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CASA Mathematics Blueprint Page 1 of 8 How do I use this document? This document contains the blueprint e.g. guidelines for the types of problems that will be on the Mathematics test in the Core Academic Skills Assessment (CASA) teacher preparation exam. The blueprint is broken down into 2 domains. Each domain has 2 standards and each standard has multiple parts. o Domain I – Numbers and Algebra Number and Quantity (Standard 9) Algebra and Functions (Standard 10) o Domain II – Geometry and Statistics Measurement and Geometry (Standard 11) Statistics and Probability (Standard 12) There is a table for each domain that details the standard and its parts. The second column unpacks each of the standards and provides additional resources online to learn, review, and/or practice a concept and/or problem solving methodology. To get the most out of this document, review each of the standards and ask yourself, ? Do I understand what this is saying? ? Can I solve a problem pertaining to this standard? If the answer is no to either question, review the information underneath “Unpacking the Standards” next to the standard. If additional help is needed, be sure to consult a tutor in the CRC. Introducing the Mathematics Portion of the CASA For the Mathematics test in the CASA, the following domains and standards are covered: Domain I – Numbers and Algebra 0005 0006 Number and Quantity (Standard 9) Algebra and Functions (Standard 10) CASA Mathematics Blueprint Standards Page 2 of 8 Unpacking the Standards Standard 9: Number and Quantity Indiana educators demonstrate knowledge of number systems, number representations, number operations, and basic number theory, including: 9.1. Recognize, What are the different number types? convert among, Explanation: Classifying numbers and order Video: https://www.youtube.com/watch?v=9orS7coe2WI various Instagrok Classify a number representations search: of rational numbers (e.g., How do you convert from a fraction to a decimal? integers, Explanation: http://cstl.syr.edu/fipse/decunit/convert/convert.htm fractions, Video: Converting between a fraction and a decimal decimals, Dogpile Dogpile results for “converting fraction to a decimal) powers). search: 9.2. 9.3. 9.4. 1 Represent rational and irrational numbers on number lines and coordinate axes. Compute fluently with rational numbers, including applying order of operations. Solve multistep problems and estimate solutions to problems using a variety of number representations. How do you represent irrational and rational numbers on a number line? blekko Represent irrational numbers on a number line search How do you represent irrational and rational numbers on a coordinate axes? Ecosia Draw irrational and rational numbers search What is order of operations? Gigablast Order of operations search Where are practice problems on order of operations? mamma1 Practice problems on order of operations search What are different ways that I can solve multi-step equations? Khan https://www.khanacademy.org/math/algebra/solving-linearAcademy equations-and-inequalities/complicated_equations/v/ex-2-multi-stepequation How would I use estimation to solve a problem? Ecosia Use estimation to solve a problem. search Why I love mamma? Mamma simultaneously searches the major search engines, analyzes the results, set the terms in the correct syntax and format and last but never least, and organizes the results in a uniform retrieval set based on relevancy and score. CASA Mathematics Blueprint Standards Unpacking the Standards 9.5. What is a factor? Bing search 9.6. 9.7. Find common factors and multiples of multidigit numbers. Recognize and represent ratio concepts (e.g., proportions, unit rates, percents). Page 3 of 8 Mathematics what is a factor How do I find the least common denominator? Using prime Explanation: Using prime factorization factorization Video: Using prime factorization Spark Notes: Additional information What is a multiple? “Math is fun” website What is a ratio? mamma search http://www.mathsisfun.com/definitions/multiple.html What is a ratio What is a proportion? mamma What is a proportion search How does a ratio compare to a proportion as well as to a percent? Google Ratio versus a percent versus a proportion Where can I find word (story) problems about ratio concepts and proportional reasoning? Google Practice problems ratio search Practice problems proportional reasoning Apply ratio concepts and proportional reasoning to solve What different methods can I use to solve word problems? mathematical Dogpile Different method for solving word problems and real-word search problems. Standard 10: Algebra and Functions Indiana educators demonstrate knowledge of mathematical expressions, basic algebraic techniques, and the use of equations and inequalities to model and solve problems, including: 10.1. Apply What is combining like terms? properties of Ixquick https://www.ixquick.com/do/search arithmetic to Type in the phrase “combine like terms”. algebraic expressions. How do I simplify an algebraic expression? Apocalx Simplify an algebraic expression What are the algebraic properties? Carrot2 Algebraic properties CASA Mathematics Blueprint Standards 10.2. Solve onevariable equations and inequalities. 10.3. Evaluate algebraic expression or a given value of a variable. 10.4. Recognize equivalent versions of algebraic expressions. 10.5. Recognize the difference between an independent and dependent variable. 10.6. Analyze and solve linear equations and systems of equations. Page 4 of 8 Unpacking the Standards What are different strategies for solving one variable equations and inequalities? Devil Finder2 Solve one variable equations and inequalities How do I evaluate an algebraic expression? eLocalFinder Evaluate an algebraic expression How do I evaluate an algebraic expression? Goofram3 Recognize equivalent versions of algebraic expressions What is an independent variable? Zoo What is an independent variable What is a dependent variable? Zoo What is a dependent variable What is a linear equation? iBoogie What is a linear equation What are the different equations of a line? Info.com What are the different equations of a line How would I solve a linear equation? iSeek4 How would I solve a linear equation 10.7. Using variables and algebraic expressions to model and solve real-world problems. 2 What are the different ways to solve a system of two equations? Graphing Elimination Substitution iSeek What are different ways to solve a system of linear equations Where are practice word (story) problems involving solving algebraic expressions? Monster Practice word problems solving algebraic expressions Crawler Warning! The search button does say “Send me to hell!” However, the search results are on point. Goofram is a metasearch engine based on Google and Wolfram Alpha. 4 If you are ever doing a research paper, iSeek is one of the ultimate search engines to use!!! 3 CASA Mathematics Blueprint Page 5 of 8 Domain II – Geometry and Statistics 0007 0008 Measurement and Geometry (Standard 11) Statistics and Probability (Standard 12) Standards Unpacking the Standards Standard 11: Measurement and Geometry Indiana educators demonstrate knowledge of principles and procedures of measurement, basic properties of two- and three-dimensional figures, and reasoning in geometry, including: 11.1. Solve How is area calculated? mathematical PolyMeta Mathematics calculate the area of a shape and real-world problems How is surface area calculated? involving area, Qrobe.it5 How do I calculate surface area surface area, and volume of How would I calculate the volume? two- and threeSearch.com Calculate the volume of a 2d figure dimensional figures. 11.2. Recognize and How do I draw a polygon on the coordinate plane? represent Searches Recognize and represent polygons on a coordinate plane polygons on a coordinate plane. 11.3. Solve problems Where are practice problems on solving problems involving scale drawings? involving scale Look Smart Practice problems scale drawings drawings. 11.4. Apply the Where can I find practice problems on applying the formulas for the circumference and formulas for the area of a circle? circumference Webcrawler Apply the formulas for the circumference and area of a circle and area of a circle. 11.5. Use facts about What are the different types of angles and what do they look like? complementary, zapmeta What are the different types of geometric angles supplementary, vertical and adjacent angles to solve multistep problems. 11.6. Apply the What is the concept of similarity? concepts of infospace What is the concept of similarity geometry similarity and congruence. What is the concept of congruence? infospace What is the concept of congruence geometry Where are practice problems involving similarity and congruence? 5 qrobe.it will proffer different search terms as you type. CASA Mathematics Blueprint Standards 11.7. Apply the Pythagorean Theorem. Page 6 of 8 Unpacking the Standards infospace Practice problems similarity and congruence geometry What is the Pythagorean Theorem? infospace What is the Pythagorean Theorem What are some practice problems using the Pythagorean Theorem? infospace Practice problems Pythagorean theorem Standard 12: Statistics and Probability Indiana educators demonstrate knowledge of collection, presentation, and interpretation of data, and of the fundamental properties of probability, including: 12.1. Display and What are different types of graphs? interpret data Zeekly What are different types of graphs presented in a variety of formats (e.g. dot plots, histograms, circle graphs). 12.2. Use and What is the mean, median and mode? interpret iBoogie What is mean median mode measures of center (e.g. What is a good method for calculating the mean, median and mode for a frequency mean, median, distribution? mode) and Findelio 6 Frequency distribution mean median mode spread (e.g. standard What is the standard deviation and how do you calculate it by hand? deviation, mamma Calculate standard deviation interquartile search range, outliers) in context. What is an interquartile range? mamma Interquartile range search 12.3. Use random sampling to draw inferences about populations. 12.4. Make inferences about populations that are based on comparisons of 6 What is an outlier? mamma search What is sampling? mamma search What is an outlier statistics What is sampling How do you make inferences about a population given a sample of the population? Google How do you make inferences about a sample population Make inferences based on the . . . Center Variability Hot Bot search Metacrawler search Make inferences based on the center Make inferences based on variability Findelio searches multiple search engines e.g. AllTheWeb, Bing, Exalead, and Entireweb and displays a directory listing after a search query. CASA Mathematics Blueprint Standards center, variability, and visual overlap of distributions. 12.5. Interpret scatter plots and estimate lines of fit for data involving two variables. 12.6. Apply fundamental properties of probability to estimate the outcomes of events. Page 7 of 8 Unpacking the Standards Visual overlap of distributions Google search Make inferences based on visual overlap of distributions The website http://bmsbrigman.weebly.com/unit-4-inferences.html includes a description of all of the above items. What is a scatter plot and how can it be used? YouTube What is a scatter plot? search What are lines of fit for data involving two variables? Deeper Web Lines of fit search What are the fundamental properties of probability? QWANT https://www.qwant.com/?q=fundamental+properties+of+probability search How to I calculate the probability of an event occurring? Khan https://www.khanacademy.org/math/probability/independentAcademy dependent-probability/basic_probability/v/basic-probability What is conditional probability? Instagrok What is conditional probability? search 12.7. Determine probabilities using various representations (e.g. Venn diagrams, tree graphs). How do you calculate probability involving AND and OR? Regents http://www.regentsprep.org/regents/math/algebra/APR8/LProbAO.htm Prep Website What is a Venn diagram? QWANT Venn diagrams search Given a Venn diagram, how to I calculate the probability of an event occurring? Yandex Use a Venn diagram to find the probability search What is a tree diagram/graph? Google What is a tree graph? search Given a tree diagram, how to do I calculate the probability of an event occurring? Video Khan Academy video on using tree diagrams In the Mathematics test, approximately 60% of the test will come from Domain 1 (Numbers and Algebra) and 40% of the test will come from Domain II (Geometry and Statistics). CASA Mathematics Blueprint Interesting websites . . . http://www.zanran.com/q/ http://www.nationmaster.com/ http://l-lists.com/en/lists/e34z3f.html Search the web for data and statistics Compare countries on anything List of metasearch engines Page 8 of 8