Algebra 2: Catapult Construction
Driving Question: How could you use ancient artillery technology to improve humanity?
Common Core State Standards – Mathematics Content Standards
Write expressions in equivalent forms to solve problems.
Driving Question: How could you use ancient artillery technology to improve humanity?
Common Core State Standards – Mathematics Content Standards
Write expressions in equivalent forms to solve problems.
- CCSS.MATH.CONTENT.HSA.SSE.B.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*
- CCSS.MATH.CONTENT.HSA.SSE.B.3.A - Factor a quadratic expression to reveal the zeros of the function it defines.
- CCSS.MATH.CONTENT.HSA.SSE.B.3.B - Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- CCSS.MATH.CONTENT.HSA.APR.A.1 - Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- CCSS.MATH.CONTENT.HSA.APR.B.2 - Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
- CCSS.MATH.CONTENT.HSA.APR.B.3 - Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
- CCSS.MATH.CONTENT.HSA.CED.A.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
- CCSS.MATH.CONTENT.HSA.CED.A.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- CCSS.MATH.CONTENT.HSA.CED.A.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
- CCSS.MATH.CONTENT.HSA.CED.A.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
- Understand solving equations as a process of reasoning and explain the reasoning.
- CCSS.MATH.CONTENT.HSA.REI.A.1 - Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
- CCSS.MATH.CONTENT.HSA.REI.B.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
- CCSS.MATH.CONTENT.HSA.REI.B.4 - Solve quadratic equations in one variable.
- CCSS.MATH.CONTENT.HSA.REI.B.4.A - Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
- CCSS.MATH.CONTENT.HSA.REI.B.4.B - Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- CCSS.MATH.CONTENT.HSA.REI.C.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- CCSS.MATH.CONTENT.HSA.REI.C.8 - (+) Represent a system of linear equations as a single matrix equation in a vector variable.
- CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
- CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
- CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
- CCSS.MATH.PRACTICE.MP4 Model with mathematics.
- CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
- CCSS.MATH.PRACTICE.MP6 Attend to precision.
- CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
- CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Chemistry: Food Chemistry
Driving Question: How can chemistry enhance the culinary arts?
Biological, chemical, and physical properties of matter result from the ability of atoms to form bonds from electrostatic forces between electrons and protons and between atoms and molecules. As a basis for understanding this concept:
a) students know atoms combine to form molecules by sharing electrons to form covalent or metallic bonds or by exchanging electrons to form ionic bonds
b) Students know chemical bonds between atoms in molecules and many large biological molecules are covalent.
c) Students know salt crystals, such as NaCl, are repeating patterns of positive and negative ions held together by electrostatic attraction.
d) Students know the atoms and molecules in liquids move in a random pattern relative to one another because the intermolecular forces are too weak to hold the atoms or molecules in a solid form.
e) Students know how to draw Lewis dot structures.
f) Students know how to predict the shape of simple molecules and their polarity from Lewis dot structures.
g) Students know how electronegativity and ionization energy relate to bond formation.
h) Students know how to identify solids and liquids held together by van der Waals forces or hydrogen bonding and relate these forces to volatility and boiling/melting point temperatures.
Organic Chemistry and Biochemistry:
The bonding characteristics of carbon allow the formation of many different organic molecules of varied sizes, shapes, and chemical properties and provide the biochemical basis of life. As a basis for understanding this concept:
a) Students know large molecules (polymers), such as proteins, nucleic acids, and starch, are formed by repetitive combinations of simple subunits.
b) Students know the bonding characteristics of carbon that result in the formation of a large variety of structures ranging from simple hydrocarbons to complex polymers and biological molecules.
c) Students know amino acids are the building blocks of proteins.
d) Students know the system for naming the ten simplest linear hydrocarbons and isomers that contain single bonds, simple hydrocarbons with double and triple bonds, and simple molecules that contain a benzene ring.
e) Students know how to identify the functional groups that form the basis of alcohols, ketones, ethers, amines, esters, aldehydes, and organic acids.
f) Students know the R-group structure of amino acids and know how they combine to form the polypeptide backbone structure of proteins.
Common Core State Standards
Reading Standards for Literacy in Science and Technical Subjects 6–12:
Writing Standards for Literacy in History/Social Studies, Science, and Technical Subjects 6–12
Production and Distribution of Writing:
Driving Question: How can chemistry enhance the culinary arts?
- By following this driving question and this path, we hope to be able to enhance the culinary arts and create our own foods. This being said, we hope to create basic foods such as ice cream, rock candy, and any other types of food that can be made in a safe manner.
- Chapter 7: Atomic Structure and Periodicity
- Chapter 8: Bonding - General Concepts
- Chapter 9: Covalent Bonds - Orbitals
- Chapter 22: Organic & Biological Molecules
Biological, chemical, and physical properties of matter result from the ability of atoms to form bonds from electrostatic forces between electrons and protons and between atoms and molecules. As a basis for understanding this concept:
a) students know atoms combine to form molecules by sharing electrons to form covalent or metallic bonds or by exchanging electrons to form ionic bonds
b) Students know chemical bonds between atoms in molecules and many large biological molecules are covalent.
c) Students know salt crystals, such as NaCl, are repeating patterns of positive and negative ions held together by electrostatic attraction.
d) Students know the atoms and molecules in liquids move in a random pattern relative to one another because the intermolecular forces are too weak to hold the atoms or molecules in a solid form.
e) Students know how to draw Lewis dot structures.
f) Students know how to predict the shape of simple molecules and their polarity from Lewis dot structures.
g) Students know how electronegativity and ionization energy relate to bond formation.
h) Students know how to identify solids and liquids held together by van der Waals forces or hydrogen bonding and relate these forces to volatility and boiling/melting point temperatures.
Organic Chemistry and Biochemistry:
The bonding characteristics of carbon allow the formation of many different organic molecules of varied sizes, shapes, and chemical properties and provide the biochemical basis of life. As a basis for understanding this concept:
a) Students know large molecules (polymers), such as proteins, nucleic acids, and starch, are formed by repetitive combinations of simple subunits.
b) Students know the bonding characteristics of carbon that result in the formation of a large variety of structures ranging from simple hydrocarbons to complex polymers and biological molecules.
c) Students know amino acids are the building blocks of proteins.
d) Students know the system for naming the ten simplest linear hydrocarbons and isomers that contain single bonds, simple hydrocarbons with double and triple bonds, and simple molecules that contain a benzene ring.
e) Students know how to identify the functional groups that form the basis of alcohols, ketones, ethers, amines, esters, aldehydes, and organic acids.
f) Students know the R-group structure of amino acids and know how they combine to form the polypeptide backbone structure of proteins.
Common Core State Standards
Reading Standards for Literacy in Science and Technical Subjects 6–12:
- CCSS.ELA-LITERACY.RST.9-10.1 - Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
- CCSS.ELA-LITERACY.RST.9-10.2 - Determine the central ideas or conclusions of a text; trace the text's explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text.
- CCSS.ELA-LITERACY.RST.9-10.3 - Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
- CCSS.ELA-LITERACY.RST.9-10.4 - Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics.
- CCSS.ELA-LITERACY.RST.9-10.5 -Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy).
- CCSS.ELA-LITERACY.RST.9-10.6 - Analyze the author's purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, defining the question the author
- CCSS.ELA-LITERACY.RST.9-10.7 - Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
- CCSS.ELA-LITERACY.RST.9-10.8 - Assess the extent to which the reasoning and evidence in a text support the author's claim or a recommendation for solving a scientific or technical problem.
- CCSS.ELA-LITERACY.RST.9-10.9 - Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts.
Writing Standards for Literacy in History/Social Studies, Science, and Technical Subjects 6–12
Production and Distribution of Writing:
- CCSS.ELA-LITERACY.WHST.9-10.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
- CCSS.ELA-LITERACY.WHST.9-10.5 - Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.
- CCSS.ELA-LITERACY.WHST.9-10.6 - Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology's capacity to link to other information and to display information flexibly and dynamically.
- CCSS.ELA-LITERACY.WHST.9-10.7 - Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.