Add and subtract fractions with like and unlike denominators (e.g., 21⁄4 – 11⁄3), and solve word problems of this kind. Multiply fractions; divide fractions in simple cases; and solve related word problems (e.g., find the area of a rectangle with fractional side lengths; determine how many 1⁄3-cup servings are in 2 cups of raisins; determine the size of a share if 9 people share a sack of rice equally or if 3 people share 1⁄2 pound of chocolate equally). Convert like measurement units within a given measurement system. Make a line plot to display a data set with fractional units of measure and interpret the data to solve problems. Geometric measurement: Understand the concept of volume, and solve word problems that involve volume. Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties. Numbering of Standards The following Mathematics Standards will be numbered continuously. The following ranges relate to the clusters found within Mathematics: Operations and Algebraic Thinking Write and interpret numerical expressions. Standards 1-2 Analyze patterns and relationships. Standard 3 Number and Operations in Base Ten Understand the place value system. Standard 4-7 Perform operations with multi-digit whole numbers and with decimals to hundredths. Standards 8-10 Number and Operations- Fractions Use equivalent fractions as a strategy to add and subtract fractions. Standards 11-12 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Standards 13-17 Measurement and Data Convert like measurement units within a given measurement system. Standard 18 Represent and interpret data. Standard 19 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Standards 20-22 Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Standards 23-24 Classify two-dimensional figures into categories based on their properties. Standards 25-26
mathematical proficiency in a developmentally-appropriate progressions of standards. Continuing the skill progressions from previous courses, the following chart represents the mathematical understandings that will be developed: Inferences and Conclusions from Data Polynomials, Rational, and Radical Relationships Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Derive the formula for the sum of a geometric series, and use the formula to solve problems. (e.g., Calculate mortgage payments.) Trigonometry of General Triangles and Trigonometric Functions Mathematical Modeling Apply knowledge of the Law of Sines and the Law of Cosines to determine distances in realistic situations. (e.g., Determine heights of inaccessible objects.) Analyze real-world situations using mathematics to understand the situation better and optimize, troubleshoot, or make an informed decision. (e.g., Estimate water and food needs in a disaster area, or use volume formulas and graphs to find an optimal size for an industrial package.) Numbering of Standards The following Mathematics Standards will be numbered continuously. The following ranges relate to the clusters found within Mathematics: Inferences and Conclusions from Data Summarize, represent, and interpret data on single count or measurement variable. Standard 1 Understand and evaluate random processes underlying statistical experiments. Standards 2-3 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Standards 4-7 Use probability to evaluate outcomes of decisions. Standards 8-9 Polynomials, Rational, and Radical Relationships Use complex numbers in polynomial identities and equations. Standards 10-11 Interpret the structure of expressions. Standards 12-13 Write expressions in equivalent forms to solve problems. Standard 14 Perform arithmetic operations on polynomials. Standard 15 Understand the relationship between zeros and factors of polynomials. Standards 16-17 Use polynomial identities to solve problems. Standards 18-19 Rewrite rational expressions. Standards 20-21
Understand solving equations as a process of reasoning and explain the reasoning. Standard 22 Represent and solve equations and inequalities graphically. Standard 23 Analyze functions using different representations. Standard 24 Trigonometry of General Triangles and Trigonometric Functions Apply trigonometry to general triangles. Standards 25-27 Extend the domain of trigonometric functions using the unit circle. Standards 28-29 Model periodic phenomena with trigonometric functions. Standard 30 Mathematical Modeling Create equations that describe numbers or relationships. Standards 31-34 Interpret functions that arise in applications in terms of a context. Standards 35-37 Analyze functions using different representations. Standards 38-40 Build a function that models a relationship between two quantities. Standard 41 Build new functions from existing functions. Standards 42-43 Construct and compare linear, quadratic, and exponential models and solve problems. Standard 44 Visualize relationships between two dimensional and three-dimensional objects. Standard 45 Apply geometric concepts in modeling situations. Standards 46-48 Inferences and Conclusions from Data Cluster Summarize, represent, and interpret data on single count or measurement variable. M.3HS.1(*) 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. Instructional Note: While students may have heard of the normal distribution, it is unlikely that they will have prior experience using it to make specific estimates. Build on students’ understanding of data distributions to help them see how the normal distribution uses area to make estimates of frequencies (which can be expressed as probabilities). Emphasize that only some data are well described by a normal distribution. Cluster Understand and evaluate random processes underlying statistical experiments. M.3HS.2(*) Understand that statistics allows inferences to be made about population parameters based on a random sample from that population. M.3HS.3(*) Decide if a specified model is consistent with results from a given data-generating process, for example, using simulation. (e.g., A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?) Instructional Note: Include comparing theoretical and empirical results to evaluate the effectiveness of a treatment.
Use functions to model relationships between quantities. Standards 25-26 Interpret functions that arise in applications in terms of a context. Standards 27-29 Analyze functions using different representations. Standards 30-31 Build a function that models a relationship between two quantities. Standards 32-33 Build new functions from existing functions. Standard 34 Construct and compare linear, quadratic, and exponential models and solve problems. Standards 35-37 Interpret expressions for functions in terms of the situation they model. Standard 38 Descriptive Statistics Summarize, represent, and interpret data on a single count or measurement variable. Standards 39-41 Investigate patterns of association in bivariate data. Standards 42-45 Summarize, represent, and interpret data on two categorical and quantitative variables. Standards 46-47 Interpret linear models. Standards 48-50 Expressions and Equations Interpret the structure of equations. Standards 51-52 Write expressions in equivalent forms to solve problems. Standard 53 Perform arithmetic operations on polynomials. Standard54 Create equations that describe numbers or relationships. Standards 55-57 Solve equations and inequalities in one variable. Standard 58 Solve systems of equations. Standard 59 Quadratic Functions and Modeling Use properties of rational and irrational numbers. Standard 60 Understand and apply the Pythagorean theorem. Standards 61-63 Interpret functions that arise in applications in terms of a context. Standards 64-66 Analyze functions using different representations. Standards 67-69 Build a function that models a relationship between two quantities. Standard 70 Build new functions from existing functions. Standards 71-72 Construct and compare linear, quadratic and exponential models and solve problems. Standard 73 Relationships between Quantities Cluster Reason quantitatively and use units to solve problems M.A18.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.