BC Education - Mathematics 10 to 12 - Shape and Space (3-D Objects and 2-D Shapes)

Applications of Mathematics 10 -
Shape and Space (3-D Objects and 2-D Shapes)

This 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 solve coordinate geometry problems involving lines and line segments.

It is expected that students will:

solve problems involving distances between points in the coordinate plane
solve problems involving midpoints of line segments
solve problems involving rise, run and slope of line segments
determine the equation of a line, given information that uniquely determines the line
solve problems using slopes of:
- parallel lines
- perpendicular lines

SUGGESTED INSTRUCTIONAL STRATEGIES

Describing linear relationships is essential to interpreting and predicting the behaviour of the world around us.

Using a geoboard, have students stretch an elastic between two posts to form a line segment, then stretch one side of the elastic around the appropriate post to form a right triangle. Have them measure the orthogonal sides by counting the posts and use the Pythagorean Theorem to find the length of the original line segment (hypotenuse of triangle).
Have students use a clinometer to measure the angle to the top of a building and connect the tangent of the angle to the slope of the line to the top of the building.
Develop a five-station carousel where each station has a different type of word problem (e.g., distance, midpoint, slope, equations of lines, parallel and perpendicular lines). Design a treasure hunt or rally to send students from station to station to solve problems. Use a point system to award prizes for the most accurate solutions.
Given an equation for a line, have students list five unique pieces or types of information that they could use to find that equation. For example, given students could list the following:
- different points on the line (6,2),(9,4),...
- slope of line is
- or the point (0,-2)
- x-intercept = 3 or the point (3,0)
- standard form of equation,
- slope intercept form is:
Have students use a graphing calculator or graphing software to explore the similar attributes of parallel or perpendicular lines. Give students six lines to graph and have them note which lines are parallel or perpendicular, analysing the similarities in their equations.
Have students use technology with dynamic geometry software to draw two lines, then rotate one line. Have them note how its slope changes as it first becomes parallel, then perpendicular to the other line.

SUGGESTED ASSESSMENT STRATEGIES

Solving problems in the coordinate plane is a natural extension of graphing, geometry, and algebraic skills. Assessment should focus students’ conceptualization of the coordinate plane and its uses in understanding the world around them.

Observe

Take note of students’ approaches to word problems that require line and segment solutions. Students should be able to explain the steps they took to translate word problems into a drawing on the coordinate system. Observe students’ abilities to draw and label clearly.

Question

For select problems, question students as to the method they used. For example, ask if the student can check a pen-and-paper solution using a graphing tool or vice versa.

Presentation

Ask students to select a graphic representation of a solution to a problem they have created. Have them present the problem to members of a small group and then teach the problem solution. Use student created problems on teacher tests where appropriate.
Ask students to create a poster that shows the relationship between a linear equation and its components.

Collect

Place information about various linear equations on file cards on a table. Give students one file card and have them list or collect cards with data related to the equation on their card.

Peer Assessment

Ask students to work in pairs using graphing calculators. Students can display graphs on their calculators, then challenge their partners to reproduce the graphs on their own calculators.
Have one student generate an equation in slope-intercept form and a partner change it to general form and vice versa. Students can check each other’s work for accuracy.