Inquiry Questions (Engaging- Debatable): How does probability relate to obtaining car insurance? (MA10-GR.HS-S.3-GLE.3-IQ.3) Why is it hard for humans to determine if a set of numbers was created randomly? Unit Strands Statistics and Probability: Conditional Probability and the Rules of Probability Concepts two-way frequency tables, associations, conclusions, categorical variables, unions, intersections, complements, events, subsets, sample space, independence, probabilities, products, conditional probability, given Generalizations My students will Understand that… Guiding Questions Factual Conceptual Two-way frequency tables provide the necessary structure to make conclusions about the association of categorical variables. (MA10-GR.HS-S.3-GLE.3-EO.a.iv) How is conditional probability represented in a two-way frequency table? How do you determine the conditional probability of A given B from a frequency table? How do you determine if two events are independent from a frequency table? Why are two-way frequency tables useful in probability? Unions, intersections and complements of events describe subsets of a sample space. How do the word “and” and “or” relate to unions and intersections? How are intersections and complements related? When is it appropriate to use unions, intersections, or complements in determining probability? Why is the addition rule related to unions, intersections and complements? Mathematicians determine the independence of events A and B by examining if the product of the probabilities of A and B equals the probability of A and B occurring together. (MA10-GR.HS-S.3-GLE.3-EO.a.iii) How can you determine if two events are independent? Why are events independent if the product of the probabilities of A and B equals the probability of A and B occurring together? Mathematicians find the probability of an event given the occurrence of another event through conditional probability. (MA10-GR.HS-S.3-GLE.3-EO.a.iii) When do we use conditional probability? How are independence and conditional probability related?
Focusing Lens(es) Structure Modeling Standards and Grade Level Expectations Addressed in this Unit MA10-GR.HS-S.1-GLE.2 MA10-GR.HS-S.4-GLE.4 MA10-GR.HS-S.4-GLE.5 Inquiry Questions (Engaging- Debatable): How might surface area and volume be used to explain biological differences in animals? (MA10-GR.HS-S.4-GLE.3-IQ.1) Unit Strands Number and Quantity: Quantities Geometry: Geometric Measurement and Dimension Geometry: Modeling with Geometry Concepts perimeter, area, volume, patterns, models, measurements, decisions Generalizations My students will Understand that… Guiding Questions Factual Conceptual Underlying and related structures of perimeter, area and volume can reveal patterns within complex objects. (MA10-GR.HS-S.4-GLE.4-EO.a, b) How does the relationship between the volumes of a cone and its corresponding cylinder help us find the volume of a pyramid? How is the area of an irregular shape measured? How can surface area be minimized while maximizing volume? (MA10-GR.HS-S.4-GLE.4-IQ.3) Why is the formula for the circumference of a circle necessary for deriving the area of a circle? Why does increasing the radius by a constant increase the volume of a cylinder more than increasing the height by the same constant? Geometric models, chosen and created with the use of appropriate measurements deepen understandings of empirical situations and improve decision-making. How are mathematical objects different from the physical objects they model? How can the geometric concepts of area and volume model density? What makes a good geometric model of a physical object or situation? (MA10-GR.HS-S.4-GLE.5-IQ.2) Why are ratios an important component of geometric modeling? Key Knowledge and Skills: My students will… What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined.