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Gary School Community Corporation Mathematics Department Unit Document Unit of Study: 5 Grade: 5th Unit Name: Geometry- Polygons and Circles Duration of Unit: 15 days UNIT FOCUS Standards for Mathematical Content Standard Emphasis Critical 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures ********* 5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter. 5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties Mathematical Process Standards: ******** PS.1: Make sense of problems and persevere in solving them. PS.2: Reason abstractly and quantitatively PS.3: Construct viable arguments and critique the reasoning of others. PS.5: Use appropriate tools strategically PS.6: Attend to Precision PS.7: Look for and make use of structure Vertical Articulation documents for K – 2, 3 – 5, and 6 – 8 can be found at: http://www.doe.in.gov/standards/mathematics (scroll to bottom) Important ********* ********* Additional Essential Questions/ Learning Targets Big Ideas/Goals • • • • Polygons can be classified according to their attributes A shape is a quadrilateral when it has exactly 4 sides and is a polygon. To be a polygon the figure must be a closed plane figure with at least three straight sides. Triangles can be named and classified according to their angles or their sides. • • • • • Geometry is the mathematics • of space and shape. • Attributes of quadrilaterals can determine how they are classified. A square is always a rectangle because a square will always have 4 right angles like a rectangle. A rectangle does not have to have 4 equal sides like a square. It can have 4 right angles without 4 equal sides. Therefore, a rectangle is not always a square. A square is always a rhombus because it has 4 equal sides like a rhombus and it is also a rectangle because it has 4 right angles like a rectangle. A rhombus does not have to have right angles like a square. It can have 4 equal sides without having 4 right angles. Therefore a rhombus is not always a square. A parallelogram can be a • • • • • What attributes are needed classify different types of quadrilaterals? What attributes are needed to classify different types of triangles? How do we use triangle sides to classify triangles? How do the angle measures of a triangle determine the way it is named? What are some examples of geometric shapes and objects in your everyday world? • What are properties of a quadrilateral? • What attributes distinguish a square from a rhombus? How are they alike? • What attributes distinguish a rectangle from a parallelogram? “I Can” Statements • • I can classify quadrilaterals according to their attributes. I can describe the attributes that distinguish different triangles. • I can determine whether a triangle is acute, right, or obtuse. • I can classify and name a triangle by measuring its angles. • I can name and identify geometric shapes and objects around me. • • I can describe, analyze, create, and compare properties of 2-D and 3-D figures. I can justify the classification of different quadrilaterals. 2 rectangle if it has 4 right angles. UNIT ASSESSMENT TIME LINE Beginning of Unit – Pre-Assessment Assessment Name: Show Me What You Know Assessment Type: Constructed Response Assessment Standards: 5.M.3, 5.G.1, 5.G.2 Assessment Description: By the conclusion of this unit, students should be able to demonstrate the following competencies: Classify quadrilaterals (square, rectangle, parallelogram, kite, trapezoid, and rhombus). Classify the different types of triangles by their attributes. Identify and sort two-dimensional and geometric figures by their properties. (circle, half/quarter circle, triangle, quadrilaterals, pentagon, hexagon) Classify two-dimensional figures in a hierarchy based on properties. Classify polygons by attribute A pre-assessment of the above skills Throughout the Unit – Formative Assessment Assessment Name: Investigating Triangles Assessment Type: Exit Ticket Assessing Standards: 5.G.1 Assessment Description: Angles are difficult, complicated figures for students to understand because they must be understood as a rotation from one place to the next, as a geometric shape, and a combination of both when measuring . Be prepared to help students identify individual angles in a triangle and deal with misconceptions about those angles. Assessment Name: Investigating Polygons Assessment Type: Exit Ticket 3 Assessing Standards: 5.G.2 Assessment Description: The purpose of this task is for students to become familiar with the properties of quadrilaterals.. They will classify two-dimensional shapes into a hierarchy based on properties. Details learned in earlier grades need to be used in the descriptions of the attributes of shapes. The more ways that students can classify and discriminate shapes, the better they can understand them. They will identify the attributes of each quadrilateral, then compare and contrast the attributes of different quadrilaterals The shapes are not limited to quadrilaterals. Assessment Name: Quadrilateral Check for Understanding Assessment Type: Selected Response, Constructed Response Assessing Standards: 5.G.2 Assessment Description: The purpose of this task is to motivate students to examine relationships among geometric properties. According to Van Heile, the students move from recognition or description to analysis. When asked to describe geometric figures, students rarely mention more than one property or describe how two properties are related. In this activity, by having to choose figures according to a pair of properties, students should go beyond simple recognition to an analysis of the properties and how they interrelate End of Unit – Summative Assessments Assessment Name: Quadrilateral Hierarchy Diagram Assessment Type: Performance Task Assessing Standards: 5.M.3, 5.G.1, 5.G.2 Assessment Description: The students will create a Hierarchy Diagram using the terms: quadrilaterals, parallelogram, non parallelograms, rectangle, square, rhombus, trapezoid, kite, and other: Classify quadrilaterals (square, rectangle, parallelogram, kite, trapezoid, and rhombus). Classify the different types of triangles by their attributes. Identify and sort two-dimensional and geometric figures by their properties. (circle, half/quarter circle, triangle, quadrilaterals, pentagon, hexagon) Classify two-dimensional figures in a hierarchy based on properties. Classify polygons by attribute PLAN FOR INSTRUCTION Unit Vocabulary 4 Key terms are those that are newly introduced and explicitly taught with expectation of student mastery by end of unit. Prerequisite terms are those with which students have previous experience and are foundational terms to use for differentiation. Key Terms for Unit Prerequisite Math Terms Rhombus Quadrilateral Area Polygon Square Triangle Rectangle Parallelogram Pentagon Hexagon Cube Trapezoid Right triangle Kite Attribute Hierarchy Unit Resources/Notes Include district and supplemental resources for use in weekly planning Targeted Process Standards for this Unit 5 PS.1: Make sense of problems and persevere in solving them Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” and "Is my answer reasonable?" They understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand how mathematical ideas interconnect and build on one another to produce a coherent whole. PS.2: Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. PS.3: Construct viable arguments and critique the reasoning of others Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They analyze situations by breaking them into cases and recognize and use counterexamples. They organize their mathematical thinking, justify their conclusions and communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. They justify whether a given statement is true always, sometimes, or never. Mathematically proficient students participate and collaborate in a mathematics community. They listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 6 PS.5: Use appropriate Tools Strategically Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. PS.6: Attend to precision Mathematically proficient students communicate precisely to others. They use clear definitions, including correct mathematical language, in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They express solutions clearly and logically by using the appropriate mathematical terms and notation. They specify units of measure and label axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently and check the validity of their results in the context of the problem. They express numerical answers with a degree of precision appropriate for the problem context. PS.7: Look for and make use of structure Mathematically proficient students look closely to discern a pattern or structure. They step back for an overview and shift perspective. They recognize and use properties of operations and equality. They organize and classify geometric shapes based on their attributes. They see expressions, equations, and geometric figures as single objects or as being composed of several objects. 7