# Number Operations and Relationships

MPS Learning Target #2, Grade 8 |

Use the Pythagorean theorem, square roots , and irrational numbers to determine lengths of sides of a triangle in problem-solving situations and explain procedures. |

MPS Target Alignment |
Grade 10 Wisconsin Sub-skill Descriptors |

A) Apply proportional reasoning and ratios in mathematical and real -world contexts. | |

B) Analyze and solve problems using percents and proportions. | |

C) Evaluate strategies, test reasonableness of results and create and evaluate numerical arguments presented in mathematical and real-world contexts. | |

D) Select and use appropriate properties, computational procedures, and modes of representation with and without context e.g., simple and compound interest, commission, percents, proportions. | |

E) Compare, perform and explain operations on real numbers with and without context e.g., transitivity, rate of change, exponential functions, scientific notation, roots, powers , reciprocals, absolute value, ratios, proportions, percents, rate of change. |

**Geometry**

MPS Learning Target #1, Grade 8 |

Perform transformations of figures, including reflections, rotations, and translations; analyze effects of transformations on the figures; and use appropriate mathematical vocabulary, symbols, and notation. |

MPS Target Alignment |
Grade 10 Wisconsin Sub-skill Descriptors |

A) Identify, describe and analyze properties of figures, relationships among figures and relationships among their parts e.g., parallel, perpendicular and congruent sides, various types of angles and triangles, complementary and supplementary angles, sum of angles in a triangle. | |

B) Present convincing geometric arguments by means of informal proof, counter-examples or other logical means. | |

C) Model problems using the Pythagorean Theorem and right triangle trigonometry. | |

D) Use proportional reasoning to solve congruence and similarity problems e.g., scale drawings and similar geometric figures. | |

E) Visualize shapes and figures in problem-solving situations. | |

F) Use transformations and symmetry to solve problems. | |

G) Use the two-dimensional rectangular coordinate system to describe and characterize properties of geometric figures. | |

H) Identify and apply symmetry about an axis. | |

I) Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships e.g., slope, intercepts, parallelism, and perpendicularity. |

**Measurement**

MPS Learning Target #2, Grade 8 |

Use the Pythagorean theorem, square roots, and irrational numbers to determine lengths of sides of a triangle in problem-solving situations and explain procedures. |

MPS Target Alignment |
Grade 10 Wisconsin Sub-skill Descriptors |

A) Identify, describe and use derived attributes to represent and solve problems e.g., speed, acceleration, density, money conversion. | |

B) Use appropriate tools to accurately determine direct and indirect measurements e.g., length, angles, elapsed time. | |

C) Use right-triangle trig functions and the Pythagorean Theorem to solve right-triangle problems. | |

D) Determine the perimeter/area of two-dimensional figures and the surface are/volume of three-dimensional figures. | |

E) Solve for angles, arcs and segments in polygons and circles . | |

F) Use formulas in applications e.g., distance, acceleration, interest. |

**Statistics and Probability**

MPS Learning Target# 3, Grade 8 |
MPS Learning Target # 4, Grade
8 |

Formulate questions that lead to data collection and analysis, design and conduct a statistical investigation, represent data in appropriate plots (e.g. line, box, scatter), and communicate the results. | Design experiments, use strategies to identify the likeliness of possible outcomes (e.g. tree diagrams, lists) of simple events, and justify the selection of the chosen strategy. |

MPS Target Alignment |
Grade 10 Wisconsin Sub-skill Descriptors |

A) Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g., histograms, line graphs , stem-and-leaf plots, scatter plots, box-and whiskers, bar charts, Venn diagrams, tables, circle graphs. | |

B) Interpret, analyze and make predictions from organized and displayed data e.g., measures of central tendency, measures of variation such as standard deviation, mean, median, mode, range, dispersion, outliers, line of best fit, percentiles. | |

C) Analyze, evaluate and critique methods and conclusions of statistical experiments e.g., randomness, sampling, techniques, surveys. | |

D) Determine the likelihood of occurrence of simple and complex events e.g., combinations and permutations, fundamental counting principle, experimental versus theoretical probability and independent, dependent and conditional probability. | |

E) Analyze outcomes based on an understanding of theoretical and experimental probability. |

## Algebraic Relationships

MPS Learning Target #5 |
MPS Learning Target #6 |
MPS Learning Target #7 |
MPS Learning Target #8 |

Represent and describe functional relationships in tables, graphical representations , and symbolic forms, and identify whether they translate into linear or exponential relationships | Use reasoning abilities to perceive patterns and identify relationships in order to generalize a rule that characterizes the rate of change among variables in functional relationships. | Represent and solve equations and inequalities using different methods (e.g. informally, graphically, using generalized properties, and with technology) and communicate why a results makes sense. | Identify, describe, and justify generalized properties and relations (e.g. commutative, associative, distributive inverses, identities). |

MPS Target Alignment |
Grade 10 Wisconsin Sub-skill Descriptors |

A) Describe, recognize, interpret and translate graphical representations of mathematical and real-world phenomena on coordinate grids, e.g., slope, intercepts, rate of change, linear and non-linear functions, and quadratic, exponential and constant functions. | |

B) Analyze, generalize and represent patterns, of change, e.g., direct and inverse variations, including numerical sequences, patterns to a given term , algebraic expressions and equations. | |

C) Solve linear and quadratic equations , linear inequalities and systems of linear equations and inequalities. | |

D) Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations and inequalities, e.g., linear, exponential, quadratic. | |

E) Translate between different representations and describe the relationship among variable quantities in a problem, e.g., tables, graphs, functional notations, formulas. | |

F) Demonstrate understanding of properties by evaluating and simplifying expressions | |

G) Demonstrate understanding of properties by solving linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities with one or two variables . |

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