| 4 | Place Value | Identify and read multi-digit whole numbers up to 1,000,000. |
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| 4 | Place Value | Write multi-digit whole numbers in standard form. |
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| 4 | Place Value | Determine the place value of each digit in a number up to 1,000,000. |
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| 4 | Place Value | Compare multi-digit whole numbers using greater than, less than, and equal to symbols. |
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| 4 | Place Value | Round multi-digit whole numbers to any given place value up to the millions. |
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| 4 | Place Value | Use place value knowledge to perform addition and subtraction of multi-digit numbers. |
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| 4 | Place Value | Understand the role of zeros as placeholders in multi-digit numbers. |
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| 4 | Place Value | Apply knowledge of base ten to understand the value of digits in different places. |
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| 4 | Addition And Subtraction | Recognize and represent the value of each digit in a multi-digit whole number. |
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| 4 | Addition And Subtraction | Identify and appropriately name the place values in multi-digit numbers. |
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| 4 | Addition And Subtraction | Compare multi-digit numbers using place value knowledge. |
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| 4 | Addition And Subtraction | Use mental math to add two-digit numbers. |
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| 4 | Addition And Subtraction | Use mental math to subtract two-digit numbers. |
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| 4 | Addition And Subtraction | Add multi-digit numbers in columns without carrying. |
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| 4 | Addition And Subtraction | Subtract multi-digit numbers in columns without borrowing. |
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| 4 | Addition And Subtraction | Add multi-digit numbers in columns including carrying over. |
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| 4 | Addition And Subtraction | Subtract multi-digit numbers in columns including borrowing. |
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| 4 | Addition And Subtraction | Solve word problems that involve multi-digit addition and subtraction. |
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| 4 | Multiplication Concepts | Understand and recognize multiplicative comparisons in word problems. |
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| 4 | Multiplication Concepts | Use visual models, like arrays, to represent multiplication problems. |
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| 4 | Multiplication Concepts | Interpret multiplication equations as comparisons, e.g., 35 = 5 × 7. |
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| 4 | Multiplication Concepts | Quickly recall multiplication facts up to 12 × 12. |
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| 4 | Multiplication Concepts | Apply properties of operations, such as the commutative and associative properties, to perform multiplication. |
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| 4 | Multiplication Concepts | Multiply one-digit numbers by multiples of 10 (e.g., 9 × 70). |
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| 4 | Multiplication Concepts | Multiply two-digit numbers by one-digit numbers. |
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| 4 | Multiplication Concepts | Use the distributive property to break down complex multiplication problems. |
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| 4 | Multiplication Concepts | Solve multiplication word problems using equations and visual representations. |
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| 4 | Multiplication Concepts | Estimate products of two-digit numbers by rounding numbers. |
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| 4 | Division Concepts | Understand and use terms like dividend, divisor, and quotient. |
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| 4 | Division Concepts | Divide objects into equal groups to understand basic division. |
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| 4 | Division Concepts | Use a number line to solve division problems. |
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| 4 | Division Concepts | Understand that division is the inverse of multiplication. |
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| 4 | Division Concepts | Recall division facts for single-digit divisors. |
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| 4 | Division Concepts | Understand and identify remainders in division problems. |
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| 4 | Division Concepts | Use the long division algorithm to solve division problems. |
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| 4 | Division Concepts | Solve division problems that result in remainders. |
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| 4 | Division Concepts | Interpret and solve division word problems, including those with remainders. |
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| 4 | Division Concepts | Estimate the quotient in a division problem by rounding. |
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| 4 | Factors And Multiples | Learn basic multiplication and its connection to factors and multiples. |
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| 4 | Factors And Multiples | Determine which numbers divide a given number with no remainder. |
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| 4 | Factors And Multiples | Identify multiples of a given number within a range. |
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| 4 | Factors And Multiples | Find all pairs of numbers that multiply to a given product. |
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| 4 | Factors And Multiples | Identify common factors between two numbers. |
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| 4 | Factors And Multiples | Find multiples common to two numbers. |
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| 4 | Factors And Multiples | Learn what prime numbers are and identify them. |
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| 4 | Factors And Multiples | Understand composite numbers and how to identify them. |
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| 4 | Factors And Multiples | Break down a number into its prime factors. |
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| 4 | Factors And Multiples | Find the largest common factor of two or more numbers. |
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| 4 | Fractions As Numbers | Recognize and generate simple fractions to represent parts of a whole. |
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| 4 | Fractions As Numbers | Place fractions correctly on a number line. |
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| 4 | Fractions As Numbers | Understand and identify equivalent fractions. |
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| 4 | Fractions As Numbers | Generate equivalent fractions with visual aids. |
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| 4 | Fractions As Numbers | Simplify fractions by finding common factors. |
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| 4 | Fractions As Numbers | Compare fractions with the same denominator. |
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| 4 | Fractions As Numbers | Compare fractions with different denominators. |
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| 4 | Fractions As Numbers | Order fractions from least to greatest and vice versa. |
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| 4 | Fractions As Numbers | Understand and represent mixed numbers and improper fractions. |
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| 4 | Fraction Operations | Recognizing and writing fractions to represent equal parts of a whole. |
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| 4 | Fraction Operations | Understanding the size of fractions with the same denominator. |
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| 4 | Fraction Operations | Identifying and generating equivalent fractions. |
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| 4 | Fraction Operations | Placing fractions on a number line. |
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| 4 | Fraction Operations | Adding fractions with the same denominator. |
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| 4 | Fraction Operations | Subtracting fractions with the same denominator. |
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| 4 | Fraction Operations | Understanding and representing mixed numbers. |
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| 4 | Fraction Operations | Adding mixed numbers with like denominators. |
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| 4 | Fraction Operations | Subtracting mixed numbers with like denominators. |
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| 4 | Fraction Operations | Solving real-world problems involving the addition and subtraction of fractions with like denominators. |
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| 4 | Decimal Concepts | Understanding how to read and interpret numbers in the tenths place. |
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| 4 | Decimal Concepts | Understanding how to read and interpret numbers in the hundredths place. |
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| 4 | Decimal Concepts | Converting fractions with a denominator of 10 to decimal notation. |
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| 4 | Decimal Concepts | Converting fractions with a denominator of 100 to decimal notation. |
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| 4 | Decimal Concepts | Converting decimal numbers in the tenths place back to fraction form. |
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| 4 | Decimal Concepts | Converting decimal numbers in the hundredths place back to fraction form. |
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| 4 | Decimal Concepts | Comparing decimal numbers to the tenths place to determine which is greater or smaller. |
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| 4 | Decimal Concepts | Comparing decimal numbers to the hundredths place to determine which is greater or smaller. |
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| 4 | Decimal Concepts | Understanding place value in decimals up to the hundredths place. |
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| 4 | Decimal Concepts | Plotting and identifying decimal numbers up to the hundredths place on a number line. |
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| 4 | Measurement And Conversion | Recognize and understand different measurement units like inches, feet, centimeters, and meters. |
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| 4 | Measurement And Conversion | Compare different units of the same type, understanding their equivalences (e.g., 12 inches = 1 foot). |
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| 4 | Measurement And Conversion | Convert measurements from larger units to smaller units and vice versa (e.g., feet to inches). |
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| 4 | Measurement And Conversion | Solve word problems involving lengths using addition or subtraction. |
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| 4 | Measurement And Conversion | Solve word problems involving weights using addition or subtraction. |
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| 4 | Measurement And Conversion | Solve word problems involving volumes using addition or subtraction. |
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| 4 | Measurement And Conversion | Understand the units of time, such as seconds, minutes, and hours. |
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| 4 | Measurement And Conversion | Solve word problems involving money using addition and subtraction. |
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| 4 | Measurement And Conversion | Understand and measure area using unit squares. |
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| 4 | Geometry And Lines | Recognize and name points on a plane. |
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| 4 | Geometry And Lines | Draw and identify straight line segments between two points. |
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| 4 | Geometry And Lines | Differentiate between parallel, perpendicular, and intersecting lines. |
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| 4 | Geometry And Lines | Recognize and name different types of angles: acute, right, obtuse, and straight. |
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| 4 | Geometry And Lines | Use a protractor to measure angles accurately. |
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| 4 | Geometry And Lines | Recognize and draw lines of symmetry in various shapes. |
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| 4 | Geometry And Lines | Categorize triangles based on side lengths and angle measures. |
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| 4 | Geometry And Lines | Categorize quadrilaterals such as squares, rectangles, and parallelograms by their properties. |
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| 4 | Geometry And Lines | Recognize and name different polygons based on the number of sides. |
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| 4 | Geometry And Lines | Draw shapes with specified properties, such as specific types of angles or parallel lines. |
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