Analyze Characteristics and Properties of 2-D and 3-D Figures
This microcredential represents a teacher’s understanding of analyzing characteristics and properties of 2-D and 3-D figures. It involves their ability to understand and respond to progressions related to analyzing characteristics and properties of 2-D and 3-D figures by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It also includes the teacher's ability to select, use, and adapt mathematics curricula and teaching materials, including the integration of mathematical tools and technology, as well as using and analyzing formative and summative assessments to determine students' understanding of analyzing the characteristics and properties of 2-D and 3-D figures. This microcredential is the third of five in the Elementary Mathematics Endorsement: Understand and Implement Concepts of Measurement Stack. These microcredentials can be earned in any order.
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Utah Effective Teaching Standards > Standard 2: Instructional Design Clarity
Element 1: Content - Demonstrating a comprehensive understanding of Utah Core Standards, communicating relevance of content, communicating clear pathways to student mastery and designing learning experiences aligned to clear learning intentions and success criteria. -
Utah Effective Teaching Standards > Standard 2: Instructional Design Clarity
Element 3: Instructional Planning - Planning high quality, personalized instructional activities that are informed by student progress data, provide multiple opportunities for students to reflect upon and assess their own growth and allow multiple opportunities and means for demonstration of competency. -
Utah Effective Teaching Standards > Standard 3: Instructional Practice
Element 1: Instructional Strategies - Using appropriate academic language and evidence-based strategies to stimulate higher-level thinking, discourse and problem solving and to scaffold learning experiences to meet the needs of all students. -
Utah Effective Teaching Standards > Standard 3: Instructional Practice
Element 3: Relevance - Providing relevant learning opportunities that value students’ interests and backgrounds and allow learner agency and choice in accessing learning and demonstrating competency.
To earn this microcredential you will need to submit three sets of evidence demonstrating your effective and consistent use of appropriate instructional strategies to teach the analysis of characteristics and properties of 2-D and 3-D figures. You will also complete a short written or video reflective analysis.
Analyzing characteristics and attributes of 2-D and 3-D figures is an integral foundation of geometry understanding.
This foundation starts with:
- Observations that geometric figures have similarities and differences,
- That many of these differences are defining attributes,
- That these figures can be connected and categorized by these attributes, and
- That these attributes can be used to create and justify statements and arguments about these figures.
Analyzing the characteristics and properties of 2-D and 3-D figures includes:
- Classifying and sorting geometric figures by characteristics and properties. (Note: There are non-defining (color) and defining attributes. Defining attributes may include open and closed figures, number and size of sides, number and size of angles, sum of interior angles, faces, edges, vertices, convex and concave, regularity, symmetry, parallel and perpendicular, etc.),
- Describing similarities and differences between figures,
- Classifying figures including subcategories and hierarchies,
- Constructing and supporting viable arguments (by modeling, drawing, creating shapes, angles, or lines while attending to properties of shapes), and
- Developing a sequence of justified statements that show truth (e.g., explain how they know a quadrilateral is a quadrilateral).
Observable characteristics of a shape that can’t be used to define the shape (e.g. color, size, orientation, etc.).
Defining Attributes:Traits or properties of a shape that make it unique and distinguishable.
Interior Angles:An angle that is located inside of a polygon.
Face:Any of the individual flat surfaces of a solid object.
Edge:A particular type of line segment joining two vertices in a polygon or 2 faces in a geometric solid.
Vertex (plural-vertices):A point where two or more line segments meet (often referred to as a corner).
Convex:A closed figure where all of its interior angles are less than 180 degrees.
Concave:A closed figure where at least one of its interior angles is more than 180 degrees.
Mrs. Barth is helping her students understand the differences between 2-D and 3-D geometric figures. In the past her students have had a difficult time connecting with the paper based resources she has used. This year she’s decided to give students a variety of 2-D and 3-D figures and ask them to sort the figures. She anticipates that one way students will sort the shape is by shapes that are flat (2-D) and shapes that are solid (3-D). She’s planned that once students have made that distinction, she will give them more hands-on activities to continue to help them solidify the characteristics of each type of figure. She’s excited to see how much more success her students have compared to previous years.
Category: Preparation and Planning
Submit the evidence below to show your preparation and planning to implement concepts of 2-D and 3-D figures.
Share a unit plan focused on analyzing characteristics and properties of 2-D and 3-D figures. The unit should include:
- Course title
- Unit title
- Selected standards for the unit, including one or more practice standards.
- Common misconceptions
- Required student prior knowledge
- How standards will be sequenced and grouped (if standards are taught together).
- Written objectives aligned to standards for each lesson of the unit, including how long each lesson is expected to take.
- Resources (tasks, activities, etc.) for each day of the unit that are aligned to the objective of that particular day.
- Description of end-of-unit assessment and how it will assess standards for the whole unit.
- Any additional summative or formal formative (collected and evaluated) assessments for the unit.
Category: Implementation
Submit TWO of the evidence options to show your implementation of concepts of 2-D and 3-D figures.
Observe 2 teachers in your building teaching lessons on analyzing characteristics and properties of 2-D and 3-D figures. This focused observation will take place in three parts: before, during, and after.
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Before the observation, preconference with the cooperating teacher. Some things to include in this discussion should be: (a) Discuss what proficiency in the standard being observed looks like for students. (b) Gather background information about what the teacher has already done to help students gain conceptual understanding. (c) Ask the teacher how they’re planning to help students progress towards proficiency during the lesson. (d) Ask the teacher what misconceptions and barriers he/she anticipates students having.
(e) Include these interview notes in your submission. -
During the lesson, do the following: (a) Take notes on what students are doing. (b) Take notes on what students are understanding. (c) Take notes on what students don’t seem to be understanding.
(d) Include these notes in your submission. -
After the lesson, complete a written reflection on the lesson. Specifically include thoughts about the following: (a) Pieces of the lesson that helped students develop understanding. (b) Some ideas on how you might be able to help students who aren’t understanding.
Submit a lesson plan that demonstrates how you have helped students become proficient in analyzing characteristics and properties of 2-D and 3-D figures. The lesson plan should clearly illustrate how the instruction effectively helps students progress from conceptual understanding towards procedural fluency. The lesson plan should include the following:
- Grade level
- Relevant standard(s)
- Intended learning outcome(s)
- Instructional materials (manipulatives, paper, etc.)
- Instructional activities (tasks, etc.)
- Written plan explaining how you will help students progress using the activities you chose
- Assessment techniques
In a separate section of the lesson plan, include citations for research supporting your instructional approach. (See the resources section for examples to cite.)
Submit student work samples that highlight how a student progressed in their understanding of analyzing characteristics and properties of 2-D and 3-D figures. The samples should include:
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Work from 1 student that shows their progression in ideas across each day of the unit. In other words, there should be an example of the student’s work for each day of the unit (at least 4).
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A written analysis of a student’s understanding for each artifact, based on the work sample collected for that day. This analysis should include: (a) The lesson taught that day. (b) The concepts explored during that lesson. (c) The representations used to enhance or demonstrate understanding.
(d) An evaluation of how well the student is understanding the concept at this point of the unit.
(e) Repeat steps a-d for each day’s artifact. -
These work samples should show how conceptual understanding was achieved.
(a) Work samples should show how students started with more concrete representation (manipulatives and pictures) before moving on to more abstract representations (numbers, expressions, algorithms, etc.)
Review Criteria
Criterion 1: Evidence demonstrates a clear content understanding that helps students move from conceptual understanding to procedural fluency.
Criterion 2: Evidence demonstrates the candidate's understanding of analyzing characteristics and properties of 2-D and 3-D figures.
Criterion 3: Evidence demonstrates the understanding of and use of effective teaching practices designed to help students analyze characteristics and properties of 2-D and 3-D figures.
Describe the effect that a deficit in analyzing characteristics and properties of 2-D and 3-D figures will have on students’ math success in future grade levels. Include at least one example standard and how that standard is affected.
Reflect on your experience analyzing the characteristics and properties of 2-D and 3-D figures across the grade levels. How might this experience affect how you plan future units of instruction?
Review Criteria
Criterion 1: The reflection indicates that the educator understands analyzing characteristics and properties of 2-D and 3-D figures standards.
Criterion 2: The reflection indicates that the educator understands the impact/importance of helping students understand characteristics and properties of 2-D and 3-D figures and how to analyze them.
https://www.schools.utah.gov/file/f0e86540-5617-4166-a701-fea403f2f848
The Utah effective Teaching Standards articulate what effective teaching and learning look like in the Utah public education system.
Progressions Documents for the Common Core Mathematics Standards
http://ime.math.arizona.edu/progressions/
Documents that break down key standards in detail and demonstrates how key concepts connect across grade levels.
NCTM Effective Mathematics Teaching Practices that Support Learning For All Students: A Focus on Elementary School
https://www.nctm.org/uploadedFiles/Conferences_and_Professional_Development/Institues/Pre-K_Grade_12_Common_Core_Series/Huinker-ElementaryKeynote_presentation.pdf
These eight mathematics teaching practices provide a framework for strengthening the teaching and learning of mathematics. This research-informed framework of teaching and learning reflects the current learning principles as well as other knowledge of mathematics teaching that has accumulated over the last two decades. In essence, these teaching practices represent a core set of high-leverage practices and essential teaching skills necessary to promote deep learning of mathematics.
Elementary and Middle School Mathematics: Teaching Developmentally John Van de Walle
Elementary and Middle School Mathematics: Teaching Developmentally illustrates how children learn mathematics, and then shows teachers the most effective methods of teaching PreK-8 math through hands-on, problem-based activities.
Utah Core Standards: Mathematics Core Guides
https://www.schools.utah.gov/curr/mathematics/core?mid=4514&tid=2
The Utah State Board of Education adopted the K-12 Utah Core Standards for Mathematics in January 2016. Core guides provide a description of the Core Standards, including concepts and skills to master, critical background knowledge and academic vocabulary. The course overview documents show the major work of the grade level and the coherence of content across grade levels.
Teaching Student-Centered Mathematics Grades K-3
Teaching Student-Centered Mathematics Grades K-3 provides practical guidance along with proven strategies for practicing teachers of kindergarten through grade 3. This volume offers brand-new material specifically written for the early grades.
Mathematics for Elementary Teachers with Activities Sybilla Beckman
This book connects the foundations of teaching elementary math and the “why” behind procedures, formulas, and reasoning so students gain a deeper understanding to bring into their own classrooms. Through her text, Beckmann teaches mathematical principles while addressing the realities of being a teacher.
Elementary Mathematics is Anything but Elementary: Content and Methods From a Developmental Perspective Damon L. Bahr and Lisa Ann DeGarcia
Elementary Mathematics is Anything but Elementary: Content and Methods From a Developmental Perspective is a comprehensive program that delivers both a content and a methods text. Serving as a professional development guide for both pre-service and in-service teachers, this text''s integrated coverage helps dissolve the line between content and methods--and consequently bolsters teachers'' confidence in their delivery of math instruction. A strong emphasis on the National Council of Teachers of Mathematics five core standards provides key information common to most state curricula relative to NCTM standards for pre-K through sixth grade. In addition, text content is based on thorough elementary mathematical scope and sequences that have been shown to be an effective means for guiding the delivery of curriculum and instruction.
The van Heile Model of the Development of Geometric Thought
https://www.cns-eoc.colostate.edu/docs/math/mathactivities/june2007/The%20van%20Hiele%20Model%20of%20the%20Development%20of%20Geometric%20Thought.pdf
The van Hiele theory describes how young people learn geometry. It postulates five levels of geometric thinking which are labeled visualization, analysis, abstraction, formal deduction and rigor. Each level uses its own language and symbols, and can be progressed from one to the next.
Understanding the Math we Teach and How to Teach It K-8 Marian Small
With this resource, new and experienced teachers alike will focus on the big ideas and practices in mathematics, deepening their own understanding and content knowledge, learn how to teach those big ideas using a student-centered, problem-solving approach, and anticipate student thinking and explore effective tools, models, and rich mathematical questions that nudge student thinking forward.
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