5.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
5.1.1.b: name the place value of a given digit from thousandths to millions;
5.1.1.c: use various models to show relationships among whole numbers, fractions, mixed numbers, and decimals (e.g., number lines, base ten blocks, Venn diagrams, hundreds boards);
5.1.1.e: model proper fractions, improper fractions, and mixed numbers;
5.1.1.f: show the relationship between improper fractions and mixed numbers;
5.1.1.h: recognize relationships among commonly used fractions and decimals.
5.1.2: Understand meanings of operations and how they relate to one another.
5.1.2.a: use commutative, associative, and identity properties;
5.1.2.b: explain and demonstrate the inverse nature of addition and subtraction;
5.1.2.c: explain and demonstrate the inverse nature of multiplication and division;
5.1.2.d: communicate the effects of addition, subtraction, multiplication, and division on size and order of numbers.
5.1.3: Solve problems, compute fluently, and make reasonable estimates.
5.1.3.c: recognize reasonable estimates for operations;
5.1.3.d: add, subtract, multiply, and divide whole numbers and decimals;
5.1.3.e: use models, benchmarks, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators;
5.2.1: Represent and analyze patterns, relations, and functions.
5.2.1.a: generalize and extend geometric and numerical patterns;
5.2.1.b: represent and analyze patterns and functions using words, tables, and graphs;
5.2.2: Represent and analyze mathematical situations and structures using algebraic symbols.
5.2.2.a: demonstrate understanding that an equation is a number sentence stating two quantities are equal;
5.2.2.d: express mathematical relationships using equations.
5.2.3: Illustrate general properties of operations.
5.2.3.a: apply commutative, associative, zero, distributive, and identity properties;
5.2.4: Analyze change in various contexts.
5.2.4.b: use a variety of methods to compare and describe situations involving constant and/or varying rates of change.
5.3.1: Analyze characteristics and properties of two- and three-dimensional shapes.
5.3.1.g: compare and contrast congruent and symmetrical geometric figures;
5.3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
5.3.2.a: describe location and movement using appropriate mathematical language;
5.3.3: Apply transformations and use symmetry to analyze mathematical situations.
5.3.3.a: investigate, predict, and describe the results of transformations of two-dimensional figures (i.e., slides, flips, turns);
5.3.3.b: describe line and rotational symmetry in two-dimensional figures;
5.3.3.c: describe a motion or a series of motions that will show that two shapes are congruent.
5.3.4: Use visualization, spatial reasoning, and geometric modeling to solve problems.
5.3.4.b: create and describe mental images of objects, patterns, and paths;
5.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.
5.4.1.a: demonstrate understanding of the concepts of length, perimeter, circumference, area, weight, capacity, volume, elapsed time, and angle measure;
5.4.2: Apply appropriate techniques, tools, and formulas to determine measurements.
5.4.2.a: apply and explain appropriate estimation strategies using standard units of measure;
5.4.2.b: select and apply appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles;
5.5.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.
5.5.1.a: collect data using observations, surveys, and experiments;
5.5.1.b: understand how data-collection methods affect the nature of the data set;
5.5.1.c: represent data using pictographs, bar graphs, tables, circle graphs, and line graphs;
5.5.1.d: interpret data displayed in pictographs, bar graphs, tables, circle graphs, and line graphs.
5.5.2: Select and use appropriate statistical methods to analyze data.
5.5.2.a: use measures of central tendency (i.e., mean, median, mode);
5.5.2.b: relate mean, median, and mode to a visual representation of a data set;
5.5.2.c: find the range of a data set.
5.5.4: Understand and apply basic concepts of probability.
5.5.4.a: describe the likelihood or chance of events as likely, unlikely, certain, equally likely, or impossible;
5.5.4.b: use a sample space to predict the probability of an event;
5.5.4.c: understand that the measure of the likelihood of an event can be represented as a number from 0-1.
Correlation last revised: 7/7/2009