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McREL Standards as Correlated to MathTrax
Yellow Squares Correlated to MathTrax
Subject: Math
Standard: Uses basic and advanced procedures while performing the process of computation
Grade Level: Middle School [7-8]
| Benchmark Label |
Benchmark |
|---|---|
| M3.3.1 | 1. Adds, subtracts, multiplies, and divides mixed numbers and fractions |
| M3.3.2 | 2. Rounds decimals and fractions |
| M3.3.3 | 3. Mentally multiplies and divides basic combinations of whole numbers with reasonable accuracy |
| M3.3.4 | 4. Uses basic estimation techniques effectively (e.g., overestimate, underestimate, range of estimations) |
| M3.3.5 | 5. Uses order of operations effectively |
| M3.3.6 | 6. Understands the nature of and similarities and differences between multiples and factors |
| M3.3.7 | 7. Uses a calculator to compare amounts proportionally |
| M3.3.8 | 8. Understands that addition and subtraction are inverses of one another as are multiplication and division; one operation undoes what the other does |
| M3.3.9 | 9. Understands the three basic meanings of the expression a/b (i.e., a is the number of units each of which has the size 1/b; a divided by b; and a compared to or in relationship to b) |
| M3.3.10 | 10. Converts fractions to decimals, percentages to fractions, fractions to percentages, percentages to decimals, decimals to percentages, common fractions and mixed numbers to decimal fractions, etc. |
| M3.3.11 | 11. Solves real-world problems involving fractions |
| M3.3.12 | 12. Solves real-world problems involving ratios |
| M3.3.13 | 13. Solves real-world problems involving proportions |
| M3.3.14 | 14. Solves real-world problems involving percents |
| M3.3.15 | 15. Selects and uses appropriate type of estimation (e.g., overestimate, underestimate, range of estimate) to solve real-world problems |
| M3.3.16 | 16. Understands and describes the purpose of algorithms (e.g., regrouping with or without manipulatives, partial products, finding the greatest common divisor) |
| M3.3.17 | 17. Solves real-world problems involving decimals |
Grade Level: High School [9-12]
| Benchmark Label |
Benchmark |
|---|---|
| M3.4.1 | 1. Adds and subtracts algebraic expressions |
| M3.4.2 | 2. Analyzes rounding errors using a calculator or computer |
| M3.4.3 | 3. Identifies the source of any discrepancy between an estimate and a calculated answer |
| M3.4.4 | 4. Understands that the reasonableness of the result of a computation can be estimated from the inputs and operations |
| M3.4.5 | 5. Solves real-world problems involving roots and exponents |
| Benchmark Label |
Benchmark |
|---|---|
| M4.3.1 | 1. Has a basic understanding of the concept of rate and how it is measured |
| M4.3.2 | 2. Understands the basic characteristics of perimeter and how perimeter is measured |
| M4.3.3 | 3. Makes effective use of a meter stick for making measurements |
| M4.3.4 | 4. Converts from one measurement to another within the same system, i.e., customary or metric (e.g., feet to miles, minutes to hours) |
| M4.3.5 | 5. Determines significant digits in measurement |
| M4.3.6 | 6. Determines the level of accuracy needed in measurement situations |
| M4.3.7 | 7. Identifies and uses appropriate measuring tools for a variety of situations |
| M4.3.8 | 8. Calculates the volumes and surface areas of rectangular solids, cylinders, cones, pyramids, prisms, and combined forms |
| M4.3.9 | 9. Estimates distances and travel times from maps and the actual size of objects from scale drawings |
| M4.3.10 | 10. Expresses answers using appropriate units of measurement (e.g., seconds, square inches, dollars per tankful) |
| M4.3.11 | 11. Reads analog and digital meters on instruments used to make direct measurements of length, volume, weight, elapsed time, rates and temperature, and chooses appropriate units for reporting various magnitudes |
| M4.3.12 | 12. Uses measuring devices to determine an object's weight, length, width, or volume in metric units |
| M4.3.13 | 13. Performs basic conversions between standard and metric involving weight, distance, and volume |
| M4.3.14 | 14. Calculates the perimeter and area of rectangles |
| M4.3.15 | 15. Calculates the perimeter and area of triangles |
| M4.3.16 | 16. Calculates the circumference and area of circles |
| M4.3.17 | 17. Solves real-world problems involving weight, distance, and volume |
| M4.3.18 | 18. Applies given measurement formulas for perimeter, area, volume, and surface area in problem situations |
| M4.3.19 | 19. Solves problems involving units of measurement and converts answers to a larger or smaller unit |
| M4.3.20 | 20. Applies absolute and relative error in problem situations involving area, volume, and surface area |
| M4.3.21 | 21. Given the dimensions of a shape, creates a scale drawing of the shape |
| M4.3.22 | 22. Understands that the scale chosen for a graph or drawing makes a big difference in how useful it is |
Grade Level: High School [9-12]
| Benchmark Label |
Benchmark |
|---|---|
| M4.4.1 | 1. Understands the basic characteristics of the concept of capacity and how it is measured |
| M4.4.2 | 2. Has a basic understanding of the concept of velocity and how it is measured |
| M4.4.3 | 3. Has a basic understanding of the concept of acceleration and how it is measured |
| M4.4.4 | 4. Determines precision and accuracy of measurements |
| M4.4.5 | 5. Analyzes absolute and relative errors in measurement |
| M4.4.6 | 6. Estimates the effects of measurement errors on calculations |
| M4.4.7 | 7. Understands that a small error in making a measurement can lead to a large error in the result (propagation of errors) |
| M4.4.8 | 8. Understands that scale drawings can help one measure distances and angles that are inconvenient to measure directly |
| M4.4.9 | 9. Understands the concept of rate and uses it in measurement situations |
| Benchmark Label |
Benchmark |
|---|---|
| M6.3.1 | 1. Understands basic characteristics of and calculates measures of central tendency (i.e., mean, median, mode) |
| M6.3.2 | 2. Understands similarities and differences between tables, bar graphs, and circle graphs |
| M6.3.3 | 3. Identifies basic trends in tables and graphs including varying rates of change, gaps, and clusters, and uses these trends to make predictions about the phenomena being graphed |
| M6.3.4 | 4. Understands that comparison of data from two groups involves comparing their middles and the spreads around them (i.e., dispersion of data) |
| M6.3.5 | 5. Interpolates or extrapolates from data presented in various forms |
| M6.3.6 | 6. Constructs, reads, and interprets data in charts, tables, plots (e.g., stem-and-leaf, box-and-whiskers, scatter), and graphs (e.g., bar, circle, line) |
Grade Level: High School [9-12]
| Benchmark Label |
Benchmark |
|---|---|
| M6.4.1 | 1. Understands the basic features of data sets (matrices) |
| M6.4.2 | 2. Understands the basic measures of dispersion (i.e., standard deviation, variance) |
| M6.4.3 | 3. Understands the basic features of outliers and procedures to deal with them |
| M6.4.4 | 4. Represents data using stem-and-leaf plots and scatter plots |
| M6.4.5 | 5. Understands that the same set of data can be represented using a variety of tables, graphs, and symbols and that different modes of representation often convey different messages |
| M6.4.6 | 6. Understands that the middle of a distribution may be misleading under certain circumstances (e.g., when data are not distributed symmetrically, when extreme high or low values exist, when the distribution is not reasonably smooth) |
| M6.4.7 | 7. Calculates measures of central tendency (i.e., mean, median, mode) for complex sets of data and analyzes the relative merits of those measures for the various data sets |
| M6.4.8 | 8. Solves real-world problems involving data matrices |
| M6.4.9 | 9. Understands basic generalizations about the nature of graphs: the position of any point on a surface can be described by two numbers; a graph represents all the values that satisfy an equation |
| Benchmark Label |
Benchmark |
|---|---|
| M8.3.1 | 1. Understands that an algebraic expression contains a variable which is a symbol representing an unknown quantity |
| M8.3.2 | 2. Understands the basic features of coordinates |
| M8.3.3 | 3. Has a basic understanding of the concept of equation |
| M8.3.4 | 4. Understands that a variable can be used as a placeholder for a specific unknown (e.g., x + 8 = 13), and as a representative of a range of values (e.g., 4t + 7) |
| M8.3.5 | 5. Understands that mathematical statements can be used to describe functional relationships for which one quantity changes when another changes |
| M8.3.6 | 6. Computes rates of change from magnitudes and magnitudes from rates of change |
| M8.3.7 | 7. Understands the common relationships that can exist between two variables and the various ways these relationships will look on a graph |
| M8.3.8 | 8. Cross-tabulates the occurrence of variables and makes a general determination whether they co-vary |
| M8.3.9 | 9. Uses substitution within given formulas and expressions with real-world problems |
| M8.3.10 | 10. Solves real-world problems involving rectangular coordinates |
| M8.3.11 | 11. Solves real-world problems involving formulas with one variable |
| M8.3.12 | 12. Simplifies algebraic expressions involving numbers and variables |
| M8.3.13 | 13. Solves simple systems of equations graphically |
Grade Level: High School [9-12]
| Benchmark Label |
Benchmark |
|---|---|
| M8.4.1 | 1. Uses appropriate terminology and notation to define functions and their properties, including domain, range, function composition, and inverses |
| M8.4.2 | 2. Understands the characteristics and uses of basic trigonometric functions |
| M8.4.3 | 3. Investigates the effects of parameter changes on the graphs of functions |
| M8.4.4 | 4. Has a basic understanding of polynomial equations |
| M8.4.5 | 5. Has a basic understanding of polar coordinates |
| M8.4.6 | 6. Determines the maximum and minimum points on a graph |
| M8.4.7 | 7. Fits a line or curve to a set of data and uses this line or curve to make predictions |
| M8.4.8 | 8. Compares and applies the numerical, symbolic, and graphical properties of a variety of functions |
| M8.4.9 | 9. Solves systems of equations and inequalities graphically, algebraically, and using matrices |
| M8.4.10 | 10. Uses a variety of algebraic and graphical methods to solve polynomial equations with real and complex roots |
| M8.4.11 | 11. Understands functional relationships for which the rate of change of one variable is dependent on how much there is of another variable (e.g., the rate of change of speed is proportional to the amount of force acting on it) |
| M8.4.12 | 12. Understands that symbolic statements in mathematics can be manipulated by rules of mathematical logic to produce other statements that preserve the basic relationships but are more easily interpreted |
| M8.4.13 | 13. Understands that symbolic statements can be combined to look for values of variables that will satisfy all of them at the same time |
| M8.4.14 | 14. Understands that any graphic or algebraic mathematical model is limited in how well it represents the world by uncertainties in measurement, neglect of some important influences, or by requiring too much computation |
| M8.4.15 | 15. Understands that when a relationship between variables is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed |
| M8.4.16 | 16. Understands that mathematical modeling is a tool that can be used to simulate how a proposed system might behave |
| M8.4.17 | 17. Understands that mathematical modeling aids in technological design by simulating how a proposed system would theoretically behave |
| M8.4.18 | 18. Understands that the basic process of creating a mathematical model involves the following components: (1) abstractions; (2) manipulating abstractions; (3) checking results; and (4) creating a new model if necessary |
| M8.4.19 | 19. Understands that it may not be easy to determine which mathematical model to use to describe data even when plenty of data is available, and that the mathematical model one chooses may require more computing power than is available |
| M8.4.20 | 20. Understands that determining the correlation between two variables involves inspecting their distributions using two-way tables or scatter plots; a correlation between two variables does not mean that one variable causes another |
| M8.4.21 | 21. Uses the technique of spatial sampling to determine the extent to which two variables have a relationship |
| M8.4.22 | 22. Constructs scatter plots for data representing two variables and makes a qualitative analysis of the relationship between the two variables |
| M8.4.23 | 23. Identifies and analyzes linear and nonlinear patterns in data using line graphs |
| M8.4.24 | 24. Constructs linear mathematical models for real-world phenomena |
| M8.4.25 | 25. Constructs nonlinear mathematical models for real-world phenomena |
| M8.4.26 | 26. Understands the formal differences between the terms "correlates with" and "causes" |
| M8.4.27 | 27. Solves real-world problems involving linear programming |
| M8.4.28 | 28. Represents real-world problems using algebraic functions and graphs of those functions |
| M8.4.29 | 29. Solves real-world problems involving polar coordinates |
| M8.4.30 | 30. Approximates solutions of equations (e.g., bisection, sign changes, successive approximations) |
URL: http://pumas.jpl.nasa.gov/ benchmarks/benchmark_search.asp Copyright: © 1996, California Institute of Technology ALL RIGHTS RESERVED Based on U.S. Government sponsored research |
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