Sorting and Describing Shapes and Objects
Strand: Shape and Space (3-D Objects and 2-D Shapes)
Outcomes: 6 and 7
Step 3: Plan for Instruction
Guiding Questions
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit the students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
A. Assessing Prior Knowledge and Skills
Before introducing new material, consider ways to assess and build on students' knowledge and skills related to 2-D shapes and 3-D objects. For example:
- How many different kinds of triangles can students draw? Have students write or discuss orally what is different about each triangle.
- How many different kinds of four-sided shapes can students draw? Have pairs of students compare their results. Which shapes could be considered part of the same group, and why?
- After the teacher makes a shape using a large geoboard template or clear geoboard on the overhead, have students use geoboards to make a shape that has something in common and not in common with the teacher's shape, and discuss.
- Using sets of geometric objects, or one set of objects used by the teacher and modelling clay for each student, have students choose or make an object that has something in common and not in common with the teacher's object, and discuss.
- Using cards that show the shapes of the faces of geometric objects, and a set of geometric objects, have students select cards that represent one of the faces of a given 3-D object. Sample face cards can be found online at http://illuminations.nctm.org/lessons/iveseen/SeenShape-AS-FaceCards.pdf.
Rather than look for preconceived right or wrong responses to these tasks, teachers should listen to their students' reasoning about why an object or shape is the same or different compared to another object or shape. Do students answer in a way that shows thoughtful analysis of attributes such as sides, faces, vertices and edges? Are students beginning to think in terms of classes of shapes or objects, generalizing about attributes that are the same or different? Are students beginning to form definitions for particular kinds of shapes based on attributes such as equal sides, regular angles or lines of symmetry, even if they do not have the mathematical language to produce conventional labels?
If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview, to determine the student's level of skill and understanding. See Sample Structured Interview: Assessing Prior Knowledge and Skills 
.
B. Choosing Instructional Strategies
Consider the following guidelines for teaching 2-D shapes and 3-D objects in Grade 3:
- Use an "Assessment for Learning" approach to ensure that students understand the learning intentions for all activities, understand what distinguishes quality work, receive descriptive feedback about their progress and have opportunities for self- and peer-assessment. For example, use the "Traffic Lights for 3-D Objects" and "Traffic Lights for 2-D Shapes" (Appendix 1, p. 31) before and after self-assessment of learning.
- Immediately after presenting a task, have students discuss the task with a partner and make predictions as to the outcome of the task.
- Have students work in partners or groups of three or four to complete tasks.
- Invite students to reflect on their predictions after a task has been completed.
- Ensure that students experience shapes and objects in different sizes and orientations. Shapes and objects that can be manipulated are a better choice for tasks than shapes that are printed on a page. Use paper shapes, clay solids, constructed solids, geometric solids, pattern blocks, tangrams, pentominoes, geoboards, attribute blocks, tessellation tiles, as well as virtual manipulatives (Internet or software programs) that can be moved around. A recommended source for virtual manipulatives is online at the National Library of Virtual Manipulatives site at http://nlvm.usu.edu/en/NAV/topic_t_3.html. Ensure that shapes include convex and concave angles, irregular polygons and a variety of quadrilaterals such as trapezoids and parallelograms. Ensure that students experience irregular 3-D objects.
- Plan a significant amount of time for students to compare strategies and outcomes as a whole class after a task has been completed. During this time, ask questions about the efficiency and mathematical thinking of particular responses to encourage greater abstraction and mathematical elegance.
- Ensure that tasks are differentiated. Students who are able to generalize about shapes and objects should have the opportunity to do so in the context of a given task and in response to questioning from the teacher. Students who rely on visual similarities between shapes and objects to complete tasks should be encouraged to do so, formulating correct responses based on visual observations rather than abstract generalizations. Both types of response are acceptable and correct at the Grade 3 level.
- Develop mathematical language for geometric shapes and objects and their properties. Many classroom communities like to adopt invented terms as common classroom language and appreciate it when the teacher honours these terms. It is also important, however, to introduce terms used by the wider mathematical community as appropriate language to use outside the context of the classroom; e.g., "The shape that we call a Bruce-angle is called a rhombus by most mathematicians." Students can look up terms and explore virtual shapes and objects using, for example, LearnAlberta's online mathematics glossary at /Resources/content/memg/index.html. The glossary has interactive demonstration applets for different kinds of polygons and clearly illustrated definitions for the terms edge, vertex and face. This can be a warm-up activity at the beginning of a lesson based in the computer lab. For example, use it as a part of Sample Learning Activity 3: Tangrams (p. 16), if you are using the virtual tangrams found at the National Library of Virtual Manipulatives site at http://nlvm.usu.edu/en/NAV/frames_asid_268_g_1_t_3.html?open=activities&from=topic_t_3.html. During any of the sample activities, learners can relate conventional and invented terms by making charts, posters or a class dictionary to create a common reference.
- Consider teaching geometry throughout the year, rather than as a discrete unit. For example, do one sample learning activity each month. Briefly review ideas already developed, using the work students produced previously, to trigger prior knowledge the next time a geometry activity is introduced.
C. Choosing Learning Activities
Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.
Grade 3
