Course Profile College and Apprenticeship Mathematics (MAP4C), Grade 12, College Preparation, Combined

Unit 3: Design

Time: 19 hours

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 Designing My Home	2 hours	AGV.01, AGV.02, AG1.04, AG2.04, AG2.06	Thinking/Inquiry Knowledge/ Understanding Communication	Explore spatial awareness involving measurement
3.2 My Home Is My Model	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 Go Figure	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 Pose For Me	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 Let’s Do A Jig (optional)	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 High Fashion	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 com