Angles and Triangles

Strand: Shape and Space (Measurement)
Outcome: 1

Strand: Shape and Space (3-D Objects and 2-D Shapes)
Outcomes: 4 and 5

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 the student has difficulty describing and providing examples of the regular and irregular polygons, including the different types of triangles, have the student construct 2-D shapes using a variety of manipulatives such as geoboards, straws and string.

By using straws and string construction, the focus is on the sides of 2-D shapes and provides a visual for students to see the essential properties; e.g., a regular polygon has all sides congruent. Have the students trace and superimpose the angles to determine congruency. Suggest that students use the corner of an index card or a protractor to determine whether triangles have obtuse, right or acute angles.

Encourage the students to use real-world objects to describe and provide examples of faces of
3-D objects that are regular and irregular polygons, including triangles of all types.

Use concept attainment (see Step 3, Section C: Choosing Learning Activities, Sample Activity 1) to aid students in describing properties of geometric concepts. It provides an opportunity for students to construct understanding of the geometric concepts and also the relationship among the concepts. Since this activity focuses attention on the properties of a given quadrilateral, students are better able to identify and sort polygons and justify their answers using sound mathematical reasoning.

If students are having difficulty identifying and sorting the polygons, have them construct one polygon, such as an equilateral triangle, out of straws or paper strips with brass fasteners. By changing the lengths of the straws or paper strips, e.g., making one side shorter or longer, students see visually the relationship between an equilateral triangle and an isosceles triangle. Have them focus on how the angles change when the side length changes (Alberta Education 1990, pp. 137–140).

Provide students with time to construct the different triangles using their protractor and ruler or straight edge so that the focus is on the size of the angles as well as the lengths of the sides; e.g., construct a right isosceles triangle. Since the lengths of the congruent sides may vary, students will have a variety of right isosceles triangles to explore as they share their constructions.

Ask guiding questions that aid students in connecting regular and irregular polygons with the different types of triangles. For example, have students sort a set of triangles into two groups, regular and irregular polygons, and justify their sorting. Also, have students construct tree diagrams to show relationships (see the tree diagram in Step 1, Big Ideas, and in Step 3, Section C: Choosing Learning Activities, Sample Activity 4).

Have students create a bulletin board display of the different types of triangles. Each student could create a triangle and place it in an appropriate cell in a chart, such as the one shown below. This helps students discover the cross-classifications that are possible when sorting triangles; i.e., they must classify each triangle by sides and by angles. They will also discover which cells in the chart are not possible to fill with any triangle.

Students could label each triangle as a regular or an irregular polygon.

Types of Triangles

	Equilateral	Isosceles	Scalene
Right
Acute
Obtuse

See Step 3, Section C: Choosing Learning Activities, Sample Activity 3: Connections among Geometric Concepts, for more information.

B. Reinforcing and Extending Learning

Strategies for Reinforcing and Extending Learning Word