Core Curriculum Content Standards
4.1.A: Number Sense
4.1.A.1: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well):
4.1.A.1.e: Absolute values
4.1.A.3: Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.
4.1.A.4: Compare and order numbers of all named types.
4.1.A.5: Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.
4.1.A.7: Construct meanings for common irrational numbers, such as p (pi) and the square root of 2.
4.1.B: Numerical Operations
4.1.B.1: Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with:
4.1.B.1.b: Mental math
4.1.B.3: Find square and cube roots of numbers and understand the inverse nature of powers and roots.
4.1.B.4: Solve problems involving proportions and percents.
4.1.B.5: Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.
4.1.C.1: Estimate square and cube roots of numbers.
4.1.C.2: Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.
4.2.A: Geometric Properties
4.2.A.1: Understand and apply concepts involving lines, angles, and planes.
4.2.A.1.a: Complementary and supplementary angles
4.2.A.1.b: Vertical angles
4.2.A.1.c: Bisectors and perpendicular bisectors
4.2.A.1.d: Parallel, perpendicular, and intersecting planes
4.2.A.1.e: Intersection of plane with cube, cylinder, cone, and sphere
4.2.A.2: Understand and apply the Pythagorean theorem.
4.2.A.3: Understand and apply properties of polygons.
4.2.A.3.a: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi
4.2.A.3.c: Sum of measures of interior angles of a polygon
4.2.A.4: Understand and apply the concept of similarity.
4.2.A.4.a: Using proportions to find missing measures
4.2.A.4.c: Models of 3D objects
4.2.A.5: Use logic and reasoning to make and support conjectures about geometric objects.
4.2.B: Transforming Shapes
4.2.B.1: Understand and apply transformations.
4.2.B.1.a: Finding the image, given the pre-image, and vice-versa
4.2.B.1.b: Sequence of transformations needed to map one figure onto another
4.2.B.1.c: Reflections, rotations, and translations result in images congruent to the pre-image
4.2.B.1.d: Dilations (stretching/shrinking) result in images similar to the pre-image
4.2.B.2: Use iterative procedures to generate geometric patterns.
4.2.B.2.c: Construction of initial stages
4.2.B.2.d: Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski’s Triangle)
4.2.C: Coordinate Geometry
4.2.C.1: Use coordinates in four quadrants to represent geometric concepts.
4.2.C.2: Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).
4.2.D: Units of Measurement
4.2.D.3: Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements.
4.2.D.4: Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.
4.2.D.6: Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).
4.2.E: Measuring Geometric Objects
4.2.E.1: Develop and apply strategies for finding perimeter and area.
4.2.E.1.a: Geometric figures made by combining triangles, rectangles and circles or parts of circles
4.2.E.1.b: Estimation of area using grids of various sizes
4.2.E.1.c: Impact of a dilation on the perimeter and area of a 2-dimensional figure
4.2.E.2: Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).
4.2.E.3: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.
4.2.E.3.a: Volume - prism, cone, pyramid
4.2.E.3.b: Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)
4.2.E.3.c: Impact of a dilation on the surface area and volume of a three-dimensional figure
4.3.A.1: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.
4.3.A.1.a: Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions
4.3.A.1.b: Finite and infinite sequences
4.3.A.1.c: Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)
4.3.A.1.d: Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)
4.3.A.1.e: Generating sequences by using calculators to repeatedly apply a formula
4.3.B: Functions and Relationships
4.3.B.1: Graph functions, and understand and describe their general behavior.
4.3.B.1.a: Equations involving two variables
4.3.B.1.b: Rates of change (informal notion of slope)
4.3.B.2: Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.
4.3.C.1: Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.
4.3.C.2: Use patterns, relations, symbolic algebra, and linear functions to model situations.
4.3.C.2.a: Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities
4.3.C.2.b: Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)
4.3.D.1: Use graphing techniques on a number line.
4.3.D.1.a: Absolute value
4.3.D.2: Solve simple linear equations informally, graphically, and using formal algebraic methods.
4.3.D.2.a: Multi-step, integer coefficients only (although answers may not be integers)
4.3.D.3: Solve simple linear inequalities.
4.3.D.4: Create, evaluate, and simplify algebraic expressions involving variables.
4.3.D.4.a: Order of operations, including appropriate use of parentheses
4.3.D.4.d: Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa
4.3.D.5: Understand and apply the properties of operations, numbers, equations, and inequalities.
4.3.D.5.c: Addition and multiplication properties of equality
4.4.A: Data Analysis
4.4.A.1: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).
4.4.A.1.a: Type of display most appropriate for given data
4.4.A.1.b: Box-and-whisker plot, upper quartile, lower quartile
4.4.A.1.c: Scatter plot
4.4.A.1.e: Finding the median and mean (weighted average) using frequency data.
4.4.A.1.f: Effect of additional data on measures of central tendency
4.4.A.3: Estimate lines of best fit and use them to interpolate within the range of the data.
4.4.A.4: Use surveys and sampling techniques to generate data and draw conclusions about large groups.
4.4.B.1: Interpret probabilities as ratios, percents, and decimals.
4.4.B.2: Determine probabilities of compound events.
4.4.B.3: Explore the probabilities of conditional events (e.g., if there are seven marbles in a bag, three red and four green, what is the probability that two marbles picked from the bag, without replacement, are both red).
4.4.B.4: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.
4.4.B.4.a: Frequency, relative frequency
4.4.B.5: Estimate probabilities and make predictions based on experimental and theoretical probabilities.
4.4.C: Discrete Mathematics-Systematic Listing and Counting
4.4.C.1: Apply the multiplication principle of counting.
4.4.C.1.a: Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class)
4.4.C.1.c: Concept of combinations (e.g., number of possible delegations of 3 out of 23 students)
Correlation last revised: 11/13/2008