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New Jersey: Grade Level Expectations - Math Grade 8

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Correlation by State

New Jersey: Grade Level Expectations - Math Grade 8

4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.

A. Number Sense

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):

Rational numbers

Percents

Roots

Absolute values

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

4. Compare and order numbers of all named types.

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

B. Numerical Operations

2. Use exponentiation to find whole number powers of numbers

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

4. Solve problems involving proportions and percents.

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

C. Estimation

1. Estimate square and cube roots of numbers.

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

4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.

A. Geometric Properties

1. Understand and apply concepts involving lines, angles, and planes.

Complementary and supplementary angles

Vertical angles

Bisectors and perpendicular bisectors

Parallel, perpendicular, and intersecting planes

2. Understand and apply the Pythagorean theorem.

3. Understand and apply properties of polygons.

Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

Sum of measures of interior angles of a polygon

4. Understand and apply the concept of similarity.

Using proportions to find missing measures

Scale drawings

B. Transforming Shapes

1. Understand and apply transformations.

Finding the image, given the pre-image, and vice-versa

Sequence of transformations needed to map one figure onto another

Reflections, rotations, and translations result in images congruent to the pre-image

Dilations (stretching/shrinking) result in images similar to the pre-image

2. Use iterative procedures to generate geometric patterns.

Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski's Triangle)

C. Coordinate Geometry

1. Use coordinates in four quadrants to represent geometric concepts.

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

D. Units of Measurement

4. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.

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).

E. Measuring Geometric Objects

1. Develop and apply strategies for finding perimeter and area.

Estimation of area using grids of various sizes

Impact of a dilation on the perimeter and area of a 2-dimensional figure

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).

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

Volume - prism, cone, pyramid

Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)

Impact of a dilation on the surface area and volume of a three-dimensional figure

4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.

A. Patterns and Relationships

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

Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

Finite and infinite sequences

Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)

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

B. Functions

1. Graph functions, and understand and describe their general behavior.

Equations involving two variables

Rates of change (informal notion of slope)

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

C. Modeling

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.

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

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)

D. Procedures

1. Use graphing techniques on a number line.

Absolute value

Arithmetic operations represented by vectors (arrows) (e.g., ""-3 + 6"" is ""left 3, right 6"")

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

Multi-step, integer coefficients only (although answers may not be integers)

3. Solve simple linear inequalities.