Oklahoma State Standards for Mathematics: Grade 5

OK.5.1. Algebraic Reasoning: Patterns and Relationships - The student will use algebraic methods to describe patterns and solve problems in a variety of contexts.

5.1.1. Describe rules that produce patterns found in tables, graphs, and models, and use variables (e.g., boxes, letters, pawns, number cubes, or other symbols) to solve problems or to describe general rules in algebraic expression or equation form.

5.1.2. Use algebraic problem-solving techniques (e.g., use a balance to model an equation and show how subtracting a number from one side requires subtracting the same amount from the other side) to solve problems.

5.1.3. Recognize and apply the commutative, associative, and distributive properties to solve problems (e.g., 3 x (2 + 4) = (3 x 2) + (3 x 4).

OK.5.2. Number Sense and Operation - The student will use numbers and number relationships to acquire basic facts. The student will estimate and compute with whole numbers, fractions, and decimals.

5.2.1. Number Sense

5.2.1.a. Apply the concept of place value of whole numbers through hundred millions (9 digits) and model, read, and write decimal numbers through the thousandths.

5.2.1.b. Represent with models the connection between fractions and decimals, compare and order fractions and decimals, and be able to convert from one representation to the other to solve problems. (e.g., use 10x10 grids, base 10 blocks).

5.2.1.c. Identify and compare integers using real world situations. (e.g., owing money, temperature, or measuring elevations above and below sea level).

5.2.1.d. Identify and apply factors, multiples, prime, and composite numbers in a variety of problem-solving situations (e.g., build rectangular arrays for numbers 1-100 and classify as prime or composite, use common factors to add fractions).

5.2.2. Number Operations

5.2.2.a. Estimate, add, or subtract decimal numbers with same and different place values to solve problems (e.g., 3.72 + 1.4, $4.56 - $2.12).

5.2.2.b. Estimate add, or subtract fractions (including mixed numbers) to solve problems using a variety of methods (e.g., use fraction strips, use area models, find a common denominator).

5.2.2.c. Estimate and find the quotient (with and without remainders) with two-digit divisors and a two- or three-digit dividend to solve application problems.

OK.5.3. Geometry - The student will apply geometric properties and relationships.

5.3.1. Compare and contrast the basic characteristics of circle and polygons (triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons).

5.3.2. Classify angles (e.g., acute, right, obtuse, straight).

OK.5.4. Measurement - The student use appropriate units of measure to solve problems in a variety of contexts.

5.4.1. Measurement

5.4.1.a. Compare, estimate, and determine the measurement of angles.

5.4.1.b. Develop and use the formula for perimeter and area of a square and rectangle to solve application problems.

5.4.1.c. Convert basic measurements of volume, mass and distance within the same system for metric and customary units (e.g., inches to feet, hours to minutes, centimeters to meters).

5.4.2. Money: Solve a variety of problems involving money.

OK.5.5. Data Analysis - The student will use data analysis, statistics and probability to interpret data in a variety of contexts.

5.5.1. Data Analysis

5.5.1.a. Compare and translate displays of data and justify the selection of the type of table of graph (e.g., charts, tables, bar graphs, pictographs, line graphs, circle graphs, Venn diagrams).

5.5.1.b. Formulate questions, design investigations, consider samples, and collect, organize, and analyze data using observation, measurement, surveys, or experiments (e.g., how far can 5th graders throw a softball based on where it first hits the ground?).

5.5.2. Probability

5.5.2.a. Determine the probability of events occurring in familiar contexts or experiments and express probabilities as fractions from zero to one (e.g., find the fractional probability of an event given a biased spinner).

5.5.2.b. Use the fundamental counting principle on sets with up to four items to determine the number of possible combinations (e.g. create a tree diagrams to see possible combinations).

5.5.3. Central Tendency: Determine the range (spread), mode (most often), and median (middle) of a set of data.

OK.PS1. Problem Solving

PS1.1. Use problem-solving approaches (e.g., act out situations, represent problems with drawings and lists, use concrete, pictorial, graphical, oral, written, and/or algebraic models, understand a problem, devise a plan, carry out the plan, look back).

PS1.2. Formulate problems from everyday and mathematical situations (e.g., how many forks are needed?, how many students are absent?, how can we share/divide these cookies?, how many different ways can we find to compare these fractions?).

PS1.3. Develop, test, and apply strategies to solve a variety of routine and non-routine problems (e.g., look for patterns, make a table, make a problem simpler, process of elimination, trial and error).

PS1.4. Verify and interpret results with respect to the original problem (e.g., students explain verbally why an answer makes sense, explain in a written format why an answer makes sense, verify the validity of each step taken to obtain a final result).

PS1.5. Distinguish between necessary and irrelevant information in solving problems (e.g., play games and discuss ''best'' clues, write riddles with sufficient information, identify unnecessary information in written story problems).

OK.PS2. Communication

PS2.1. Express mathematical ideas coherently and clearly to peers, teachers, and others (e.g., with verbal ideas, models or manipulatives, pictures, or symbols).

PS2.2. Extend mathematical knowledge by considering the thinking and strategies of others (e.g., agree or disagree, rephrase another student's explanation, analyze another student's explanation).

PS2.3. Relate manipulatives, pictures, diagrams, and symbols to mathematical ideas.

PS2.4. Represent, discuss, write, and read mathematical ideas and concepts. Start by relating everyday language to mathematical language and symbols and progress toward the use of appropriate terminology (e.g., ''add more'' becomes ''plus'', ''repeated addition'' becomes ''multiplication'', ''fair share'' becomes ''divide'', ''balance the equation'' becomes ''solve the equation'').

OK.PS3. Reasoning

PS3.1. Explain mathematical situations using patterns and relationships (e.g., identify patterns in situations, represent patterns in a variety of ways, extend patterns to connect with more general cases).

PS3.2. Demonstrate thinking processes using a variety of age-appropriate materials and reasoning processes (e.g., manipulatives, models, known facts, properties and relationships, inductive [specific to general], deductive [general to specific], spatial, proportional, logical reasoning [''and'' ''or'' ''not''] and recursive reasoning).

PS3.3. Make predictions and draw conclusions about mathematical ideas and concepts. Predictions become conjectures and conclusions become more logical as students mature mathematically.

OK.PS4. Connections

PS4.1. Relate various concrete and pictorial models of concepts and procedures to one another (e.g., use two colors of cubes to represent addition facts for the number 5, relate patterns on a hundreds chart to multiples, use base-10 blocks to represent decimals).

PS4.2. Link concepts to procedures and eventually to symbolic notation (e.g., represent actions like snap, clap, clap with symbols A B B, demonstrate 3x4 with a geometric array, divide a candy bar into 3 equal pieces that represent one piece as 1/3).

PS4.3. Recognize relationships among different topics within mathematics (e.g., the length of an object can be represented by a number, multiplication facts can be modeled with geometric arrays, can be written as .5 and 50%).

PS4.4. Use mathematical strategies to solve problems that relate to other curriculum areas and the real world (e.g., use a timeline to sequence events, use symmetry in art work, explore fractions in quilt designs and to describe pizza slices).

OK.PS5. Representation

PS5.1. Create and use a variety of representations appropriately and with flexibility to organize, record, and communicate mathematical ideas (e.g., dramatizations, manipulatives, drawings, diagrams, tables, graphs, symbolic representations).

PS5.2. Use representations to model and interpret physical, social, and mathematical situations (e.g., counters, pictures, tally marks, number sentences, geometric models; translate between diagrams, tables, charts, graphs).