Gary School Community Corporation Mathematics Department Unit Document. Unit Number: 8 Grade: 2


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1 Gary School Community Corporation Mathematics Department Unit Document Unit Number: 8 Grade: 2 Unit Name: YOU SEE IT!!! (2D & 3D Shapes) Duration of Unit: 18 days UNIT FOCUS Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two and threedimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. Standards for Mathematical Content 2.G.1: Identify, describe, and classify two and three  dimensional shapes (triangle, square, rectangle, cube, right rectangular prism) according to the number and shape of faces and the number of sides and/or vertices. Draw two  dimensional shapes. 2.G.2: Create squares, rectangles, triangles, cubes, and right rectangular prisms using appropriate materials. 2.G.3: Investigate and predict the result of composing and decomposing two  and three  dimensional shapes Standard Emphasis Critical Important Additional X X X 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.4: Model with mathematics PS.5: Use appropriate tools strategically PS.6: Attend to Precision PS.7: Look for and make use of structure
2 PS.8: Look for and express regularity in repeated reasoning Big Ideas/Goals Shapes can be analyzed and manipulated using their attributes. Shapes can classified by their vertices, sides and faces. Shapes can be classifed as 2dimensional or 3 dimensional. Essential Questions/ Learning Targets How do you identify and describe plane and solid figures? How are geometric shapes used in our lives? How are a rectangular prism and a pyramid similar? I Can Statements I can tell the difference between features that show the shape and features that do not show the shape. I can use features to build shapes. I can use features to draw shapes. I can build a new shape using two 2dimensional shapes. (rectangle, square, trapezoid, triangle, ½ circle, ¼ circle) I can build a new shape using two 3dimensional shapes. (cube, right rectangular prism, right circular cone, right circular cylinder). I can take a shape I have made from two shapes and change it to make a new shape. Color Key: Knowledge Reasoning Performance Product UNIT ASSESSMENT TIME LINE
3 Beginning of Unit PreAssessment Assessment Name: MClass (MOY Data) Assessment Type: PreAssessments Assessment Standards: 2.G.1; 2.G.2; 2.G.3 Assessment Description: Questions on the preassessment may include identifying and describing basic and threedimensional objects; understanding and categorizing twodimensional objects based on attributes; identifying and drawing points, lines, and line segments; and portioning shapes into equal areas, and using fraction to identify equal parts of a shape. The preassessment can be used throughout the unit to show what students know at the beginning, during the unit and at the end of the unit. Have students to change the color of their writing utensil to show growth, or the underline new information that is added. Throughout the Unit Formative Assessment Assessment Name: Geoboard Geometry Guru Assessment Type: Exit Ticket Assessing Standards: 2.G.1; 2.G.3 Assessment Description: Students should begin to use what they have learned about properties from the previous activities to be able to begin to classify shapes. Begin with shapes learned in previous grades and move up to focusing on quadrilaterals. Before beginning this task, students should be familiar with common quadrilaterals and the identification of their sides and angles. Also, they should be able to use a geoboard and transfer that information to paper. Some students may need specific instructions on how to transfer figures to the paper (e.g. counting the spaces between dots and directionality). Finally, students should be able to make multiple representations of the same shape with variance in size and orientation, and still determine it to be the same shape based on its attributes. Then students can use the same concept to build 3D shapes. Assessment Name: Shapes Are Everywhere
4 Assessment Type: Performance Task Assessing Standards: 2.G.2 Assessment Description: Students will use real life Famous figures and See how many threedimensional shapes could be identified from the picture. Then model for the students how to build a geometric threedimensional shape by using toothpicks and gumdrops. Explain to the students that the toothpicks will be the edges of the shape and the gumdrops will be the vertices. (See Lesson Plans for additional details. Show the class pictures of real life objects. Assessment Name: Can You Find It? Assessment Type: Performance Task Assessing Standards: 2.G.2; 2.G.3 Assessment Description: Students will create different geometric shapes in grids and label them. You may wish to open this lesson by reading a book such as Shape Spotter by Megan Bryant, The Story of Goldie Locks and the Three Squares by Grace Maccarone, or a similar book. Then, students will use the Can You Find It? student resource sheet to locate a rectangle, square, triangle, hexagon, pentagon, a quadrilateral that does not look like a rectangle or square, trapezoid, rhombus, a different looking hexagon, and a different looking trapezoid. They may color each shape a different color and then put some type of marking on all of the quadrilaterals, or you may want them to color all quadrilaterals the same color. rs/blm_40.pdf End of Unit Summative Assessments Assessment Name: Geometric Shapes Summative Assessment Assessment Type: Selected Response and Constructed Response Assessing Standards: 2.G.1; 2.G.2; 2.G.3 Assessment Description: The summative assessment consists of five selected response questions and a brief constructed response. The students will apply their knowledge of threedimensional geometric shapes. This will include knowing the number of faces, vertices, and edges along with the proper name for each threedimensional solid.
5 PLAN FOR INSTRUCTION Unit Vocabulary 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 Identify Classify Shape (cube, right, rectangular prism) Vertices Dimensional Shape Create Investigate Predict Features Difference Plane Figures Solid Figures Prerequisite Math Terms Describe Shapes (triangle, square, rectangle) Faces Sides Composing and decomposing Show Unit Resources/Notes Include district and supplemental resources for use in weekly planning 2.G.2 2.G.3 Targeted Process Standards for this Unit 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
6 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. PS.4: Model with mathematics Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas. Mathematically proficient students apply what they know and are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, twoway tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results
7 make sense, possibly improving the model if it has not served its purpose. 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. PS.8: Look for and express regularity in repeated reasoning Mathematically proficient students notice if calculations are repeated and look for general methods and shortcuts. They notice regularity in mathematical problems and their work to create a rule or formula. Mathematically proficient students maintain oversight of the process, while attending to the details as they solve a problem. They continually evaluate the reasonableness of their intermediate results.
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