Overview. Essential Questions. Grade 1 Mathematics, Quarter 2, Unit 2.2 Exploring Shapes and Their Attributes

Transcription

1 Exploring Shapes and Their Attributes Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Distinguish between defining and nondefining attributes. Build and draw shapes that have defining attributes. Compose two-dimensional shapes or threedimensional shapes to create a composite shape. Compose new shapes from a composite shape. Partition circles and rectangles into equal halves or equal fourths. Use appropriate words and phrases to describe the equal shares (halves, fourths, quarters, half of, fourth of, quarter of). Understand that decomposing into more equal shares will create smaller shares. Mathematical Practices to Be Integrated 3 Construct viable arguments and critique the reasoning of others. Create composite shapes and communicate how they were created to others. Communicate the reasoning that determined how a shape was portioned into equal halves or fourths. 7 Look for and make use of structure. Sort 2-D and 3-D shapes by their attributes and explain your reasoning. Essential Questions What are attributes of all? (e.g., rectangles) How can you build and draw shapes with specific attributes? How can you use shapes to create new shapes? How can circles or rectangles be partitioned into equal shares? How can you sort a group of shapes? Providence Public Schools D-45

2 Exploring Shapes and Their Attributes (7 9 days) Standards Common Core State Standards for Mathematical Content Geometry 1.G Reason with shapes and their attributes. 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. 4 4 Students do not need to learn formal names such as right rectangular prism. 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. Common Core State Standards for Mathematical Practice 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 are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, 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. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 8 equals the well remembered , in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see D-46 Providence Public Schools

3 Exploring Shapes and Their Attributes (7 9 days) Grade 1 Mathematics, Quarter 2, Unit 2.2 complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Clarifying the Standards Prior Learning In Kindergarten, students described objects in the environment using names of shapes. They used terms like above, beside, in front of, behind, and next to to describe the shapes positions. Kindergarteners named shapes regardless of size or orientation. They identified flat shapes as two-dimensional and solids as three-dimensional. Students analyzed and compared two-dimensional and three-dimensional shapes according to their attributes. They built shapes from components (sticks, balls of clay) and drew shapes. They composed simple shapes to make larger ones. Current Learning Reasoning about attributes of and composing and decomposing geometric shapes is a critical area in Grade 1. Students distinguish between defining attributes (e.g., triangles are closed and three sided) and nondefining attributes (e.g., color, orientation, overall size). They build shapes that have defining attributes. They compose two-dimensional and three-dimensional shapes to create a composite shape. They also compose a new shape incorporating the composite shapes previously made. Students partition circles and rectangles into two and four equal shares, and they describe the shares using the words halves, fourths, and quarters. They also use the phrases half of, fourth of, and quarter of to describe the shares and describe the whole as two or four of the shares. Future Learning In Grade 2, students will draw shapes with specific attributes (number of equal faces, number of angles, and number of sides), and they will identify quadrilaterals and pentagons. Students will view rectangles in terms of equal groups of rows and columns. and they will partition circles and rectangles into thirds. They will use the terms half of and third of to describe equal shares, and they will view the whole as two halves, three thirds, or four fourths. Students will understand that equal parts of the same whole may not be the same shape. Additional Findings The geometric and spatial knowledge children bring to school should be expanded by explorations, investigations, and discussions shapes and structures in the classroom. Students should use their notions of geometric ideas to become more proficient in describing, representing, and navigating their environment. They should learn to represent 2D and 3D shapes through drawings, block constructions, dramatizations, and words. They should explore shapes by decomposing them and creating new ones. Their knowledge of direction and position should be refined through the use of spoken language to locate objects by giving and following multi-step directions. (Principles and Standards for School Mathematics, p. 97) First grade children are more likely than older children to think of contrasting forms by counting the number of sides and corners. As children move through the grades, they are less likely to notice such attributes. (A Research Companion to Principles and Standards for Mathematics, p. 161) Providence Public Schools D-47

4 Exploring Shapes and Their Attributes (7 9 days) Assessment When constructing an end-of-unit assessment, be aware that the assessment should measure your students understanding of the big ideas indicated within the standards. The CCSS for Mathematical Content and the CCSS for Mathematical Practice should be considered when designing assessments. Standards-based mathematics assessment items should vary in difficulty, content, and type. The assessment should comprise a mix of items, which could include multiple choice items, short and extended response items, and performance-based tasks. When creating your assessment, you should be mindful when an item could be differentiated to address the needs of students in your class. The mathematical concepts below are not a prioritized list of assessment items, and your assessment is not limited to these concepts. However, care should be given to assess the skills the students have developed within this unit. The assessment should provide you with credible evidence as to your students attainment of the mathematics within the unit. Build and draw shapes to possess defining attributes Compose 2D and 3D shapes to create a composite shape Compose a new shapes from a composite shape Partition circles and rectangles into equal halves and fourths Describe shares using the words halves, fourths, and quarters Determine what happens to the whole when it is decomposed into equal shares Learning Objectives Instruction Students will be able to: Distinguish between defining and non-defining attributes. Build and draw shapes that possess defining attributes. Compose two-dimensional (2D) shapes: rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles. Compose three dimensional (3D) shapes: cubes, right rectangular prisms, right circular cones, and right circular cylinders. Create a composite shape from 2D or 3D shapes. Compose new shapes from composite shapes. Partition circles and rectangles into two and four equal shares. Describe shares using the words halves, fourths, and quarters. Describe shares using the phrases half of, fourth of, and quarter of. Describe what happens to the whole when it is decomposed into equal shares. Demonstrate understanding of the concepts and skills learned in this unit. D-48 Providence Public Schools

5 Exploring Shapes and Their Attributes (7 9 days) Grade 1 Mathematics, Quarter 2, Unit 2.2 Resources envision Math Grade 1, Pearson Education, Inc., 2009 Topic 8 Teacher Edition, Geometry Resource Masters Student Edition pages Also see Section I, Supplemental Materials Lesson 08-11A Building With Solid Figures Topic 19 Teacher Edition, Fractional Parts Resource Masters Student Edition pages Also see Section I, Supplemental Materials Lesson 19-3A Making Halves and Fourths of Rectangles and Circles Teacher Resources Binder Investigations in Number, Data, and Space Grade 1, Pearson Education, Inc., 2008 Implementing Investigations in Grade 1 Implementation Guide Unit 2 Teacher Edition, Making Shapes and Designing Quilts Investigation 1, Composing and Decomposing 2D Shapes Investigation 2, Describing and Sorting Shapes Unit 9 Teacher Edition, Blocks and Boxes Investigation 1, Comparing and Constructing 3D Shapes Investigation 2, Building a Block Town Also see Section I, Supplemental Materials Lesson 2.3A Cones and Cylinders Pearson Online Success Net, Exam View Assessment Suite Note: The district resources may contain content that goes beyond the standards addressed in this unit. See the Planning for Effective Instructional Design and Delivery and Assessment for information and resources to refer to when planning your unit and individual lessons. Materials Chart paper, pattern blocks, construction paper, glue, geometric solids, geoblocks, plane shape cards, pattern blocks, large construction paper, envelopes or closeable plastic bags Providence Public Schools D-49

6 Exploring Shapes and Their Attributes (7 9 days) Instructional Considerations Key Vocabulary defining attributes non-defining attributes solid figure vertex vertices equal parts fourth half halves quarter unequal parts Planning for Effective Instructional Design and Delivery In grade 1, reasoning about attributes of, and composing and decomposing geometric shapes is a critical area of instructional focus as defined by the Common Core State Standards. The Common Core State Standards state that students compose and decompose plane or solid figures and build understanding of part-whole relationships as well as the properties of the original and composite shape. As students combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different. Fill the Hexagons is an activity where students fill several hexagons using pattern blocks. Quick Images with Shapes helps students in developing visual images of, and language for describing 2D shapes. It provides repeated opportunities to identify names and attributes of 2D shapes. Investigations Activities and Center Activities: Students should be engaged in ongoing and repetitive practice of the skills and concepts in this unit. Investigations Activities (Start With/Get To, Collect 20 Together, Roll and Record Subtraction, Five in a Row, Compare Dots, and Compare) and one or two envision Math Center Activities are made available throughout this unit. Choose one or two envision Math Center Activities that reinforce the CCSS addressed in this topic. The Implementing Investigations Resource guide provides detailed information on the activities and routines and variations that can be used to support the Common Core State Standards. In Lesson 8-2 (TE, page 199), use identifying similarities and differences to practice sorting plane shapes and identifying their properties. As part of the Interactive Learning, model sorting plane shapes by classifying using defining and non-defining attributes. Help the students create and post a Classification Chart that demonstrates the traits of sorting plane figures by sides and corners. Use teacher created common tasks as formative assessments to monitor student progress and understanding of critical content and essential questions. Use data from formal and informal assessments to guide your instruction and planning. For planning considerations, read through the teacher editions for suggestions about scaffolding techniques, using additional examples, and differentiated instruction as suggested by the envision and Investigations resources. D-50 Providence Public Schools

7 Exploring Shapes and Their Attributes (7 9 days) Grade 1 Mathematics, Quarter 2, Unit 2.2 Notes Providence Public Schools D-51

8 Exploring Shapes and Their Attributes (7 9 days) D-52 Providence Public Schools