Skip to Content.
Link back to Home.
Home  |   Directories  |   Data  |   Reports  |   Programs  |   Online Services   |   Contact Us
Main content begins below.
Numbers & Operations | Algebra | Geometry | Measurement | Data Analysis & Probablity Print version

Fourth Grade

Number and Operation

Content Standard 1.0 The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Learning Expectations:

  • 1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
  • 1.2 Understand meanings of operations and how they relate to one another.
  • 1.3 Solve problems, compute fluently, and make reasonable estimates.

Accomplishments

4.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

  1. read and write numbers from hundredths to hundred-thousands;
  2. recognize the place value of a given digit from hundredths to hundred-thousands;
  3. compare and order whole numbers using the appropriate symbols (i.e., >, <, = );
  4. model fractions as parts of unit wholes, as part of a set, as locations on number lines, and as divisions of whole numbers;
  5. recognize and generate equivalent forms of whole numbers and commonly used fractions and decimals;
  6. use models to compare and order commonly used fractions;
  7. use concrete and pictorial representations to compare decimals;
  8. use various models to represent, order, and compare whole numbers and commonly used fractions and mixed numbers (e.g., number lines, base ten blocks, Venn diagrams, hundreds boards);
  9. communicate and use mathematical language and symbols correctly.

4.1.2 Understand meanings of operations and how they relate to one another.

  1. explain the relationship between addition and subtraction;
  2. explain the relationship between multiplication and division;
  3. communicate the effects of addition, subtraction, multiplication, and division on size and order of numbers.

4.1.3 Solve problems, compute fluently, and make reasonable estimates.

  1. use strategies to estimate the results of whole-number computations;
  2. explain the reasonableness of results;
  3. add and subtract fractions with like denominators;
  4. multiply and divide efficiently and accurately with single-digit whole numbers;
  5. add, subtract, and multiply decimals (includes monetary units);
  6. select appropriate methods and tools for computing with whole numbers (e.g., mental computation, estimation, calculators, paper and pencil, guess and check);
  7. solve real-world problems involving one-step addition, subtraction, and multiplication;
  8. identify missing information and/or too much information in real-world problems;
  9. apply logical reasoning to solve real-world problems;
  10. select the appropriate computational and operational method to solve problems;
  11. solve real-world problems using whole numbers, fractions, and decimals.

Fourth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

  • 4.1.spi.1. represent whole numbers to 9999;
  • 4.1.spi.2. compare and order whole numbers to 9999 using the appropriate symbol (<, >, =);
  • 4.1.spi.3. solve one-step real-world problems involving addition or subtraction of whole numbers.

at Level 2, the student is able to

  • 4.1.spi.4. read and write numbers from hundred-thousands to hundredths;
  • 4.1.spi.5. identify the place value of a given digit from hundred-thousands to hundredths;
  • 4.1.spi.6. identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as divisions of whole numbers;
  • 4.1.spi.7. multiply efficiently and accurately with single-digit whole numbers;
  • 4.1.spi.8. use estimation to select a reasonable solution to a whole number computation involving addition, subtraction, or multiplication;
  • 4.1.spi.9. add and subtract decimals (includes monetary units);
  • 4.1.spi.10. represent whole numbers up to 10,000 in expanded form ( 1000’s + 100’s + 10’s + 1’s);
  • 4.1.spi.11. add and subtract fractions with like denominators.

at Level 3, the student is able to

  • 4.1.spi.12. represent numbers as both improper fractions and mixed numbers;
  • 4.1.spi.13. generate equivalent forms of whole numbers, commonly used fractions, and decimals;
  • 4.1.spi.14. solve one-step real-world problems involving addition, subtraction, or multiplication of whole numbers and/or decimals.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

  • 4.1.tpi.1. explain the relationship between of addition and subtraction;
  • 4.1.tpi.2. explain the relationship between multiplication and addition;
  • 4.1.tpi.3. explain the relationship between multiplication and division.

at Level 2, the student is able to

  • 4.1.tpi.4. use concrete and pictorial representations to compare decimals;
  • 4.1.tpi.5. use various models to represent, order, and compare whole numbers and commonly used fractions and mixed numbers;
  • 4.1.tpi.6 identify missing information or too much information in real-world problems
  • 4.1.tpi.7. communicate and use mathematical symbols correctly.

at Level 3, the student is able to

  • 4.1.tpi.8. select appropriate methods and tools for computing with whole numbers;
  • 4.1.tpi.9. communicate the effects of addition, subtraction, multiplication, and division;
  • 4.1.tpi.10. select the appropriate computational and operational methods to solve problems.

Algebra

Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Learning Expectations:

  • 2.1 Understand patterns, relations, and functions.
  • 2.2 Represent and analyze mathematical situations and structures using algebraic symbols.
  • 2.3 Illustrate general properties of operations.
  • 2.4 Analyze change in various contexts.

Accomplishments

4.2.1 Understand patterns, relations, and functions.

  1. generalize and extend geometric and numerical patterns;
  2. represent and analyze patterns and functions using words, tables, and graphs;
  3. identify and describe a function rule.

4.2.2 Represent and analyze mathematical situations and structures using algebraic symbols.

  1. interpret and solve open sentences that involve addition, subtraction, multiplication, and division;
  2. represent the idea of a variable as an unknown quantity using a letter or a symbol;
  3. demonstrate an understanding that an equation is a number sentence stating two quantities are equal.

4.2.3 Illustrate general properties of operations.

  1. apply commutative, associative, zero, and identity properties.

4.2.4 Analyze change in various contexts.

  1. investigate how a change in one variable relates to a change in a second variable.

Fourth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

4.2.spi.1. solve open sentences involving addition and subtraction.

at Level 2, the student is able to

  • 4.2.spi.2. extend numerical and geometric patterns;
  • 4.2.spi.3. determine the function rule for data in a function table
  • 4.2.spi.4. connect open sentences to real-world situations;
  • 4.2.spi.5. solve open sentences involving multiplication and division.

at Level 3, the student is able to

4.2.spi.6. apply basic function rules.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

4.2.tpi.1. apply commutative, associate, zero, and identify properties

at Level 2, the student is able to

  • 4.2.tpi.2. generalize geometric and numerical patterns.5.2.tpi.2. represent and analyze patterns and functions using words, tables, and graphs;
  • 4.2.tpi.3. demonstrate an understanding that an equation is a number sentence stating two quantities are equal;
  • 4.2.tpi.4 identify and describe a function rule;
  • 4.2.tpi.5 investigate how a change in one variable relates to a change in a second variable.

at Level 3, the student is able to

  • 4.2.tpi.6. demonstrate understanding that an equation is a number sentence stating two quantities are equal;
  • 4.2.tpi.7. represent the idea of a variable as an unknown quantity using a letter or a symbol.

Geometry

Content Standard 3.0 The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

Learning Expectations:

  • 3.1 Analyze characteristics and properties of two- and three-dimensional shapes.
  • 3.2 Specify locations and describe spatial relationships using coordinate geometry.
  • 3.3 Apply transformations and use symmetry to analyze mathematical situations.
  • 3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.

Accomplishments

4.3.1 Analyze characteristics and properties of two- and three-dimensional shapes.

  1. identify, compare, and analyze attributes of two- and three-dimensional shapes;
  2. develop and use mathematical language to describe the attributes of geometric figures;
  3. draw points, lines, line segments, rays, and angles;
  4. describe characteristics of lines and angles (e.g., parallel, perpendicular, intersecting, right, acute, obtuse);
  5. describe and compare properties of two- and three-dimensional geometric figures;
  6. investigate and describe the results of subdividing and combining two-dimensional geometric figures;
  7. recognize congruent geometric figures;
  8. draw lines of symmetry for two-dimensional geometric figures.

4.3.2 Specify locations and describe spatial relationships using coordinate geometry.

  1. use appropriate mathematical language to find and specify points on a grid using whole number coordinates.

4.3.3 Apply transformations and use symmetry to analyze mathematical situations.

  1. investigate, predict, and describe the results of transformations of two-dimensional geometric figures (i.e., slides, flips, turns);
  2. describe a motion that will show that two shapes are congruent.

4.3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.

  1. construct and draw two- and three-dimensional geometric figures;
  2. create and describe mental images of objects, patterns, and paths;
  3. use geometric models to solve real-world problems.

Fourth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

4.3.spi.1. identify points, lines, and rays.

at Level 2, the student is able to

  • 4.3.spi.2. recognize congruent geometric figures;
  • 4.3.spi.3. identify lines of symmetry for two-dimensional geometric figures;
  • 4.3.spi.4. identify the result of a transformation (flip or slide) that has been applied to a simple two-dimensional geometric shape.

at Level 3, the student is able to

  • 4.3.spi.5. identify two- or three-dimensional shapes given defining attributes;
  • 4.3.spi.6. locate and specify points in Quadrant I of a coordinate system.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

  • 4.3.tpi.1. draw and describe lines, line segments, rays, and angles;
  • 4.3.tpi.2. draw lines of symmetry for two-dimensional geometric figures.

at Level 2, the student is able to

  • 4.3.tpi.3. develop and use mathematical language to describe the attributes of geometric figures;
  • 4.3.tpi.4. describe characteristics of lines, rays, and angles;
  • 4.3.tpi.5. describe and compare properties of two- and three-dimensional geometric figures;
  • 4.3.tpi.6. construct or draw the mirror image of a two-dimensional geometric figure or pattern.

at Level 3, the student is able to

  • 4.3.tpi.7. investigate and describe the results of subdividing and combining two-dimensional geometric figures;
  • 4.3.tpi.8. identify, compare, and analyze attributes of two- and three-dimensional shapes;
  • 4.3.tpi.9. describe a motion that will show that two shapes are congruent.

Measurement

Content Standard 4.0 The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

Learning Expectations:

  • 4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.
  • 4.2 Apply appropriate techniques, tools, and formulas to determine measurements.

Accomplishments

4.4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.

  1. demonstrate understanding of the concepts of length, perimeter, area, weight, capacity, volume, time, and angle measure;
  2. apply appropriate estimation strategies using standard units of measure;
  3. demonstrate understanding that measurements are approximations;
  4. demonstrate understanding of the relationships among the units within a system of linear measurement;
  5. explore perimeter and area using a variety of models (e.g., geoboards, graph paper).

4.4.2 Apply appropriate techniques, tools, and formulas to determine measurements.

  1. select and use tools to measure weight and volume;
  2. measure length to the nearest 1/4 inch;
  3. tell time to the nearest minute;
  4. read and record temperature using Fahrenheit and Celsius scales;
  5. develop strategies for estimating the perimeters and areas of geometric figures;
  6. apply the formula for finding the area of a rectangle;
  7. solve real-world problems involving measurement and elapsed time to the quarter hour.

Fourth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

4.4.spi.1. read temperature using Fahrenheit and Celsius scales.

at Level 2, the student is able to

  • 4.4.spi.2. find the perimeter of rectangles;
  • 4.4.spi.3. tell time on the minute;
  • 4.4.spi.4. measure length to the nearest ¼ inch or nearest centimeter;
  • 4.4.spi.5. use estimation to determine if a length or volume measurement is reasonable;
  • 4.4.spi.6. solve real-world problems involving addition and subtraction of measurements;
  • 4.4.spi.7. solve real-world problems involving elapsed time to the quarter-hour.

at Level 3, the student is able to

  • 4.4.spi.8. apply the formula for finding area of a rectangle;
  • 4.4.spi.9. select the appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

4.4.tpi.1. select and use appropriate benchmarks to estimate length measurements.

at Level 2, the student is able to

  • 4.4.tpi.2. demonstrate understanding of the concepts of length, perimeter, area, weight, capacity, volume, time, and angle measure;
  • 4.4.tpi.3. develop strategies for estimating the perimeters and areas of geometric figures;
  • 4.4.tpi.4. communicate an understanding of the relationships among the units within a system of linear measurement.

at Level 3, the student is able to

4.4.tpi.5. explore how perimeter and area of a rectangle change when its dimensions change.

Data Analysis & Probability

Content Standard 5.0 The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Learning Expectations:

  • 5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.
  • 5.2 Select and use appropriate statistical methods to analyze data.
  • 5.3 Develop and evaluate inferences and predictions that are based on data.
  • 5.4 Understand and apply basic concepts of probability.

Accomplishments

4.5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

  1. collect data using observations, surveys, and experiments;
  2. understand how data-collection methods affect the nature of the data set;
  3. represent data using tables, pictographs, line graphs, and bar graphs;
  4. interpret data displayed in tables, pictographs, line graphs, and bar graphs;
  5. evaluate how well various representations show the collected data.

4.5.2 Select and use appropriate statistical methods to analyze data.

  1. explore measures of central tendency (i.e., mean, median, mode).

4.5.3 Make and justify predictions based on data.

  1. make predictions based on data;
  2. design investigations to address a question.

4.5.4 Understand and apply basic concepts of probability.

  1. describe the likelihood or chance of events as certain, possible, or impossible;
  2. explain whether an event is likely or unlikely;
  3. predict the probability of outcomes of simple experiments.

Fourth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

4.5.spi.1. interpret data displayed in bar graphs and pictographs.

at Level 2, the student is able to

  • 4.5.spi.2. connect data in tables to pictographs, line graphs, or bar graphs;
  • 4.5.spi.3. determine the most likely, least likely, or equally likely outcomes in simple experiments;
  • 4.5.spi.4. select all possible outcomes of a simple experiment (i.e., spinner, coin toss, number or color cube).

at Level 3, the student is able to

4.5.spi.5. determine the median of a data set;

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

4.5.tpi.1. collect data using observations, surveys, and experiments;

at Level 2, the student is able to

  • 4.5.tpi.2. construct bar graphs and line graphs from data in a table;
  • 4.5.tpi.3. evaluate how well various representations show the collected data.

at Level 3, the student is able to

  • 4.5.tpi.4. understand how data collection methods affect the nature of the data set;
  • 4.5.tpi.5. design investigations to address a question;
  • 4.5.tpi.6. explain differences in measures of center (mean, median, mode).

Tennessee.gov  |   Search Tennessee.gov  |  A to Z Directory  |  Policies  |  Survey  |  Help  |  Site Map  |  Contact

Link to contact information.