1.0 Numbers and Operations

4.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

4.1.2 Understand meanings of operations and how they relate to one another.

4.1.3 Compute fluently and make reasonable estimates.

2.0 Algebra

4.2.1 Understand patterns, relations, and functions.

4.2.2 Represent and analyze mathematical situations and structures using algebraic symbols.

4.2.3 Illustrate general properties of operations.

4.2.4 Analyze change in various contexts.

3.0 Geometry

4.3.1 Analyze characteristics and properties of two- and three- dimensional shapes.

4.3.2 Specify locations and describe spatial relationships using coordinate geometry.

4.3.3 Apply transformations and use symmetry to analyze mathematical situations.

4.3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.

4.0 Measurement

4.4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.4.2 Apply appropriate techniques, tools, and formulas to determine measurements.

5.0 Data Analysis and Probability

4.5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

4.5.2 Select and use appropriate statistical methods to analyze data.

4.5.3 Develop and evaluate inferences and predictions that are based on data.

4.5.4 Understand and apply basic concepts of probability.

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4.1.1a Read and write numbers from hundred-thousands to hundredths,

(millions to thousandths).

Read and write in Roman Numerals.

4.1.1b Name the place value of a given digit from hundred-thousands to hundredths.

4.1.1c Compare and order whole numbers using the appropriate symbols (i.e. >, <, +) (and symbols for less than and equal to and greater than and equal to).

4.1.1d Model fractions as parts of unit wholes, as part of a set, as locations on numbers lines, and as divisions of whole numbers.

4.1.1e Recognize and generate equivalent formulas of whole numbers and commonly used fractions and decimals.

4.1.1f Use models to compare and order commonly used fractions.

4.1.1g Compare and order commonly used decimals using the appropriate symbols (i.e. .>, <, =) (and symbols for less than and equal to & greater than and equal to).

4.1.1h Use various models to identify, order, and compare whole numbers and commonly used fractions and mixed numbers (e.g. number lines, base ten blocks, Venn diagrams, hundred boards).

4.1.1i Communicate and use mathematical terms and symbols correctly.

Read and write percentages (multiples of 5 and <100).

Explain the relationship among fractions, decimals, and percents.

4.1.2a Explain the relationship between multiplication and addition.

4.1.2b Explain the relationship between multiplication and division.

Explain the relationship between subtraction and division.

4.1.2c Communicate the effects of addition, subtraction, multiplication, and division on size and order of numbers.

4.1.3a Use strategies to estimate the results of whole-number computations (add, subtract, multiply, and divide).

Round numbers to nearest 10, 100, 1000.

4.1.3b Explain the reasonableness of the results.

4.1.3c Add and subtract fractions with like denominators.

4.1.3d Multiply and divide efficiently and accurately with single-digit whole numbers.

Recall multiplication facts through 12 X 12 and division facts.

Multiply 3 digits by 2 digits.

Divide 3 digits by 2 and 3 digits.

4.1.3e Add, subtract, and multiply decimals (including monetary units). [to hundredths].

4.1.3f Select appropriate methods and tools for computing with whole numbers (e.g. mental computation, estimation, calculators, paper and pencil).

4.1.3g Solve real world problems involving one-step addition, subtraction, and multiplication.

4.1.3h Identify missing information and/or too much information in real-world problems.

4.1.3i Apply logical reasoning to solve real-world problems.

4.1.3j Select the appropriate computational and operational methods to solve problems.

4.1.3k Solve real world problems using whole numbers,

fractions, and decimals.

4.2.1a Generalize and extend geometric and numerical patterns.

Use patterns to develop strategies to remember multiplic facts.

4.2.1b Represent and analyze patterns and functions using words, tables, and graphs.

4.2.1c Identify and describe a function rule.

4.2.2a Interpret and solve open sentences that involve addition, subtraction, multiplication, and division.

4.2.2b Represent the idea of a variable as an unknown quantity using a letter or a symbol.

4.2.2c Demonstrate an understanding that an equation is a number sentence stating two quantities are equal.

4.2.3a Apply commutative, zero, and identity properties.

& associative.