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Interactive Mathematics Program Curriculum Framework

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Interactive Mathematics Program Curriculum Framework Interactive Mathematics Program Curriculum Framework School: __Delaware STEM Academy________ Curricular Tool: _IMP________ Grade or Course _Year 1 (grade 9) Unit Concepts / Standards Alignment Essential Questions Assessments Big Ideas from IMP Unit One: Patterns Timeline: 6 weeks Interpret expressions that represent a quantity in terms of its Patterns emphasizes extended, open-ended Can students use variables and All assessments are context. CC.A-SSE.1 exploration and the search for patterns. algebraic expressions to listed at the end of the Important mathematics introduced or represent concrete situations, curriculum map. Understand that a function from one set (called the domain) reviewed in Patterns includes In-Out tables, generalize results, and describe to another set (called the range) assigns to each element of functions, variables, positive and negative functions? the domain exactly one element of the range. If f is a function numbers, and basic geometry concepts Can students use different and x is an element of its domain, then f(x) denotes the output related to polygons. Proof, another major representations of functions— of f corresponding to the input x. The graph of f is the graph theme, is developed as part of the larger symbolic, graphical, situational, of the equation y = f(x). CC.F-IF.1 theme of reasoning and explaining. and numerical—and Students’ ability to create and understand understanding the connections Recognize that sequences are functions, sometimes defined proofs will develop over their four years in between these representations? recursively, whose domain is a subset of the integers. For IMP; their work in this unit is an important example, the Fibonacci sequence is defined recursively by start. Can students use function f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. CC.F-IF.3 notation? This unit focuses on several mathematical Can students model, and Write a function that describes a relationship between two ideas: computing with signed quantities. CC.F-BF.1 Finding, analyzing, and generalizing numbers? geometric and numeric patterns Determine an explicit expression, a recursive process, or Analyzing and creating In-Out tables Can students solve equations steps for calculation from a context. CC.F-BF.1a Using variables in a variety of ways, using trial and error? including to express generalizations Write arithmetic and geometric sequences both recursively Developing and using general and with an explicit formula, use them to model situations, principles for working with variables, and translate between the two forms. CC.F-BF.2 including the distributive property Working with order-of-operations rules Know precise definitions of angle, circle, perpendicular line, for arithmetic parallel line, and line segment, based on the undefined Using a concrete model to understand notions of point, line, distance along a line, and distance and do arithmetic with positive and around a circular arc.CC.G-CO.1 negative integers Applying algebraic ideas, including In- Out tables, in geometric settings Developing proofs concerning Copyright © 2013 by 4-D-1 Unit Concepts / Standards Alignment Essential Questions Assessments Big Ideas from IMP consecutive sums and other topics Unit Two: Game of Pig Timeline: 7 weeks Represent data with plots on the real number line (dot plots, As an introduction to the probability Can students apply basic All assessments are histograms, and box plots). CC.S-ID.1 concepts and skills needed to analyze the methods for calculating listed at the end of the game of Pig, students work on a variety of probabilities? curriculum map. Distinguish between correlation and causation. CC.S-ID.9 problems involving chance occurrences. Can students construct area Through these experiences, they develop an models and tree diagrams? Decide if a specified model is consistent with results from a understanding of the concept of expected given data-generating process, e.g. using simulation. For value and learn to calculate expected value Can students distinguish example, a model says a spinning coin falls heads up with using an area model. They also encounter between theoretical and probability 0.5. Would a result of 5 tails in a row cause you some real-life “games,” such as buying experimental probabilities? to question the model? CC.S-IC.2 insurance and playing the lottery, and Can students plan and carry out discover that in such situations, expected simulations? Describe events as subsets of a sample space (the set of value may not be the sole criterion for outcomes) using characteristics (or categories) of the making a decision. Can students collect and analyze outcomes, or as unions, intersections, or complements of In the unit activities, students explore these data? other events (“or,” “and,” “not”). CC.S-CP.1 important mathematical ideas: Can students construct Learning what constitutes a “complete frequency bar graphs? Understand that two events A and B are independent if the strategy” for a game and developing probability of A and B occurring together is the product of and analyzing strategies Can students calculate, and their probabilities, and use this characterization to determine Calculating probabilities as fractions, interpret expected value? if they are independent. CC.S-CP.2 decimals, and percents by emphasizing Can students apply the concept equally likely outcomes and by of expected value to real-world Understand the conditional probability of A given B as P(A constructing mathematical models, situations? and B)/P(B), and interpret independence of A and B as including area models and tree saying that the conditional probability of A given B is the diagrams same as the probability of A, and the conditional probability Determining whether events are of B given A is the same as the probability of B. CC.S-CP.3 independent Using the idea of “in the long run” to Find the conditional probability of A given B as the fraction develop the concept of expected value of B’s outcomes that also belong to A and interpret the and calculating and interpreting answer in terms of the model. CC.S-CP.6 expected values Solving problems involving conditional Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and probability B), and interpret the answer in terms of the model. CC.S- Making and interpreting frequency bar CP.7 – supplementary lesson is being developed by the graphs publisher Using simulations to estimate probabilities and compare strategies Copyright © 2013 by 4-D-2 Unit Concepts / Standards Alignment Essential Questions Assessments Big Ideas from IMP Apply the general Multiplication Rule in a uniform Comparing the theoretical analysis of a probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), situation with experimental results and interpret the answer in terms of the model. CC.S-CP.8 - Examining how the number of trials in unit supplement to be developed a simulation affects the results Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. CC.S- MD.1 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. CC.S-MD.2 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. CC.S-MD.3 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. CC.S-MD.5 Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. CC.S-MD.5a Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. CC.S-MD.5b Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). CC.S-MD.6 Copyright © 2013 by 4-D-3 Unit Concepts / Standards Alignment Essential Questions Assessments Big Ideas from IMP Analyze decisions and strategies using probability concepts (e.g. product testing, medical testing, pulling a hockey goalie at the end of a game). CC.S-MD.7 Unit Three: The Overland Trail Timeline: 7 weeks Use units as a way to understand problems and to guide the Building on students’ work in Patterns, this Can students interpret graphs All assessments are solution of multi-step problems; choose and interpret units unit develops the central mathematical idea and use graphs to represent listed at the end of the consistently in formulas; choose and interpret the scale and of functions and their representations. situations? curriculum map. the origin in graphs and data displays. CC.N-Q.1 Students will move among the following Can students relate graphs to four “faces” of functions: situations, graphs, their equations, with emphasis Define appropriate quantities for the purpose of descriptive tables and rules. on linear relationships? modeling. CC.N-Q.2 The focus of this unit is on linear functions. Can students solve pairs of Interpret parts of an expression, such as terms, factors, and Students will use starting values and rate of linear equations by graphing? coefficients. CC.A-SSE.1a change to characterize linear functions, Can students fit equations to build In-Out tables, draw graphs, and write data, both with and without Use the structure of an expression to identify ways to rewrite equations to represent specific contexts.
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