Essentials of Mathematics
10 -
Geometry Project
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 complete a project that includes a 2-D plan and a 3-D model of some physical
structure
It is expected that students
will:
- measure lengths using
both SI Metric and Imperial units
- estimate measurements
of objects in SI and Imperial systems including:
- draw top, front and side
views for both 3-D rod or block objects and their sketches
- sketch and build 3-D
designs using isometric dot paper
- determine the relationships
among linear scale factors, areas, surface areas, and volumes of similar figures
and objects
- enlarge or reduce a
dimensioned object according to a specified scale
- solve problems involving
linear dimensions, area, and volume
- interpret drawings and
use the information to solve problems
- complete a project that
includes a 2-D plan and a 3-D model of some physical structure
SUGGESTED
INSTRUCTIONAL STRATEGIES
The ability to make sense
of 2-D and 3-D scale representations is an important skill for solving construction
problems. Study of geometry gives students opportunities to acquire a sense
of proportion and shape.
- Provide students with
a 3-D model using straight lines, and ask students to produce top, front,
and side views in 1:1 scale.
- Ask students to produce
a 2:1 and a 1:2 version of the same view.
- Using examples of simple
3-D objects, ask students to produce 2-D representations to a simple scale.
- Ask students to find
the surface areas and volumes of several objects (e.g., cuisinaire rods, dice,
shoebox, blocks).
- Provide drawings of
simple 3-D objects, and ask students to build models of the objects using
blocks. Have them solve for missing measurements, either directly or by calculation.
- Provide students with
the dimensions of a helium or hot-air balloon (e.g., the Hindenberg) and have
them calculate the volume of gas needed to inflate it (volume).
- Provide students with
the dimensions of a local landmark (e.g., the HR MacMillan Planetarium) and
ask them to calculate the volume of paint that would be needed to cover it
(surface area).
- Ask students to calculate
the length of fencing (perimeter) that would be required to surround a well-known
structure (e.g., Stonehenge), if the fence remains exactly 75m away from the
outer perimeter of the structure.
SUGGESTED
ASSESSMENT STRATEGIES
Being able to measure using
instruments and modeling 2-D and 3-D objects is fundamental to applying mathematics
practically. Students should be able to devise a plan to construct a 3-D object.
Observe
- Notice how students
are able to grasp the concept of scale. Use simple 3-D objects such as small
blocks or toys to observe if students are understanding view point and scale.
Collect
- Have students create
a 3-D model from given plans. Use materials such as firm cardboard, wax, soap
or modeling clay. Use a rubric to assess how well the students meet the criteria
previously identified for spatial understanding.
Question
- Ask students to comment
on advantages and difficulties of working with scale models and note to what
extent they are able to list them. Ask them to describe how they overcame
difficulties.
Self Assessment
- Ask students to estimate
and record how far they can throw an object. Then have students complete the
activity and measure the distance. Repeat this activity with golf clubs and
balls, hockey pucks, and empty boxes. Have students examine their recording
and notice how the measurements are becoming more closely aligned.
RECOMMENDED
LEARNING RESOURCES
Comprehensive learning resources
for this course are currently under development. As an interim measure, schools
are encouraged to use the teacher-developed learning resources distributed to
schools (student and teacher resources). Please note that the student materials
require photocopying for student use.
Software
©
2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000
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