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New Jersey Math Standards - 4th Grade
MathScore aligns to the New Jersey Math Standards for 4th 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
4.1.4 A. Number Sense1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well).
• Whole numbers through millions
• Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 16) as part of a whole, as a subset of a set, and as a location on a number line (Fraction Pictures )
• Decimals through hundredths (Making Change 2 , Counting Money )
2. Demonstrate an understanding of place value concepts. (Place Value , Decimal Place Value )
3. Demonstrate a sense of the relative magnitudes of numbers. (Number Comparison , Order Numbers , Order Large Numbers , Order Decimals , Fraction Comparison , Compare Decimals )
4. Understand the various uses of numbers.
• Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor)
5. Use concrete and pictorial models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number.
6. Compare and order numbers. (Number Comparison , Order Numbers , Order Large Numbers , Order Decimals , Fraction Comparison , Compare Decimals )
7. Explore settings that give rise to negative numbers.
• Temperatures below 0°, debts
• Extension of the number line (Compare Integers )
4.1.4 B. Numerical Operations
1. Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.
• Addition and subtraction: joining, separating, comparing (Basic Word Problems )
• Multiplication: repeated addition, area/array (Arithmetic Word Problems , Basic Word Problems 2 , Understanding Multiplication )
• Division: repeated subtraction, sharing (Arithmetic Word Problems , Basic Word Problems 2 , Understanding Division )
2. Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as "skip counting" and "repeated subtraction") and then commit them to memory. (Beginner Multiplication , Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
3. Construct, use, and explain procedures for performing whole number calculations and with:
• Pencil-and-paper
• Mental math
• Calculator (Long Addition , Long Subtraction , Multiplication By One Digit , Long Multiplication , Long Division By One Digit )
4. Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.
• Addition of 3-digit numbers (Long Addition to 1000 , Long Addition , Basic Addition to 1000 )
• Subtraction of 3-digit numbers (Long Subtraction , Basic Subtraction to 1000 , Long Subtraction to 1000 )
• Multiplication of 2-digit numbers (Multiplication By One Digit , Long Multiplication )
• Division of 3-digit numbers by 1-digit numbers (Long Division By One Digit , Division with Remainders )
5. Construct and use procedures for performing decimal addition and subtraction. (Decimal Addition , Decimal Subtraction )
6. Count and perform simple computations with money.
• Standard dollars and cents notation (Making Change , Making Change 2 )
7. Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
8. Check the reasonableness of results of computations.
9. Use concrete models to explore addition and subtraction with fractions. (Requires outside materials )
10. Understand and use the inverse relationships between addition and subtraction and between multiplication and division. (Inverse Equations 1 , Inverse Equations 2 )
4.1.4 C. Estimation
1. Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.
2. Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the results of computations. (Rounding Numbers , Rounding Large Numbers , Decimal Rounding to .01 , Money Addition , Money Subtraction )
3. Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. (Estimated Multiply Divide Word Problems )
4. Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.
Geometry and Measurement
4.2.4 A. Geometric Properties1. Identify and describe spatial relationships of two or more objects in space.
• Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)
• Relative shapes and sizes
• Shadows (projections) of everyday objects
2. Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.
• Vertex, edge, face, side, angle
• 3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid
• 2D figures - square, rectangle, circle, triangle, quadrilateral, pentagon, hexagon, octagon (Geometric Shapes , Polygon Names )
• Inclusive relationships - squares are rectangles, cubes are rectangular prisms
3. Identify and describe relationships among two-dimensional shapes.
• Congruence
• Lines of symmetry
4. Understand and apply concepts involving lines, angles, and circles.
• Point, line, line segment, endpoint
• Parallel, perpendicular (Parallel and Perpendicular Lines )
• Angles - acute, right, obtuse
• Circles - diameter, radius, center (Circle Measurements )
5. Recognize, describe, extend, and create space-filling patterns.
4.2.4 B. Transforming Shapes
1. Use simple shapes to cover an area (tessellations).
2. Describe and use geometric transformations (slide, flip, turn).
3. Investigate the occurrence of geometry in nature and art.
4.2.4 C. Coordinate Geometry
1. Locate and name points in the first quadrant on a coordinate grid.
2. Use coordinates to give or follow directions from one point to another on a map or grid.
4.2.4 D. Units of Measurement
1. Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.
2. Select and use appropriate standard units of measure and measurement tools to solve real- life problems
• Length - fractions of an inch (1/8, 1/4, 1/2), mile, decimeter, kilometer
• Area - square inch, square centimeter
• Volume - cubic inch, cubic centimeter
• Weight - ounce
• Capacity - fluid ounce, cup, gallon, milliliter
3. Develop and use personal referents to approximate standard units of measure (e.g., a common paper clip is about an inch long).
4. Incorporate estimation in measurement activities (e.g., estimate before measuring).
5. Solve problems involving elapsed time. (Time Intervals )
4.2.4 E. Measuring Geometric Objects
1. Determine the area of simple two-dimensional shapes on a square grid.
2. Distinguish between perimeter and area and use each appropriately in problem-solving situations. (Perimeter and Area Word Problems )
3. Measure and compare the volume of three-dimensional objects using materials such as rice or cubes. (Requires outside materials )
Patterns and Algebra
4.3.4 A. Patterns1. Recognize, describe, extend, and create patterns.
• Descriptions using words, number sentences/expressions, graphs, tables, variables (e.g., shape, blank, or letter) (Function Tables , Function Tables 2 )
• Sequences that stop or that continue infinitely
• Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11, . . . or 800, 400, 200, . . .) (Patterns: Numbers )
• Sequences can often be extended in more than one way (e.g., the next term after 1, 2, 4, . . . could be 8, or 7, or … )
4.3.4 B. Functions and Relationships
1. Use concrete and pictorial models to explore the basic concept of a function.
• Input/output tables, T-charts
• Combining two function machines
• Reversing a function machine
4.3.4 C. Modeling
1. Recognize and describe change in quantities.
• Graphs representing change over time (e.g., temperature, height) (Line Graphs )
• How change in one physical quantity can produce a corresponding change in another (e.g., pitch of a sound depends on the rate of vibration)
2. Construct and solve simple open sentences involving any one operation (e.g., 3 x 6 = __, n = 15 ÷ 3, 3 x __ = 0, 16 - c = 7). (Missing Factor , Missing Term , Missing Operator , Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 )
4.3.4 D. Procedures
1. Understand, name, and apply the properties of operations and numbers.
• Commutative (e.g., 3 x 7 = 7 x 3) (Commutative Property 2 )
• Identity element for multiplication is 1 (e.g., 1 x 8 = 8)
• Associative (e.g., 2 x 4 x 25 can be found by first multiplying either 2 x 4 or 4 x 25) (Associative Property 2 )
• Division by zero is undefined
• Any number multiplied by zero is zero.
2. Understand and use the concepts of equals, less than, and greater than in simple number sentences.
• Symbols ( = , < , > ) (Compare Expressions )
Data Analysis, Probability, and Discrete Mathematics
4.4.4 A. Data Analysis1. Collect, generate, organize, and display data in response to questions, claims, or curiosity.
• Data collected from the school environment
2. Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.
• Pictograph, bar graph, line plot, line graph, table (Tally and Pictographs , Bar Graphs , Line Graphs )
• Average (mean), most frequent (mode), middle term (median) (Mean, Median, Mode )
4.4.4 B. Probability
1. Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability.
• Likely, unlikely, certain, impossible, improbable, fair, unfair
• More likely, less likely, equally likely
• Probability of tossing "heads" does not depend on outcomes of previous tosses
2. Determine probabilities of simple events based on equally likely outcomes and express them as fractions. (Probability )
3. Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color).
• What students think will happen (intuitive)
• Collect data and use that data to predict the probability (experimental)
• Analyze all possible outcomes to find the probability (theoretical)
4.4.4 C. Discrete Mathematics-Systematic Listing and Counting
1. Represent and classify data according to attributes, such as shape or color, and relationships.
• Venn diagrams
• Numerical and alphabetical order
2. Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation.
• Organized lists, charts, tree diagrams
• Dividing into categories (e.g., to find the total number of rectangles in a grid, find the number of rectangles of each size and add the results)
4.4.4 D. Discrete Mathematics-Vertex-Edge Graphs and Algorithms
1. Follow, devise, and describe practical sets of directions (e.g., to add two 2-digit numbers).
2. Play two-person games and devise strategies for winning the games (e.g., "make 5" where players alternately add 1 or 2 and the person who reaches 5, or another designated number, is the winner).
3. Explore vertex-edge graphs and tree diagrams.
• Vertex, edge, neighboring/adjacent, number of neighbors
• Path, circuit (i.e., path that ends at its starting point)
4. Find the smallest number of colors needed to color a map or a graph.
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