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TIMSS 2019 Mathematics Framework

Mary Lindquist, Ray Philpot, Ina V.S. Mullis, and Kerry E. Cotter

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Mathematics Content Domains–Fourth Grade

Exhibit 1.2 shows the TIMSS Mathematics—Fourth Grade content domains and the target percentages of assessment score points devoted to each. Each content domain consists of topic areas, and each topic area in turn includes several topics. Across the fourth grade mathematics assessment, each topic receives approximately equal weight.

Exhibit 1.2: Target Percentages of the TIMSS 2019 Mathematics Assessment Devoted to Content Domains at the Fourth Grade

Fourth Grade Content Domains Percentages
Number 50%
Measurement and Geometry 30%
Data 20%

Number

Number provides the foundation of mathematics in primary school. The number content domain consists of three topic areas. The fifty percent of the assessment devoted to number is apportioned as follows:

  • Whole numbers (25%)
  • Expressions, simple equations, and relationships (15%)
  • Fractions and decimals (10%)

Whole numbers are the predominant component of the number domain and students should be able to compute with whole numbers of reasonable size as well as use computation to solve problems. Prealgebra concepts also are part of the TIMSS assessment at the fourth grade, including understanding the concept of variable (unknowns) in simple equations, and initial understandings of relationships between quantities. However, because objects and quantities often do not come in whole numbers, it is also important for students to understand fractions and decimals. Students should be able to compare, add, and subtract familiar fractions and decimals to solve problems.

Whole Numbers

  1. Demonstrate knowledge of place value (2-digit to 6-digit numbers); represent whole numbers with words, diagrams, number lines, or symbols; order numbers.
  2. Add and subtract (up to 4-digit numbers), including computation in simple contextual problems.
  3. Multiply (up to 3-digit by 1-digit and 2-digit by 2-digit numbers) and divide (up to 3-digit by 1-digit numbers), including computation in simple contextual problems.
  4. Solve problems involving odd and even numbers, multiples and factors of numbers, rounding numbers (up to the nearest ten thousand), and making estimates.
  5. Combine two or more properties of numbers or operations to solve problems in context.

Expressions, Simple Equations, and Relationships

  1. Find the missing number or operation in a number sentence (e.g., 17 + w = 29).
  2. Identify or write expressions or number sentences to represent problem situations that may involve unknowns.
  3. Identify and use relationships in a well-defined pattern (e.g., describe the relationship between adjacent terms and generate pairs of whole numbers given a rule).

Fractions and Decimals

  1. Recognize fractions as parts of wholes or collections; represent fractions using words, numbers, or models; compare and order simple fractions; add and subtract simple fractions, including those set in problem situations. (Fractions may have denominators of 2, 3, 4, 5, 6, 8, 10, 12, or 100.)
  2. Demonstrate knowledge of decimal place value including representing decimals using words, numbers, or models; compare, order, and round decimals; add and subtract decimals, including those set in problem situations. (Decimals may have one or two decimal places, allowing for computations with money.)

Measurement and Geometry

We are surrounded by objects of different shapes and sizes, and geometry helps us visualize and understand the relationships between shapes and sizes. Measurement is the process of quantifying attributes of objects and phenomena (e.g., length and time).

The two topic areas in measurement and geometry are as follows:

  • Measurement (15%)
  • Geometry (15%)

At the fourth grade, students should be able to use a ruler to measure length; solve problems involving length, mass, capacity, and time; calculate areas and perimeters of simple polygons; and use cubes to determine volumes. Students should be able to identify the properties and characteristics of lines, angles, and a variety of two- and three-dimensional shapes. Spatial sense is integral to the study of geometry, and students will be asked to describe and draw a variety of geometric figures. They also should be able to analyze geometric relationships and use these relationships to solve problems.

Measurement

  1. Measure and estimate lengths (millimeters, centimeters, meters, kilometers); solve problems involving lengths.
  2. Solve problems involving mass (gram and kilogram), volume (milliliter and liter), and time (minutes and hours); identify appropriate types and sizes of units and read scales.
  3. Solve problems involving perimeters of polygons, areas of rectangles, areas of shapes covered with squares or partial squares, and volumes filled with cubes.

Geometry

  1. Identify and draw parallel and perpendicular lines; identify and draw right angles and angles smaller or larger than a right angle; compare angles by size.
  2. Use elementary properties, including line and rotational symmetry, to describe, compare, and create common two-dimensional shapes (circles, triangles, quadrilaterals, and other polygons).
  3. Use elementary properties to describe and compare three-dimensional shapes (cubes, rectangular solids, cones, cylinders, and spheres) and relate these with their two-dimensional representations.

Data

The explosion of data in today’s information society has resulted in a daily bombardment of visual displays of quantitative information. Often the Internet, newspapers, magazines, textbooks, reference books, and articles have data represented in charts, tables, and graphs. Students need to understand that graphs and charts help organize information or categories and provide a way to compare data.

The data content domain consists of two topic areas:

  • Reading, interpreting, and representing data (15%)
  • Using data to solve problems (5%)

At the fourth grade, students should be able to read and recognize various forms of data displays. Given a simple question, students should be able to collect, organize, and represent the data in graphs and charts to address the question. Students should be able to use data from one or more sources to solve problems.

Reading, Interpreting, and Representing Data

  1. Read and interpret data from tables, pictographs, bar graphs, line graphs, and pie charts.
  2. Organize and represent data to help answer questions.

Using Data to Solve Problems

  1. Use data to answer questions that go beyond directly reading data displays (e.g., solve problems and perform computations using data, combine data from two or more sources, draw conclusions based on data).