Compose Shapes Unit of Study: 3-Dimensional Shapes Global Concept Guide: 2 of 3

Content Development “Composing and decomposing shapes require spatial visualization, an important foundation of geometry. Children compose shapes when they put them together. Decomposing shapes involves determining which shapes could have been put together to make a given shape” (Go Math, p. 453C). Children will have success with geometry if they are regularly seeing, manipulating, and describing three-dimensional shapes. Sinclair (2003) reported that students must bring some explicit mathematical knowledge to the process. That is, an intuition about a generalization involves more than observed evidence” (p. 192). Inquiry and investigation of 3-dimensional shapes will build explicit knowledge that will later lead to generalizations about geometry and shapes.

Day 1  How can you combine three-dimensional shapes to make new shapes?  Use Go Math Lesson 11.2, pp  Essentials: Students should each have their own 3-dimensional figures to assist with investigating and composing shapes.  Teachers should be carefully observing the ways in which the learner engages with the figures and their ability to decipher shapes once composed. Can they see them differently?  Extend the Math, p. 463 provides an excellent opportunity to engage in small group investigation and discussion about flat and curved surfaces.

Day 2  How can you use a combined shape to build a new shape?  Go Math Lesson 11.3, pp  Using concrete objects, children explain their reasoning as they identify attributes and the positions of the shapes in the new construction.  Can a cone go on top of a cube? Can a cube go on top of a cone? Explain (A cone has an apex so a cube cannot set on top of the cone without falling.)  Why would cylinders in a combined shape be standing vertically rather than horizontally? (They would roll and not stay combined.)  Focus on prepositional phrases to assist with clarify the position of shapes in a combined figure.  Watch for students who may only focus on the orientation (vertical, horizontal, etc) of the blocks instead of their relative positions(next to, on top of, etc).  You may choose to wrap up with Mid-Chapter Checkpoint, p. 468.

Day 3  What strategies can you use to help deconstruct (take apart) a combined shape?  Go Math Lesson 11.3, pp  Students will break apart complicated figures into shapes, they will analyze the structure of a single entity as well as several composite shapes. The shape is defined by the sum of its parts—connect the constructed model (3-d) with a pictured shape (2-d). Facilitate discussion of making generalizations about ways to identify 3-d figures when pictured as 2-d.

Enrich/Reteach/Intervention  Students with excellent spatial reasoning could engage in “Send a Problem”. Working with a partner, each builds a new shape. Swap tables to repeat the figure started by their partner. Next, they record in their math journals a 2-d representation and identify the individual shapes used in the composite figure.  Students struggling to visualize the faces of a 3-d shape may require a bit more intervention. Go Math, Lesson 11.4, p. 469B Tier 1 Reteach may be appropriate.

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