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, “ 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

Essential Question: How can you combine three-dimensional shapes to make new shapes?

  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?

   Engage: Go Math Lesson 11.2, Extend the Math p. 463 provides an excellent opportunity to engage in small group investigation and discussion about flat and curved surfaces.

Building Conceptual Knowledge/Independent Practice: Go Math On Your Own p.463 #4-8 and Problem Solving p. 464 #9-12. Students will determine which 3D shape is composed of the given 3D shapes. Possible Closure: Go Math Math Journal p. 464 By the end of Day 1, students should be able to identify a 3D shape composed from other 3D shapes.

Day 2

Essential Question: How can you use a combined shape to build a new shape?

       Focus on prepositional phrases to assist with clarifying 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).

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.) Engage: Go Math Lesson 11.3, Enrich p. 465B (TE Manual). Students will build a structure from 3D shapes. Partners will combine their composed 3D shapes into a new 3D shape. Students will describe the new composed 3D shape with their partner.  Drawing the 3D shapes can be difficult for 1 depict the composed shape. st graders, a suggestion is to use the 3D shape cards from the lesson, I’ve Seen that Shape Before p. 14, to cut out the appropriate shape and glue together to Building Conceptual Knowledge: Go Math, Share and Show p. 466 #1-3. Ask students, “Is there another way the shapes can be placed?”  Emphasize the shapes can be flipped or rotated after the combined shape has been repeated. Independent Practice: Go Math On Your Own p. 467 #4-7 Closure: Go Math Mid-Chapter Checkpoint p. 468 By the end of Day 2, students should be able to use combined shapes to build a new three dimensional shape.

Day 3

Essential Question: What strategies can you use to help deconstruct (take apart) a combined shape?

  Engage: Go Math Enrich p. 469B. Students will build a composite shape from cubes, cones, cylinders, and rectangular prisms and keep the composite shape hidden from a partner. The composite shape is revealed to the partner and the partner has to rebuild the figure and identify the shapes.  The teacher needs to make sure the students are using precise language when describing the 3D shapes. Building Conceptual Knowledge: Go Math Lesson 11.4, Try Another Problem p. 470 #1,2. Students will identify the 3D shapes from the given constructed/composite shape. Facilitate a discussion about how students know which 3D shapes are used to build the tower. Use the guiding questions on p. 470 (TE Manual).  Independent Practice: Go Math On Your Own p. 472 #8-11.  Closure: Discuss #10 from the independent practice- different views or orientations of the same shape. By the end of Day 3, students should be able to identify 3D shapes from a constructed/composite shape.

Students should take the performance task on this day. Give to small groups or individually while others are working.

Enrich/Reteach/Intervention

Use your anecdotal notes and observations from the previous three days to plan the reteach lessons.  Reteach/Intervention:  Go Math Lesson 11.4 p. 469B Tier 1. The teacher is using 3D shapes to create a composite shape. The teacher provides each student a 2D representation of one of the shapes and the student has identify where it is located.  Go Math Language Support p. 469B  Enrich:  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.

Literature for your Classroom Library

Dayle Ann Dodds Moira Anderson