TWO AND THREE DIMENSIONAL SHAPES

  • LEARNING AND INSTRUCTIONAL GOALS

    • ENDURING UNDERSTANDINGS:
      Three dimensional objects have capacity. Second and third shapes are a way to measure space. Mathematics is a language of its own that we use to solve problems.

      ESSENTIAL QUESTIONS
      How are two dimensional objects different from three dimensional objects?
      What are the parts of two and three dimensional objects?
      In what ways does calculating volume help us in every day life?
      How do we measure the space an object takes up?
      How do we use two and three dimensional objects in our world?
      How can surface area and volume help you to make decisions in your life?
      Given some measurements of a shape, how can we calculate missing measurements?

      STUDENTS WILL KNOW/UNDERSTAND:
      The vocabulary related to 2 and 3 dimensional shapes.
      The difference between 2 and 3 dimensional.
      The difference between 1 (linear), 2, and 3 dimensional measurement.
      How does the shape of an object affect the volume?
      Understand and apply the Pythagorean Theorem.

      STUDENTS WILL BE ABLE TO:
      Use formulas to find area, surface area and/or volume.
      Be able to decide if a given net will fold into a given solid.
      Be able to create nets that will fold into a given shape.
      Know the appropriate units for linear, area and volume.
      Be able to use vocabulary associated with lines and shapes.
      Be able to identify second and third shapes.
      Be able to differentiate among area, surface, and volume.
      Communicate verbally and in writing, their process for problem solving using their understanding about second and third shapes.

      MAINE LEARNING RESULTS:
      Students know and use properties of polygons.
      Students know and use angle properties of parallel lines to solve problems and determine geometric relationship.
      Students know and use the Pythagorean Theorem.
      Students find the volume and surface area of prisms, pyramids, cylinders, and other figures composed of these solids.
      Students understand and use the concept of scale drawings to enlarge or reduce two-dimensional plane figures.

  • ASSESSMENTS

    • FORMATIVE:
      Pretest: Lesson 1 used to determine current level of knowledge and understanding of geometry concepts.
      Triple-Entry Journal: Lesson 2, 3 (record vocabulary), lesson 5 (students will record vocabulary associated with the Pythagorean Theorem), lesson 7 (students will demonstrate their thinking as they develop an aquatic habitat).
      Quick Write: Lesson 3 (record students’ process for applying learning about dilating an object), lesson 5 (students will share what they know about right angles).
      Build Models: Lesson 5 (students will create a concrete model of the Pythagorean Theorem), lesson 7 (students will design and illustrate geometric habitats).
      Think-Pair-Share: Lesson 2 (activate prior knowledge), lesson 6 (students will recall elements of and process for using the Pythagorean Theorem).
      Give One, Get One: Lesson 2 (solidify concepts or future application), lesson 6 (review unit to date and prepare for geometry project).
      Knowledge Rating Guide: Lesson 4 (gage students’ current level of understanding and compare following the lesson).
      Two-Column Notes: Lesson 4 (journal size paper with lines formatted in four rows and students will record their understanding of angle measures and rules for finding them).
      Creative Writing Prompt: Lesson 5 (students will express their understanding of the importance of the radical, what its function is).
      Problematic Situation: Lesson 6 (students will problem solve using the Pythagorean Theorem).
      Coding: Lesson 5 (students will read about the Pythagorean Theorem and code for J+, put in journal because it’s new, C-I made a connection, ? – I don’t understand/I wonder, checkmark – I know this).
      Museum Walk: Lesson 7 (students will ask questions about peers aquatic designs).
      Journal writing: Lesson 7 (students will respond to at least two questions about their design posed by their peers).

      SUMMATIVE:
      Post test: Same test except for word problem.

  • TECHNOLOGY INTEGRATION
  • LITERACY SUPPORT

    • Math Journals
      Two-Column Notes (adapted for math)
      Problem Solving Template
      Triple-Entry Journal (adapted for math)
      Vocabulary/concept entries
      RAFT: Role, Audience, Format, Topic
      Semantic Feature Analysis
      Think-Pair-Share
      Give One, Get One
      Interactive Word Wall
      Problematic Situation
      Save the Last Word

      ACTIVE LEARNING EVENTS:
      Students will activate prior knowledge using a matching up activity for formulas and shapes.
      Students will record definition and formulas in their journals.
      Students will transform two dimensional objects on a coordinate graph.
      Students will use tools to create parallel lines and transversals.
      Students will find the measure of all angles given the measure of one angle when working with parallel lines with a transversal.
      Students will prove the Pythagorean Theorem using graph paper and a right triangle.
      Students will use the Pythagorean Theorem to form two lengths into a right angle.
      Students will demonstrate their understanding of geometry by designing and problem solving an aquatic habitat for a pair of sea creatures.


  • INSTRUCTIONAL SEQUENCE



TWO AND THREE DIMENSIONAL SHAPES


Name of Instructor(s):

Marielle Edgecomb

   
Subject:Geometry
   
Grade Level: 8th
   
Duration: 3 Weeks
   
Videos:  
Two and Three Dimensional Shapes—Literacy Support: Multi-Column Notes, Two-Column Notes, Triple-Entry Vocabulary Journal
   
Rationale and Context:
This unit engages students in an in-depth study of the characteristics of two dimensional and three dimensional shapes. It is designed to help students understand the differences among area, surface area and volume. Students will explore the building blocks of shapes and will solve real world problems related to volume and surface area. The instructor uses Give One, Get One, RAFT, Semantic Feature Analysis, Frayer Model, Think-Pair-Share, Triple-Entry Journals, and Word Walls. Technology integration includes the use of an interactive white board, document camera, virtual manipulatives, and OER resources.

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