participation in group activities
Oral explanation of problem solving strategies
Response to teacher directed questions
 Using iPads, mini whiteboards, or at the board to share problem solving strategies
Reflection logs / 3-5 Lesson assessment questions/Exit ticket
ACE Homework assignments
End of Investigation Quizzes
Unit Tests
End of Investigation reflections