IO Project

Curriculum

Science

6?1 Design and carry out an investigation in which variables are identified and controlled, and that provides a fair test of the question being investigated.

6?2 Recognize the importance of accuracy in observation and measurement; and apply suitable methods to record, compile, interpret and evaluate observations and measurements.

Topic D: Evidence and Investigation
Overview
Students sharpen their skills in observing and interpreting what they see by investigating evidence of human and animal activity. They explore and analyze indoor and outdoor environments as they look for footprints, markings, evidence of disturbance and things that are left behind. Through these studies, students learn to pose questions, devise investigations, recognize patterns and discrepancies, and think logically about what they have observed.

Curriculum

Mathematics

Number Concepts: Develop a number sense for decimals and common fractions, explore integers and show number sense for whole numbers

*Number Operations: Apply arithmetic operations on whole numbers and decimals in solving problems

*Patterns & Relations: Use relationships to summarize, generalize and extend patterns including those found in music and art

*Shape & Space (3D/2D): Use visualization and symmetry to solve problems involving classification and sketching

*Shape & Space (3D/2D): Classify triangles according to the measures of their angles

*Shape & Space (Transformations): Create patterns and designs that incorporate symmetry. tesselations and reflections

Grade Nine:

Number (Number Concepts)
General Outcome
Explain and illustrate the structure and the interrelationship of the sets of numbers within the rational number system.
Specific Outcomes
1. Give examples of numbers that satisfy the conditions of natural, whole, integral and rational numbers, and show that these numbers comprise the rational number system. [C, CN, PS, R]
2. Describe, orally and in writing, whether or not a number is rational. [C, R]

Number (Number Operations)General Outcome
Use a scientific calculator or a computer to solve problems involving rational numbers.
Specific Outcomes
7. Document and explain the calculator keying sequences used to perform calculations involving rational numbers. [C, PS, T]
8. Solve problems, using rational numbers in meaningful contexts. [CN, PS]

Patterns and Relations (Patterns)
General Outcome
Generalize, design and justify mathematical procedures, using appropriate patterns, models and technology.
Specific Outcomes
1. Use logic and divergent thinking to present mathematical arguments in solving problems. [C, PS, R]
2. Model situations that can be represented by first-degree expressions. [CN, PS]
3. Write equivalent forms of algebraic expressions, equations, with rational coefficients. [C, CN, R]

Patterns and Relations (Variables and Equations)
General Outcome
Solve and verify linear equations and inequalities in
one variable.
Specific Outcomes
4. Illustrate the solution process for a first-degree, single-variable equation, using concrete materials or diagrams. [PS, R, V]
5. Solve and verify first-degree, single-variable equations of forms, such as:
· ax = b + cx
· a(x + b) = c
· ax + b = cx + d
· a(bx + c) = d(ex + f)
· a
x b =
where a, b, c, d, e and f are all rational numbers (with a focus on integers), and use equations of this type to model and solve problem situations. [C, PS, V]
6. Solve, algebraically, first-degree inequalities in one variable, display the solutions on a number line and test the solutions. [PS, R, V]

Statistics and Probability (Data Analysis)

General Outcome
Collect and analyze experimental results expressed in
two variables, using technology, as required.
Specific Outcomes
1. Design, conduct and report on an experiment to
investigate a relationship between two variables.
[C, CN, PS]
2. Create scatterplots for discrete and continuous
variables. [C, V]
3. Interpret a scatterplot to determine if there is an
apparent relationship. [E, R]
4. Determine the lines of best fit from a scatterplot
for an apparent linear relationship, by:
· inspection
· using technology (equations are not expected).
[E, PS, T]
5. Draw and justify conclusions from the line of best
fit. [C, R]
6. Assess the strengths, weaknesses and biases of
samples and data collection methods. [C, R, T]
7. Critique ways in which statistical information and
conclusions are presented by the media and other
sources. [C, CN]

General Outcome
Explain the use of probability and statistics in the
solution of complex problems.
Specific Outcomes
8. Recognize that decisions based on probability may
be a combination of theoretical calculations,
experimental results and subjective judgements.
[PS, R]
9. Demonstrate an understanding of the role of
probabil

Curriculum

Fine Arts

ANALYSIS: Students will study and analyze the individual character of natural objects or forms.

ANALYSIS: Students will study and analyze the individual character of natural objects or forms.

UNITY: Students will create unity by integrating the parts of a composition into the whole.

Task

The Vitruvian Man

Leonardo Da Vinci's Vitruvian Man "is a world renowned drawing with accompanying notes created by Leonardo da Vinci around the year 1492 as recorded in one of his journals. It depicts a nude male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man" (http://en.wikipedia.org/wiki/Vitruvian_man).

Recreate Da Vinci's Vitruvian Man with a fully clothed adult male. Determine the extent to which Da Vinci's proportions still hold today.

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Activity

Today's Adult Male

With a partner and a digital camera locate an adult male and photograph him in the positions described below:

1. Have the subject stand upright with his legs together and his arms straight out to the sides for your first image.
2. Next, have your subject open his legs until his height has been decreased by 1/14 of his original height. Then have him raise his arms until his middle fingers touch the level of the top of his head.
3. Be sure all appropriate calculations are thought out before approaching your subject. A spreadsheet is really handy for getting all the information coordinated before you start your measurements.

*NOTE: to get the best results use a model with bright clothing and photograph against a white wall.*

See the following site for guidance http://partner.galileo.org/tips/davinci/ourwork.html

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Activity

Verifying DaVinci's Claims

Once you have acquired the images needed, determine if the following ten statements are true.

The preceding is the complete translation of the text accompanying Leonardo DaVinci's Vitruvian Man. It is actually a translation of Vitruvius, as Leonardo's drawing was originally an illustration for a book on the works of Vitruvius.

1. The length of a man''s outspread arms is equal to his height.
2. From the roots of the hair to the bottom of the chin is a tenth of a man's height.
3. From the bottom of the chin to the top of a man's head is one eighth of his height.
4. The greatest width of the shoulders contains in itself the fourth part of the man.
5. From the elbow to the tip of the hand will be the fifth part of a man.
6. From the elbow to the angle of the armpit will be the eighth part of the man.
7. The whole hand will be the tenth part of the man.
8. The foot is the seventh part of the man.
9. From the sole of the foot to below the knee will be the fourth part of the man.
10. The distance from the bottom of the chin to the nose and from the roots of the hair to the eyebrows is, in each case the same, and like the ear, a third of the face.
11. The space between the legs will be an equilateral triangle.

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Task

Vitruvian Me - The Vitruvian Student

You have already taken an picture of an adult male and taken all of his measurements and compared them to DaVinci’s Vitruvian Man, now it is time to determine how you measure up to the Vitruvian Man. You will need to relate Vitruvius’ theories of proportion to yourself and your partner.

You will create a presentation that includes all the data from this task including digital images, precise measurements, a summary of proportions and your supported conclusions. Make sure you enter all your data into a spreadsheet where you will determine what the proportions are for the Vitruvian Student.

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Activity

Picture Yourself

With a partner and a digital camera photograph yourself in the positions described below:

1. Stand upright with your legs together and your arms straight out to the sides for your first image.
2. Next, stand with your legs open until your height has been decreased by 1/14 of your original height. Then raise your arms until your middle fingers touch the level of the top of your head.
3. Once again a spreadsheet is really handy for getting all the information coordinated before you start your measurements.

With a partner and a digital camera photograph yourself in the positions described below:

1. Stand upright with your legs together and your arms straight out to the sides for your first image.
2. Next, stand with your legs open until your height has been decreased by 1/14 of your original height. Then raise your arms until your middle fingers touch the level of the top of your head.
3. Once again a spreadsheet is really handy for getting all the information coordinated before you start your measurements.

*NOTE: to get the best results wear bright clothing and photograph against a white wall.*

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Activity

Measuring Up

Determine if the following ten following statements were true. The statements are a complete translation of the text accompanying Leonardo DaVinci's Vitruvian Man. It is actually a translation of Vitruvius, as Leonardo's drawing was originally an illustration for a book on the works of Vitruvius.

1. The length of a man's outspread arms is equal to his height.
2. From the roots of the hair to the bottom of the chin is a tenth of a man's height.
3. From the bottom of the chin to the top of a man's head is one eighth of his height.
4. The greatest width of the shoulders contains in itself the fourth part of the man.
5. From the elbow to the tip of the hand will be the fifth part of a man.
6. From the elbow to the angle of the armpit will be the eighth part of the man.
7. The whole hand will be the tenth part of the man.
8. The foot is the seventh part of the man.
9. From the sole of the foot to below the knee will be the fourth part of the man.
10. The distance from the bottom of the chin to the nose and from the roots of the hair to the eyebrows is, in each case the same, and like the ear, a third of the face.
11. The space between the legs will be an equilateral triangle.

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Activity

The Vitruvian Student Determine how you measured up to the Vitruvian Man and relate Vitruvius' theories of proportions to yourself. Create a presentation that includes all data from the task including digital images, precise measurements, a summary of proportions and their supported conclusions.
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The Vitruvian Man

	1	2	3	4
Fraction, Ratio and Proportion Conceptual Understanding	Does not realize that he/she needs to establish the unit of measurement. (eg. The question "What is the unit of measurement?" does not make sense) Uses the additive principle when working with fractions, ratios and proportions. (eg. doesn't realize that equivalency is established through the operations of multiplication and division).	Uncertain of the unit of measurement. (eg. The question, "What is the unit of measurement?" makes sense but the student doesn't know the unit of measurement.) Confuses additive and multiplicative principle when working with fractions, ratios and proportions.	Establishes the unit of measurement. (eg. The question, "What is the unit of measurement?" makes sense and the student can articulate.) Applies the multiplicative principle when working with fractions, ratios and proportions.	Establishes, clearly articulates and consistently applies the unit of measurement. (eg. The question, "What is the unit of measurement?" makes sense and the student can articulate what it is and provide additional examples to support their knowing.) Applies the multiplicative principle when working with fractions, ratios and proportions and demonstrates how this works itself out using algebra and equivalency.
Representation	Images are not proportional or combined	Images are proportional and combined.	Images are proportional and accurately combined	Images are clear, focused, proportional and accurately combined
Computation and Execution	Enters discrete data into spreadsheet but computes comparisons by hand or calculator. Makes errors in computation serious enough to flaw the solution. Provides no evidence of how he/she arrived at his/her solution.	Follows a prescribed procedure for entering data into a spreadsheet and performing calculations. Provides evidence of how he/she arrived at their solution however it is inconsistent or unclear.	Sets up spreadsheet and enters data into a spreadsheet and performs calculations using cell variables. Provides evidence of how he/she that clearly supports his/her solution.	Sets up spreadsheet and enters data into a spreadsheet and performs calculations in a variety of ways using the cell variables and functions. Provides evidence of multiple ways to solve the problem.
Communication	Explanation rambled without a clear focus.	Explanation was redundant or hard to follow in places.	Explanation was well organized, flowed logically and was easy to follow.	Explanation was clear, concise providing an in depth understanding of meaning.
Task Management	Struggles to follow management plan to manage time, gather resources and follow the given task for each team member.	Follows a task management plan to manage time, select resources and decide on which tasks team members will undertake.	Creates and follows a task management plan to manage time, determine resources and allocate tasks to team members.	Creates and follows a comprehensive, detailed task management plan to manage time, determine resources and allocate tasks to team members.

Vitruvian Me - The Vitruvian Student

	1	2	3	4
Fraction, Ratio and Proportion Conceptual Understanding	Does not realize that he/she needs to establish the unit of measurement. (eg. The question "What is the unit of measurement?" does not make sense) Uses the additive principle when working with fractions, ratios and proportions. (eg. doesn't realize that equivalency is established through the operations of multiplication and division).	Uncertain of the unit of measurement. (eg. The question, "What is the unit of measurement?" makes sense but the student doesn't know the unit of measurement.) Confuses additive and multiplicative principle when working with fractions, ratios and proportions.	Establishes the unit of measurement. (eg. The question, "What is the unit of measurement?" makes sense and the student can articulate.) Applies the multiplicative principle when working with fractions, ratios and proportions.	Establishes, clearly articulates and consistently applies the unit of measurement. (eg. The question, "What is the unit of measurement?" makes sense and the student can articulate what it is and provide additional examples to support their knowing.) Applies the multiplicative principle when working with fractions, ratios and proportions and demonstrates how this works itself out using algebra and equivalency.
Representation	Images are not proportional or combined	Images are proportional and combined.	Images are proportional and accurately combined	Images are clear, focused, proportional and accurately combined
Computation and Execution	Enters discrete data into spreadsheet but computes comparisons by hand or calculator. Makes errors in computation serious enough to flaw the solution. Provides no evidence of how he/she arrived at his/her solution.	Follows a prescribed procedure for entering data into a spreadsheet and performing calculations. Provides evidence of how he/she arrived at their solution however it is inconsistent or unclear.	Sets up spreadsheet and enters data into a spreadsheet and performs calculations using cell variables. Provides evidence of how he/she that clearly supports his/her solution.	Sets up spreadsheet and enters data into a spreadsheet and performs calculations in a variety of ways using the cell variables and functions. Provides evidence of multiple ways to solve the problem.
Communication	Explanation rambled without a clear focus.	Explanation was redundant or hard to follow in places.	Explanation was well organized, flowed logically and was easy to follow.	Explanation was clear, concise providing an in depth understanding of meaning.
Task Management	Struggles to follow management plan to manage time, gather resources and follow the given task for each team member.	Follows a task management plan to manage time, select resources and decide on which tasks team members will undertake.	Creates and follows a task management plan to manage time, determine resources and allocate tasks to team members.	Creates and follows a comprehensive, detailed task management plan to manage time, determine resources and allocate tasks to team members.