Posted: Tue, 07/03/2018 - 2:11pm Updated: Thu, 03/14/2019 - 2:03pm

This Teacher Resource Guide has been developed to provide supporting materials to help educators successfully implement the Indiana Academic Standards for Finite. These resources are provided to help you in your work to ensure all students meet the rigorous learning expectations set by the Indiana Academic Standards. Use of these resources are optional; teachers should decide which resources will work best in their classroom for their students.

The resources on this webpage are for illustrative purposes only, to promote a base of clarity and common understanding. Each item illustrates a standard but please note that the resources are not intended to limit interpretation or classroom applications of the standards.

The links compiled and posted on this webpage have been provided by classroom teachers, the Department of Education, and other sources. The IDOE has not attempted to evaluate any posted materials. They are offered as samples for your reference only and are not intended to represent the best or only approach to any particular issue. The IDOE does not control or guarantee the accuracy, relevance, timeliness, or completeness of information contained on a linked website; does not endorse the views expressed or services offered by the sponsor of a linked website; and cannot authorize the use of copyrighted materials contained in linked websites. Users must request such authorization from the sponsor of the linked website.

SETS

Activities, Examples, or Resources

FM.S.1: Know and use the concepts of sets, elements, and subsets.

FM.S.2: Perform operations on sets (union, intersection, complement, cross product) and illustrate using Venn diagrams.

MATRICES

Activities, Examples, or Resources

FM.MA.1: Add, subtract, and multiply matrices of appropriate dimensions (i.e. up to 3x3 matrices). Multiply matrices by scalars. Calculate row and column sums for matrix equations.

FM.MA.2: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers.

FM.MA.3: Understand the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

FM.MA.4: Solve problems represented by matrices using row-reduction techniques and properties of matrix multiplication, including identity and inverse matrices.

FM.MA.5: Use matrices to solve real-world problems that can be modeled by a system of equations (i.e. up to 3 linear equations) in two or three variables using technology.

FM.MA.6: Build and use matrix representations to model polygons, transformations, and computer animations.

NETWORKS

Activities, Examples, or Resources

FM.N.1: Use networks, traceable paths, tree diagrams, Venn diagrams, and other pictorial representations to find the number of outcomes in a problem situation.

FM.N.2: Optimize networks in different ways and in different contexts by finding minimal spanning trees, shortest paths, and Hamiltonian paths including real-world problems.

FM.N.3: Use critical-path analysis in the context of scheduling problems and interpret the results.

FM.N.4: Construct and interpret directed and undirected graphs, decision trees, networks, and flow charts that model real-world contexts and problems.

FM.N.5: Use graph-coloring techniques to solve problems.

The Poor Cartographer

FM.N.6: Construct vertex-edge graph models involving relationships among a finite number of elements.  Describe a vertex-edge graph using an adjacency matrix.  Use vertex-edge graph models to solve problems in a variety of real-world settings.

OPTIMIZATION

Activities, Examples, or Resources

FM.O.1: Use bin-packing techniques to solve problems of optimizing resource usage.

FM.O.2: Use geometric and algebraic techniques to solve optimization problems with and without technology.

FM.O.3: Use the Simplex method to solve optimization problems with and without technology.

PROBABILITY

Activities, Examples, or Resources

FM.P.1: Use Markov chains to solve problems with and without technology.

FM.P.2: Understand and use the addition rule to calculate probabilities for mutually exclusive and non mutually exclusive events.

FM.P.3: Understand and use the multiplication rule to calculate probabilities for independent and dependent events. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Medical Testing

FM.P.4: Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.

FM.P.5: Calculate the probabilities of complementary events.

Even or Odd?

FM.P.6: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

The Expected Value Spinner

FM.P.7: Analyze decisions and strategies using probability concepts.  Analyze probabilities to interpret odds and risk of events.

FM.P.8: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events.

FM.P.9: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

Winner, Winner!

FM.P.10: Use the relative frequency of a specified outcome of an event to estimate the probability of the outcome and apply the law of large numbers in simple examples.