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New Jersey Math Standards - 5th Grade
MathScore aligns to the New Jersey Math Standards for 5th 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
4.1.5 A. Number Sense1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well).
• 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 , Making Change 2 , Unit Cost )
3. Demonstrate a sense of the relative magnitudes of numbers.
4. 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 )
5. Develop and apply number theory concepts in problem solving situations.
• Primes, factors, multiples (Prime Numbers , Prime Factoring , Greatest Common Factor , Factoring , Least Common Multiple )
6. Compare and order numbers. (Order Numbers , Order Large Numbers , Order Decimals , Compare Mixed Values , Positive Number Line , Fraction Comparison , Compare Decimals )
4.1.5 B. Numerical Operations
1. Recognize the appropriate use of each arithmetic operation in problem situations. (Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 , Word Problems With Remainders , Fraction Word Problems , Fraction Word Problems 2 )
2. Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with:
• Pencil-and-paper
• Mental math
• Calculator (Basic Fraction Addition , Fraction Addition , Basic Fraction Subtraction , Fraction Subtraction , Decimal Addition , Decimal Subtraction )
3. Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number. (Long 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. Check the reasonableness of results of computations.
6. Understand and use the various relationships among operations and properties of operations. (Associative Property 2 , Commutative Property 2 )
4.1.5 C. Estimation
1. Use a variety of estimation strategies for both number and computation. (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
4.2.5 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.
• 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). (Congruent And Similar Triangles )
4.2.5 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.
4.2.5 C. Coordinate Geometry
1. Create geometric shapes with specified properties in the first quadrant on a coordinate grid.
4.2.5 D. Units of Measurement
1. Select and use appropriate units to measure angles and area.
2. Convert measurement units within a system (e.g., 3 feet = ___ inches). (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion )
3. Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). (Temperature Conversion )
4. Use measurements and estimates to describe and compare phenomena.
4.2.5 E. Measuring Geometric Objects
1. Use a protractor to measure angles.
2. Develop and apply strategies and formulas for finding perimeter and area.
• Square
• Rectangle
3. Recognize that rectangles with the same perimeter do not necessarily have the same area and vice versa. (Compare Rectangle Area and Perimeter )
4. 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
4.3.5 A. Patterns1. Recognize, describe, extend, and create patterns involving whole numbers.
• Descriptions using tables, verbal rules, simple equations, and graphs (Function Tables , Function Tables 2 )
4.3.5 B. Functions & Relationships
1. Describe arithmetic operations as functions, including combining operations and reversing them.
2. Graph points satisfying a function from T-charts, from verbal rules, and from simple equations.
4.3.5 C. Modeling
1. Use number sentences to model situations.
• Using variables to represent unknown quantities (Algebraic Word Problems )
• Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations (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 )
• Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly) (Requires outside materials )
4.3.5 D. Procedures
1. Solve simple linear equations with manipulatives and informally
• Whole-number coefficients only, answers also whole numbers (Linear Equations )
• Variables on one side of equation (Single Variable Equations )
Data Analysis, Probability, and Discrete Mathematics
4.4.5 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 (Bar Graphs , Line Graphs )
• Range, median, and mean (Mean, Median, Mode )
3. Respond to questions about data and generate their own questions and hypotheses.
4.4.5 B. Probability
1. Determine probabilities of events.
• Event, probability of an event (Probability )
• Probability of certain event is 1 and of impossible event is 0 (Probability )
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 )
• Given data obtained experimentally, what is the likely distribution of items in the bag
3. Model situations involving probability using simulations (with spinners, dice) and theoretical models.
4.4.5 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
2. Explore the multiplication principle of counting in simple situations by representing all possibilities in an organized way (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).
4.4.5 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.
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