All the resources on this page come from the GADOE Framework 5th Grade Unit 5 Overview. Reviewing this information before or during planning can help ensure your instruction is aligned with the standards and is at the depth expected.

Unit 5 Overview

In this unit students will:

• Identify similarities and differences among two-dimensional figures.

• Reason about attributes (properties) of two-dimensional figures.

• Have experiences discussing properties of two-dimensional figures.

• Build upon their fourth-grade knowledge and create a hierarchy diagram.

• Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classify two-dimensional figures into categories based on their properties.

Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: attribute, category, subcategory, hierarchy, (properties)-rules about how numbers work, two dimensional. From previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube and trapezoid.

From Teaching Student Centered Mathematics, page 186, Van de Walle & Lovin, 2006

1. Shapes exist in great variety. There are many different ways to describe attributes of shapes. The more ways one can classify and discriminate shapes, the better one understands them.

2. Shapes have properties that can be used when describing and analyzing them. Awareness of these properties helps us appreciate shapes in our world. Properties can be explored and analyzed in a variety of ways.

3. An analysis of geometric properties leads to deductive reasoning in a geometric environment.

For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview.

STANDARDS FOR MATHEMATICAL PRACTICE

This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.

1. Make sense of problems and persevere in solving them. Students make sense of problems involving two-dimensional figures based on their geometric properties.

2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning about rational relationships among geometric properties. Students go beyond simple recognition to an analysis of the properties and how they interrelate.

3. Construct viable arguments and critique the reasoning of others. Students construct and critiques arguments regarding their knowledge of triangles and the ability to belong to one or more of the categories and sub-categories.

4. Model with mathematics. Students use tables to identify and draw all three types of triangles comparing their attributes in mathematical and real-world contexts.

5. Use appropriate tools strategically. Students select and use tools such as tables and the quadrilateral hierarchy to represent situations involving the categories and sub-categories of two-dimensional figures.

6. Attend to precision. Students attend to the geometric precision when classifying twodimensional figures in the hierarchy.

7. Look for and make use of structure. Students relate the attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

8. Look for and express regularity in repeated reasoning. Students relate new experiences to experiences with similar contexts when studying the hierarchy of polygons based on properties.

***Mathematical practices 1 and 6 should be evident in EVERY lesson***

STANDARDS FOR MATHEMATICAL CONTENT

Classify two-dimensional figures into categories based on their properties

MGSE5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

MGSE5.G.4 Classify two-dimensional figures in a hierarchy based on properties (polygons, triangles and quadrilaterals).

BIG IDEAS

• Two-Dimensional figures are classified by their properties.

• Two-Dimensional figures can fit into more than one category.

• Identify and describe properties of two-dimensional figures more precisely

ESSENTIAL QUESTIONS

• How can plane figures be categorized and classified?

• What is a quadrilateral?

• What are the properties of quadrilaterals?

• How can you classify different types of quadrilaterals?

• How are quadrilaterals alike and different?

• How can angle and side measures help us to create and classify triangles?

• Where is geometry found in your everyday world?

• What careers involve the use of geometry?

• Why are some quadrilaterals classified as parallelograms?

• Why are kites not classified as parallelograms?

• Why is a square always a rectangle?

• What are ways to classify triangles?

CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge experience related to the concepts and skills identified below. It may be necessary to pre-assess to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas. Details learned in earlier grades need to be used in the descriptions of the attributes of shapes. The more the students can classify and discriminate shapes, the better they can understand them.

• describe, analyze, create, and compare properties of two-dimensional figures

• compare and classify figures by their sides and angles

• examine the presence or absence of parallel and perpendicular lines

• examine the presence or absence of angles of a specified size to classify two-dimensional shapes

• classify two-dimensional shapes in a hierarchy based on properties

Fluency: Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Fluent problem solving does not necessarily mean solving problems within a certain time limit, though there are reasonable limits on how long computation should take. Fluency is based on a deep understanding of quantity and number.

Deep Understanding: Teachers teach more than simply “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives. Therefore, students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of foundational mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.

Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency. Fluency implies a much richer kind of mathematical knowledge and experience.

Number Sense: Students consider the context of a problem, look at the numbers in a problem, make a decision about which strategy would be most efficient in each particular problem. Number sense is not a deep understanding of a single strategy, but rather the ability to think flexibly between a variety of strategies in context.

Fluent students:

• flexibly use a combination of deep understanding, number sense, and memorization.

• are fluent in the necessary baseline functions in mathematics so that they are able to spend their thinking and processing time unpacking problems and making meaning from them.

• are able to articulate their reasoning.

• find solutions through a number of different paths.

For more about fluency, see: http://www.youcubed.org/wpcontent/uploads/2015/03/FluencyWithoutFear-2015.pdf and: https://bhi61nm2cr3mkdgk1dtaov18- wpengine.netdna-ssl.com/wp-content/uploads/nctm-timed-tests.pdf

STRATEGIES FOR TEACHING AND LEARNING

Classify two-dimensional figures into categories based on their properties.

MGSE5.G.3 This standard calls for student to reason about the attributes (properties) of shapes. Student should have experiences discussing the property of shapes and explaining their reasoning.

MGSE5.G.4 This standard builds on what was done in 4th grade. Figures from previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube and trapezoid.

For example, explain how a right triangle can be both scalene and isosceles, but not equilateral.

SELECTED TERMS AND SYMBOLS

The following terms are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them.

The terms below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real-life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers. Due to the preponderance of advantages, inclusive definitions are used. For example, the inclusive definition of trapezoid specifies that it is a quadrilateral with at least one pair of parallel sides. For a great illustration and justification of this approach, see http://safeshare.tv/v/ss56aa7885e3e9c.

• acute angle

• acute triangle

• congruence/congruent

• equilateral triangle

• hexagon

• irregular polygon

• isosceles triangle

• kite

• obtuse angle

• parallel lines

• parallelogram

• pentagon

• perpendicular lines

• plane figure

• polygon

• quadrilateral

• rectangle

• regular polygon

• right angle

• right triangle

• rhombus/rhombi

• scalene triangle

• square

• triangle

• trapezoid

• two-dimensional

• vertex

Mathematics Glossary:

http://www.corestandards.org/Math/Content/mathematics-glossary/glossary