Wisconsin State Standards for Mathematics: Grade 5

WI.A. Mathematical Processes: Students in Wisconsin will draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies, including reasoning, oral and written communication, and the use of appropriate technology, when solving mathematical, real-world and non-routine problems.

A.8.1. Use reasoning abilities to evaluate information; perceive patterns; identify relationships; formulate questions for further exploration; evaluate strategies; justify statements; test reasonableness of results; defend work.

A.8.2. Communicate logical arguments clearly to show why a result makes sense.

A.8.3. Analyze non-routine problems by modeling, illustrating, guessing, simplifying, generalizing, shifting to another point of view, etc.

A.8.4. Develop effective oral and written presentations that include appropriate use of technology; the conventions of mathematical discourse (e.g., symbols, definitions, labeled drawings); mathematical language; clear organization of ideas and procedures; understanding of purpose and audience.

A.8.5. Explain mathematical concepts, procedures, and ideas to others who may not be familiar with them.

A.8.6. Read and understand mathematical texts and other instructional materials and recognize mathematical ideas as they appear in other contexts.

WI.B. Number Operations and Relationships: Students in Wisconsin will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem solving.

B.8.1. Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions, and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential).

B.8.2. Perform and explain operations on rational numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value).

B.8.3. Generate and explain equivalencies among fractions, decimals, and percents.

B.8.4. Express order relationships among rational numbers using appropriate symbols (>, <).

B.8.5. Apply proportional thinking in a variety of problem situations that include, but are not limited to ratios and proportions (e.g., rates, scale drawings, similarity); percents, including those greater than 100 and less than one (e.g., discounts, rate of increase or decrease, sales tax).

B.8.6. Model and solve problems involving number-theory concepts such as prime and composite numbers; divisibility and remainders; greatest common factors; least common multiples.

B.8.7. In problem-solving situations, select and use appropriate computational procedures with rational numbers such as calculating mentally; estimating; creating, using, and explaining algorithms; using technology (e.g., scientific calculators, spreadsheets).

WI.C. Geometry: Students in Wisconsin will be able to use geometric concepts, relationships and procedures to interpret, represent, and solve problems.

C.8.1. Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) by naming, defining, and giving examples; comparing, sorting, and classifying them; identifying and contrasting their properties (e.g., symmetrical, isosceles, regular); drawing and constructing physical models to specifications; explaining how these figures are related to objects in the environment.

C.8.2. Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent faces).

C.8.3. Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features.

C.8.4. Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures.

C.8.5. Locate objects using the rectangular coordinate system.

WI.D. Measurement: Students in Wisconsin will select and use appropriate tools (including technology) and techniques to measure things to a specified degree of accuracy. They will use measurements in problem-solving situations.

D.8.1. Identify and describe attributes in situations where they are not directly or easily measurable (e.g., distance, area of an irregular figure, likelihood of occurrence).

D.8.2. Demonstrate understanding of basic measurement facts, principles, and techniques including the following approximate comparisons between metric and US Customary units (e.g., a liter and a quart are about the same; a kilometer is about six-tenths of a mile); knowledge that direct measurement produces approximate, not exact, measures; the use of smaller units to produce more precise measures.

D.8.3. Determine measurement directly using standard units (metric and US Customary) with these suggested degrees of accuracy lengths to the nearest mm or 1/16 of an inch; weight (mass) to the nearest 0.1 g or 0.5 ounce; liquid capacity to the nearest ml; angles to the nearest degree; temperature to the nearest C or F; elapsed time to the nearest second.

D.8.4. Determine measurements indirectly using estimation; conversion of units within a system (e.g., quarts to cups, millimeters to centimeters); ratio and proportion (e.g., similarity, scale drawings); geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area); the Pythagorean relationship; geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles).

WI.E. Statistics and Probability: Students in Wisconsin will use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.

E.8.1. Work with data in the context of real-world situations by formulating questions that lead to data collection and analysis; designing and conducting a statistical investigation; using technology to generate displays, summary statistics, and presentations.

E.8.2. Organize and display data from statistical investigations using appropriate tables, graphs, and/or charts (e.g., circle, bar or line for multiple sets of data); appropriate plots (e.g., line, stem-and-leaf, box, scatter).

E.8.3. Extract, interpret, and analyze information from organized and displayed data by using frequency and distribution, including mode and range; central tendencies of data (mean and median); indicators of dispersion (e.g., outliers).

E.8.4. Use the results of data analysis to make predictions; develop convincing arguments; draw conclusions.

E.8.5. Compare several sets of data to generate, test, and, as the data dictate, confirm or deny hypotheses.

E.8.6. Evaluate presentations and statistical analyses from a variety of sources for credibility of the source; techniques of collection, organization, and presentation of data; missing or incorrect data; inferences; possible sources of bias.

E.8.7. Determine the likelihood of occurrence of simple events by using a variety of strategies to identify possible outcomes (e.g., lists, tables, tree diagrams); conducting an experiment; designing and conducting simulations; applying theoretical notions of probability (e.g., that four equally likely events have a 25% chance of happening).

WI.F. Algebraic Relationships: Students in Wisconsin will discover, describe, and generalize simple and complex patterns and relationships. In the context of real-world problem situations, the student will use algebraic techniques to define and describe the problem to determine and justify appropriate solutions.

F.8.1. Work with algebraic expressions in a variety of ways, including using appropriate symbolism, including exponents and variables; evaluating expressions through numerical substitution; generating equivalent expressions; adding and subtracting expressions.

F.8.2. Work with linear and nonlinear patterns and relationships in a variety of ways, including representing them with tables, with graphs, and with algebraic expressions, equations, and inequalities; describing and interpreting their graphical representations (e.g., slope, rate of change, intercepts); using them as models of real-world phenomena; describing a real-world phenomenon that a given graph might represent.

F.8.3. Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation).

F.8.4. Use linear equations and inequalities in a variety of ways, including writing them to represent problem situations and to express generalizations; solving them by different methods (e.g., informally, graphically, with formal properties, with technology); writing and evaluating formulas (including solving for a specified variable); using them to record and describe solution strategies.

F.8.5. Recognize and use generalized properties and relations, including additive and multiplicative property of equations and inequalities; commutativity and associativity of addition and multiplication; distributive property; inverses and identities for addition and multiplication; transitive property.