Louisiana State Standards for Mathematics: Grade 8

LA.N. Number and Number Relations: In problem-solving investigations, students demonstrate an understanding of the real number system and communicate the relationships within that system using a variety of techniques and tools.

N-1-M. Demonstrating that a rational number can be expressed in many forms, and selecting an appropriate form for a given situation (e.g., fractions, decimals, and percents).

N-1-M-GLE 1. Compare rational numbers using symbols (i.e., <, </=, =, >/=, >) and position on a number line (N-1-M) (N-2-M)

N-1-M-GLE 2. Use whole number exponents (0-3) in problem-solving contexts (N-1-M) (N-5-M)

N-2-M. Demonstrating number sense and estimation skills to describe, order, and compare rational numbers (e.g., magnitude, integers, fractions, decimals, and percents).

N-2-M-GLE 1. Compare rational numbers using symbols (i.e., <, </=, =, >/=, >) and position on a number line (N-1-M) (N-2-M)

N-2-M-GLE 3. Estimate the answer to an operation involving rational numbers based on the original numbers (N-2-M) (N-6-M)

N-3-M. Reading, writing, representing, and using rational numbers in a variety of forms (e.g., integers, mixed numbers, and improper fractions).

N-3-M-GLE 4. Read and write numbers in scientific notation with positive exponents (N-3-M)

N-4-M. Demonstrating a conceptual understanding of the meaning of the basic arithmetic operations (add, subtract, multiply and divide) and their relationships to each other.

N-4-M-GLE 5. Simplify expressions involving operations on integers, grouping symbols, and whole number exponents using order of operations (N-4-M)

N-5-M. Applying an understanding of rational numbers and arithmetic operations to real-life situations.

N-5-M-GLE 2. Use whole number exponents (0-3) in problem-solving contexts (N-1-M) (N-5-M)

N-5-M-GLE 6. Identify missing information or suggest a strategy for solving a real-life, rational-number problem (N-5-M)

N-5-M-GLE 8. Solve real-life problems involving percentages, including percentages less than 1 or greater than 100 (N-8-M) (N-5-M)

N-5-M-GLE 9. Find unit/cost rates and apply them in real-life problems (N-8-M) (N-5-M) (A-5-M)

N-6-M. Constructing, using, and explaining procedures to compute and estimate with rational numbers employing mental math strategies.

N-6-M-GLE 3. Estimate the answer to an operation involving rational numbers based on the original numbers (N-2-M) (N-6-M)

N-7-M. Selecting and using appropriate computational methods and tools for given situations involving rational numbers (e.g., estimation, or exact computation using mental arithmetic, calculator, computer, or paper and pencil).

N-8-M. Demonstrating a conceptual understanding and applications of proportional reasoning (e.g., determining equivalent ratios, finding a missing term of a given proportion).

N-8-M-GLE 7. Use proportional reasoning to model and solve real-life problems (N-8-M)

N-8-M-GLE 8. Solve real-life problems involving percentages, including percentages less than 1 or greater than 100 (N-8-M) (N-5-M)

N-8-M-GLE 9. Find unit/cost rates and apply them in real-life problems (N-8-M) (N-5-M) (A-5-M)

N-8-M-GLE 18. Apply rate of change in real-life problems, including density, velocity, and international monetary conversions (M-1-M) (N-8-M) (M-6-M)

N-8-M-GLE 30. Construct, interpret, and use scale drawings in real-life situations (G-5-M) (M-6-M) (N-8-M)

LA.A. Algebra: In problem-solving investigations students demonstrate an understanding of concepts and processes that allow them to analyze, represent, and describe relationships among variable quantities and to apply algebraic methods to real-world situations.

A-1-M. Demonstrating a conceptual understanding of variables, expressions, equations, and inequalities (e.g., symbolically represent real-world problems as linear terms, equations, or inequalities).

A-1-M-GLE 10. Write real-life meanings of expressions and equations involving rational numbers and variables (A-1-M) (A-5-M)

A-1-M-GLE 11. Translate real-life situations that can be modeled by linear or exponential relationships to algebraic expressions, equations, and inequalities (A-1-M) (A-4-M) (A-5-M)

A-2-M. Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs, manipulatives, and/or standard algebraic procedures).

A-2-M-GLE 12. Solve and graph solutions of multi-step linear equations and inequalities (A-2-M)

A-2-M-GLE 14. Construct a table of x- and y-values satisfying a linear equation and construct a graph of the line on the coordinate plane (A-3-M) (A-2-M)

A-3-M. Representing situations and number patterns with tables, graphs, and verbal and written statements, while exploring the relationships among these representations (e.g., multiple representations for the same situation).

A-3-M-GLE 13. Switch between functions represented as tables, equations, graphs, and verbal representations, with and without technology (A-3-M) (P-2-M) (A-4-M)

A-3-M-GLE 14. Construct a table of x- and y-values satisfying a linear equation and construct a graph of the line on the coordinate plane (A-3-M) (A-2-M)

A-4-M. Analyzing tables and graphs to identify relationships exhibited by the data and making generalizations based upon these relationships.

A-4-M-GLE 11. Translate real-life situations that can be modeled by linear or exponential relationships to algebraic expressions, equations, and inequalities (A-1-M) (A-4-M) (A-5-M)

A-4-M-GLE 13. Switch between functions represented as tables, equations, graphs, and verbal representations, with and without technology (A-3-M) (P-2-M) (A-4-M)

A-4-M-GLE 15. Describe and compare situations with constant or varying rates of change (A-4-M)

A-4-M-GLE 16. Explain and formulate generalizations about how a change in one variable results in a change in another variable (A-4-M)

A-4-M-GLE 38. Sketch and interpret a trend line (i.e., line of best fit) on a scatterplot (D-2-M) (A-4-M) (A-5-M)

A-5-M. Demonstrating the connection of algebra to the other strands and to real-life situations.

A-5-M-GLE 9. Find unit/cost rates and apply them in real-life problems (N-8-M) (N-5-M) (A-5-M)

A-5-M-GLE 10. Write real-life meanings of expressions and equations involving rational numbers and variables (A-1-M) (A-5-M)

A-5-M-GLE 11. Translate real-life situations that can be modeled by linear or exponential relationships to algebraic expressions, equations, and inequalities (A-1-M) (A-4-M) (A-5-M)

A-5-M-GLE 29. Solve problems involving lengths of sides of similar triangles (G-5-M) (A-5-M)

A-5-M-GLE 38. Sketch and interpret a trend line (i.e., line of best fit) on a scatterplot (D-2-M) (A-4-M) (A-5-M)

A-5-M-GLE 47. Represent the nth term in a pattern as a formula and test the representation (P-1-M) (P-2-M) (P-3-M) (A-5-M)

LA.M. Measurement: In problem-solving investigations, students demonstrate an understanding of the concepts, processes, and real-life applications of measurement.

M-1-M. Applying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to real-world experiences.

M-1-M-GLE 17. Determine the volume and surface area of prisms and cylinders (M-1-M) (G-7-M)

M-1-M-GLE 18. Apply rate of change in real-life problems, including density, velocity, and international monetary conversions (M-1-M) (N-8-M) (M-6-M)

M-2-M. Demonstrating an intuitive sense of measurement (e.g., estimating and determining reasonableness of measures).

M-2-M-GLE 19. Demonstrate an intuitive sense of the relative sizes of common units of volume in relation to real-life applications and use this sense when estimating (M-2-M) (G-1-M)

M-3-M. Selecting appropriate units and tools for tasks by considering the purpose for the measurement and the precision required for the task (e.g., length of a room in feet rather than inches).

M-3-M-GLE 20. Identify and select appropriate units for measuring volume (M-3-M)

M-4-M. Using intuition and estimation skills to describe, order, and compare formal and informal measures (e.g., ordering cup, pint, quart, gallon; comparing a meter to a yard).

M-4-M-GLE 21. Compare and estimate measurements of volume and capacity within and between the U.S. and metric systems (M-4-M) (G-1-M)

M-5-M. Converting from one unit of measurement to another within the same system (Comparisons between systems, customary and metric, should be based on intuitive reference points, not formal computation.).

M-5-M-GLE 22. Convert units of volume/capacity within systems for U.S. and metric units (M-5-M)

M-6-M. Demonstrating the connection of measurement to the other strands and to real-life situations.

M-6-M-GLE 18. Apply rate of change in real-life problems, including density, velocity, and international monetary conversions (M-1-M) (N-8-M) (M-6-M)

M-6-M-GLE 30. Construct, interpret, and use scale drawings in real-life situations (G-5-M) (M-6-M) (N-8-M)

LA.G. Geometry: In problem-solving investigations, students demonstrate an understanding of geometric concepts and applications involving one-, two-, and three-dimensional geometry, and justify their findings.

G-1-M. Using estimation skills to describe, order, and compare geometric measures.

G-1-M-GLE 19. Demonstrate an intuitive sense of the relative sizes of common units of volume in relation to real-life applications and use this sense when estimating (M-2-M) (G-1-M)

G-1-M-GLE 21. Compare and estimate measurements of volume and capacity within and between the U.S. and metric systems (M-4-M) (G-1-M)

G-2-M. Identifying, describing, comparing, constructing, and classifying geometric figures and concepts.

G-2-M-GLE 23. Define and apply the terms measure, distance, midpoint, bisect, bisector, and perpendicular bisector (G-2-M)

G-2-M-GLE 24. Demonstrate conceptual and practical understanding of symmetry, similarity, and congruence and identify similar and congruent figures (G-2-M)

G-3-M. Making predictions regarding transformations of geometric figures (e.g., make predictions regarding translations, reflections, and rotations of common figures).

G-3-M-GLE 25. Predict, draw, and discuss the resulting changes in lengths, orientation, angle measures, and coordinates when figures are translated, reflected across horizontal or vertical lines, and rotated on a grid (G-3-M) (G-6-M)

G-3-M-GLE 26. Predict, draw, and discuss the resulting changes in lengths, orientation, and angle measures that occur in figures under a similarity transformation (dilation) (G-3-M) (G-6-M)

G-4-M. Constructing two- and three-dimensional models.

G-4-M-GLE 27. Construct polyhedra using 2-dimensional patterns (nets) (G-4-M)

G-5-M. Making and testing conjectures about geometric shapes and their properties.

G-5-M-GLE 28. Apply concepts, properties, and relationships of adjacent, corresponding, vertical, alternate interior, complementary, and supplementary angles (G-5-M)

G-5-M-GLE 29. Solve problems involving lengths of sides of similar triangles (G-5-M) (A-5-M)

G-5-M-GLE 30. Construct, interpret, and use scale drawings in real-life situations (G-5-M) (M-6-M) (N-8-M)

G-5-M-GLE 31. Use area to justify the Pythagorean theorem and apply the Pythagorean theorem and its converse in real-life problems (G-5-M) (G-7-M)

G-5-M-GLE 32. Model and explain the relationship between the dimensions of a rectangular prism and its volume (i.e., how scale change in linear dimension(s) affects volume) (G-5-M)

G-6-M. Demonstrating an understanding of the coordinate system (e.g., locate points, identify coordinates, and graph points in a coordinate plane to represent real-world situations).

G-6-M-GLE 25. Predict, draw, and discuss the resulting changes in lengths, orientation, angle measures, and coordinates when figures are translated, reflected across horizontal or vertical lines, and rotated on a grid (G-3-M) (G-6-M)

G-6-M-GLE 26. Predict, draw, and discuss the resulting changes in lengths, orientation, and angle measures that occur in figures under a similarity transformation (dilation) (G-3-M) (G-6-M)

G-6-M-GLE 33. Graph solutions to real-life problems on the coordinate plane (G-6-M)

G-7-M. Demonstrating the connection of geometry to the other strands and to real-life situations (e.g., applications of the Pythagorean Theorem).

G-7-M-GLE 17. Determine the volume and surface area of prisms and cylinders (M-1-M) (G-7-M)

LA.D. Data Analysis, Probability, and Discrete Math: In problem-solving investigations, students discover trends, formulate conjectures regarding cause-and-effect relationships, and demonstrate critical thinking skills in order to make informed decisions.

D-1-M. Systematically collecting, organizing, describing, and displaying data in charts, tables, plots, graphs, and/or spreadsheets.

D-1-M-GLE 34. Determine what kind of data display is appropriate for a given situation (D-1-M)

D-1-M-GLE 35. Match a data set or graph to a described situation, and vice versa (D-1-M)

D-1-M-GLE 36. Organize and display data using circle graphs (D-1-M)

D-1-M-GLE 37. Collect and organize data using box-and-whisker plots and use the plots to interpret quartiles and range (D-1-M) (D-2-M)

D-2-M. Analyzing, interpreting, evaluating, drawing inferences, and making estimations, predictions, decisions, and convincing arguments based on organized data (e.g., analyze data using concepts of mean, median, mode, range, random samples, sample size, bias, and data extremes).

D-2-M-GLE 37. Collect and organize data using box-and-whisker plots and use the plots to interpret quartiles and range (D-1-M) (D-2-M)

D-2-M-GLE 38. Sketch and interpret a trend line (i.e., line of best fit) on a scatterplot (D-2-M) (A-4-M) (A-5-M)

D-2-M-GLE 39. Analyze and make predictions from discovered data patterns (D-2-M)

D-2-M-GLE 40. Explain factors in a data set that would affect measures of central tendency (e.g., impact of extreme values) and discuss which measure is most appropriate for a given situation (D-2-M)

D-2-M-GLE 41. Select random samples that are representative of the population, including sampling with and without replacement, and explain the effect of sampling on bias (D-2-M) (D-4-M)

D-3-M. Describing informal thinking procedures (e.g., solving elementary logic problems using Venn diagrams, tables, charts, and/or elementary logic operatives to solve logic problems in real-life situations; reach valid conclusions in elementary logic problems involving and, or, not, if/then).

D-4-M. Analyzing various counting and enumeration procedures with and without replacement (e.g., find the total number of possible outcomes or possible choices in a given situation).

D-4-M-GLE 41. Select random samples that are representative of the population, including sampling with and without replacement, and explain the effect of sampling on bias (D-2-M) (D-4-M)

D-4-M-GLE 42. Use lists, tree diagrams, and tables to apply the concept of permutations to represent an ordering with and without replacement (D-4-M)

D-4-M-GLE 43. Use lists and tables to apply the concept of combinations to represent the number of possible ways a set of objects can be selected from a group (D-4-M)

D-5-M. Comparing experimental probability results with theoretical probability (e.g., representing probabilities of concrete situations as common fractions, investigating single-event and multiple-event probability, using sample spaces, geometric figures, tables, and/or graphs).

D-5-M-GLE 44. Use experimental data presented in tables and graphs to make outcome predictions of independent events (D-5-M)

D-5-M-GLE 45. Calculate, illustrate, and apply single- and multiple-event probabilities, including mutually exclusive, independent events and non-mutually exclusive, dependent events (D-5-M)

D-6-M. Demonstrating the connection of data analysis, probability, and discrete math to other strands and to real-life situations.

LA.P. Patterns, Relations, and Functions: In problem-solving investigations, students demonstrate an understanding of patterns, relations, and functions that represent and explain real-world situations.

P-1-M. Describing, extending, analyzing, and creating a wide variety of numerical, geometrical, and statistical patterns (e.g., skip counting of rational numbers and simple exponential number patterns).

P-1-M-GLE 46. Distinguish between and explain when real-life numerical patterns are linear/arithmetic (i.e., grows by addition) or exponential/geometric (i.e., grows by multiplication) (P-1-M) (P-4-M)

P-1-M-GLE 47. Represent the nth term in a pattern as a formula and test the representation (P-1-M) (P-2-M) (P-3-M) (A-5-M)

P-2-M. Describing and representing relationships using tables, rules, simple equations, and graphs.

P-2-M-GLE 13. Switch between functions represented as tables, equations, graphs, and verbal representations, with and without technology (A-3-M) (P-2-M) (A-4-M)

P-2-M-GLE 47. Represent the nth term in a pattern as a formula and test the representation (P-1-M) (P-2-M) (P-3-M) (A-5-M)

P-3-M. Analyzing relationships to explain how a change in one quantity results in a change in another (e.g., change in the dimensions of a rectangular solid affects the volume).

P-3-M-GLE 47. Represent the nth term in a pattern as a formula and test the representation (P-1-M) (P-2-M) (P-3-M) (A-5-M)

P-3-M-GLE 48. Illustrate patterns of change in dimension(s) and corresponding changes in volumes of rectangular solids (P-3-M)

P-4-M. Demonstrating the pervasive use of patterns, relations, and functions in other strands and in real-life situations.

P-4-M-GLE 46. Distinguish between and explain when real-life numerical patterns are linear/arithmetic (i.e., grows by addition) or exponential/geometric (i.e., grows by multiplication) (P-1-M) (P-4-M)