The Mathematics Curriculum in Primary and Lower Secondary Grades

The current mathematics curriculum in Lithuania was approved in 2008. According to the national curriculum, mathematics education in primary school (Grades 1 to 4) aims to help students develop calculating, reasoning, and formalizing skills, as well as visual, spatial, and statistical thinking.¹ The curriculum is based on the premise that understanding and applying mathematical concepts, models, methods, and relationships will allow students to better understand the world, solve everyday life problems, and adopt a culture of human thought and action that was developed over centuries. Knowledge gained in various mathematical content areas will help students orient themselves in everyday life, and prepare for further studies in mathematics, the natural sciences, and technology.

Student skill objectives include communicating and collaborating using mathematical concepts as a means of conveying information, using mathematical vocabulary and symbols, adopting elements of mathematical reasoning, and learning to solve simple problems from everyday life that correspond to personal experience and interests. Students are expected to develop an appreciation of the importance of mathematics in their own lives and the lives of others, and its applications in various spheres of practical human endeavor. Overall, the curriculum aims to help students grow to value the honesty, perseverance, and creativity needed for intellectual work, and aspire to additional mathematical knowledge and skills.

The primary school curriculum comprises several mathematics content areas: numbers; expressions, equations, and inequalities; geometry; measurement; and statistics. When studying numbers, students focus on developing their skills in mental and written calculations in order to learn the names and components of arithmetic operations and the concepts of numbers, digits, and fractions (however, students do not apply arithmetic operations to fractions in primary school). Exhibit 1 summarizes the knowledge content and specialized skills students learn in mathematics in Grades 3 to 4.

Exhibit 1: Mathematics Learning Objectives and Expectations, Grades 3–4

Content Area	Objectives and Expectations
Numbers	Read and write natural numbers up to 10,000, simple fractions with denominators of 2, 3, 4, 5, 6, 7, 8, 9, 10, and 100, and decimal fractions with no more than two digits after the decimal point Compare numbers of the same type, correctly using symbols such as <, >, or = Identify how close a given number is to which multiple of 10, 100, or 1,000 Carry out practical counting tasks Add and subtract natural numbers, multiply and divide by one-digit and two-digit numbers, and round three-digit and four-digit numbers (e.g., 100 or 1,000) Solve simple real life and abstract problems, and estimate and check the results of calculations Explain the appearance of remainders from division in the context of concrete situations
Expressions, Equations, and Inequalities	Calculate values of simple numerical expressions or quantities Depict everyday practical and mathematical situations using simple numerical expressions Use the commutative and distributive properties of addition and multiplication when rearranging simple numerical expressions Solve simple equations and inequalities using more than one variable by guessing the answer and checking the result
Geometry	Recognize and draw points, segments, triangles, rectangles, squares, circles, cubes, parallelepipeds, pyramids, cones, and spheres Show elements of triangles and rectangles (e.g., side, angle, and vertex) in models and sketches Show radii of circles, and edges, vertices, and walls of cubes, parallelepipeds, and prisms in sketches Identify symmetry in objects or geometric plane figures Apply knowledge of plane and solid figures to solving simple problems
Measurement	Read and write measurement results correctly Draw segments of a given length, rectangles of given dimensions, and circles of a given radius Estimate parameters of simple objects (e.g., length, width, and volume in liters) without using measuring instruments Solve simple problems in which measurements are needed to carry out operations Use calendars and schedules Calculate average speed given distance and elapsed time Calculate perimeter of triangles and quadrilaterals and area of rectangles
Statistics	Collect data from the surrounding environment and display in frequency tables Read information from bar graphs, pictograms, and frequency tables, and represent given (or collected) data in bar graphs Answer simple questions and draw simple conclusions based on given (or collected) data

The basic education curriculum (Grades 5 to 10) emphasizes acquiring knowledge of various mathematical content areas for use in everyday life, and building a strong foundation for the study of other subjects, such as the natural sciences and technology. Student skill objectives include communicating and collaborating, using mathematical vocabulary and symbols, adopting elements of mathematical methods and reasoning, conducting mathematical investigations in everyday life, solving mathematical problems, and understanding and applying mathematical relationships.

The curriculum conveys the need for students to understand the historical evolution of mathematics, and to explore ideas about modern areas of mathematics that might contribute to advances in natural, social, and computer sciences. Students should recognize the importance of mathematics for society, its objectivity, and its practical applicability in various areas of human activity. Mathematics instruction in Grades 5 to 10 aims to motivate students to seek mathematical knowledge and develop openness, perseverance, positive attitudes toward change, willpower, motivation, and responsibility. It emphasizes the need for students to learn and remain interested in other subjects, which are built on a mathematical foundation.

The basic education curriculum divides mathematical knowledge and skills into the following content areas: Numbers; Expressions, Equations, Inequalities, and Their Systems; Relationships and Functions; Geometry; Measurement; Statistics; and Probability Theory. The curriculum further divides general skills and attitudes into knowledge and understanding, mathematical communication, mathematical reasoning, problem solving, and the ability to learn and develop interest in mathematics. Exhibit 2 summarizes the knowledge content and specialized skills students learn in mathematics in Grades 7 to 8.

Exhibit 2: Mathematics Learning Objectives and Expectations, Grades 7–8

Content Area	Objectives and Expectations
Numbers	Read, write, and compare rational numbers, place them on a number line, round them to a specified digit, and use them in arithmetic calculations Raise rational numbers to a whole number power Find square or cube roots of rational numbers Continue to develop problem solving skills involving percentages Use a calculator to carry out various calculations and to check results
Expressions, Equations, and Inequalities	Calculate values of simple numerical and algebraic expressions that may include two or three arithmetic operators, exponents, square roots, brackets, and one or two variables Rearrange terms in polynomials and factor them in simple cases Apply attributes of whole number exponents, and square and cube roots in simple cases Solve first-degree equations and equations in the form of A(x)B(x) = 0, where A(x), B(x) are first-degree binomials; and ax² = b and ax³ = b (a, b > 0) Solve simple first-degree inequalities
Relationships and Functions	Represent two directly or inversely proportional quantities with tables, graphs, or formulas, and apply the concept of proportionality Draw a figure symmetrical to one given by applying point or line symmetry
Geometry	Classify angles, triangles, and quadrangles according to given attributes Apply properties of adjacent and vertical angles and parallel lines in solving simple problems Explore properties of triangles (isosceles and equilateral) and quadrilaterals (parallelograms and trapezoids), and apply the properties of congruence to triangles and symmetry to figures (point and line) Prove simple statements by using geometric properties (e.g., triangle congruence, the sum of triangle or quadrilateral angles, and the Pythagorean theorem) Draw right triangles or quadrilateral prisms, cylinders, cones, spheres, and regular pyramids and name their elements Make models of right triangles or quadrilateral prisms, regular pyramids, and other regular solid figures
Measurement	Read and write results of measurements in both standard and nonstandard units Estimate parameters of simple objects in the real world, with and without measuring instruments Use formulas to calculate perimeter and area of triangles, parallelograms, trapezoids, and circles Understand and use properties of length, width, and area Apply measurement scales to solving problems that require finding length (perimeter) or area of figures Calculate the sum of the angles in triangles or quadrilaterals Calculate the volume and surface area of right prisms and cylinders Establish relationships among various units of measurement Add and subtract measurements in the same units and multiply and divide measurements in any units Calculate speed, distance, and time using relevant formulas
Statistics	Find and analyze diverse statistical information from different sources Interpret and evaluate sample characteristics Display data and find numerical characteristics using spreadsheets
Probability Theory	Make subsets of several elements, with elements taken from different sets or from the same set Distinguish whether order in a subset is important Use the rule of multiplication when calculating a number of subsets when the order of subset elements is important Understand the concepts underlying probability experiments and their outcomes Conduct experiments, learn how to calculate relative frequency of outcomes, and draw simple conclusions about the likelihood of each outcome