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New Jersey Math Standards - 7th Grade
MathScore aligns to the New Jersey Math Standards for 7th 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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View the New Jersey Math Standards at other levels.
Number and Numerical Operations
4.1.7 A. Number Sense1. Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well):
• Rational numbers (Percentage Pictures )
• Percents (Percentage Pictures )
• Whole numbers with exponents (Exponent Basics )
2. Demonstrate a sense of the relative magnitudes of numbers.
3. Understand and use ratios, 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 , Ratios )
4. Compare and order numbers of all named types. (Compare Mixed Values , Compare Mixed Values 2 , Positive Number Line , Number Line , Compare Integers )
5. Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number. (Fraction Simplification , Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Percentages )
6. Understand that all fractions can be represented as repeating or terminating decimals. (Fractions to Decimals , Repeating Decimals )
4.1.7 B. Numerical Operations
1. Use and explain procedures for performing calculations with integers and all number types named above with:
• Pencil-and-paper
• Mental math
• Calculator (Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
2. Use exponentiation to find whole number powers of numbers. (Exponent Basics )
3. Understand and apply the standard algebraic order of operations, including appropriate use of parentheses. (Using Parentheses , Order Of Operations )
4.1.7 C. Estimation
1. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.
Geometry and Measurement
4.2.7 A. Geometric Properties1. Understand and apply properties of polygons.
• Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi (Quadrilateral Angles , Quadrilateral Types )
• Regular polygons (Polygon Names )
2. Understand and apply the concept of similarity.
• Using proportions to find missing measures (Proportions 2 )
• Scale drawings
• Models of 3D objects
3. Use logic and reasoning to make and support conjectures about geometric objects.
4.2.7 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
4.2.7 C. Coordinate Geometry
1. Use coordinates in four quadrants to represent geometric concepts. (Ordered Pairs , Line Segments )
2. Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units). (Translations and Reflections )
4.2.7 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 )
2. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.
3. Recognize that all measurements of continuous quantities are approximations.
4.2.7 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
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 )
Patterns and Algebra
4.3.7 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 (Function Tables , Function Tables 2 )
• Finite and infinite sequences
• Generating sequences by using calculators to repeatedly apply a formula
4.3.7 B. Functions and Relationships
1. Graph functions, and understand and describe their general behavior.
• Equations involving two variables
4.3.7 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 manipulatives, tables, graphs, verbal rules, algebraic expressions/equations/inequalities (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , 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 )
4.3.7 D. Procedures
1. Use graphing techniques on a number line.
• Absolute value (Absolute Value 1 )
• Arithmetic operations represented by vectors (arrows) (e.g., "-3 + 6" is "left 3, right 6")
2. Solve simple linear equations informally and graphically.
• Multi-step, integer coefficients only (although answers may not be integers) (Single Variable Equations 2 , Single Variable Equations 3 )
• Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology
3. Create, evaluate, and simplify algebraic expressions involving variables.
• Order of operations, including appropriate use of parentheses (Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 )
• Substitution of a number for a variable (Variable Substitution )
4. Understand and apply the properties of operations, numbers, equations, and inequalities.
• Additive inverse
• Multiplicative inverse
Data Analysis, Probability, and Discrete Mathematics
4.4.7 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
2. Make inferences and formulate and evaluate arguments based on displays and analysis of data.
4.4.7 B. Probability
1. Interpret probabilities as ratios, percents, and decimals. (Probability , Probability 2 )
2. Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.
• Frequency, relative frequency
3. Estimate probabilities and make predictions based on experimental and theoretical probabilities.
4. Play and analyze probability-based games, and discuss the concepts of fairness and expected value.
4.4.7 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)
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.
4.4.7 D. Discrete Mathematics-Vertex-Edge Graphs and Algorithms
1. Use vertex-edge graphs to represent and find solutions to practical problems.
• Finding the shortest network connecting specified sites
• 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
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