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1 Skills available for California fourth-grade math standards Standards are in bold, followed by a list of the IXL math skills that are aligned to that standard. Students can practice these skills online at Standards: 1997 California Content Standards 4.NS Number Sense 4.NS.1.0 Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers: 4.NS.1.1 Read and write whole numbers in the millions. Number sense: Word names for numbers (Fourth grade - A.3) 4.NS.1.2 Order and compare whole numbers and decimals to two decimal places. Money: Put money amounts in order (Third grade - N.6) Decimals: Inequalities with decimals (Third grade - T.5) Decimals: Put decimal numbers in order (Third grade - T.6) Number sense: Compare numbers up to billions (Fourth grade - A.9) Money: Compare money amounts (Fourth grade - M.1) 4.NS.1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Number sense: Rounding (Fourth grade - A.6) 4.NS.1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate. Addition: Estimate sums: word problems (Fourth grade - B.9) Subtraction: Estimate differences: word problems (Fourth grade - C.7) 4.NS.1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0). Fractions: Fractions of a number (Third grade - S.10) Fractions: Fractions of a number - word problems (Third grade - S.11) Fractions and mixed numbers: Equivalent fractions (Fourth grade - Q.1) Fractions and mixed numbers: Patterns of equivalent fractions (Fourth grade - Q.2) Fractions and mixed numbers: Fractions review (Fourth grade - Q.4) 4.NS.1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or.50; 7/4 = 1 3/4 = 1.75). Decimals: Convert between decimals and fractions (Third grade - T.2) 4.NS.1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. Fractions and mixed numbers: Fractions review (Fourth grade - Q.4) 4.NS.1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing"). Place values and number sense: Understanding integers (Fifth grade - A.8) Place values and number sense: Compare integers (Fifth grade - A.9) Integers: Number lines with integers (Sixth grade - C.3) 4.NS.1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places. Fractions and mixed numbers: Fractions review (Fourth grade - Q.4) Decimals: Decimal number lines (Fourth grade - T.5) 4.NS.2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals: 4.NS.2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. Decimals: Add and subtract decimals (Third grade - T.7) Decimals: Add and subtract decimals - word problems (Third grade - T.8) Decimals: Add three or more decimal numbers (Third grade - T.9) Addition: Estimate sums (Fourth grade - B.8) Subtraction: Estimate differences (Fourth grade - C.6) Money: Add and subtract money amounts (Fourth grade - M.3) 1 of 6 9/29/12 6:08 AM

2 Money: Making change (Fourth grade - M.5) Money: Price lists with addition and subtraction (Fourth grade - M.6) 4.NS.2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer. Money: Round money amounts (Fourth grade - M.2) 4.NS.3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations: 4.NS.3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers. Addition: Add numbers up to millions (Fourth grade - B.1) Addition: Addition: fill in the missing digits (Fourth grade - B.3) Addition: Add 3 or more numbers up to millions (Fourth grade - B.5) Addition: Choose numbers with a particular sum (Fourth grade - B.7) Subtraction: Subtract numbers up to millions (Fourth grade - C.1) Subtraction: Subtraction: fill in the missing digits (Fourth grade - C.3) Subtraction: Choose numbers with a particular difference (Fourth grade - C.5) Mixed operations: Mentally add and subtract numbers ending in zeroes (Fourth grade - F.8) 4.NS.3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results. Multiplication: Multiplication facts to 12 (Fourth grade - D.1) Multiplication: Choose the multiples of a given number up to 12 (Fourth grade - D.3) Multiplication: Multiply 1-digit numbers by larger numbers (Fourth grade - D.5) Multiplication: Multiply a 2-digit number by a 2-digit number: complete the missing steps (Fourth grade - D.10) Multiplication: Multiply a 2-digit number by a 2-digit number (Fourth grade - D.11) Multiplication: Choose numbers with a particular product (Fourth grade - D.13) Multiplication: Multiply a 2-digit number by a larger number: complete the missing steps (Fourth grade - D.14) Multiplication: Multiply a 2-digit number by a larger number (Fourth grade - D.15) Multiplication: Multiply numbers ending in zeroes (Fourth grade - D.17) Multiplication: Multiply numbers ending in zeroes: word problems (Fourth grade - D.18) Multiplication: Multiply 3 numbers up to 2 digits each (Fourth grade - D.19) Multiplication: Inequalities with multiplication (Fourth grade - D.20) Division: Division facts to 12 (Fourth grade - E.1) Division: Division facts to 12: word problems (Fourth grade - E.2) Division: Properties of division (Fourth grade - E.3) Division: Divide larger numbers, one-digit divisors (Fourth grade - E.4) Division: Divide by 1-digit numbers: complete the table (Fourth grade - E.6) Division: Divide by 1-digit numbers: interpret remainders (Fourth grade - E.7) Division: Choose numbers with a particular quotient (Fourth grade - E.8) Division: Divide numbers ending in zeroes, one-digit divisors (Fourth grade - E.9) Division: Inequalities with division (Fourth grade - E.20) 4.NS.3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers. Multiplication: Multiply a 2-digit number by a larger number: word problems (Fourth grade - D.16) 4.NS.3.4 Solve problems involving division of multidigit numbers by one-digit numbers. Division: Divide larger numbers, one-digit divisors: word problems (Fourth grade - E.5) 4.NS.4.0 Students know how to factor small whole numbers: 4.NS.4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3). Number theory: Prime factorization (Fifth grade - K.2) 4.NS.4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. Number sense: Prime and composite numbers (Fourth grade - A.5) 4.AF Algebra and Functions 4.AF.1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences: 2 of 6 9/29/12 6:08 AM

3 4.AF.1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable). Algebra: Write variable expressions (Fourth grade - G.1) Algebra: Write variable expressions: word problems (Fourth grade - G.2) 4.AF.1.2 Interpret and evaluate mathematical expressions that now use parentheses. Algebra: Evaluate variable expressions (Fourth grade - G.3) Algebra: Simplify expressions using order of operations and parentheses (Fourth grade - G.4) 4.AF.1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. 4.AF.1.4 Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships. 4.AF.1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given. Algebra: Evaluate variable expressions (Fourth grade - G.3) Functions: Function tables (Fourth grade - H.2) Functions: Write linear functions (Fourth grade - H.3) 4.AF.2.0 Students know how to manipulate equations: 4.AF.2.1 Know and understand that equals added to equals are equal. Addition: Properties of addition (Fourth grade - B.4) Algebra: Solve variable equations (Fourth grade - G.6) 4.AF.2.2 Know and understand that equals multiplied by equals are equal. Multiplication: Properties of multiplication (Fourth grade - D.7) Algebra: Solve variable equations (Fourth grade - G.6) 4.MG Measurement and Geometry 4.MG.1.0 Students understand perimeter and area: 4.MG.1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm²), square meter (m²), square kilometer (km²), square inch (in²), square yard (yd²), or square mile (mi²). Geometry: Area of squares and rectangles (Fourth grade - P.18) 4.MG.1.2 Recognize that rectangles that have the same area can have different perimeters. Geometry: Rectangles: relationship between perimeter and area (Sixth grade - Z.25) 4.MG.1.3 Understand that rectangles that have the same perimeter can have different areas. Geometry: Rectangles: relationship between perimeter and area (Sixth grade - Z.25) 4.MG.1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes. Geometry: Perimeter (Fourth grade - P.17) Geometry: Area of complex figures (with all right angles) (Fourth grade - P.19) Geometry: Use area and perimeter to determine cost (Fourth grade - P.23) 4.MG.2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures: Data and graphs: Coordinate graphs (Second grade - R.1) Graphs: Coordinate graphs I (Third grade - P.1) Graphs: Coordinate graphs II (Third grade - P.2) 4.MG.2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line). Functions: Graph linear functions (Fourth grade - H.4) 4.MG.2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates. Coordinate graphs: Coordinate graphs as maps (Fourth grade - I.4) 4.MG.2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates. Coordinate graphs: Coordinate graphs as maps (Fourth grade - I.4) 3 of 6 9/29/12 6:08 AM

4 4.MG.3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems: 4.MG.3.1 Identify lines that are parallel and perpendicular. Geometry: Parallel, perpendicular, intersecting (Fourth grade - P.27) 4.MG.3.2 Identify the radius and diameter of a circle. Geometry: Parts of a circle (Fourth grade - P.16) 4.MG.3.3 Identify congruent figures. Geometry: Congruent (Second grade - T.5) Geometry: Similar and congruent (Third grade - R.5) Geometry: Similar and congruent (Fourth grade - P.9) 4.MG.3.4 Identify figures that have bilateral and rotational symmetry. Geometry: Symmetry (Second grade - T.4) Geometry: Symmetry (Third grade - R.4) Geometry: Rotational symmetry (Fourth grade - P.24) Geometry: Lines of symmetry (Fourth grade - P.25) 4.MG.3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90, 180, 270, and 360 are associated, respectively, with 1/4, 1/2, 3/4, and full turns. Geometry: Acute, right, obtuse, and straight angles (Fourth grade - P.11) Geometry: Angles of 90, 180, 270, and 360 degrees (Fourth grade - P.12) Geometry: Measure angles with a protractor (Fourth grade - P.13) 4.MG.3.6 Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid. Geometry: Which 3-dimensional figure is being described? (Fourth grade - P.5) Geometry: Count and compare sides, edges, faces, and vertices (Fourth grade - P.8) Geometry: Nets of 3-dimensional figures (Fourth grade - P.10) 4.MG.3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes. Geometry: Types of triangles (Fourth grade - P.2) 4.MG.3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid). Geometry: Which 2-dimensional shape is being described? (Fourth grade - P.4) 4.SDAP Statistics, Data Analysis, and Probability 4.SDAP.1.0 Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings: 4.SDAP.1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts. Coordinate graphs: Coordinate graphs review (Fourth grade - I.1) Coordinate graphs: Relative coordinates (Fourth grade - I.3) Data, charts, and graphs: Interpret line graphs (Fourth grade - J.2) Data, charts, and graphs: Create line graphs (Fourth grade - J.3) Data, charts, and graphs: Interpret bar graphs (Fourth grade - J.4) Data, charts, and graphs: Create bar graphs (Fourth grade - J.5) Data, charts, and graphs: Interpret line plots (Fourth grade - J.6) Data, charts, and graphs: Create line plots (Fourth grade - J.7) Data, charts, and graphs: Choose the best type of graph (Fourth grade - J.11) 4.SDAP.1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets. Probability and statistics: Mean, median, mode, and range (Third grade - U.2) Probability and statistics: Interpret charts to find mean, median, mode, and range (Third grade - U.3) Probability and statistics: Mean, median, mode, and range (Fourth grade - V.3) Probability and statistics: Interpret charts to find mean, median, mode, and range (Fourth grade - V.4) 4.SDAP.1.3 Interpret one- and two-variable data graphs to answer questions about a situation. Data, charts, and graphs: Interpret bar graphs (Fourth grade - J.4) 4 of 6 9/29/12 6:08 AM

5 4.SDAP.2.0 Students make predictions for simple probability situations: 4.SDAP.2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams). Probability and statistics: Combinations (Fourth grade - V.5) 4.SDAP.2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3 /4). Probability and statistics: Calculate probability (Fourth grade - V.1) Probability and statistics: Make predictions (Fourth grade - V.2) 4.MR Mathematical Reasoning 4.MR.1.0 Students make decisions about how to approach problems: 4.MR.1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Mixed operations: Word problems with extra or missing information (Fourth grade - F.5) Logical reasoning: Find the order (Fourth grade - K.3) Patterns: Geometric growth patterns (Fourth grade - L.1) Patterns: Increasing growth patterns (Fourth grade - L.2) Patterns: Numeric patterns: word problems (Fourth grade - L.3) Patterns: Mixed patterns review (Fourth grade - L.5) 4.MR.1.2 Determine when and how to break a problem into simpler parts. Mixed operations: Multi-step word problems (Fourth grade - F.4) 4.MR.2.0 Students use strategies, skills, and concepts in finding solutions: 4.MR.2.1 Use estimation to verify the reasonableness of calculated results. Multiplication: Estimate products (Fourth grade - D.8) Division: Estimate quotients, one-digit divisors (Fourth grade - E.10) Division: Estimate quotients (Fourth grade - E.21) 4.MR.2.2 Apply strategies and results from simpler problems to more complex problems. Addition: Addition patterns over increasing place values (Fourth grade - B.6) Subtraction: Subtraction patterns over increasing place values (Fourth grade - C.4) 4.MR.2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Number sense: Inequalities with number lines (Fourth grade - A.8) Mixed operations: Inequalities involving addition, subtraction, multiplication, and division (Fourth grade - F.9) Data, charts, and graphs: Read a table (Fourth grade - J.1) Data, charts, and graphs: Frequency charts (Fourth grade - J.8) Data, charts, and graphs: Stem-and-leaf plots (Fourth grade - J.9) Data, charts, and graphs: Circle graphs (Fourth grade - J.10) Fractions and mixed numbers: Compare fractions (Fourth grade - Q.5) Fractions and mixed numbers: Mixed number review (Fourth grade - Q.9) 4.MR.2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work. Number sense: Convert between place values (Fourth grade - A.2) 4.MR.2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. Multiplication: Estimate products: word problems (Fourth grade - D.9) Mixed operations: Estimate sums, differences, products, and quotients: word problems (Fourth grade - F.3) 4.MR.2.6 Make precise calculations and check the validity of the results from the context of the problem. Addition: Add numbers up to millions: word problems (Fourth grade - B.2) Subtraction: Subtract numbers up to millions: word problems (Fourth grade - C.2) 4.MR.3.0 Students move beyond a particular problem by generalizing to other situations: 4.MR.3.1 Evaluate the reasonableness of the solution in the context of the original situation. Multiplication: Multiply a 2-digit number by a 2-digit number: word problems (Fourth grade - D.12) 5 of 6 9/29/12 6:08 AM

6 Mixed operations: Addition, subtraction, multiplication, and division word problems (Fourth grade - F.2) 4.MR.3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. Multiplication: Multiplication patterns over increasing place values (Fourth grade - D.6) Division: Division patterns over increasing place values (Fourth grade - E.12) 4.MR.3.3 Develop generalizations of the results obtained and apply them in other circumstances. Functions: Input/output tables with addition, subtraction, multiplication, and division (Fourth grade - H.1) For more information about IXL, go to or send an to orders@ixl.com. 6 of 6 9/29/12 6:08 AM