Components

5-7 Benchmark

Number Sense

• Demonstrate understanding of integers, fractions, decimals, percents, place value of decimals, and properties of the rational number system using pictures and symbols.

• Compare and order integers, fractions, and decimals.

• Understand the concepts of prime and composite numbers, factors and multiples, and divisibility rules.

• Understand and apply the concepts of ratio and direct proportion.

• Understand operations on non-negative rational numbers.

• Add, subtract, multiply, and divide non-negative fractions and decimals using rules for order of operation.

• Use mental arithmetic, pencil and paper, calculator, or computer as appropriate to the task involving non-negative rational numbers.

• Identify situations involving non-negative rational numbers in which estimation is sufficient and computation is not required.

• Use estimation to predict computation results and to determine the reasonableness of answers involving non-negative rational numbers, for example, estimating a tip.

Measurement

• Understand the concepts of and the relationships among perimeter, area, and volume and how changes in one dimension affect perimeter, area, and/or volume.

• Measure objects and events directly or using indirect methods such as calculating and applying procedures for determining perimeter, area, and volume.

• Understand the concept of rate and how to calculate rates and determine units.

• Understand that precision is related to the unit of measurement used and the calibration of the measurement tool.

• Know when to estimate and use estimation to obtain reasonable approximations, for example, estimating the length and width of the playground to approximate its area.

• Understand the appropriate uses of standard units of measurement for both direct and indirect measurement.

• Understand the relationship among units within both the U.S. and metric systems.

• Select and use tools that will provide an appropriate degree of precision, for example, using meters vs. kilometers.

Geometric Sense

• Use the properties and relationships of plane geometry to describe shapes and figures including angles, degrees in a circle, triangles, isosceles, equilateral, or quadrilateral.

• Identify, describe, or draw objects in the surrounding environment in geometric terms, for example, producing a simple scale drawing of a classroom.

• Understand symmetry, congruence, and similarity.

• Perform geometric constructions using a variety of tools and technologies, such as paper folding, computer software, straightedge, compass.

• Identify and describe location of objects on coordinate grids in any of the four quadrants.

• Understand and apply simple geometric transformations using combinations of translations (slides), or reflections (flips), or rotations (turns).

Probability and Statistics

• Know how to calculate numerical measures of chance for simple events.

• Understand procedures for counting outcomes to determine probabilities.

• Know how to conduct experiments and simulations and to compare results with mathematical expectations.

• Collect a random sample of data that represents a described population.

• Organize and display data in appropriate forms, such as frequency tables, circle graphs, and stem-and-leaf plots.

• Calculate and appropriately use range.

• Identify how statistics can be used to support different points of view.

• Predict outcomes of experiments and simulations and compare the predictions to experimental results.

• Understand and make inferences based on analysis of experimental results, statistical data, and simple graphical representations.

Algebraic Sense

• Recognize, extend, and create patterns and sequences.

• Generalize and express rules describing patterns and sequences.

• Represent equalities and inequalities symbolically using =, >, <, £ , ³

• Use variables to write simple expressions, equations, and inequalities, for example, 3x > 18.

• Evaluate expressions and formulas.

• Solve single-variable equations.

Components

5-7 Benchmark

Investigate situations

• Solve challenging problems that require perseverance.

• Solve problems involving integration of topics, such as probability, statistics, geometry and number sense.

• Develop and use a variety of strategies and combination of strategies (e.g. guess-check-revise, work backwards, solve a simple problem and generalize, write an equation, organized list, use proportional reasoning).

Formulate questions and define the problem

• Define problems and identify irrelevant information in problem situations.

• Clarify the problem and identify the question being asked.

• Distinguish between relevant and irrelevant information.

Construct solutions

• Use technology (e.g. graphing calculators, spreadsheets) to find and analyze data or represent information.

• Solve problems involving multiple steps.

Components

5-7 Benchmark

Analyze information

• Validate thinking and mathematical ideas using patterns, relationships, and counter-examples.

Predict results

• Develop conjectures based on analysis of new problem situations (e.g. in context of learning divisibility rules, formulate a rule for divisibility by 6 and develop arguments to support their rule).

• Generate and organize data to test a conjecture (e.g. measure a random sample of 8 th graders to test the conjecture “The average height of an 8 th grader is 5'7”.”)

Draw conclusions and verify results

• Support arguments and justify results using inductive reasoning.

• Organize and clarify mathematical information by reflecting, writing, and discussing.

• Reflect on and evaluate procedures and results through writing and discussion.

Components

5-7 Benchmark

Gather information

• Formulate questions and develop a plan for collecting and communicating relevant data.

• Use diagrams, oral narratives, symbolic representations, and written logs to clearly and effectively express ideas.

• Use available technology to browse, select, and retrieve information.

Organize and interpret information

• Organize and clarify mathematical information by reflecting and discussing (e.g. during class discussion about probability, student presents oral justification for inferences made from experimental data).

Represent and share information

• Use both everyday and mathematical language appropriate to the audience.

Components

5-7 Benchmark

Relate concepts and procedures within mathematics

• Connect conceptual and procedural understandings among different mathematical content areas (e.g. apply ratios and proportions to indirect measurement tasks).

• Relate and use different mathematical models and representations for the same situation.

Relate mathematical concepts and procedures to other disciplines

• Identify mathematical patterns and relationships in other disciplines (e.g. show the relationship between coordinate grids and maps).

• Use mathematical thinking and modeling in other disciplines.

• Understand the contributions to mathematics by different cultures.

Related mathematical concepts and procedures to real life situations

• Recognize the use of mathematics outside the classroom and within several occupational/career areas (e.g. banking, engineering).