Number, Operation, and Quantitative Reasoning 
5.1 Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. 
5.1.A  use place value to read, write, compare, and order whole numbers through the billions place 
5.1.B  use place value to read, write, compare, and order decimals through the thousandths place 
5.2 Number, operation, and quantitative reasoning. The student uses fractions in problemsolving situations. 
5.2.A  generate equivalent fractions 
5.2.B  compare two fractional quantities in problemsolving situations using a variety of methods, including common denominators 
5.2.C  use models to relate decimals to fractions that name tenths, hundredths, and thousandths 
5.3 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. 
5.3.A  use addition and subtraction to solve problems involving whole numbers and decimals 
5.3.B  use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology) 
5.3.C  use division to solve problems involving whole numbers (no more than twodigit divisors and threedigit dividends without technology) 
5.3.D  identify prime factors of a whole number and common factors of a set of whole numbers 
5.3.E  model and record addition and subtraction of fractions with like denominators in problemsolving situations 
5.4 Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. 
5.4.A  round whole numbers and decimals through tenths to approximate reasonable results in problem situations 
5.4.B  estimate to solve problems where exact answers are not required 

Patterns, Relationships, and Algebraic Thinking 
5.5 Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns and relationships. 
5.5.A  use pictures to make generalizations about determining all possible combinations 
5.5.B  use lists, tables, charts, and diagrams to find patterns and make generalizations, such as a procedure for determining equivalent fractions 
5.5.C  identify prime and composite numbers using concrete models and patterns in factor pairs 
5.6 Patterns, relationships, and algebraic thinking. The student describes relationships mathematically. 
5.6.A  select from and use diagrams and number sentences to represent reallife situations 

Geometry and Spatial Reasoning 
5.7 Geometry and spatial reasoning. The student generates geometric definitions using critical attributes. 
5.7.A  identify critical attributes, including parallel, perpendicular, and congruent parts of geometric shapes and solids 
5.7.B  use critical attributes to define geometric shapes or solids 
5.8 Geometry and spatial reasoning. The student models transformations. 
5.8.B  describe the transformation that generates one figure from the other when given two congruent figures 
5.9 Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and locations of points on a plane. The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers. 
5.9.A  locate and name points on a coordinate grid using ordered pairs of whole numbers 

Measurement 
5.10 Measurement. The student selects and uses appropriate units and procedures to measure volume. 
5.10.A  measure volume using models of cubic units 
5.11 Measurement. The student applies measurement concepts. 
5.11.A  measure to solve problems involving length (including perimeter), weight, capacity, time, temperature, and area 
5.11.B  describe numerical relationships between units of measure within the same measurement system, such as an inch is onetwelfth of a foot 

Probability and Statistics 
5.12 Probability and statistics. The student describes and predicts the results of a probability experiment. 
5.12.A  use fractions to describe the results of an experiment 
5.12.B  use experimental results to make predictions 
5.13 Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. 
5.13.A  use tables of related number pairs to make line graphs 
5.13.B  describe characteristics of data presented in tables and graphs, including the shape and spread of the data and the middle number 
5.13.C  graph a given set of data using an appropriate graphical representation such as a picture or line 

Underlying processes and mathematical tools 
5.14 Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. 
5.14.A  identify the mathematics in everyday situations 
5.14.B  use a problemsolving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness 
5.14.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. 
5.15 Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language. 
5.15.B  relate informal language to mathematical language and symbols 
5.16 Underlying processes and mathematical Tools. The student uses logical reasoning to make sense of his or her world. 
5.16.A  make generalizations from patterns or sets of examples and nonexamples 