| 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 problem-solving situations. |
| 5.2.A - generate equivalent fractions |
| 5.2.B - compare two fractional quantities in problem-solving 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 two-digit divisors and three-digit 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 problem-solving 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 real-life 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 one-twelfth 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 |
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| 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 problem-solving 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 problem-solving 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 |
