# Transformations

**Strand:** Shape and Space (Transformations)

**Outcomes:** 5, 6

## 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

**Congruence**

If the student is having difficulty with congruence, provide many opportunities for him or her to use concrete materials that are congruent, such as congruent pattern blocks or tiles. Place the congruent shape in a variety of orientations to reinforce the concept that shapes remain congruent when the orientation changes. Connect the work done with concrete materials to diagrams. Have the student draw the two congruent shapes using square or isometric dot paper.

To create congruent shapes, have the student draw a design on folded paper, cut it out and verify that the two shapes have the same shape and size. When matching congruent shapes to select congruent pairs or to identify corresponding sides and vertices, have the students cut out the shapes and superimpose on over the other. If the student is unable to cut out the shape because it is in a book, provide tracing paper so that he or she can trace the 2-D shape and superimpose it on other shapes to determine congruency and the corresponding sides and vertices.

**Symmetry**

If the student is having difficulty with symmetry, reinforce the connection to congruence by using folded paper to create symmetrical designs. Explain that the fold forms the axis of symmetry. Have the student identify symmetrical shapes by folding them. Provide tracing paper for the student to trace shapes out of books and then fold the cut out shapes to determine if they are symmetrical.

Use a variety of manipulatives to address the different learning styles. Provide experiences with folded paper, Miras, pattern blocks and geoboards. Ask probing questions to encourage the students to explain their thinking. Connect the manipulation of objects to diagrams by having the students draw the designs created.

When creating a symmetrical shape without manipulatives, have the students create half a design on grid paper and draw a vertical axis of symmetry along one of the sides of the design. Remind the students that the other half of the design must be congruent to the half design drawn. Review that congruent shapes have corresponding vertices. Have the students complete the other half by visually counting the spaces of corresponding vertices from the axis of symmetry. Continue work with vertical axes of symmetry until the students understand the process. Then include horizontal lines of symmetry as the students create and complete symmetric designs. Oblique lines of symmetry may be too difficult for some students so professional discretion must be used.

### B. Reinforcing and Extending Learning

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

Strategies for Reinforcing and Extending Learning