Number, Operation, and Quantitative Reasoning 
4.1 Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. 
4.1.A  use place value to read, write, compare, and order whole numbers through the millions place 
4.2 Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects. 
4.2.A  generate equivalent fractions using pictorial models 
4.2.B  model fraction quantities greater than one using pictures 
4.2.C  compare and order fractions using pictorial models 
4.2.D  relate decimals to fractions that name tenths and hundredths using models

4.3 Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers and decimals. 
4.3.A  use addition and subtraction to solve problems involving whole numbers 
4.3.B  add and subtract decimals to the hundredths place using pictorial models 
4.4 Number, operation, and quantitative reasoning. The student multiplies and divides to solve meaningful problems involving whole numbers. 
4.4.A  model factors and products using arrays and area models 
4.4.B  represent multiplication and division situations in picture, word, and number form 
4.4.C  recall and apply multiplication facts through 12 x 12 
4.4.D  use multiplication to solve problems involving twodigit numbers 
4.4.E  use division to solve problems involving onedigit divisors 
4.5 Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. 
4.5.A  round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations 
4.5.B  estimate a product or quotient beyond basic facts 

Patterns, Relationships, and Algebraic Thinking 
4.6 Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division. 
4.6.B  solve division problems related to multiplication facts (fact families), such as 9 x 9 = 81 and 81 รท 9 = 9 
4.6.C  use patterns to multiply by 10 and 100 
4.7 Patterns, relationships, and algebraic thinking. The student uses organizational structures to analyze and describe patterns and relationships. The student is expected to describe the relationship between two sets of related data such as ordered pairs in a table.

4.7.A  describe the relationship between two sets of related data, such as ordered pairs in a table 

Geometry and Spatial Reasoning 
4.8 Geometry and spatial reasoning. The student identifies and describes lines, shapes, and solids using formal geometric language. 
4.8.A  identify right, acute, and obtuse angles 
4.8.B  identify models of parallel and perpendicular lines 
4.8.C  describe shapes and solids in terms of vertices, edges, and faces 
4.9 Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. 
4.9.B  use translations, reflections, and rotations to verify that two shapes are congruent 
4.9.C  use reflections to verify that a shape has symmetry 
4.10 Geometry and spatial reasoning. The student recognizes the connection between numbers and points on a number line. The student is expected to locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths. 
4.10.A  locate and name points on a number line using whole numbers, fractions such as halves 

Measurement 
4.11 Measurement. The student selects and uses appropriate units and procedures to measure weight and capacity. 
4.11.A  estimate and measure weight using standard units, including ounces, pounds, grams, and kilograms 
4.11.B  estimate and measure capacity using standard units, including milliliters, liters, cups, pints, quarts, and gallons 
4.12 Measurement. The student applies measurement concepts. The student is expected to measure to solve problems involving length, including perimeter, time, temperature, and area. 
4.12.A  measure to solve problems involving length, including perimeter, time, temperature, and area 

Probability and Statistics 
4.13 Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. 
4.13.A  list all possible outcomes of a probability experiment, such as tossing a coin 
4.13.B  use a pair of numbers to compare favorable outcomes to all possible outcomes such as four heads out of six tosses of a coin 
4.13.C  interpret bar graphs 

Underlying Processes and Mathematical Tools 
4.14 Underlying processes and mathematical tools. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school. 
4.14.A  identify the mathematics in everyday situations 
4.14.B  use a problemsolving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness 
4.14.C  select or develop an appropriate problemsolving strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. 
4.15 Underlying processes and mathematical tools. The student communicates about Grade 4 mathematics using informal language. 
4.15.B  relate informal language to mathematical language and symbols. 
4.16 Underlying Processes and Mathematical Tools. The student uses logical reasoning to make sense of his or her world. 
4.16.A  make generalizations from patterns or sets of examples and nonexamples 