The Math Team aligned the previous version of the Illinois ABE/ASE Content Standards with the Common Core State Standards through a process of research, discussion, and revision. The membership included: Joshua Anderson Waukegan Public Library Dr. Tania Giordani College of Lake County Emilie McCallister Joliet Junior College Dr. Sharon Bryant City Colleges of Chicago Mark Harrison Urbana Adult Education Serkies Central Illinois Adult Education Service Center Gagnon Richland Community College Elizabeth Hobson Elgin Community College The ICCB would like to thank the following individuals and organizations for their leadership and assistance throughout the project: Dr. Haynie, Math Team Leader Dawn Hughes, Project Leader Central Illinois Adult Education Service Center (CIAESC)
(Grade Levels 4.0 – 5.9) Standard Number MATH STANDARD Reference Example of How Adults Use This OPERATIONS AND ALGEBRAIC THINKING (OA) Use the four operations with whole numbers to solve problems. 3.OA.1 Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. CC.4.OA.1 ESS01.03.02 CCR.OA.C Calculating the total number of items in batches (e.g., 5 crates with 16 boxes to a crate) 3.OA.2 Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. CC.4.OA.2 ESS01.03.02 ESS01.03.05 CCR.OA.C Planning a neighborhood party 3.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. CC.4.OA.3 ESS01.03.02 ESS01.03.05 CCR.OA.C Planning what kind of pizza or sandwiches to order for an employee luncheon Gain familiarity with factors and multiples. 3.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. CC.4.OA.4 ESS01.03.02 CCR.OA.C Figuring how many ways change from $100 can be given/made Generate and analyze patterns.
Functions presented as expressions can many important phenomena. Two important families of functions characterized by laws of growth are linear functions, which grow at a constant rate, and exponential functions, which grow at a constant percent rate. Linear functions with a constant term of zero describe proportional relationships. A graphing utility or a computer algebra system can be used to experiment with properties of these functions and their graphs and to build computational models of functions, including recursively defined functions. Connections to Expressions, Equations, Modeling, and Coordinates - Determining an output value for a particular input involves evaluating an expression; finding inputs that yield a given output involves solving an equation. Questions about when two functions have the same value for the same input lead to equations, whose solutions can be visualized from the intersection of their graphs. Because functions describe relationships between quantities, they are frequently used in modeling. Sometimes functions are defined by a recursive process, which can be displayed effectively using a spreadsheet or other technology. Conceptual Category IV – Modeling Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data. A model can be very simple, such as writing total cost as a product of unit price and number bought, or using a geometric shape to describe a physical object like a coin. Even such simple models involve making choices. It is up to us whether to model a coin as a three-dimensional cylinder, or whether a two-dimensional disk works well enough for our purposes. Other situations—modeling a delivery route, a production schedule, or a comparison of loan amortizations—need more elaborate models that use other tools from the mathematical sciences. Real-world situations are not organized and labeled for analysis; formulating tractable models, representing such models, and analyzing them is appropriately a creative process. Like every such process, this depends on acquired expertise as well as creativity.
5.S.ID.2 Use statistics appropriate to the of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CC.S.ID.2 Understanding there are no “true” measures for statistical quantities (i.e., home values, expected wages, expected prices, expected profits or losses) 5.S.ID.3 Interpret differences in center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). CC.S.ID.3 CCR.S.ID.E Understanding there are no “true” measures for statistical quantities (i.e., home values, expected wages, expected prices, expected profits or losses) 5.S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. CC.S.ID.4 ESS04.07.01 Tracking one’s daily expenses personal financial choices to data from an ideal spender’s purchase log Summarize, represent, and interpret data on two categorical and quantitative variables. 5.S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* CC.S.ID.5 CCR.S.ID.E Looking at reports on stock market to see if they reflect the trends represented
Result Unknown Change Unknown Start Unknown Add to Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now? 2 + 3 = ? Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two? 2 + ? = 5 Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before? ? + 3 = 5 Take from Five apples were on the table. I ate two apples. How many apples are on the table now? 5 – 2 = ? Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat? 5 – ? = 3 Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before? ? – 2 = 3 Total Unknown Addend Unknown Both Addends Unknown Put Together/ Take Apart Three red apples and two green apples are on the table. How many apples are on the table? 3 + 2 = ? Five apples are on the Three are red and the rest are green. How many apples are green? 3 + ? = 5, 5 – 3 = ? Grandma has five flowers. How many can she put in her red vase and how many in her blue vase? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 = 4 + 1 5 = 2 + 3, 5 = 3 + 2 Difference Unknown Bigger Unknown Smaller Unknown Compare (“How many more?” version): Lucy has two apples. has five apples. How many more apples does Julie have than Lucy? (Version with “more”): Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have? (Version with (Version with “more”): Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?
Arrays, Area There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle? If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it? If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it? Compare A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long? A red hat $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? General a b = ? a ? = p and p a = ? ? b = p and p b = ? Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition Commutative property of addition Additive identity property of 0 Existence of additive inverses Associative property of multiplication (a + b) + c = a + (b + c) a + b = b + a a + 0 = 0 + a = a For every a there exists –a so that a + (–a) = (–a) + a = 0. (a b) c = a (b c)