standards and Learning Objectives
This unit is designed as a two week introduction to the surface area and volume unit of a Geometry class. There are other standards, Algebra I, Algebra II, and Integrated Chemistry Physics standards that are addressed in the unit, but only the Geometry standards are being assessed.
Mathematics and SCIENCE Standards
Geometry
G.TS.1 Describe relationships between the faces, edges, and vertices of three-dimensional solids. Create a net for a given three-dimensional solid. Describe the three-dimensional solid that can be made from a given net (or pattern).
Algebra I
AI.F.2 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. Identify independent and dependent variables and make predictions about the relationship.
AII.EL.5 Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship.
ICP.3.1 Describe how we use macroscopic properties of matter to model microscopic processes.
G.TS.1 Describe relationships between the faces, edges, and vertices of three-dimensional solids. Create a net for a given three-dimensional solid. Describe the three-dimensional solid that can be made from a given net (or pattern).
- Students will be able to identify multiple nets and their corresponding solid.
- Students will be able to deduce that the surface area is the same as the area of the corresponding net.
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Students will be able to analyze how changes in one dimension of a solid affect the surface area and volume.
- Students will be able to correctly apply surface area and volume to real-life scenarios.
Algebra I
AI.F.2 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. Identify independent and dependent variables and make predictions about the relationship.
- Students will be able to graph and describe the relationship between surface area-to-volume ratio and linear measure (side length or radius).
AII.EL.5 Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship.
- Students will be able to graph an exponential function.
ICP.3.1 Describe how we use macroscopic properties of matter to model microscopic processes.
- Students will be able to explain how material can be made hydrophobic due to microscale properties.
Learning Objectives
Size and Scale
N.S.1. Learners will be able to relate the size of nano-sized objects to objects encountered in daily life (macro-scale).
Structure of Matter
N.S.2. Learners will compare surface-area-to-volume ratios of different sized objects and explain that surface-area-to-volume ratios play a role in the unique properties of objects at the nano-scale.
Forces and Interactions
N.S.3. Learners will be able to explain why (intensive) properties of matter can change at the nano-scale (for example: properties like boiling point, reactivity, malleability, fluorescence, magnetism).
Methods
N.S.4. Learners will recognize that scientists and engineers were unable to study the nano-scale until advances in technology made it possible.
N.S.1. Learners will be able to relate the size of nano-sized objects to objects encountered in daily life (macro-scale).
- Students will be able to compare objects in terms of size and justify their reasoning.
Structure of Matter
N.S.2. Learners will compare surface-area-to-volume ratios of different sized objects and explain that surface-area-to-volume ratios play a role in the unique properties of objects at the nano-scale.
- Students will be able to use Excel to demonstrate patterns and relationships between volume, SA, and SA/V ratio in context.
Forces and Interactions
N.S.3. Learners will be able to explain why (intensive) properties of matter can change at the nano-scale (for example: properties like boiling point, reactivity, malleability, fluorescence, magnetism).
- Students will be able to describe how properties change at the nano-scale.
Methods
N.S.4. Learners will recognize that scientists and engineers were unable to study the nano-scale until advances in technology made it possible.
- Students will be able to describe the impact of advances in technology on aspects of the mobile phone market.
21st Century Skills
TC.1. Students will be able to collaborate with others. Group members are expected to propose new ideas and provide feedback on the ideas of others during the gallery walk. A rubric will be created based on these properties so that students can be assessed by both their group members and their teacher.
TC.2. Students will be able to communicate effectively. During the final presentation, each group will be assessed by the teacher based on their abilities to clearly explain their prediction for the cell phone of the future and justify their prediction in concrete nanoscience research and information from the past. Students will also be required to justify their reasoning in written form on a final paper.
TC.3. Students will demonstrate creativity in the explanation of their unique cell phone. The students' new design must be something relatively innovative, unknown, and/or unseen in the current cell phone market. Students will measure each others design via peer review.
TC.4. Students will make connections across academic subjects. For example, students will be able to state how various chemical properties of molecules will affect the resulting surface-area-to-volume mathematical computations.
TC.2. Students will be able to communicate effectively. During the final presentation, each group will be assessed by the teacher based on their abilities to clearly explain their prediction for the cell phone of the future and justify their prediction in concrete nanoscience research and information from the past. Students will also be required to justify their reasoning in written form on a final paper.
TC.3. Students will demonstrate creativity in the explanation of their unique cell phone. The students' new design must be something relatively innovative, unknown, and/or unseen in the current cell phone market. Students will measure each others design via peer review.
TC.4. Students will make connections across academic subjects. For example, students will be able to state how various chemical properties of molecules will affect the resulting surface-area-to-volume mathematical computations.