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New Jersey Math Standards - 8th Grade
MathScore aligns to the New Jersey Math Standards for 8th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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Number and Numerical Operations
4.1.8 A. Number Sense1. 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 (Percentage Pictures )
• Percents (Percentage Pictures )
• Exponents
• Roots
• Absolute values (Absolute Value 1 )
• Numbers represented in scientific notation (Scientific Notation )
2. Demonstrate a sense of the relative magnitudes of numbers.
3. Understand and use ratios, rates, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations. (Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Proportions 1 , Proportions 2 , Simple Interest , Compound Interest , Distance, Rate, and Time )
4. Compare and order numbers of all named types. (Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Estimating Square Roots )
5. Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number. (Percentages )
6. Recognize that repeating decimals correspond to fractions and determine their fractional equivalents.
• 5/7 = 0.714285714285… = 0.714285 (Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Repeating Decimals )
7. Construct meanings for common irrational numbers, such as π (pi) and the square root of 2. (Circle Area , Circle Circumference )
4.1.8 B. Numerical Operations
1. Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with:
• Pencil-and-paper
• Mental math
• Calculator (Scientific Notation 2 , Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
2. Use exponentiation to find whole number powers of numbers. (Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases )
3. Find square and cube roots of numbers and understand the inverse nature of powers and roots. (Estimating Square Roots , Perfect Squares )
4. Solve problems involving proportions and percents. (Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Proportions 1 , Proportions 2 , Mixture Word Problems )
5. Understand and apply the standard algebraic order of operations, including appropriate use of parentheses. (Using Parentheses , Order Of Operations )
4.1.8 C. Estimation
1. Estimate square and cube roots of numbers. (Estimating Square Roots )
2. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.
3. Recognize the limitations of estimation and assess the amount of error resulting from estimation.
Geometry and Measurement
4.2.8 A. Geometric Properties1. Understand and apply concepts involving lines, angles, and planes.
• Complementary and supplementary angles (Angle Measurements )
• Vertical angles (Angle Measurements )
• Bisectors and perpendicular bisectors
• Parallel, perpendicular, and intersecting planes
• Intersection of plane with cube, cylinder, cone, and sphere
2. Understand and apply the Pythagorean theorem. (Pythagorean Theorem )
3. Understand and apply properties of polygons.
• Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi (Quadrilateral Angles )
• Regular polygons (Polygon Angles )
• Sum of measures of interior angles of a polygon (Polygon Angles )
• Which polygons can be used alone to generate a tessellation and why
4. Understand and apply the concept of similarity.
• Using proportions to find missing measures (Solving For Angles , Proportions 2 )
• Scale drawings
• Models of 3D objects
5. Use logic and reasoning to make and support conjectures about geometric objects.
6. Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).
• Congruent angles or line segments
• Midpoint of a line segment
7. Create two-dimensional representations (e.g., nets or projective views) for the surfaces of three-dimensional objects.
4.2.8 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.
• Fractals (e.g., the Koch Snowflake)
• Self-similarity
• Construction of initial stages
• Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski's Triangle)
4.2.8 C. Coordinate Geometry
1. Use coordinates in four quadrants to represent geometric concepts. (Line Segments )
2. Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units). (Translations and Reflections )
4.2.8 D. Units of Measurement
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"). (Time Intervals , Train Problems )
2. Use approximate equivalents between standard and metric systems to estimate measurements (e.g., 5 kilometers is about 3 miles).
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. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.
5. Recognize that all measurements of continuous quantities are approximations.
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). (Distance, Rate, and Time )
4.2.8 E. Measuring Geometric Objects
1. Develop and apply strategies for finding perimeter and area.
• Geometric figures made by combining triangles, rectangles and circles or parts of circles (Irregular Shape Areas , Perimeter and Area of Composite Figures )
• Estimation of area using grids of various sizes
• Impact of a dilation on the perimeter and area of a 2-dimensional figure (Area And Volume Proportions )
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). (Rectangular Solids , Triangular Prisms , Cylinders )
3. Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.
• Volume - prism, cone, pyramid (Rectangular Solids , Triangular Prisms )
• Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base) (Rectangular Solids , Triangular Prisms )
• Impact of a dilation on the surface area and volume of a three-dimensional figure (Area And Volume Proportions )
4. Use formulas to find the volume and surface area of a sphere.
Patterns and Algebra
4.3.8 A. Patterns1. 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) (Patterns: Numbers )
• Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)
• Generating sequences by using calculators to repeatedly apply a formula
4.3.8 B. Functions and Relationships
1. Graph functions, and understand and describe their general behavior.
• Equations involving two variables
• Rates of change (informal notion of slope) (Determining Slope )
2. Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.
4.3.8 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. (Linear Equations )
2. Use patterns, relations, symbolic algebra, and linear functions to model situations.
• Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Applied Linear Equations 1 , Nonlinear Functions , Number Line Inequalities , Algebraic Sentences 2 , Algebraic Sentences )
• 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) (Compound Interest )
4.3.8 D. Procedures
1. Use graphing techniques on a number line.
• Absolute value (Number Line Inequalities )
• 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) (Single Variable Equations 2 , Single Variable Equations 3 )
• Simple literal equations (e.g., A = lw) (Distance, Rate, and Time )
• Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology
3. Solve simple linear inequalities. (Single Variable Inequalities )
4. Create, evaluate, and simplify algebraic expressions involving variables.
• Order of operations, including appropriate use of parentheses (Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 )
• Distributive property (Distributive Property , Distributive Property 2 )
• Substitution of a number for a variable (Variable Substitution )
• Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa (Algebraic Sentences 2 , Algebraic Sentences )
5. Understand and apply the properties of operations, numbers, equations, and inequalities.
• Additive inverse
• Multiplicative inverse
• Addition and multiplication properties of equality
• Addition and multiplication properties of inequalities
Data Analysis, Probability, and Discrete Mathematics
4.4.8 A. Data Analysis1. Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).
• Type of display most appropriate for given data
• Box-and-whisker plot, upper quartile, lower quartile
• Scatter plot
• Calculators and computer used to record and process information
• Finding the median and mean (weighted average) using frequency data.
• Effect of additional data on measures of central tendency (Batting Averages )
2. Make inferences and formulate and evaluate arguments based on displays and analysis of data sets.
3. Estimate lines of best fit and use them to interpolate within the range of the data.
4. Use surveys and sampling techniques to generate data and draw conclusions about large groups.
4.4.8 B. Probability
1. Interpret probabilities as ratios, percents, and decimals. (Probability , Probability 2 )
2. Determine probabilities of compound events. (Probability 2 )
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). (Object Picking Probability )
4. Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.
• Frequency, relative frequency
5. Estimate probabilities and make predictions based on experimental and theoretical probabilities.
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
1. Apply the multiplication principle of counting.
• 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)
• Factorial notation
• Concept of combinations (e.g., number of possible delegations of 3 out of 23 students)
2. Explore counting problems involving Venn diagrams with three attributes (e.g., there are 15, 20, and 25 students respectively in the chess club, the debating team, and the engineering society; how many different students belong to the three clubs if there are 6 students in chess and debating, 7 students in chess and engineering, 8 students in debating and engineering, and 2 students in all three?).
3. Apply techniques of systematic listing, counting, and reasoning in a variety of different contexts.
4.4.8 D. Discrete Mathematics-Vertex-Edge Graphs and Algorithms
1. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems.
• Finding the shortest network connecting specified sites
• Finding a minimal route that includes every street (e.g., for trash pick-up)
• Finding the shortest route on a map from one site to another
• Finding the shortest circuit on a map that makes a tour of specified sites
• Limitations of computers (e.g., the number of routes for a delivery truck visiting n sites is n!, so finding the shortest circuit by examining all circuits would overwhelm the capacity of any computer, now or in the future, even if n is less than 100)
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