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New Jersey Math Standards - 6th Grade
MathScore aligns to the New Jersey Math Standards for 6th 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
4.1.6 A. Number Sense1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well).
• All integers (Compare Integers )
• All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers (Fraction Pictures )
• All decimals
2. Recognize the decimal nature of United States currency and compute with money. (Making Change , Unit Cost )
3. Demonstrate a sense of the relative magnitudes of numbers.
4. Explore the use of ratios and proportions in a variety of situations. (Proportions 1 , Ratios )
5. Understand and use whole-number percents between 1 and 100 in a variety of situations. (Percentages , Percentage Pictures , Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Simple Interest )
6. Use whole numbers, fractions, and decimals to represent equivalent forms of the same number. (Basic Fraction Simplification , Fraction Simplification , Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line )
7. Develop and apply number theory concepts in problem solving situations.
• Primes, factors, multiples (Prime Numbers , Prime Factoring , Factoring , Divisibility Rules )
• Common multiples, common factors
• Least common multiple, greatest common factor (Greatest Common Factor , Least Common Multiple )
8. Compare and order numbers. (Order Decimals , Compare Mixed Values , Positive Number Line , Fraction Comparison , Compare Decimals , Compare Integers )
4.1.6 B. Numerical Operations
1. Recognize the appropriate use of each arithmetic operation in problem situations. (Fraction Word Problems , Fraction Word Problems 2 , Algebraic Word Problems , Distance, Rate, and Time , Batting Averages )
2. Construct, use, and explain procedures for performing calculations with fractions and decimals with:
• Pencil-and-paper
• Mental math
• Calculator (Money Multiplication , Money Division , Fraction Addition , Fraction Subtraction , Fraction Multiplication , Fraction Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division )
3. Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number. (Long Division , Long Division with Remainders , Small Decimal Division )
4. Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
5. Find squares and cubes of whole numbers. (Perfect Squares )
6. Check the reasonableness of results of computations.
7. Understand and use the various relationships among operations and properties of operations. (Distributive Property , Distributive Property 2 , Basic Distributive Property )
8. Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses. (Using Parentheses , Order Of Operations )
4.1.6 C. Estimation
1. Use a variety of strategies for estimating both quantities and the results of computations. (Rounding Large Numbers , Decimal Rounding to .01 , Decimal Rounding , Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction )
2. Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. (Estimated Multiply Divide Word Problems )
3. Determine the reasonableness of an answer by estimating the result of operations.
4. Determine whether a given estimate is an overestimate or an underestimate.
Geometry and Measurement
4.2.6 A. Geometric Properties1. Understand and apply concepts involving lines and angles.
• Notation for line, ray, angle, line segment
• Properties of parallel, perpendicular, and intersecting lines (Parallel and Perpendicular Lines )
• Sum of the measures of the interior angles of a triangle is 180° (Triangle Angles )
2. Identify, describe, compare, and classify polygons and circles.
• Triangles by angles and sides (Triangle Types )
• Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi (Quadrilateral Types )
• Polygons by number of sides. (Polygon Names )
• Equilateral, equiangular, regular
• All points equidistant from a given point form a circle
3. Identify similar figures. (Congruent And Similar Triangles )
4. Understand and apply the concepts of congruence and symmetry (line and rotational).
5. Compare properties of cylinders, prisms, cones, pyramids, and spheres.
6. Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives.
7. Identify a three-dimensional shape with given projections (top, front and side views).
8. Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).
4.2.6 B. Transforming Shapes
1. Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.
2. Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.
4.2.6 C. Coordinate Geometry
1. Create geometric shapes with specified properties in the first quadrant on a coordinate grid.
4.2.6 D. Units of Measurement
1. Select and use appropriate units to measure angles, area, surface area, and volume.
2. Use a scale to find a distance on a map or a length on a scale drawing.
3. Convert measurement units within a system (e.g., 3 feet = ___ inches). (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion )
4. Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). (Temperature Conversion )
5. Use measurements and estimates to describe and compare phenomena.
4.2.6 E. Measuring Geometric Objects
1. Use a protractor to measure angles.
2. Develop and apply strategies and formulas for finding perimeter and area.
• Triangle, square, rectangle, parallelogram, and trapezoid (Triangle Area , Parallelogram Area , Perimeter , Trapezoids )
• Circumference and area of a circle (Circle Area , Circle Circumference )
3. Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders. (Rectangular Solids , Cylinders )
4. Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa. (Compare Rectangle Area and Perimeter )
5. Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).
Patterns and Algebra
4.3.6 A. Patterns1. Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.
• Descriptions using tables, verbal rules, simple equations, and graphs (Function Tables , Function Tables 2 )
• Formal iterative formulas (e.g., NEXT = NOW * 3)
• Recursive patterns, including Pascal's Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, . . . (where NEXT = NOW + PREVIOUS)
4.3.6 B. Functions and Relationships
1. Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).
4.3.6 C. Modeling
1. Use patterns, relations, and linear functions to model situations.
• Using variables to represent unknown quantities (Algebraic Word Problems , Algebraic Sentences )
• Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities (Algebraic Sentences 2 , Algebraic Sentences )
2. Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.
• Changes over time (Requires outside materials )
• Relations between quantities (Requires outside materials )
• Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly) (Requires outside materials )
4.3.6 D. Procedures
1. Solve simple linear equations with manipulatives and informally.
• Whole-number coefficients only, answers also whole numbers (Linear Equations )
• Variables on one or both sides of equation (Single Variable Equations , Single Variable Equations 2 )
2. Understand and apply the properties of operations and numbers.
• Distributive property (Distributive Property , Distributive Property 2 , Basic Distributive Property )
• The product of a number and its reciprocal is 1
3. Evaluate numerical expressions. (Using Parentheses , Order Of Operations , Variable Substitution )
4. Extend understanding and use of inequality.
• Symbols ( ≥ , ≠ , ≤ ) (Algebraic Sentences 2 )
Data Analysis, Probability, and Discrete Mathematics
4.4.6 A. Data Analysis1. Collect, generate, organize, and display data.
• Data generated from surveys
2. Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.
• Bar graph, line graph, circle graph, table, histogram (Bar Graphs , Line Graphs )
• Range, median, and mean (Mean, Median, Mode )
• Calculators and computers used to record and process information
3. Respond to questions about data, generate their own questions and hypotheses, and formulate strategies for answering their questions and testing their hypotheses.
4.4.6 B. Probability
1. Determine probabilities of events.
• Event, complementary event, probability of an event
• Multiplication rule for probabilities (Probability 2 )
• Probability of certain event is 1 and of impossible event is 0 (Probability )
• Probabilities of event and complementary event add up to 1
2. Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).
• Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked (Probability , Probability 2 )
• Given data obtained experimentally, what is the likely distribution of items in the bag
3. Explore compound events. (Probability 2 )
4. Model situations involving probability using simulations (with spinners, dice) and theoretical models.
5. Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.
4.4.6 C. Discrete Mathematics-Systematic Listing and Counting
1. Solve counting problems and justify that all possibilities have been enumerated without duplication.
• Organized lists, charts, tree diagrams, tables
• Venn diagrams
2. Apply the multiplication principle of counting.
• Simple situations (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).
• Number of ways a specified number of items can be arranged in order (concept of permutation)
• Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21)
3. List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person's hand once).
4.4.6 D. Discrete Mathematics-Vertex-Edge Graphs and Algorithms
1. Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.
2. Analyze vertex-edge graphs and tree diagrams.
• Can a picture or a vertex-edge graph be drawn with a single line? (degree of vertex)
• Can you get from any vertex to any other vertex? (connectedness)
3. Use vertex-edge graphs to find solutions to practical problems.
• Delivery route that stops at specified sites but involves least travel
• Shortest route from one site on a map to another
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