Board Approved - April 24, 2003 For best printing results, click here (pdf).
MATHEMATICS K-10 – Grade Level Expectations
Grade 6	Grade 7	Grade 8
NUMBER SENSE	NUMBER SENSE	NUMBER SENSE
number and numeration	number and numeration	number and numeration
§ use models to explain equivalencies of fractions, decimals, and percents § identify, compare, and order non-negative whole numbers, fractions, and decimals § use models to describe primes, composites, factors, and multiples, and determine divisibility by 2, 4, 5, 8, and 10 § use objects, pictures, and symbols to create equivalent ratios in part:whole context § find missing values within proportional conditions using ratios and rates	§ use models to show understanding of non-negative fractions, decimals, percents, place value, and absolute value § use pictures and symbols to demonstrate properties of the rational number system § use exponents and scientific notation to explore representation of relatively large and small numbers § identify fraction, decimal, ratio, and percent equivalencies § compare and order whole numbers, fractions, and decimals § use models to describe prime and composite numbers, factors and multiples, and determine divisibility § express numbers in factored form including all factor pairs	§ compare and order symbolically or on a number line whole, rational, and decimal numbers, and integers § use pictures and symbols to demonstrate properties of the rational number system § find the least common multiple and greatest common divisor/factor for a pair of positive integers § apply associative, commutative, identify, inverse, and distributive properties to simplify and complete rational number operations § translate between simple fraction, mixed number, and improper fraction formats in representing and interpreting rational numbers § uses factors, multiples, and prime factorization to simplify and solve rational number computations, e.g., writes 28/48 in reduced form § create and solve whole number proportions
computation	computation	computation
§ add, subtract, multiply, and divide whole numbers § add, subtract, and multiply decimals, fractions, and mixed numbers § calculate simple percentages § use models to demonstrate the meaning of division of simple fractions and decimals § use order of operations to simplify arithmetic expressions with whole numbers § justify the use of mental arithmetic, paper and pencil, calculator or computer as appropriate for a given situation	§ add, subtract, multiply, and divide non-negative whole numbers, decimals, fractions, and mixed numbers using order of operations § justify the use of mental arithmetic, paper and pencil, calculator or computer as appropriate for a given situation involving non-negative rational numbers	§ effectively and efficiently perform the operations for whole, rational, decimal, and integer computations § use exponential notation to represent and calculate whole number powers of numbers § apply mental arithmetic to compute simple percentages such as 10%, 25%, 33.5%, 50%, 75%
estimation	estimation	estimation
§ determine and justify the reasonableness of answers by estimating results prior to actual computation with whole numbers and fractions	§ identify situations involving non-negative rational numbers in which estimation is sufficient and computation is not required § determine and justify the reasonableness of answers by estimating results prior to actual computation with non-negative rational numbers	§ give estimates for values involving unit multiples using mental mathematics, e.g., if 5 bottles costs $10, then 7 bottles cost $14 § select and choose the type of number needed for a given situation, judging whether exact answer or estimate is needed for a given situation § determine and justify the reasonableness of answers by estimating results prior to actual computation with non-negative rational numbers
MEASUREMENT	MEASUREMENT	MEASUREMENT
attributes and dimensions	attributes and dimensions	attributes and dimensions
§ describe relationships among perimeter, area, and volume § determine area and volume when given dimensions of the object or space measured in U.S. or metric units of measurement § determine the area of irregular shapes using customary and metric units of measurement § apply the concept of ratio when constructing scale models using customary or metric units of measurement	§ develop and use formulas for perimeter and area of polygons and circles § develop and use formulas for volume and surface area of prisms and cylinders § solve problems using rates and determine the appropriate units	§ measure sides of triangles indirectly using the Pythagorean theorem § know the number of degrees in a circle, triangle, and quadrilateral § apply formulas for perimeter and area for triangles, standard quadrilaterals, and circles and surface area and volume for prisms, cylinders, cones, and spheres § use scales and ratios involving known measures to estimate or calculate measures of objects for which no direct information is given, e.g., how much does a large can of juice cost if the small can costs 25¢, when both cans are shown
approximation and precision	approximation and precision	approximation and precision
§ explain how precision depends on the calibration of the measurement tool	§ describe and justify methods used to obtain reasonable approximations when given no exact measures	§ describe and justify methods used to obtain reasonable approximations when given no exact measures
systems and tools	systems and tools	systems and tools
§ determine which U.S. or metric unit of measurement will result in the most appropriate measurement for a given situation § use a protractor to measure angles	§ make conversions within U.S. Customary and within Metric Systems	§ select appropriate units for the measurement of common situations involving length, area, volume, weight, capacity, and mass § measure angles to the nearest degree with a protractor and estimate angle measurements to the nearest 10º § illustrate conversion between metric measures using powers of ten and movement of the decimal point, e.g., 42.31 cm = 0.4231 m
GEOMETRIC SENSE	GEOMETRIC SENSE	GEOMETRIC SENSE
properties and relationships	properties and relationships	properties and relationships
§ identify and describe figures that are similar, congruent, or symmetric § identify the number of degrees in a circle, triangle, and quadrilateral § compare, contrast, classify, and construct 2-D figures, such as isosceles, equilateral, and scalene triangles	§ construct and describe symmetric, congruent, and similar geometric figures using appropriate tools and computer software § identify and describe geometric shapes found in the environment § compare, contrast, and classify 3-D figures	§ construct and describe symmetric, congruent and similar geometric figures using appropriate tools and computer software § visualize (verbally and through sketches) the planar cross section of a geometric solid in a given direction § employ similarity and the Pythagorean theorem to find indirect measures § represent relationships between corresponding parts of similar triangles and use proportions to find unknown measures in such triangles § describe and classify 3-D figures using their defining attributes: faces, edges, angles, vertices, angle measures, and measures of faces § model and sketch 2-D versions of 3-D figures and 3-D figures from 2-D views
locations and transformations	locations and transformations	locations and transformations
§ describe the location of points on coordinate grids using letters and numbers on axes § describe simple transformations using combinations of translations, reflections, and rotations	§ describe the location of points on coordinate grids (first quadrant) § describe and construct simple transformations using combinations of translations, reflections, and rotations	§ use a coordinate system to graph linear expressions and represent properties of lines (parallelism/perpendicularity) § describe and construct simple transformations for complex figures using combinations of translations, reflections, and rotations
PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS
probability	probability	probability
§ display the sample space of a probability experiment by making a table or using a diagram § conduct simulations to determine probabilities	§ calculate the probability that an event will occur in experimental and theoretical situations § compare experimental and theoretical results § explore independent and dependent events	§ determine situations involving probabilities known as certain and impossible § evaluate the probability of a simple event using lists of outcomes
statistics	statistics	statistics
§ form a random sample from a described population § collect, organize, and display data using the appropriate forms § identify the effects of outliers on the mean and median § compute mean, median, mode, and/or range as appropriate in describing simple data	§ implement an investigation in which a random sample of data representing a described population is collected § collect, organize, and display data using appropriate form § calculate and demonstrate the appropriate use of mean, median, mode, and range as appropriate in describing a set of data	§ represent the central tendencies and spread of data using a variety of graphs, including box-and-whisker plots § describe changes in a graph from one reporting point to the adjacent reporting point, e.g., describe the growth in population in one decade versus the next decade § collect random samples and describe the population it depicts § recognize the type of data involved in a situation, count or measure, and choose the appropriate type of graph to represent it, e.g., describe a data set that requires a bar graph rather than line graph § calculate and apply the mean, median, mode, and range for a set of data, e.g., find the average height and range of heights for a sample of students in a class
prediction and inference	prediction and inference	prediction and inference
§ predict outcomes of simple experiments and simulations and compare the predictions to experimental results § make inferences based on experimental results	§ predict outcomes of experiments and simulations and compare the predictions to experimental results § make and justify inferences based on experimental results	§ analyze information to predict outcomes of experiments or simulations § make decisions based on inferences from analysis of experimental results and statistical data
ALGEBRAIC SENSE	ALGEBRAIC SENSE	ALGEBRAIC SENSE
patterns	patterns	patterns
§ recognize and extend number patterns and sequences § use relationships found among sets of numbers to extend patterns on t-tables and function machines	§ recognize, extend, create, and represent number patterns using tables, graphs, and rules	§ describe and extend number patterns based on constant additions of the same term
representations	representations	representations
§ write rules for data found on t-tables and function machines § express relationships between numbers using =, ¹, >, or < § describe variables found in simple inequalities and formulas § translate a given problem situation into a simple mathematical equation and find the problem	§ describe variables found in simple inequalities and formulas	§ translate between equivalent forms of expressions and equations using basic properties of equality and operation § translate representations easily between numerical, graphical, symbolic, and verbal forms in problem-solving situations § write an equation representing a specified relationship between quantities, e.g., what number when multiplied by 4, then increased by 2, is 38
operations	operations	operations
§ evaluate simple expressions using pictorial representations § use pictures and/or words to describe solutions to single-variable equations	§ evaluate simple expressions and formulas § solve simple equations and inequalities containing one variable	§ set up and solve one- and two-step linear equations representing real-life situations (with integral coefficients), e.g., 5x + 2 = 37 § find the value associated with a variable in a formula given values for the other variables in the formula § graph inequalities (including absolute value) on the number line, e.g., shade all points on the line where |x| + 2 < 7
PROBLEM SOLVING	PROBLEM SOLVING	PROBLEM SOLVING
investigate situations