### 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: Exhibit an understanding of the place-value structure of the base-ten number system by:

A.1.1.1.a: reading, modeling, writing, and interpreting whole numbers up to 10,000

A.1.1.1.b: comparing and ordering numbers up to 1,000

A.1.1.1.c: recognizing the position of a given number in the base-ten number system and its relationship to benchmark numbers such as 10, 50, 100, 500

A.1.1.2: Use whole numbers by using a variety of contexts and models (e.g., exploring the size of 1,000 by skip-counting to 1,000 using hundred charts or strips 10 or 100 centimeters long).

A.1.1.4: Identify the relationship among commonly encountered factors and multiples (e.g., factor pairs of 12 are 1 x 12, 2 x 6, 3 x 4; multiples of 12 are 12, 24, 36).

A.1.1.5: Use visual models and other strategies to recognize and generate equivalents of commonly used fractions and mixed numbers (e.g., halves, thirds, fourths, sixths, eighths, and tenths).

A.1.1.6: Demonstrate an understanding of fractions as parts of unit wholes, parts of a collection or set, and as locations on a number line.

A.1.1.7: Use common fractions for measuring and money (e.g., using fractions and decimals as representations of the same concept, such as half of a dollar = 50 cents)

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

A.1.2.1: Use a variety of models to show an understanding of multiplication and division of whole numbers (e.g., charts, arrays, diagrams, and physical models [i.e., modeling multiplication with a variety of pictures, diagrams, and concrete tools to help students learn what the factors and products represent in various contexts]).

A.1.2.2: Find the sum or difference of two whole numbers between 0 and 10,000.

A.1.2.3: Solve simple multiplication and division problems (e.g., 135 ÷.(ٱ= 5

A.1.2.4: Identify how the number of groups and the number of items in each group equals a product.

A.1.2.5: Demonstrate the effects of multiplying and dividing on whole numbers (e.g., to find the total number of legs on 12 cats, 4 represents the number of each [cat] unit, so 12 x 4 = 48 [leg] units).

A.1.3: Compute fluently and make reasonable estimates.

A.1.3.1: Choose computational methods based on understanding the base-ten number system, properties of multiplication and division, and number relationships.

A.1.3.2: Use strategies (e.g., 6 x 8 is double 3 x 8) to become fluent with the multiplication pairs up to 10 x 10.

A.1.3.4: Demonstrate reasonable estimation strategies for measurement, computation, and problem solving.

### B: Algebra

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

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

B.1.1.5: Recognize and use the commutative property of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5?).

B.1.1.6: Create, describe, and extend numeric and geometric patterns including multiplication patterns.

B.1.1.7: Represent simple functional relationships:

B.1.1.7.a: solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit)

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

B.1.2.2: Recognize and use the commutative and associative properties of addition and multiplication (e.g., "If 5 x 7 = 35, then what is 7 x 5? And if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?").

B.1.2.3: Explore the ways that commutative, distributive, identity, and zero properties are useful in computing with numbers.

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

B.1.3.1: Model problem situations with objects and use representations such as pictures, graphs, tables, and equations to draw conclusions.

### 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: Describe and compare the attributes of plane and solid geometric figures to show relationships and solve problems:

C.1.1.1.a: identify, describe, and classify polygons (e.g., pentagons, hexagons, and octagons)

C.1.1.1.b: identify lines of symmetry in two-dimensional shapes

C.1.1.1.c: explore attributes of quadrilaterals (e.g., parallel and perpendicular sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square)

C.1.1.1.d: identify right angles

C.1.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

C.1.2.2: Use ordered pairs to graph, locate specific points, create paths, and measure distances within a coordinate grid system.

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

C.1.3.1: Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.

C.1.3.2: Identify and describe the line of symmetry in two- and three-dimensional shapes.

### D: Measurement

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

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

D.1.1.3: Identify time to the nearest minute (elapsed time) and relate time to everyday events.

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

D.1.2.2: Estimate measurements.

### 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: Collect and organize data using observations, measurements, surveys, or experiments.

E.1.1.2: Represent data using tables and graphs (e.g., line plots, bar graphs, and line graphs).

E.1.1.3: Conduct simple experiments by determining the number of possible outcomes and make simple predictions:

E.1.1.3.a: identify whether events are certain, likely, unlikely, or impossible

E.1.1.3.b: record the outcomes for a simple event and keep track of repetitions

E.1.1.3.d: use the results to predict future events

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

E.1.2.1: Apply and explain the uses of sampling techniques (e.g., observations, polls, tally marks) for gathering data.

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

E.1.4.1: Discuss the degree of likelihood of events and use terminology such as "certain," "likely," "unlikely".

Correlation last revised: 1/20/2017

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