The Mathematics Curriculum in Primary and Lower Secondary Grades

Finland recognizes the significant influences of mathematics education on students’ intellectual growth and their ability to advance purposeful activity and social interaction. According to the National Core Curriculum for Basic Education, the purpose of mathematics instruction is to offer opportunities to develop mathematical thinking and learn mathematical concepts and problem solving methods. The goal of instruction is to develop creative and precise thinking and guide the student in finding, formulating, and solving problems.⁴ Mathematics instruction progresses systematically to create a lasting foundation for the assimilation of mathematical concepts and structures. The nature of the discipline brings together student experiences and systems of thought with the abstract system of mathematics. Problems that arise in everyday situations, and that can be resolved with the aid of mathematical thinking or operations, are examined. Information and Communications Technology (ICT) are used to support student learning.

In the first and second grades, mathematics instruction focuses on mathematical thinking as well as concentration, listening, and communication skills, while providing a basis for the formulation of mathematical concepts and structures. During these first two years the core content is as follows:

Numbers and Calculations—Number and number symbols; properties of numbers; comparison, classification, ordering, and use of manipulatives to break down and assemble numbers; the decimal system; addition and subtraction, and using natural numbers; multiplication and basic multiplication tables; division using concrete tools; methods of calculating, including blocks and decimal tools, number lines, mental calculation, and pencil and paper; and introducing basic concepts of fractions using manipulatives
Algebra—Identifying patterns, ratios, and correlations pictorially; and simple number sequences
Geometry—Observing and describing spatial relationships; observing, describing, and naming geometric shapes in the environment; recognizing, explaining, and naming two- and three-dimensional figures; basic geometric concepts such as point, line segment, line, half line, and angle; making, drawing, and tracing two-dimensional figures and recognizing and constructing three-dimensional figures; and simple reflections and dilations
Measurement—Principles of measurement; length, mass, area, volume, time, and price; use of measuring devices; comparisons of units of measurement; and analysis of measurement results
Data Processing and Statistics—Looking for, collecting, and storing data; and reading simple tables and diagrams and presenting collected data as a graph

The core objectives of mathematics instruction in the third through fifth grades are to develop mathematical thinking, introduce mathematical modeling, strengthen basic calculation skills, reinforce the concept of number, and provide a basis for assimilating the concepts and structures of mathematics. During these years the core content of instruction includes:

Numbers and Calculations—Developing the concept of the decimal system, introduction to the base-60 system, and telling time; classification and organization of numbers; multiplication; ratios, division into parts, and divisibility; algorithms and mental calculation; the concept of the fraction and conversion of fractions; the concept of decimal fractions; the relationship between fractions, decimal fractions, and percentages; addition, subtraction, and multiplication of fractions and decimal fractions; division by natural numbers; evaluating, checking, and rounding the results of calculations; use of parentheses; and the concept of negative whole numbers
Algebra—The concept of the algebraic expression; the interpretation and writing of number sequences, regularities, ratios, and correlations; and using deduction to solve simple linear equations and inequalities
Geometry—Dilations; similarity and scale; reflections across a line and around a point and symmetry; congruence; the circle and its parts; parallel and perpendicular lines; measurement and classification of angles; classification of different types of polygons; circumference, perimeter, and area; geometric properties of two- and three-dimensional figures; reinforcement of the principle of measurement; use, comparison, and conversion of units of measurement; evaluation of measurement results; and revision of measurements
Data Processing, Statistics, and Probability—Searching for, gathering, storing, and presenting data; the Cartesian coordinate system; reading simple tables and diagrams; concept and computation of the arithmetic mean; classification and organization of data; introduction to the concepts of mode and median; and experiences with classical and statistical probability

The core objectives of mathematics instruction in the sixth through ninth grades are to deepen the understanding of mathematical concepts and further develop modeling skills with an emphasis on everyday mathematical problems, to provide experiences that encourage students to think mathematically, and to develop the ability to express mathematical ideas precisely. The core content of instruction during these four years includes:

Thinking Skills and Methods—Processes that demand logical thinking, such as classification, comparison, organization, measurement, constructing, modeling, and articulating rules and correlations; the interpretation and use of concepts to make comparisons and correlations; the interpretation and production of mathematical texts; introduction to proof, including justified conjectures and experiments, systematic trial-and-error method, demonstrating incorrectness, and direct proof; solving combinatorial problems; use of tools and drawings to investigate problems; and the history of mathematics
Numbers and Calculations—Strengthening basic calculation skills; natural numbers, whole numbers, rational numbers, and real numbers; negative numbers, absolute values, and reciprocals; time calculations and intervals; prime numbers, division of numbers into prime factors, and rules for divisibility; reduction of fractions, conversion of fractions and decimal fractions as common fractions; multiplication and division with fractions and decimal fractions; simplification of expressions; ratio and proportion; strengthening the concept of percentage and calculating percentages; rounding and estimation; using a calculator; powers using whole number exponents; and the concept of root and square root calculations
Algebra—Expressions and their simplification, exponential expressions and their simplification, and the concept of polynomials; addition, subtraction, and multiplication of polynomials; concept of variables; calculating the value of an expression; equation, inequality, domain, and range; solving a first-degree equation and an incomplete quadratic equation; proportionality; simultaneous equations and their solution algebraically and graphically, and study and formulation of number sequences
Functions—Observing correlation and presentation by means of variables; concept of the function; presenting a set of coordinates in a coordinate system; interpreting simple functions and drawing their graphs in a coordinate system; investigating the graph of a function, including the function’s root, largest and smallest values, increasing and decreasing functions; linear functions; and direct and inverse proportionality
Geometry—Relationships between angles; concepts related to triangles and quadrilaterals; regular polygons; the circle and related concepts; calculating the perimeter and area of plane figures; naming and classifying three-dimensional figures; calculating the volume and surface area of a three-dimensional figure; similarity and congruence; geometric constructions; depictions of congruence, including reflections, rotation, and transformation; the Pythagorean theorem; relationships between triangles and circles; and trigonometry and solving right triangles
Probability and Statistics—Concept of probability; frequency and relative frequency; determining average, mode, and median; concept of dispersion; interpretation of graphs; and gathering and adapting information, and presentation in a usable form