# 2-D Shapes

**Strand:** Shape and Space (3-D Objects and 2-D Shapes)

**Outcomes:** 6, 8

## Step 5: Follow-up on Assessment

### Guiding Questions

- What conclusions can be made from assessment information?
- How effective have instructional approaches been?
- What are the next steps in instruction?

### A. Addressing Gaps in Learning

If students are still struggling with recognizing the properties of 2-D shapes, try activities such as "What's My Shape?" in which a shape is pasted inside a piece of construction paper that is folded in half. A set of shapes, including the "secret shape" are spread out on a table or desk. Students ask the student leader, with the secret shape, questions that can be answered "yes" or "no." The question cannot be, "Is this one the secret shape?" As they are given answers, the students can eliminate shapes from the group until they are down to one remaining shape, which they may test against the secret shape hidden inside the folded construction paper.

This activity adapted from John A. Van de Walle, LouAnn H. Lovin, *Teaching Student-Centered Mathematics: Grades K–3*, 1e (p. 195). Published by Allyn and Bacon, Boston, MA. Copyright © 2006 by Pearson Education. Reprinted by permission of the publisher.

### B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades. Consider strategies, such as the following.

- Provide tips for parents on how to reinforce the students' knowledge of the properties of 2-D shapes. These properties are often not part of the parents' daily life and so they are not likely to be able to reinforce their students’ learning in this strand unless you provide them information about what the students are doing and the learning objectives of these sorting activities. Make sure they understand that it is the concepts that the students are developing, not the mathematical terminology, such as "parallel", "perpendicular," or "concave." They may need to be reminded of some of the discoveries about shapes that are so easily taken for granted, such as that the points on the circumference of a circle are all equidistant from its centre point and how one can draw a circle with a pencil and piece of string.
- Have the students sort other objects such as buttons, stones or trading cards using two attributes.

- Have the students do activities with pattern blocks or tangrams, to compose or decompose composite figures. There are books available with composite shapes to reproduce in order of difficulty. There are some "tangram tangles" puzzles provided in the
*Diagnostic Mathematics Program, Division I, Geometry *book on pages 116 to 124. If you do not have commercial tangrams for students, the tangram tangles are preceded by directions for tearing a square into the seven tangram shapes. There is also one example that can be used for tracing them onto plastic lids or a plastic sheet, then the shapes can be cut apart. Students like the commercial shapes, particularly the translucent ones made for overhead use as well as individual use. There are also tangram activities on Web sites.
- Integrate the work from patterns with geometry by having students review repeating patterns using squares, circles and triangles. In simple patterns, each of these three repeating shapes is the same size, colour and is in the same orientation. Later, make the patterns more complex by varying the size, colour and orientation (Del Grande and Morrow 1993).
- Have the students explore squares on the geoboard. Did they discover ones that have four, eight and twelve pegs on the boundaries? A similar exploration of rectangles may follow. Explain what is meant by pegs on the inside of the shape (only the ones that are not touching the bands). Then challenge students to make triangles with one peg inside, two pegs inside, then three and search for others, such as six inside pegs.

This activity adapted with permission from *Geometry and Spatial Sense* (p. 13) by John Del Grande and Lorna Morrow, copyright 1993 by the National Council of Teachers of Mathematics.