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## New Jersey Math Standards - 3rd Grade

MathScore aligns to the New Jersey Math Standards for 3rd 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

4.1.3 A. Number Sense
1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well).
• Whole numbers through hundred thousands
• Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as (Fraction Pictures )
2. Demonstrate an understanding of whole number place value concepts. (Place Value )
3. Identify whether any whole number is odd or even. (Odd or Even )
4. Explore the extension of the place value system to decimals through hundredths. (Decimal Place Value )
5. Understand the various uses of numbers.
• Counting, measuring, labeling (e.g., numbers on baseball uniforms)
6. Compare and order numbers. (Number Comparison , Order Numbers to 1000 , Order Numbers , Fraction Comparison , Basic Fraction Comparison )
4.1.3 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
• Multiplication: repeated addition, area/array (Understanding Multiplication )
• Division: repeated subtraction, sharing (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"). (Skip Counting , Beginner Multiplication , Understanding Multiplication )
3. Construct, use, and explain procedures for performing whole number calculations with:
• Pencil-and-paper
• Mental math
• Calculator (Long Addition to 1000 , Long Addition , Long Subtraction , Multiplication By One Digit , Basic Addition to 1000 , Basic Subtraction to 1000 , Long Subtraction to 1000 )
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 by 1-digit numbers (Multiplication By One Digit )
5. Count and perform simple computations with money.
• Cents notation (¢) (Making Change 2 , Counting Money )
6. Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
7. Check the reasonableness of results of computations.
4.1.3 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 result of computations. (Rounding Numbers , Estimated Addition , Estimated 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

4.2.3 A. Geometric Properties
1. 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
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, pentagon, hexagon, octagon (Geometric Shapes , Polygon Names )
3. Identify and describe relationships among two-dimensional shapes.
• Same size, same shape
• Lines of symmetry
4. Understand and apply concepts involving lines, angles, and circles.
• Line, line segment, endpoint
5. Recognize, describe, extend, and create space-filling patterns.
4.2.3 B. Transforming Shapes
1. Describe and use geometric transformations (slide, flip, turn).
2. Investigate the occurrence of geometry in nature and art.
4.2.3 C. Coordinate Geometry
1. Locate and name points in the first quadrant on a coordinate grid.
4.2.3 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 (1/4, 1/2), mile, decimeter, kilometer
• Area - square inch, square centimeter
• Weight - ounce
• Capacity - fluid ounce, cup, gallon, milliliter
3. Incorporate estimation in measurement activities (e.g., estimate before measuring).
4.2.3 E. Measuring Geometric Objects
1. Determine the area of simple two-dimensional shapes on a square grid.
2. Determine the perimeter of simple shapes by measuring all of the sides. (Perimeter )
3. Measure and compare the volume of three-dimensional objects using materials such as rice or cubes. (Requires outside materials )

## Patterns and Algebra

4.3.3 A. Patterns
1. Recognize, describe, extend, and create patterns.
• Descriptions using words and number sentences/expressions (Function Tables , Function Tables 2 )
• 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 )
4.3.3 B. Functions and Relationships
1. Use concrete and pictorial models to explore the basic concept of a function.
• Input/output tables, T-charts (Function Tables , Function Tables 2 )
4.3.3 C. Modeling
1. Recognize and describe change in quantities.
• Graphs representing change over time (e.g., temperature, height) (Line Graphs )
2. Construct and solve simple open sentences involving addition or subtraction (e.g., 3 + 6 = __, n = 15 - 3, 3 + __ = 3, 16 - c = 7). (Missing Term , Basic Word Problems )
4.3.3 D. Procedures
1. Understand 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)
• Any number multiplied by zero is zero
2. Understand and use the concepts of equals, less than, and greater than to describe relations between numbers.
• Symbols ( = , < , > ) (Number Comparison , Order Numbers to 1000 , Order Numbers )

## Data Analysis, Probability, and Discrete Mathematics

4.4.3 A. Data Analysis
1. Collect, generate, organize, and display data in response to questions, claims, or curiosity.
• Data collected from the classroom environment
2. Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.
• Pictograph, bar graph, table (Tally and Pictographs , Bar Graphs )
4.4.3 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
• More likely, less likely, equally likely
2. 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) (Probability )
• Collect data and use that data to predict the probability (experimental)
4.4.3 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
4.4.3 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. Explore vertex-edge graphs
• Vertex, edge
• Path
3. Find the smallest number of colors needed to color a map.

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