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TIMSS 2019 Mathematics Framework

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

Download TIMSS 2019 Mathematics Framework (pdf)

Mathematics Content Domains–Eighth Grade

Exhibit 1.3 shows the TIMSS Mathematics—Eighth 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 eighth grade mathematics assessment, each topic receives approximately equal weight.

Exhibit 1.3: Target Percentages of the TIMSS 2019 Mathematics Assessment Devoted to Content Domains at the Eighth Grade

Eighth Grade Content Domains Percentages
Number 30%
Algebra 30%
Geometry 20%
Data and Probability 20%

Number

At the eighth grade, the thirty percent of the assessment devoted to number consists of three topic areas:

  • Integers (10%)
  • Fractions and decimals (10%)
  • Ratio, proportion, and percent (10%)

Building on the number content domain at the fourth grade, eighth grade students should have developed proficiency with more advanced whole number concepts and procedures as well as extended their mathematical understanding of rational numbers (integers, fractions, and decimals). Students also should understand and be able to compute with integers. Fractions and decimals are an important part of daily life and being able to compute with them requires an understanding of the quantities the symbols represent. Students should understand that fractions and decimals are single entities like whole numbers. A single rational number can be represented with many different written symbols, and students need to be able to recognize the distinctions among interpretations of rational numbers, convert between them, and reason with them. Students should be able to solve problems involving ratios, proportions, and percents.

Integers

  1. Demonstrate understanding of properties of numbers and operations; find and use multiples and factors, identify prime numbers, evaluate positive integer powers of numbers, evaluate square roots of perfect squares up to 144, and solve problems involving square roots of whole numbers.
  2. Compute and solve problems with positive and negative numbers, including through movement on the number line or various models (e.g., losses and gains, thermometers).

Fractions and Decimals

  1. Using various models and representations, compare and order fractions and decimals, and identify equivalent fractions and decimals.
  2. Compute with fractions and decimals, including those set in problem situations.

Ratio, Proportion, and Percent

  1. Identify and find equivalent ratios; model a given situation by using a ratio; divide a quantity according to a given ratio.
  2. Solve problems involving proportions or percents, including converting between percents and fractions or decimals.

Algebra

The thirty percent of the assessment devoted to algebra is comprised of two topic areas:

  • Expressions, operations, and equations (20%)
  • Relationships and functions (10%)

Patterns and relationships are pervasive in the world around us and algebra enables us to express these mathematically. Students should be able to solve real world problems using algebraic models and explain relationships involving algebraic concepts. They need to understand that when there is a formula involving two quantities, if they know one quantity, they can find the other either algebraically or by substitution. This conceptual understanding can extend to linear equations for calculations about things that expand at constant rates (e.g., slope). Functions can be used to describe what will happen to a variable when a related variable changes.

Expressions, Operations, and Equations

  1. Find the value of an expression or a formula given values of the variables.
  2. Simplify algebraic expressions involving sums, products, and powers; compare expressions to determine if they are equivalent.
  3. Write expressions, equations, or inequalities to represent problem situations.
  4. Solve linear equations, linear inequalities, and simultaneous linear equations in two variables, including those that model real life situations.

Relationships and Functions

  1. Interpret, relate and generate representations of linear functions in tables, graphs, or words; identify properties of linear functions including slope and intercepts.
  2. Interpret, relate and generate representations of simple non-linear functions (e.g., quadratic) in tables, graphs, or words; generalize pattern relationships in a sequence using numbers, words, or algebraic expressions.

Geometry

Extending the understanding of shapes and measures assessed at the fourth grade, eighth grade students should be able to analyze the properties of a variety of two- and three-dimensional figures and calculate perimeters, areas, and volumes. They should be able to solve problems and provide explanations based on geometric relationships, such as congruence, similarity, and the Pythagorean theorem.

The geometry content domain at the eighth grade consists of one topic area:

  • Geometric shapes and measurements (20%)

Geometric Shapes and Measurements

At eighth grade, geometric shapes include circles; scalene, isosceles, equilateral, and right-angled triangles; trapezoids, parallelograms, rectangles, rhombuses, and other quadrilaterals; as well as other polygons including pentagons, hexagons, octagons, and decagons. They also include three-dimensional shapes—prisms, pyramids, cones, cylinders, and spheres. One- and two-dimensional figures can be presented in the Cartesian plane.

  1. Identify and draw types of angles and pairs of lines and use the relationships between angles on lines and in geometric figures to solve problems, including those involving the measures of angles and line segments; solve problems involving points in the Cartesian plane.
  2. Identify two-dimensional shapes and use their geometric properties to solve problems, including those involving perimeter, circumference, area, and the Pythagorean Theorem.
  3. Recognize and draw images of geometric transformations (translations, reflections, and rotations) in the plane; identify congruent and similar triangles and rectangles and solve related problems.
  4. Identify three-dimensional shapes and use their geometric properties to solve problems, including those involving surface area and volume; relate three-dimensional shapes with their two-dimensional representations.

Data and Probability

Increasingly, the more traditional forms of data display (e.g., bar graphs, line graphs, pie graphs, pictographs) are being supplemented by an array of new graphic forms (e.g., infographics). By the eighth grade, students should to be able to read and extract the important meaning from a variety of visual displays. It is also important for eighth grade students to be familiar with the statistics underlying data distributions and how these relate to the shape of data graphs. Students should know how to collect, organize, and represent data. Students also should have an initial grasp of some concepts related to probability.

The data and probability content domain contains two topic areas:

  • Data (15%)
  • Probability (5%)

Data

  1. Read and interpret data from one or more sources to solve problems (e.g., interpolate and extrapolate, make comparisons, draw conclusions).
  2. Identify appropriate procedures for collecting data; organize and represent data to help answer questions.
  3. Calculate, use, or interpret statistics (i.e., mean, median, mode, range) summarizing data distributions; recognize the effect of spread and outliers.

Probability

  1. For simple and compound events: a) determine theoretical probability (based on equally likely outcomes, e.g., rolling a fair die) or b) estimate the empirical probability (based on experimental outcomes).

Calculator Use at the Eighth Grade

Continuing the practice of previous TIMSS assessments, at the fourth grade students will not be permitted to use calculators. This includes both paperTIMSS and eTIMSS. At the eighth grade, students will be permitted to use calculators, although the mathematics items are developed to be calculator neutral−do not advantage or disadvantage students whether or not they have calculators. In paperTIMSS, consistent with past TIMSS assessments, students at the eighth grade may bring their own calculators to the assessment. In eTIMSS, students at the eighth grade will have access to a calculator provided as part of the on-screen interface and will not be permitted to bring their own calculators. The on-screen calculator includes the four basic functions (+ , − , ×, ÷) and a square root key. The eventual transition to eTIMSS will result in calculators being standardized.