Grade 7 - Shape and Space (3-D Objects and 2-D Shapes)

The sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will link angle measurements to the properties of parallel lines.

It is expected that students will:

measure and classify pairs of angles, complementary angles (90°), or supplementary angles (180°)
identify and name pairs of angles pertaining to parallel lines and transversals, including:
- corresponding angles
- vertically opposite angles
- interior angles on the same side of the transversal
- exterior angles on the same side of the transversal
- interior alternate angles
describe the relationships between the pairs of angles pertaining to parallel lines and transversals
use mathematical reasoning to determine the measures of angles in a diagram
perform calculations with angle measures
construct angle bisectors and perpendicular bisectors
explain in more than one way why the sum of the measures of the angles of a triangle is 180°

To view the prescribed learning outcomes for Shape and Space (3-D Objects and 2-D Shapes) in other grades click on an icon below.

SUGGESTED INSTRUCTIONAL STRATEGIES

Geometric models can provide a perspective that can make an abstract representation of the world more easily understood. As students construct, draw, measure, compare, and classify figures, they develop more meaningful definitions for relationships among figures and are more able to use these ideas to develop informal conjectures. Students should be challenged to analyse their thinking about lines and angles and justify their explanations.

Have students create tessellations using trapezoids, triangles, or parallelograms (pattern blocks). Have them discuss the segments and angles created in their figures. Ask them to present information to answer the following questions:
- Which lines are parallel?
- Which lines are transversals?
- Which angles are interior alternate or supplementary pairs?
- Which angles are complimentary or supplementary?
- Which lines are interior or exterior?
Have students transfer the tessellations to paper and label them. Have them use the pattern blocks to identify the equal angles. Ask them to measure only one angle, and then, using previous knowledge, ask them to discuss how to calculate the remaining angles. Have them label all the angle sizes in their tessellations.
Have students integrate art with geometry by creating designs by bisecting angles and lines.
To introduce angles and prompt discussion, have students stand in a circle with one person in the middle. Pull three strings from the middle to serve as radii. Have students pass the strings around the circle to create different angles.

SUGGESTED ASSESSMENT STRATEGIES

Geometry is the study of objects, motions, and relationships in a spatial environment. As students become more skilled at connecting the physical world to abstract representations, they demonstrate how well they have developed spatial awareness. As they work and talk together, students can share ideas, draw conclusions, and analyse their activities.

Observe

Find pictures in magazines that show a variety of angles and lines. Have students present and describe the pictures to the class. Record the extent to which students use vocabulary appropriately.
Have groups of students model with metre-sticks the variety of angles and intersecting lines. Observe the students to ensure that they use correct definitions and examples.

Collect

Collect student line designs that use bisection. Look for accuracy in their construction process.
Give the students a worksheet that contains randomly mixed pictures of angles and names. Have students complete the worksheet by matching the appropriate pairs.