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This schoolwide project will be facilitated by the Mathematics teacher. Students will work in heterogeneous teams of four and given an opportunity to decide which type of bridge they will design and construct. The project is divided into four (4) stages: Research through Webquest, Bridge Design, Bridge Construction with Testing, and Multimedia Presentation.
Each team of four students will design using a software and build a model bridge of wooden toothpicks from specification given in the Building Rules and Code. During this project, students will utilize the following math skills:
Each team will present their model bridge accompanied by a multimedia presentation to an audience of their peers, parents, and teachers. Afterwhich, the audience will witness the destruction of their bridges that will then justify their design.
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1. Students will enhance their technology experience by creating multimedia representation of project and design.
2. Students will recognize real world application of mathematical concepts and principles.
3. Students will learn to conduct multiple research and data collection.
4. Students will develop spatial visualization, intuition, and learn to make good judgment.
5. Student will collaborate effectively in small groups and exhibit communication skills/techniques.
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1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
1.1 Students use properties of numbers to demonstrate whether assertions are true or false.2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
3.0 Students solve equations and inequalities involving absolute values.
4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
19.0 Students know the quadratic formula and are familiar with its proof by completing the square.
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
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1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
4.0 Students prove basic theorems involving congruence and similarity.
5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
6.0 Students know and are able to use the triangle inequality theorem.
7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
14.0 Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.
2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
12.0 Students use trigonometry to determine unknown sides or angles in right triangles.
13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.
14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.
1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.
5.0 Students determine the mean and the standard deviation of a normally distributed random variable.
6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.
7.0 Students compute the variance and the standard deviation of a distribution of data.
1. Basic operations and concepts
2. Social, ethical, and human issues
3. Technology productivity tools
4. Technology communications tools
5. Technology research tools
6. Technology problem-solving and decision-making tools
d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton's third law).
e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.
f. Students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth's gravitational force causes a satellite in a circular orbit to change direction but not speed).
g. Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.
History and Social Science
Chronological and Spatial Thinking
1. Students compare the present with the past, evaluating the consequences of past events and decisions and determining the lessons that were learned.
2. Students analyze how change happens at different rates at different times; understand that some aspects can change while others remain the same; and understand that change is complicated and affects not only technology and politics but also values and beliefs.
3. Students use a variety of maps and documents to interpret human movement, including major patterns of domestic and international migration, changing environmental preferences and settlement patterns, the frictions that develop between population groups, and the diffusion of ideas, technological innovations, and goods.
4. Students relate current events to the physical and human characteristics of places and regions.
1. Students show the connections, causal and otherwise, between particular historical events and larger social, economic, and political trends and developments.
2. Students recognize the complexity of historical causes and effects, including the limitations on determining cause and effect.
1.0 Writing Strategies
Research and Technology
1.6 Develop presentations by using clear research questions and creative and critical research strategies (e.g., field studies, oral histories, interviews, experiments, electronic sources).
1.7 Use systematic strategies to organize and record information (e.g., anecdotal scripting, annotated bibliographies).
1.8 Integrate databases, graphics, and spreadsheets into word-processed documents.
Evaluation and Revision
1.9 Revise text to highlight the individual voice, improve sentence variety and style, and enhance subtlety of meaning and tone in ways that are consistent with the purpose, audience, and genre.
1.0 Listening and Speaking Strategies
1.8 Use effective and interesting language, including:
a. Informal expressions for effect
b. Standard American English for clarity
c. Technical language for specificity
We would like to extend our deep-felt appreciation to the following for making this project possible:
Building Toothpick Bridges by Jeanne Pollard (Dale Seymour Publications)
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