Course Profile College and Apprenticeship Mathematics (MAP4C), Grade 12, College Preparation, Combined
Unit 3: Design
Time: 19 hours
Activity
3.1 | Activity 3.2 | Activity 3.3 | Activity 3.4
| Activity 3.5 | Activity
3.6
Unit Description
Students design and
construct physical models to expand their knowledge of geometry and
measurement. Connections are made to the fields of construction, fashion
design, and machining. Students take a three-dimensional object and make a
two-dimensional representation of it. They expand their knowledge of
measurement by using both the metric and imperial systems.
Ontario Catholic School Graduate Expectations: 1d, 1g, 2b, 2c, 3b, 3c, 4a, 4b, 4f, 7b.
Unit Synopsis Chart
|
Activity |
Time |
Learning Expectations |
Assessment Categories |
Focus |
|
3.1 |
2 hours |
AGV.01, AGV.02,
AG1.04, AG2.04, AG2.06 |
Thinking/Inquiry Knowledge/
Understanding Communication |
Explore spatial
awareness involving measurement |
|
3.2 |
7 hours |
AGV.01, AGV.02,
AG1.01, AG1.02, AG1.04, AG2.03, AG2.05, AG2.06 |
Knowledge/
Understanding Application |
Construct a
three-dimensional model based on a two-dimensional plan |
|
3.3 |
1.25 hours |
AGV.01, AGV.02,
AG1.01, AG1.03, AG2.01 |
Knowledge/
Understanding Thinking/Inquiry Application Communication |
Create patterns of
combined geometric shapes related to interior decorating |
|
3.4 |
2.5 hours |
AGV.01, AGV.02,
AG1.02, AG2.04, AG2.05 |
Knowledge/
Understanding Application |
Represent a
three-dimensional shape in an orthographic drawing |
|
3.5 |
2.5 hours |
AGV.01, AGV.02,
AG1.02, AG2.02 |
Knowledge/
Understanding Thinking/Inquiry Application |
Design a physical
model of a piece of equipment given constraints |
|
3.6 |
6.25 hours |
AGV.01, AGV.02,
AG1.01, AG1.02, AG1.03, AG1.04, AG2.01, AG2.02, AG2.06 |
Knowledge/
Understanding Application Thinking/Inquiry Communication |
Summative
Assessment |
Activity
3.1: Designing My Home
Time: 1.5 hours
Description
Students develop an understanding of area, perimeter, and spatial
awareness and gain a working knowledge of imperial measurement by designing a
ranch-style home with a minimum area of 1300 ft2 and a maximum area
of 2000 ft2.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE2b - read,
understand, and use written materials effectively;
CGE4b - demonstrate
flexibility and adaptability;
CGE3c - think
reflectively and creatively to evaluate situations and solve problems.
Strand(s): Applications of Geometry, Measurement, and Trigonometry
Overall
Expectations
AGV.01 - demonstrate
an understanding of the relationship between three-dimensional objects and
their two-dimensional representations;
AGV.02 - solve
problems involving measurement.
Specific
Expectations
AG1.04 - design and
construct physical models of things (e.g., structures, equipment, furniture),
satisfying given constraints and using concrete materials, design software, or
drawing software;
AG2.04 - demonstrate
a working knowledge of the measurement of length and area in the imperial
system, in relation to application (e.g., design, construction);
AG2.06 - use
calculators effectively in solving problems involving measurement, and judge
the reasonableness of the answers produced.
Prior Knowledge & Skills
·
operations
involving fractions;
·
measuring
fractions of an inch;
·
the concept of
scale diagrams.
Planning Notes
·
Students require
graph paper for the presentation diagram. Each square on the graph paper
represents 2 ft. by 2 ft. to enable students to fit most designs on one sheet
of paper. Book computer time and/or a computer with a data projector for the
pre-assignment activity. For scaled plans of their house, students need scales
(rulers), set squares, and T-squares for constructing right angles and drawing
accurate scale representations, as well as masking tape to tape their plans to
their desk. A drafting board would be ideal. Before the actual activity starts,
students can make a scale diagram of the classroom to review the concept of
scale diagrams.
·
Even though
students may live in a house, few are familiar with house design. As a
pre-activity, students find and hand in three or four house plans that are
within the size range of that in the activity. House plans can be found on the
Internet (see Resources). Students analyse and determine the rationale for the
designer’s layout and room sizes. Students can list features they like and
dislike in each house plan, such as a bad location of washrooms, small rooms,
window placements, or too much distance between the kitchen and dining room. In
a teacher-directed analysis, students discuss designing a functional house. If
time and resources permit, the teacher may choose to use
component 4. Students should be told that they are going to physically
construct their models in Activity 3.2.
Teaching/Learning Strategies
To ensure students
keep on track and progress appropriately, they do not proceed to the next step
of the assignment until the segment they are presently working on has been
completed and approved by the teacher. This will ensure that students do not
forget important components in the design process. Each step is essential in
the proper production of a home design. Students must work individually to
ensure that they experience each step of the design process. The teacher
suggests an appropriate scale for the floor plan (1/8" = 1 ft), which will
be different than the scale for the grid-paper presentation diagram.
Teacher
Facilitation
Most building
materials and supplies are measured and sold using imperial measurements.
Students’ experience with this type of measure will determine how in-depth
teaching of this concept will need to be.
Student Activity
Students design a
one-floor (ranch style) home with an area ranging from 1300–2000 square feet.
The home is to contain the following rooms with the following size
specifications:
·
1 living room 150
ft2 – 600 ft2;
·
1 dining room 100
ft2 – 225 ft2;
·
1 kitchen 100 ft2
– 400 ft2;
·
3 bedrooms 90 ft2
– 169 ft2;
·
1 bathroom 50 ft2
– 100 ft2;
·
1 laundry room 60
ft2 – 100 ft2.
1) Bubble Diagram
Students determine
the locations of the rooms. Bubbles are used to determine a rough location of
each room. Locations are based on how the family will best function during
their daily lives in the student’s house. Students write a brief summary to
explain the rationale behind the room locations. Dimensions are not needed at
this time. This diagram can be distributed to the class as an example of what
is expected. Hallway areas are of no concern in this component.
2) Presentation
Diagram
In this component,
students use graph paper to plan scale versions of their designs. Each square
has a scale of 2 feet by 2 feet. Students manipulate room size areas to fit the
specifications and include the area of the hallways. Students produce a
drawing, which differs from the bubble diagram and include dimensions for each
room (e.g., BEDROOM 20 ft × 10 ft).
3) Floor Plan
Students reproduce their presentation diagrams on at least 11.5" ×
17" paper using scales, T-squares, and set squares. Floor plans are to be
neat, accurate, and to a scale of 1/8' = 1 foot.
4) Computer
Reproduction (optional)
Students reproduce
their floor plans using design software.
Assessment & Evaluation of Student Achievement
The activity
should be assessed formatively, and can focus on the categories of:
· Thinking/Inquiry: The degree to which students demonstrate their understanding of the problem by meeting the minimum/maximum area criteria.
· Knowledge/Understanding: The accuracy to which diagrams are drawn to scale.
Accommodations
· Teachers should refer to the student’s Individual Education Plan (IEP) and use the recommendations to make any necessary accommodations for individuals.
· Students with vision challenges can be given work with large print or simplifying the complexity of diagrams.
Resources
www.coolhouseplans.com
www.dreamhomesource.com
www.homestyles.com
www.homeplanfinder.com
www.thehousedesigners.com
Activity
3.2: My Home is My Model
Time: 5 hours
Description
Teams of students
develop an understanding of how three-dimensional models are constructed from
two-dimensional diagrams by building a scale model of the home that was
designed in Activity 3.1. A plan of one of the group members’ houses is to be
used as the plan for the model. After the model is completed, the team chooses
a type of flooring for each room and determines the cost of materials and
labour.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE1d - develop
attitudes and values founded on Catholic social teaching and act to promote
social responsibility, human solidarity, and the common good;
CGE1g - understand
that one’s purpose or call in life comes from God and strive to discern and
live out this call throughout life’s journey;
CGE2b - read,
understand, and use written materials effectively;
CGE2c - present
information and ideas clearly and honestly and with sensitivity to others;
CGE3b - create,
adapt, and evaluate new ideas in light of the common good;
CGE4a - demonstrate
a confident and positive sense of self and respect for the dignity and welfare
of others;
CGE4b - demonstrate
flexibility and adaptability;
CGE4f - apply
effective communication, decision-making, problem-solving, time, and resource
management skills;
CGE7b - accept
accountability for one’s own actions.
Strand(s): Applications of Geometry,
Measurement, and Trigonometry
Overall
Expectations
AGV.01 - demonstrate
an understanding of the relationship between three-dimensional objects and
their two-dimensional representations;
AGV.02 - solve
problems involving measurement.
Specific
Expectations
AG1.01 - identify,
through observation and measurement, the uses of geometric shapes and the
reasons for those uses, in a variety of applications (e.g., production design,
architecture, fashion);
AG1.02 - represent
three-dimensional objects in a variety of ways (e.g., front, side, and top
views: perspective drawings; scale models), using concrete material and design
or drawing software;
AG1.04 - design and
construct physical models of things (e.g., structures, equipment, furniture),
satisfying given constraints and using concrete materials, design software, or
drawing software;
AG2.03 - demonstrate
an understanding of the use of the imperial system in a variety of applications
(e.g., bolt and screw sizes; tool sizes; quantities of soil, water or cement);
AG2.05 - perform
required conversions between the imperial system and the metric system, as
necessary within projects and applications;
AG2.06 - use
calculators effectively in solving problems involving measurement, and judge
the reasonableness of the answers produced.
Prior Knowledge & Skills
·
percents and
calculation of area;
·
converting
measurements from actual measurements to their scale values.
Planning Notes
·
Obtain all
construction materials and tools for building models. Students use glue guns to
put their projects together. You may need sticks to use as beams or have
students do this as part of the pre-construction preparation. Many lumber
companies cut the sticks to order. A suggested size for
sticks: ¼ inch by ½ inch by 12 inches can be used to represent an 8-foot
two-by-four.
·
Provide glue
guns, small handsaws for cutting the sticks, scales (ruler), T-squares, and set
squares. Since glue guns and small handsaws are being used, safety issues must
be addressed in class. A small hand level may be useful to make walls plum.
·
FOAM CORE Bristol
board can be an alternative to sticks; however, sticks are recommended because
of their resemblance to the actual building materials.
·
If unable to
obtain the sticks, have school technical classes or a local lumber store cut
the material.
·
Building codes
should be assigned or researched at this time.
·
One of the
student’s plans is to be chosen as the blueprint for the model. This may be a
teacher or group decision.
·
Students are to
be divided into groups. You may want to have some groups delegate tasks in such
a way that Parts 2 and 3 are performed simultaneously by different teams in the
class.
·
Contact a
flooring store and make arrangements so that students can call or investigate
the possible choices for their houses.
·
Set due dates for
the different phases so that students can use their time productively.
Teaching/Learning Strategies
Teacher Facilitation
Before Part 1
begins, pick a floor plan and estimate the amount of lumber required to build
the walls for that plan’s model so that students understand what to calculate
and why. Framing building codes addressing doors, windows, and stud spacing for
walls are supplied by the teacher to assist in estimating the amount of lumber
needed. Discuss why material waste is inevitable and unavoidable in both the
frame construction phase and the installation of flooring. For Part 2, use
cardboard as the base for the model. It may be necessary to explain how corners
of walls are built by doubling two-by-fours on one of the wall’s end. Before
students start Part 3 calculations, review the conversion from square feet to
square yards. Students should also be made aware that taxes of material costs
(15% GST and PST) and labour
costs (8% PST) are not the same.
Student Activity
Students construct a
model of a house by following one group member’s plans. After the model is
completed, they find the cost of installing at least three different types of
flooring in the home.
Part 1
Seventy-five minutes
is recommended for this part. The group chooses a plan to use as a blueprint
for their model. They submit a report in writing, explaining the rationale
behind their choice. In the report, they also calculate how many 8-foot
two-by-fours they will need. To calculate this they need to know how far apart
studs are to be. They can research the local building code or the teacher can
determine this. Eighteen inches apart is the standard in many municipalities.
Eight-foot ceilings are also minimum standards in many communities.
Part 2
A time of
approximately 225 minutes is recommended for this part. Using the chosen floor
plan, students pick their building materials and construct their models. Models
represent the frame of the house with no interior or exterior wall coverings.
Part 3
This part of the
assignment may be researched on the Internet, completed at home by phone, or
completed by visiting a flooring showroom with the store manager’s permission.
After the models have been constructed, groups decide on the type of flooring
that is to be installed in each room. They hand in their decisions in chart
form. Below is an example of a format that you can use.
|
Room |
Dimensions and Area |
Type of Floor |
Unit Cost |
Total Cost of Flooring |
Cost of Installation |
Cost of Flooring and Installation |
Taxes |
Total Cost |
|
Dining Room |
12 ft. x 18 ft. =
216 sq. ft. |
oak |
$5.99/ sq. ft. |
$1293.84 |
$2.99 × 216 =
$645.84 |
$1939.68 |
$239.28 |
$2178.96 |
|
Bedroom 1 |
13 ft. x 13 ft.=
139 sq. ft. or 15.5 sq. yds |
carpet |
$25/sq. yd. |
$387.50 |
$50 |
$437.50 |
$58.12 |
$495.63 |
|
etc. |
|
|
|
|
|
|
|
|
In their report,
students justify their choice of flooring for each room.
Assessment & Evaluation Student
Achievement
Formative:
· Application can be assessed based on the degree to which students can create their three-dimensional model based on their two-dimensional design.
· Inquiry/Problem Solving can be assessed based on the degree to which their model satisfies the given constraints.
· Communication can be assessed by the clarity with which students are able to identify the use of geometric shapes and provide reasons for these uses.
· Knowledge/Understanding can be assessed based on the accuracy of their measurements and their model.
Summative
· A quiz can be used to assess the accuracy of their conversions between imperial and metric units (Knowledge/Understanding).
Activity
3.3: Go Figure
Time: 1.25 hours
Description
Students develop an
understanding of measurement and surface area by assuming the role of floor
designer to come up with different floor patterns given various shapes of tile.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE2b - read,
understand, and use written materials effectively;
CGE3c - think
reflectively and creatively to evaluate situations and solve problems;
CGE4b - demonstrate
flexibility and adaptability;
CGE5b - think
critically about the meaning and purpose of work.
Strand(s): Applications of Geometry,
Measurement, and Trigonometry
Overall Expectations
AGV.01 - demonstrate
an understanding of the relationship between three-dimensional objects and
their two-dimensional representations;
AGV.02 - solve
problems involving measurement.
Specific
Expectations
AG1.01 - identify,
through observation and measurement, the uses of geometric shapes and the
reasons for those uses, in a variety of applications (e.g., product design,
architecture, fashion);
AG1.03 - create
nets, plans, and patterns from physical models related to a variety of
applications (e.g., fashion design, interior decorating, building
construction), using design or drawing software;
AG2.01 - solve
problems related to the perimeter and area of plane figures, and the surface
area and volume of prisms, pyramids, cylinders, spheres, and cones, including
problems involving combinations of these objects.
Prior Knowledge & Skills
·
the use of set
squares and protractors to draw the different shapes;
·
knowledge of
geometric shapes according to their proper names.
Planning Notes
Students require
graph paper to sketch their patterns. They also require set squares to draw
30º, 45º, 60º, and 90° angles. Students can work more efficiently if they can
work on drafting boards. If drafting boards are not available, they can use
T-squares to draw parallel lines. Bristol board is required to create the
shapes for the pattern. Scissors must be made available for this activity.
Teaching/Learning Strategies
There are two stages
in this design activity. The first stage involves sketching different patterns
using various shapes of different sizes. The second stage involves drawing the
scale version of the pattern on Bristol board and placing the cut shapes on the
pattern. Students present two to three different patterns. They must work
individually to ensure uniqueness of their design. Students cannot proceed to
the next stage unless the teacher has approved the sketch.
Teacher
Facilitation
The teacher must
stress accuracy because the shapes must fit together. Offer constructive
criticism of the patterns before allowing students to proceed to the next
phase.
Student Activity
The teacher hands
out these diagrams of possible tile shapes.
1) Students sketch different patterns with the
tile shapes and come up with two or three different designs.
2) Once the sketching is done, students start a
scaled drawing of their pattern to see if the combination of tiles actually
fits the pattern they designed. The following diagram shows a pattern that can
be created with the given tiles. The design is to be placed in a specific area,
such as a foyer, bathroom, etc.
Follow-Up Activity
This activity can be
extended to include volume and surface area by supplementing it with questions
from the textbook or other resources. Students can also bring in
three-dimensional shapes, such as beverage cans or boxed foods that have their
volumes listed on them. Students calculate the volumes of these items and
compare the results to the listed values on the three-dimensional shape. Have
students give reasons for why there is a discrepancy between the listed values
and their calculated value.
Assessment & Evaluation of
Student Achievement
· By requiring students to identify shapes and to describe the tiling pattern, the teacher can assess Communication based on the clarity and completeness of responses.
· The accuracy of the nets that are created can be used to assess Knowledge/Understanding.
· Application can be assessed based on the degree to which students can identify shapes and calculate the perimeter, area, and surface area using the appropriate formula.
· Inquiry/Problem Solving can be assessed based on their understanding of the design elements needed to determine perimeter, area, and volume.
Accommodations
Shapes could be
pre-cut.
Activity
3.4: Pose For Me
Time: 2.5 hours
Description
Students develop an
understanding of three-dimensional representation by taking various
measurements of an object and representing it as an orthographic drawing with
the top, front, and side views. They also develop an understanding of the
relationship between imperial and metric measurements.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE2b - read,
understand, and use written materials effectively;
CGE5b - think
critically about the meaning and purpose of work;
CGE7b - accept
accountability for one’s own actions.
Strand(s): Applications of Geometry,
Measurement, and Trigonometry
Overall
Expectations
AGV.01 - demonstrate
an understanding of the relationship between three-dimensional objects and
their two-dimensional representations;
AGV.02 - solve
problems involving measurement.
Specific
Expectations
AG1.02 - represent
three-dimensional objects in a variety of ways (e.g., front, side and top
views; perspective drawings; scale models), using concrete materials and design
or drawing software;
AG2.04 - demonstrate
a working knowledge of the measurement of length and area in the imperial
system, in relation to application;
AG2.05 - perform
required conversions between the imperial system and the metric system, as
necessary within projects and applications.
Prior Knowledge & Skills
·
accurately
measuring features of objects using various measuring devices;
·
drawing front,
top, and side views of objects;
·
calculating
ratios (for scaling purposes).
Planning Notes
Students require
measuring devices, such as scales and measuring tapes. Graph paper is required
for sketching purposes. If using design or drawing software, book computer time
and/or a computer with a screen projector. If using drafting boards or a desk,
provide scales (rulers), set squares, and T-squares so that the student may
construct right angles and draw accurately scaled orthographic representations
of objects. Masking tape is needed to tape plans to desks. A drafting board
would be more appropriate.
Teaching/Learning Strategies
The four
stages in this design activity are:
1) sketch the top, front, and side views
(orthographic) of the object;
2) measure the object and record the
measurements;
3) draw the scaled top, front, and side views
(orthographic) on grid paper;
4) draw the actual scaled layout of the top,
front, and side views of the object.
Students work individually so that they have the opportunity to measure
and use the different measuring devices. The object should be at least the size
of the paper so that students have to scale down the measurements of the object
to fit the views on one sheet of paper. Students do not proceed to the next
stage until the segment they are presently working on has been completed and
approved by the teacher.
Teacher
Facilitation
The teacher may have
to teach students how to draw orthographic views and provide further
instruction in using the measuring devices. Review scaling of an object (e.g.,
If a 1:2 scale is used, then a 20 cm length would be 10 cm on paper).
Student Activity
Students take various measurements of an object
in the room (e.g., podium, box, computer mouse, overhead projector, student
desk, etc.) and draw front, top, and side views to represent the object. The
teacher may make their own objects to give to students. The following diagram
is an example of an object the teacher can use. Hidden lines should be used to
reveal features that are hidden on a certain view.
The object must be
at least the size of the paper in order to ensure the use of scaling. Students
may bring an object from home. The object should not be too intricate since it
has to be represented on paper. The activity consists of the following
components:
1) Sketching
Orthographic Views (Top, Front, and Side Views of the Object)
Students draw a
rough sketch of top, front, and side views of the object. In this component,
measurements are not necessary. Students should only be concerned with how
their views will look on paper.
2) Object
Measurement and Recording of Measurements
Students measure
certain details of the object, including length, width, thickness, location of
holes, depth of holes, steps in the object, grooves, etc. Students may use
callipers to measure holes. If a small cylindrical shape is to be measured,
they may want to use a micrometer. For straight details, they may only need to
use a simple scale (ruler). The measurements should be recorded for use on the
scale layout.
3) Scale Layout of
Orthographic Views on Grid Paper
Using the
measurements that were recorded, students represent their sketched orthographic
views on grid paper, keeping in mind the scale they will require. They will
have to scale down the object in order to get the three views on the grid
paper. Each grid on the paper will have a value in order to accommodate the
views (e.g., 5 mm per block). Students place the dimensions in their proper
locations.
4) Presentation of
Orthographic Views
Students reproduce
their scale layouts on 11" × 8.5" paper, using scales (ruler),
T-squares, and set squares. It would be preferable for students to use a drafting
table. The drawing should contain the dimensions and it is to be neat,
accurate, and to scale.
5) Computer
Reproduction
Students reproduce
their floor plans using design software if they did not do so as an optional
component of Activity 3.1.
Follow-up Activity
Students measure the
object using both metric and imperial measures and then calculate the area of
each surface. The surface area should be in appropriate units (i.e., square
feet, square yards, square metres).
Assessment & Evaluation of Student
Achievement
This activity must be assessed as a Math task based on the stated expectations of the activity, and not as a Drafting task.
· Knowledge/Understanding can be assessed based on the accuracy of the use of scale in the drawing.
· Application can be assessed based on the degree to which the Orthographic Views represent the three-dimensional object.
· Requiring students to describe the shapes that make up their orthographic views and to explain the process of how they created the three views can be used to assess Communication.
Resources
Giesecke,
F., A. Mitchell, H.C. Spencer, I.L. Hill, R.O. Loving, J.T. Dygdon, and J.E.
Novak. Principles of Engineering
Graphics, 2nd ed. Prentice
Hall, 1994. ISBN 0-02-342820-1
Grout, D., P.
Resetarits, and J. James. AUTOCAD
Drafting. Glencoe/McGraw-Hill, 1995.
ISBN 0-02-677135- 7
Activity
3.5: Let’s Do A Jig (optional)
Time: 2.5 hours
Description
Students practise
their designing skills by designing a device that will allow them to hold a
manufactured part in place in order to precisely drill four holes.
Note: This activity is optional because it is geared to teachers with a
technical or manufacturing background.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE2b - read,
understand, and use written materials effectively;
CGE3c - think
reflectively and creatively to evaluate situations and solve problems;
CGE4b - demonstrate
flexibility and adaptability.
Strand(s): Applications of Geometry,
Measurement, and Trigonometry
Overall Expectations
AGV.01 - demonstrate
an understanding of the relationship between three-dimensional objects and
their two-dimensional representations;
AGV.02 - solve
problems involving measurement.
Specific
Expectations
AG1.02 - represent three-dimensional objects in a variety of ways (e.g.,
front, side, and top views; perspective drawing; scale models), using concrete
materials and design or drawing software;
AG2.02 - demonstrate accuracy and precision in working with metric
measures.
Prior
Knowledge & Skills
·
drawing top,
front, and side views of objects;
·
knowledge of how
to use set squares, T-squares, and measuring scales.
Planning
Notes
Students require
graph paper for sketching. If using design or drawing software, book computer
time and/or a computer with a data projector for your class. If using drafting
boards or a desk, provide scales (rulers), set squares, T-squares, and masking
tape.
Teaching/Learning
Strategies
The three
stages in this design activity are:
1) sketch the top, front, and side views
(orthographic views) of the jig and fixture;
2) draw a scaled layout on grid paper of the
top, front, and side views (orthographic) of the jig and fixture;
3) draw a presentation layout of the top, front,
and side views of the jig and fixture.
The teacher gives formative feedback to students at each stage – a
requirement before proceeding to the next stage. This will ensure that students
do not forget important components in the design process. Each step of the
activity is essential in the design of a jig and fixture. Students work
individually to ensure uniqueness of their design. Students can use catalogues
of fixtures and fasteners to assist in their design. These can be obtained from
a local industry or off the Internet.
Teacher Facilitation
The teacher introduces
the topic of jigs and fixtures to students. Students can also research jigs and
fixtures on the Internet. The following specifics should be stressed:
·
Jigs are special
devices that determine location dimensions, which are produced by machining or
fastening operations; they determine where cuts or holes will be made
repeatedly in the production of a part. This will ensure every piece that is
processed is identical. The first piece will have its cuts and holes in the
same place as the thousandth piece.
·
Fixtures are
devices that hold parts during machining or assembly. Jigs can also perform the
function of fixtures.
·
Jigs and fixtures
reduce the set-up time resulting in increased productivity.
·
Students must
know what jig feet, drill bushings, and spring plungers are.
Student Activity
Students design a device that will allow them to drill four holes in the
manner described. The device acts as a guide. The location and depth of the
holes never change, regardless of whether it is the first piece or the
hundredth piece being produced. There should be the capability of holding the
work being processed in place so it does not move. The following is what the
piece should look like once the drilling is done:
The four holes are
15 mm in diameter. The two middle holes are 35 mm deep, while the other two are
30 mm deep. The piece is 40 mm thick. Use appropriate jig feet, drill bushing,
and spring plungers. The jig feet are needed in order for the jig to stand with
a stable base. The drill bushing is needed to protect the jig itself from the
drilling and to restrict the depth of the hole in the work piece. All these
items can be located in any fixture catalogue. Remind students that the drill
bit is extending 40 mm out of the drill chuck.
1) Sketch
In this part of the
activity, students roughly sketch their jig and fixture. Students do not use
rulers for this component. The ruler will only slow down the free flow of
ideas, which the student will try to convey on paper. At this stage, it is not
necessary to consider scale and the actual dimensions. Once the idea is
sketched and checked by the teacher, students roughly sketch the top, front,
and side views (orthographic view) of the jig and fixture. Sketches are also
checked by the teacher.
2) Scale Layout of
the Jig and Fixture
Students use graph
paper to draw scale versions of their jig and fixture. At this stage, students
have a better understanding of the actual sizes of certain sized bushings, jig
feet, or spring plungers and whether they can be used in their design. Students
manipulate their jig sizes and locations to meet specifications. Students place
their dimensions in their proper locations. Students do not proceed to the next
stage in the assignment until the segment they are presently working on has
been completed and approved.
3) Presentation of
Orthographic Views
In this final stage,
students reproduce their scale layouts of the jig and fixture on at least
8.5" × 11" sized paper using scales (rulers), T-squares, and set
squares. This drawing should contain the dimensions and it is to be neat,
accurate, and to scale.
4) Computer
Reproduction (optional)
In this component,
students reproduce their floor plans using design software, or math software.
Assessment & Evaluation of
Student Achievement
·
Knowledge/Understanding
of accuracy and precision in working with metric measures can be assessed by
correct dimensions in all diagrams.
·
An accurate scale
drawing demonstrates the Knowledge/Understanding of how to solve problems
involving measurement.
·
Demonstrating an
understanding of the relationship between the three-dimensional objects and
their two-dimensional representations shows proper Application of orthographic
representation.
Resources
http://www.reidtoolcom/PDF/CuttingToolsDrillBushings.pdf,
pp. 20-23
Activity
3.6: Summative Assessment
Time: 6.25 hours
Description
Students apply their
understanding of nets, plans, and patterns from physical models by creating a
personal design of either a piece of clothing or furniture.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE2b - read,
understand, and use written materials effectively;
CGE2c - present
information and ideas clearly and honestly and with sensitivity to others;
CGE3c - think
reflectively and creatively to evaluate situations and solve problems;
CGE4b - demonstrate
flexibility and adaptability;
CGE4f - apply
effective communication, decision-making, problem-solving, time, and resource
management skills;
CGE5b - think
critically about the meaning and purpose of work;
CGE5g - achieve
excellence, originality, and integrity in one’s own work and support these
qualities in the work of others.
Strand(s): Applications of Geometry and
Measurement
Overall
Expectations
AGV.01 - demonstrate
an understanding of the relationship between three-dimensional objects and
their two-dimensions representations;
AGV.02 - solve
problems involving measurement.
Specific
Expectations
AG1.01 - identify,
through observation and measurement, the uses of geometric shapes and the
reasons for those uses, in a variety of applications (e.g., product design,
architecture, fashion);
AG1.02 - represent
three-dimensional objects in a variety of ways (e.g., front, side, and top
views; perspective drawings; scale models), using concrete materials and design
or drawing software;
AG1.03 - create
nets, plans, and patterns from physical models related to a variety of drawing
applications (e.g., fashion design, interior decorating, building
construction), using design or drawing software;
AG1.04 - design and
construct physical models of things (e.g., structures, equipment, furniture),
satisfying given constraints and using concrete materials, design software, or
drawing software;
AG2.02 - demonstrate
accuracy and precision in working with metric measures;
AG2.06 - use
calculators effectively in solving problems involving measurement, and judge
the reasonableness of the answers produced.
Prior Knowledge & Skills
·
determining the
perimeter and area of shapes;
·
a working
knowledge of per cent;
·
drawing nets;
·
drawing front,
top, and side views of three-dimensional objects.
Planning Notes
·
Specify a mark-up
of forty per cent on clothing or furniture.
·
If using a
computer design program, book computers equipped with the necessary programs.
·
The assessment
component of this unit is completed in three parts. First, students plan the
creation of a piece of clothing or furniture. Once students attain approval on
their project, they begin the second part, which is the creation of a small
scale version of their item. Third, students hand in pencil-and-paper tasks set
out for them in the activity.
·
Students call
retail stores in the community to determine the prices of similar items for the
follow-up activity. Retailers may not forward mark-up information to consumers.
Teaching/Learning Strategies
Student Activity
Students choose a
piece of clothing or furniture to design (e.g., shirts, chair, etc.). Students
then write a proposal of the necessary steps they must go through to create
their design. The proposal includes:
·
identification of
the geometric shapes required for designing their product;
·
a scale drawing
of the various shapes that make up their design;
·
three
perspectives (front, back, and side) of the three-dimensional shape to give an
accurate vision of the item (for a piece of clothing, the side view is not
needed);
·
a scaled-down net
of the item using Bristol board (keep the excess materials). For furniture,
students can make two-dimensional representations of each part of the
furniture;
·
a list of the
necessary materials to create the full-scale item.
Teacher
Facilitation
Assist students in
the design and creation of their item by approving the proposals. Ensure that
students have a reasonable item in mind and that their goals are attainable.
Once students have attained approval, they may begin creating their item.
Have the necessary
materials ready. For students to create the fashion item they have chosen they
must have a needle and thread to sew their design together. Students who have
chosen a piece of furniture will need carpenter glue to secure their pieces.
Paper-and-Pencil
Task
(a) Determine the surface area of your item.
(b) Calculate the surface area of the materials.
Describe how you determined your answer.
(c) Record all materials that you used in your
project and the approximate cost of the materials needed to construct the
design. (The teacher gives approximate value of material per square unit.)
(d) Calculate the perimeter of the design.
(e) Estimate the amount of material needed.
(f) Estimate a value that you would sell the item
for and justify your reasoning.
(g) If you were required to make 1000 replicas of
your design, how would this change the amount you were asking for your item?
Justify your reasoning.
Follow-up Activity
(a) Research the selling price of
a piece of clothing/furniture comparable to yours.
(b) How does your price compare to
the price that you found? Explain why there is such a difference between what
it costs to make the item versus what it cost to buy it.
(c) The mark-up on the item in this activity is 40
%. How does this mark-up compare to the mark-ups of similar items in retail
stores? Students will have to call retail stores in the community.
Assessment & Evaluation of
Student Achievement
In this summative assessment, several opportunities exist for the
evaluation of all of the knowledge and skill categories. Criteria to be
assessed in the activity might include:
·
Determining
perimeter and surface area of the design (Thinking/Inquiry/Problem Solving)
·
Accuracy of
calculations (Knowledge/Understanding)
·
Accuracy of nets
(Knowledge/Understanding)
·
Judging the
reasonableness of results (Inquiry)
·
Identification of
the geometric shapes required in designing the product (Knowledge)
·
A scale drawing
of the various shapes that make up the design (Application)
·
Drawing the three
perspectives (front, back, and side) of the three-dimensional shapes to give an
accurate vision of the item (Application)
·
Creating a
scaled-down net of the product using Bristol board (Application)
Rubric
|
Criteria |
Level 1 (50-59%) |
Level 2 (60-69%) |
Level 3 (70-79%) |
Level 4 (80-100%) |
|
Communication - clarity in explanations and justifications of their proposal |
- explanations and justifications have limited clarity |
- explanations and justifications have some clarity |
- explanations and justifications most often clear |
- explanations and justifications are consistently clear |
|
Problem Solving - estimating the value of the item - estimating the value of the design feature |
- estimate is minimally accurate - estimate is based on limited design features |
- estimate is somewhat accurate - estimate is based on some design features |
- estimate is generally accurate estimate is based on most design features |
- estimate is thoroughly accurate - estimate is based on all or almost all design features |
|
Application - scale is used to create the design |
- a limited number of items are scaled appropriately |
- some items are scaled appropriately |
- most items are scaled appropriately |
- all or almost all of the items are scaled appropriately |
Note: A student whose achievement is below Level 1 (50%) has not met the
expectations for this assignment or activity.