Unit 9: May/June Solid Shapes


 Aldous Byrd
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1 Approximate time: 45 weeks Connections to Previous Learning: Students have experience studying attributes and names of flat shapes (2dimensional). Focus of the Unit: Students will extend knowledge of flat (2dimensional) shapes to name, compose, analyze, and compare 3dimensional shapes. They will build shapes from components or smaller shapes, and connect them to objects within their environment. Connections to Subsequent Learning: Students will use their knowledge of shapes and their attributes to distinguish between shapes, and use those defining attributes to build and draw other shapes. They will also compose twodimensional or threedimensional shapes from other 2 and 3dimensional shapes. In first grade, students will begin decomposing circles and rectangles into equal, smaller shares (beginning fractions). From the K6, Geometry progression document pg.67 From experiences with varied examples of these shapes (e.g., the variants shown in the margin), students extend their initial intuitions to increasingly comprehensive and accurate intuitive concept images of each shape category. These richer concept images support students ability to perceive a variety of shapes in their environments and describe these shapes in their own words. MP7 This includes recognizing and informally naming threedimensional shapes, e.g., balls, boxes, cans. Such learning might also occur in the context of solving problems that arise in construction of block buildings and in drawing pictures, simple maps, and so forth. Students also begin to name and describe threedimensional shapes with mathematical vocabulary, such as sphere, cube, cylinder, and cone. K.G.1 They identify faces of threedimensional shapes as twodimensional geometric figures K.G.4 and explicitly identify shapes as twodimensional ( flat or lying in a plane) or threedimensional ( solid ). K.G.3 A second important area for kindergartners is the composition of geometric figures. Students not only build shapes from components, but also compose shapes to build pictures and designs. Initially lacking competence in composing geometric shapes, they gain abilities to combine shapes first by trial and error and gradually by considering components into pictures. At first, side length is the only component considered. Later experience brings an intuitive appreciation of angle size. Major Standards Supporting Standards Additional Standards Page 1
2 Standard(s): Desired Outcomes Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. K.G.2 Correctly name shapes regardless of their orientations or overall size. K.G.3 Identify shapes as twodimensional (lying in a plane, flat ) or three dimensional ( solid ). Analyze, compare, create, and compose shapes K.G.4 Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length) K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.6 Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle? Routines: Know number names and the count sequence. K.CC.1 Count to 100 by ones and tens K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). Centers: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.5 Fluently add and subtract within 5 Work with numbers to gain foundations for place value. K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = ); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Know number names and the count sequence. K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). Major Standards Supporting Standards Additional Standards Page 2
3 Transfer: Students will apply Knowledge of twodimensional shapes to threedimensional shapes to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length). Modeling of shapes in the world by building shapes from components and drawing shapes. Understandings: Students will understand that Threedimensional shapes have unique attributes. Threedimensional shapes have specific names regardless of their orientations or overall size. Shapes can be used to build pictures, designs and other shapes. Shapes can be built from components. Essential Questions: What determines the difference between 2dimensional and 3dimensional shapes? Why is mathematical language critical when describing 2dimensional and 3dimensional shapes? Highlighted Mathematical Practices: (Practices to be explicitly emphasized are indicated with an *.) 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. Students reason about the attributes of 3dimensional figures by counting faces, edges and corners. * 3. Construct viable arguments and critique the reasoning of others. Students construct arguments by defending the way they have sorted shapes, when sorting flat and solid figures. They critique each other s reasoning when discussing if they agree or disagree with the way others have sorted. 4. Model with mathematics. Students use informal language to describe attributes of flat and solid shapes. Students will build complex shapes from simpler shapes using geometric tools. In addition, students study the shapes by composing them from 2dimensional figures. They model when they can describe how real world objects have shapes or are composed of shapes. 5. Use appropriate tools strategically. Students will use their geometric figures and component parts to construct, describe and replicate 3dimensional figures. * 6. Attend to precision. Students build geometric shapes from other size/orientation of shapes. They will use this knowledge to build a richer vocabulary to describe 3dimensional shapes in their own words. 7. Look for and make use of structure. Students will examine the structure of 3dimensional shapes and use the structure to discuss similarities and differences between the figures. 8. Look for and express regularity in repeated reasoning. Major Standards Supporting Standards Additional Standards Page 3
4 Prerequisite Skills/Concepts: Students will compose, analyze, and compare flat shapes to build descriptive knowledge of geometric attributes Advanced Skills/Concepts: Students will determine defining attributes of 3dimensional figures. Knowledge: Students will know Attributes of flat and solid shapes (K.G.4) Names of 2 and 3dimensional shapes (K.G.2) WIDA Standard: English Language Learners Skills: Students will be able to do Analyze and compare 2 and 3dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts, and other attributes. (K.G.4) Model shapes in the world by building shapes from components and drawing shapes. (K.G.5) Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. (K.G.1) Identify shapes as flat or solid. (K.G.3) English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. English language learners would benefit from: The teacher describing objects in the environment using the names of shapes and labeling the shape. Students looking for other objects that are the same shape as the one the teacher shared, vebalizing the shape name. The teacher identifying shapes as twodimensional (flat) or three dimensional (solid) and showing examples of threedimensional shapes. Students looking for additional examples of 3D shapes. The teacher showing threedimensional shapes of different sizes and describing their similarities and differences. Students analyzing and comparing two different sized shapes describing their parts (number of sides and vertices/"corners") and other attributes such as length of sides. Students building shapes from materials such as clay. The teacher modeling how a larger shape can be composed of two smaller shapes and students building a larger shapes using two or more simple shapes. Students repeatedly verbalizing the names of the smaller shapes used to compose the larger shape. Major Standards Supporting Standards Additional Standards Page 4
5 Academic Vocabulary: Critical Terms: Attribute Side Length Orientation Square Circle Triangle Rectangle Hexagon Cube Cone Cylinder Sphere Supplemental Terms: Assessment PreAssessments Formative Assessments Summative Assessments SelfAssessments Sample Lesson Sequence Major Standards Supporting Standards Additional Standards Page 5
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