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United States

The Mathematics Curriculum in Primary and Lower Secondary Grades

In the United States, the curriculum frameworks of individual states vary. Mathematics standards across the states increasingly emphasize learning mathematical content in the context of real-world situations while also focusing on computational thinking and mathematical fluency to solve problems and foster a deeper understanding.21

Many state curricula are moving toward a more unified approach. The Common Core State Standards for Mathematics (CCSSM)f were developed in order to bring greater focus and coherence to the teaching of mathematics. While not all states have adopted the CCSSM, and they are only guidelines for states in the development of their curriculum frameworks, they have widely influenced mathematics education in the United States. They describe knowledge and skills that mathematics educators at all levels should seek to develop in their students. In addition, the Council of Chief State School Officers has developed a list of tools, resources, and practices to help states implement Common Core State Standards.22

Exhibits 2 and 3 (on the following pages) summarize the topics that were commonly included in states’ mathematics curricula during the 2014–2015 school year. The mathematics topics in the exhibits are based on the TIMSS 2015 Curriculum Questionnaires, the curriculum frameworks for five of the most populous states—California, Florida, Massachusetts, New York, and Texas—and the CCSSM.f Exhibit 2 focuses on upper elementary school (the Grades 3 to 5 band), and Exhibit 3 focuses on middle school (the Grades 6 to 8 band) in order to cover the mathematics topics that are generally included in the curriculum frameworks for the two TIMSS grades (Grades 4 and 8). These grade bands were selected because the curriculum grade structure in the United States varies by state for both mathematics and science, and some topics are taught across grade levels.

Additional topics not included in the exhibits appear in some states’ curricula. Moreover, specific curriculum frameworks at the state and district levels may include detailed grade-level instructional benchmarks, approaches to learning, and instructional resource material.

Exhibit 2: Mathematics Curriculum Topics in Upper Elementary School*

Area of Mathematics Topics
Numbers
  • Concepts of whole numbers, including place value and ordering
  • Adding, subtracting, multiplying, and/or dividing with whole numbers
  • Concepts of multiples and factors; odd and even numbers
  • Concepts of fractions (fractions as parts of a whole or of a collection, or as a location on a number line)
  • Adding and subtracting with fractions; comparing and ordering fractions
  • Concepts of decimals, including place value and ordering
  • Number sentences (finding the missing number, modeling simple situations with number sentences)
  • Number patterns (extending number patterns, finding missing terms)
Geometry
  • Parallel and perpendicular lines
  • Comparing and drawing angles
  • Elementary properties of common geometric shapes
  • Graphing points on the coordinate plane to solve real-world and mathematical problems
Measurement and Data
  • Solving problems involving measurement, estimation of intervals of time, money, and mass
  • Converting like measurement units within a given measurement system
  • Measurement using mathematical tools (e.g., ruler and protractor)
  • Finding and estimating areas, perimeters, and volumes
  • Organizing data in pictographs, bar graphs, and line plots
  • Reading data from tables, pictographs, and bar graphs
  • Drawing conclusions from data displays
*Upper elementary school refers to Grades 3 to 5. State curricula differ in their grade structuring; some states specify topics should be taught within a certain grade band (e.g., Grades 3 to 5), while others specify topics that should be taught at specific grades.
NOTE: Curriculum topics listed in this exhibit are based on the TIMSS 2015 Curriculum Questionnaire; the state curriculum frameworks in California, Florida, Massachusetts, New York, and Texas; and the Common Core State Standards for Mathematics (CCSSM). With the exception of Texas, these states, along with 39 others, had adopted the CCSSM as of 2013.23 The topics listed are not exhaustive, as curriculum frameworks vary by state.

Exhibit 3: Mathematics Curriculum Topics in Middle School*

Area of Mathematics Topics
Numbers
  • Understanding negative numbers in the context of real-world contexts (e.g., temperature, height below sea level), including absolute value
  • Comparing and ordering rational numbers
  • Computing with rational numbers (fractions, decimals, and integers)
  • Concepts of irrational numbers
  • Concepts of problem solving involving ratios, proportions, and percent
Algebra
  • Simplifying and evaluating algebraic expressions
  • Working with radicals and integer exponents
  • Solving simple linear equations
  • Solving simple linear inequalities
  • Basic understanding of simultaneous (two variables) equations (graphical method only)
  • Concepts of numeric, algebraic, and geometric patterns or sequences (extension, missing terms, generalization of patterns)
  • Representation of functions as ordered pairs, tables, graphs, words, or equations
  • Qualitative understanding of properties of functions (slopes, intercepts, etc.)
Geometry
  • Properties of geometric two- and three-dimensional shapes (triangles, quadrilaterals, and other common polygons)
  • Basic understanding of congruent and similar figures
  • Understanding and applying the Pythagorean Theorem
  • Relationships between three-dimensional shapes and their two-dimensional representations
  • Using appropriate measurement formulas for perimeters, circumferences, areas, surface areas, and volumes
  • Translation, reflection, and rotation
Statistics and Probability
  • Characteristics of data sets including mean, median, range, and shape of distribution
  • Interpreting data sets (drawing conclusions, making predictions, and estimating values between and beyond given data points)
  • Using random sampling to draw inferences about a population
  • Developing, using, and evaluating probability models
  • Investigating patterns of association in bivariate data
*Middle school refers to Grades 6 to 8. State curricula differ in their grade structuring; some states specify that topics should be taught within a certain grade band (e.g., Grades 6 to 8), while others specify topics that should be taught at specific grades.
NOTE: Curriculum topics listed in this exhibit are based on the TIMSS 2015 Curriculum Questionnaire; the state curriculum frameworks in California, Florida, Massachusetts, New York, and Texas; and the Common Core State Standards for Mathematics (CCSSM). With the exception of Texas, these states, along with 39 others, had adopted the CCSSM as of 2013.24 The topics listed are not exhaustive, as curriculum frameworks vary by state.