### A: Number and Operations

#### A.1: Students will understand numerical concepts and mathematical operations

A.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

A.1.1.1: Compare and order using concrete or illustrated models:

A.1.1.1.a: whole numbers (to millions)

A.1.1.1.b: common fractions (halves, thirds, fourths, eighths)

A.1.1.1.c: decimals (thousandths)

A.1.1.2: Demonstrate understanding of the magnitude of the value of numbers from thousandths to millions, including common fractions.

A.1.1.4: Interpret percents as part of a hundred (i.e., find decimal and percent equivalents for common fractions, explain how they represent the same value, and compute a given percent of a whole number).

A.1.1.5: Identify and represent on a number line decimals, fractions, and mixed numbers.

A.1.1.6: Identify prime and composite numbers to 50.

A.1.2: Understand the meaning of operations and how they relate to one another.

A.1.2.1: Explain and perform whole number division and express remainders as a whole number or a fractional part as appropriate to the context of real-life problems.

A.1.2.4: Find the factors and multiples of whole numbers.

A.1.2.6: Identify and represent on a number line decimals, fractions, and mixed numbers.

A.1.2.7: Demonstrate proficiency with division, including one- and two-digit divisors.

A.1.2.8: Solve simple problems involving the addition and subtraction of fractions and mixed numbers.

A.1.2.9: Represent and use fractions and decimals in equivalent forms.

A.1.3: Compute fluently and make reasonable estimates.

A.1.3.1: Add, subtract, multiply, and divide whole numbers.

A.1.3.3: Use estimation strategies to verify the reasonableness of calculated results.

A.1.3.4: Explain how the estimation strategy impacts the result.

A.1.3.5: Relate the basic arithmetic operations to one another (e.g., multiplication and division are inverse operations).

A.1.3.6: Simplify numerical expressions using order of operations.

### B: Algebra

#### B.1: Students will understand algebraic concepts and applications.

B.1.1: Understand patterns, relations, and functions.

B.1.1.1: Identify and graph ordered pairs in the first quadrant of the coordinate plane.

B.1.1.2: Describe, represent, and analyze patterns and relationships.

B.1.1.3: Identify, describe, and continue patterns presented in a variety of formats (e.g., numeric, visual, oral, written, kinesthetic, pictorial).

B.1.1.4: Generate a pattern using a written description.

B.1.2: Represent and analyze mathematical situations and structures using algebraic symbols.

B.1.2.3: Understand the differences between the symbols for "less than", "less than or equal to", "greater than", and "greater than or equal to".

B.1.3: Use mathematical models to represent and understand quantitative relationships.

B.1.3.1: Use mathematical models to represent and explain mathematical concepts and procedures.

B.1.3.2: Understand and use mathematical models such as:

B.1.3.2.a: the number line to model the relationship between rational numbers and rational number operations

B.1.3.2.d: graphs, tables, and charts to describe data

B.1.3.3: Demonstrate how a situation can be represented in more than one way.

B.1.4: Analyze changes in various contexts.

B.1.4.1: Recognize and create patterns of change from everyday life using numerical or pictorial representations.

B.1.4.2: Generalize patterns of change and recognize the same general patterns presented in different representations.

### C: Geometry

#### C.1: Students will understand geometric concepts and applications.

C.1.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

C.1.1.1: Identify, describe, and classify two-dimensional shapes and three-dimensional figures by their properties.

C.1.3: Apply transformations and use symmetry to analyze mathematical situations.

C.1.3.1: Identify line of symmetry in simple geometric figures.

### D: Measurement

#### D.1: Students will understand measurement systems and applications.

D.1.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

D.1.1.1: Understand properties (e.g., length, area, weight, volume) and select the appropriate type of unit for measuring each using both U.S. customary and metric systems.

D.1.1.4: Perform one-step conversions within a system of measurement (e.g., inches to feet, centimeters to meters).

D.1.2: Apply appropriate techniques, tools, and formulas to determine measurements.

D.1.2.1: Solve measurement problems using appropriate tools involving length, perimeter, weight, capacity, time, and temperature.

D.1.2.2: Select and use strategies to estimate measurements including length, distance, capacity, and time.

### E: Data Analysis and Probability

#### E.1: Students will understand how to formulate questions, analyze data, and determine probabilities.

E.1.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

E.1.1.1: Construct, read, analyze, and interpret tables, charts, graphs, and data plots.

E.1.1.2: Construct, interpret, and analyze data from graphical representations and draw simple conclusions using bar graphs, line graphs, circle graphs, frequency tables, and Venn diagrams.

E.1.1.3: Display, analyze, compare, and interpret different data sets, including data sets of different sizes.

E.1.1.4: Organize and display single-variable data in appropriate graphs and representations.

E.1.1.5: Organize, read, and display numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including correct titles, labels, and intervals or categories including:

E.1.1.5.a: frequency tables

E.1.1.5.b: stem and leaf plots

E.1.1.5.c: bar, line, and circle graphs

E.1.1.5.e: pictorial displays

E.1.1.5.f: charts and tables

E.1.1.6: Formulate questions and identify data to be collected to correctly answer a question.

E.1.2: Select and use appropriate statistical methods to analyze data.

E.1.2.1: Organize and display single-variable data in appropriate graphs and representations and determine which types of graphs are appropriate for various data sets.

E.1.3: Develop and evaluate inferences and predictions that are based on data.

E.1.3.8: List all possible outcomes of simple events.

E.1.4: Understand and apply basic concepts of probability.

E.1.4.1: Determine probabilities through experiments and/or simulations and compare the results with mathematical expressions.

E.1.4.3: Identify simple experiments where the probabilities of all outcomes are equal.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.