5th Grade Math standards


       umber Sense



1.0     Students compute with very large and very small numbers, positive integers,   decimals, and          fractions and understand the relationship between decimals, fractions, and percents.          They understand the relative magnitudes of numbers:


             1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.

             1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and                                explain why they represent the same value; compute a given percent of a whole number.

             1.3 Understand and compute positive integer powers of nonnegative integers; compute examples as repeated                                  multiplication.

             1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime                           factors by using exponents to show multiples of a factor (e.g., 24 = 2 × 2 × 2 × 3 = 23 × 3).

             1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.



2.0    Students perform calculations and solve problems involving addition, subtraction, and          simple multiplication and division of fractions and decimals:


             2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from                           negative integers; and verify the reasonableness of the results.

             2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit                           divisors.

             2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of                           fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the                                   simplest form.

             2.4 Understand the concept of multiplication and division of fractions.

             2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving              problems.






1.0    Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results:


             1.1 Use information taken from a graph or equation to answer questions about a problem situation.

             1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable                           by substitution.

             1.3 Know and use the distributive property in equations and expressions with variables.

             1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.

             1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting                      ordered pairs of integers on a grid.




             easurement and Geometry

1.0 Students understand and compute the volumes and areas of simple objects:


             1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula                           for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a                                 parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the                           parallelogram).

             1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the                           surface area for these objects.

             1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic                                 centimeter [cm 3], cubic meter [m3], cubic inch [in 3], cubic yard [yd3]) to compute the volume of rectangular                           solids.

             1.4 Differentiate between, and use appropriate units of measures for, two- and three-dimensional objects (i.e.,                             find the perimeter, area, volume).



2.0    Students identify, describe, and classify the properties of, and the relationships          between, plane and solid geometric figures:


             2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using                                        appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).

             2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360°                           and use this information to solve problems.

             2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.



      tatistics, Data Analysis, and Probability


1.0    Students display, analyze, compare, and interpret different data sets, including data sets of different sizes:


             1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may                             differ.

             1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle                                graphs) explain which types of graphs are appropriate for various data sets.

             1.3 Use fractions and percentages to compare data sets of different sizes.

             1.4 Identify ordered pairs of data from a graph and interpret the meaning of the datain terms of the situation                             depicted by the graph.

             1.5 Know how to write ordered pairs correctly; for example, (x, y).




                    athematical Reasoning


1.0    Students make decisions about how to approach problems:


             1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing                           and prioritizing information, and observing patterns.

             1.2 Determine when and how to break a problem into simpler parts.


2.0 Students use strategies, skills, and concepts in finding solutions:


             2.1 Use estimation to verify the reasonableness of calculated results.

             2.2 Apply strategies and results from simpler problems to more complex problems.

             2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to                                        explain mathematical reasoning.

             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.

             2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a                                     specified degree of accuracy.

             2.6 Make precise calculations and check the validity of the results from the context of the problem.


3.0 Students move beyond a particular problem by generalizing to other situations:


             3.1 Evaluate the reasonableness of the solution in the context of the original situation.

             3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by                              solving similar problems.

             3.3 Develop generalizations of the results obtained and apply them in other circumstances.








Structural Features of Informational Materials

2.1 Identify structural patterns found in informational text (e.g., compare and contrast, cause and effect, sequential or chronological order, proposition and support) to strengthen comprehension.

Comprehension and Analysis of Grade-Level-Appropriate Text

2.2 Use appropriate strategies when reading for different purposes (e.g., full comprehension, location of information, personal enjoyment).

2.3 Make and confirm predictions about text by using prior knowledge and ideas presented in the text itself, including illustrations, titles, topic sentences, important words, and foreshadowing clues.

2.4 Evaluate new information and hypotheses by testing them against known information and ideas.

2.5 Compare and contrast information on the same topic after reading several passages or articles.

2.6 Distinguish between cause and effect and between fact and opinion in expository text.

2.7 Follow multiple-step instructions in a basic technical manual (e.g., how to use computer commands or video games).


lgebra and Functions