#### 4.1: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

4.1.8 A: Number Sense

4.1.8 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):

4.1.8 A.1.a: Rational numbers

4.1.8 A.1.b: Percents

4.1.8 A.1.d: Roots

4.1.8 A.1.e: Absolute values

4.1.8 A.3: Understand and use ratios, rates, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.

4.1.8 A.4: Compare and order numbers of all named types.

4.1.8 A.5: Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.

4.1.8 A.7: Construct meanings for common irrational numbers, such as pi and the square root of 2.

4.1.8 B: Numerical Operations

4.1.8 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:

4.1.8 B.1.a: Pencil-and-paper

4.1.8 B.1.b: Mental math

4.1.8 B.1.c: Calculator

4.1.8 B.3: Find square and cube roots of numbers and understand the inverse nature of powers and roots.

4.1.8 B.4: Solve problems involving proportions and percents.

4.1.8 B.5: Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

4.1.8 C: Estimation

4.1.8 C.1: Estimate square and cube roots of numbers.

4.1.8 C.2: Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

#### 4.2: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

4.2.8 A: Geometric Properties

4.2.8 A.1: Understand and apply concepts involving lines, angles, and planes.

4.2.8 A.1.a: Complementary and supplementary angles

4.2.8 A.1.b: Vertical angles

4.2.8 A.1.c: Bisectors and perpendicular bisectors

4.2.8 A.1.d: Parallel, perpendicular, and intersecting planes

4.2.8 A.2: Understand and apply the Pythagorean theorem.

4.2.8 A.3: Understand and apply properties of polygons.

4.2.8 A.3.a: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

4.2.8 A.3.c: Sum of measures of interior angles of a polygon

4.2.8 A.4: Understand and apply the concept of similarity.

4.2.8 A.4.a: Using proportions to find missing measures

4.2.8 A.4.b: Scale drawings

4.2.8 A.6: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).

4.2.8 A.6.b: Midpoint of a line segment

4.2.8 A.7: Create two-dimensional representations (e.g., nets or projective views) for the surfaces of three-dimensional objects.

4.2.8 B: Transforming Shapes

4.2.8 B.1: Understand and apply transformations.

4.2.8 B.1.a: Finding the image, given the pre-image, and vice-versa

4.2.8 B.1.b: Sequence of transformations needed to map one figure onto another

4.2.8 B.1.c: Reflections, rotations, and translations result in images congruent to the pre-image

4.2.8 B.1.d: Dilations (stretching/shrinking) result in images similar to the pre-image

4.2.8 C: Coordinate Geometry

4.2.8 C.1: Use coordinates in four quadrants to represent geometric concepts.

4.2.8 C.2: Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).

4.2.8 D: Units of Measurement

4.2.8 D.1: Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4'3" plus 7'10" equals 12'1").

4.2.8 E: Measuring Geometric Objects

4.2.8 E.1: Develop and apply strategies for finding perimeter and area.

4.2.8 E.1.a: Geometric figures made by combining triangles, rectangles and circles or parts of circles

4.2.8 E.1.c: Impact of a dilation on the perimeter and area of a 2-dimensional figure

4.2.8 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).

4.2.8 E.3: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.

4.2.8 E.3.a: Volume - prism, cone, pyramid

4.2.8 E.3.b: Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)

#### 4.3: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

4.3.8 A: Patterns

4.3.8 A.1: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.

4.3.8 A.1.a: Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

4.3.8 A.1.c: Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)

4.3.8 A.1.d: Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)

4.3.8 B: Functions and Relationships

4.3.8 B.1: Graph functions, and understand and describe their general behavior.

4.3.8 B.1.a: Equations involving two variables

4.3.8 B.1.b: Rates of change (informal notion of slope)

4.3.8 B.2: Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.

4.3.8 C: Modeling

4.3.8 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.

4.3.8 C.2: Use patterns, relations, symbolic algebra, and linear functions to model situations.

4.3.8 C.2.a: Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities

4.3.8 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)

4.3.8 D: Procedures

4.3.8 D.1: Use graphing techniques on a number line.

4.3.8 D.1.a: Absolute value

4.3.8 D.2: Solve simple linear equations informally, graphically, and using formal algebraic methods.

4.3.8 D.2.a: Multi-step, integer coefficients only (although answers may not be integers)

4.3.8 D.2.b: Simple literal equations (e.g., A = lw)

4.3.8 D.2.c: Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology

4.3.8 D.3: Solve simple linear inequalities.

4.3.8 D.4: Create, evaluate, and simplify algebraic expressions involving variables.

4.3.8 D.4.a: Order of operations, including appropriate use of parentheses

4.3.8 D.4.b: Distributive property

4.3.8 D.4.c: Substitution of a number for a variable

4.3.8 D.4.d: Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa

4.3.8 D.5: Understand and apply the properties of operations, numbers, equations, and inequalities.

4.3.8 D.5.b: Multiplicative inverse

4.3.8 D.5.c: Addition and multiplication properties of equality

#### 4.4: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

4.4.8 A: Data Analysis

4.4.8 A.1: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).

4.4.8 A.1.a: Type of display most appropriate for given data

4.4.8 A.1.b: Box-and-whisker plot, upper quartile, lower quartile

4.4.8 A.1.e: Finding the median and mean (weighted average) using frequency data.

4.4.8 A.1.f: Effect of additional data on measures of central tendency

4.4.8 A.2: Make inferences and formulate and evaluate arguments based on displays and analysis of data sets.

4.4.8 A.3: Estimate lines of best fit and use them to interpolate within the range of the data.

4.4.8 A.4: Use surveys and sampling techniques to generate data and draw conclusions about large groups.

4.4.8 B: Probability

4.4.8 B.1: Interpret probabilities as ratios, percents, and decimals.

4.4.8 B.2: Determine probabilities of compound events.

4.4.8 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).

4.4.8 B.5: Estimate probabilities and make predictions based on experimental and theoretical probabilities.

4.4.8 B.6: Play and analyze probability-based games, and discuss the concepts of fairness and expected value.

4.4.8 C: Discrete Mathematics-Systematic Listing and Counting

4.4.8 C.1: Apply the multiplication principle of counting.

4.4.8 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)

4.4.8 C.1.b: Factorial notation

4.4.8 C.1.c: Concept of combinations (e.g., number of possible delegations of 3 out of 23 students)

Correlation last revised: 5/18/2018

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