LUMINAMATH COMPETITION CURRICULAR MATHEMATICS SUBJECT
Chapter 1: Using numbers in elementary calculations  

Subchapter  Content 
1.1. Writing, reading and forming numbers up to 1000 

1.2 Comparing numbers in the 01000 range  Comparing some groups of objects by placing the elements one under the other, circling
the common parts, matching;

1.3. Ordering numbers in the 01000 range, using positioning on the number axis, estimations, approximations 

1.4. Carrying out additions and subtractions, mentally and in writing, in the 01000 range, using counting and/or grouping whenever necessary 

1.5. Perform multiplications and divisions in the 01000 range by repeated additions/subtractions 

1.6. Using mathematical names and symbols (sum, total, terms of a sum, difference, remainder, minus, decrement, product, factors of a product, quotient, divided, divisor, <, >, =, +, , ·, :) in solving and/or composing problems 

Chapter 2: Highlighting the geometric characteristics of some objects located in the surrounding space  

Subchapter  Content 
2.1. Locating objects by establishing coordinates relative to a given reference system, using learned phrases 

2.2. Highlighting some simple characteristics specific to flat geometric shapes and geometric bodies identified in different contexts 

Chapter 3: Identifying of phenomena/relations/regularities/structures in the immediate environment  

Subchapter  Content 
3.1. Solving problems by investigating, observing and generalizing patterns or regularities in the immediate environment 

Chapter 4: Generating simple explanations using elements of logic  

Subchapter  Content 
4.1. Describing a work plan using some scientific terms, graphical representations and the logical operators "and", "or", "not" 

Chapter 5: Solving problems starting with sorting and representing data  

Subchapter  Content 
5.1. Solving problems of the type a±b=x; a±b±c=x in the 0  1000 range; a·b=x; a:b=x, in the 0  100 range 

Chapter 6: Using Conventional Standards for Measurement and Estimation  

Subchapter  Content 
6.1. Use of nonconventional measures to determine and compare masses, lengths and capacities 

6.2. Using units of measure to determine, compare, and order the durations of various events 

6.3. Completing valueequivalent exchanges through standard and nonstandard conventional representations and through the use of money in simple revenueexpendituretype gameproblems, with numbers from the 0  1000 range 

6.4. Identifying and usage of common units of measurement for length, capacity, mass (meter, centimeter, liter, milliliter, kilogram, gram) and appropriate tools 

Chapter 1: Identifying some relationships/regularities in the immediate environment  

Subchapter  Content 
1.1. Observing some patterns / regularities from everyday life, to create own reasonings 

1.2. Applying a rule to continue repetitive patterns 

Chapter 2: Using numbers in calculations  

Subchapter  Content 
2.1. Recognizing of natural numbers in the 010000 range and subunit or equiunit fractions with denominators less than or equal to 10 

2.2. Comparison of natural numbers in the 0 – 10000 range, respectively of subunit or equiunit fractions that have the same denominator, less than or equal to 10 

2.3. Addition and subtraction of natural numbers in the 0  10000 range or with fractions with the same denominator 

2.4. Performing multiplications of numbers in the 0  10000 range and divisions using the multiplication table and the division table respectively 

Chapter 3: Exploring the geometric characteristics of some objects located in the immediate environment  

Subchapter  Content 
3.1. Locating objects in space and in representations, in familiar situations 

3.2. Exploring simple features of geometric shapes and solids in familiar contexts 

Chapter 4: Using Conventional Standards for Measurement and Estimation  

Subchapter  Content 
4.1. The use of standardized tools and measurement units, in concrete situations 

4.2. Operating standardized units of measurement, without conversions 

Chapter 5: Solving problems in familiar situations  

Subchapter  Content 
5.1. Use of specific terminology and mathematical symbols in solving and/or composing simple reasoning problems 

5.2. Recording in tables some observed daily data 

5.3. Solving problems with studied arithmetic operations, focusing on 0  10000 

Chapter 1: Identifying some relationships/regularities in the immediate environment  

Subchapter  Content 
1.1. Generation of repetitive patterns / regularities 

Chapter 2: Using numbers in calculations  

Subchapter  Content 
2.1. Recognizing natural numbers in the 0  1000000 range and fractions with denominators less than or equal to 10, respectively equal to 100 

2.2. Comparing natural numbers in the 0 – 1000000 range, respectively of fractions that have the same numerator or the same denominator, less than or equal to 10 or denominator equal to 100 

2.3. Ordering the natural numbers in the 0 – 1000000 range and, respectively, the fractions that have the same numerator or the same denominator, less than or equal to 10 or denominator equal to 100 

2.4. Addition and subtraction of natural numbers in the 0  1000000 range or with fractional numbers 

2.5. Multiplication of numbers in the 0  1000000 range when the factors have at most three digits and division of onedigit or twodigit numbers 

Chapter 3: Exploring the geometric characteristics of some objects located in the immediate environment  

Subchapter  Content 
3.1. Locating objects in space and symbols in various representations 

3.2. Exploring the characteristics, relationships and properties of geometric shapes and solids identified in different contexts 

Chapter 4. Use of conventional standards for measurements and estimates  

Subchapter  Content 
4.1. The use of standardized tools and measurement units, in concrete situations, including for the validation of transformations 

4.2. Working with standardized units of measure, using transformations 

Chapter 5: Solving problems in familiar situations  

Subchapter  Content 
5.1. Usage of specific terminology and mathematical symbols in solving and/or composing problems with various reasoning 

5.2. Organizing of data in tables and their graphical representation 

5.3. Solving problems with the arithmetic operations studied, in the 0 – 1000000 range 

Chapter 1: Identifying some data, quantities and mathematical relationships, in the context in which they appear  

Specific skills  Content 
1.1. Identifying natural numbers in various contexts 

1.2. Identifying ordinary or decimal fractions in various contexts 

1.3. Identifying elementary geometric notions and units of measurement in different contexts 

Chapter 2: The processing of quantitative, qualitative, structural mathematical data contained in various informational sources  

Specific skills  Content 
2.1. Performing calculations with natural numbers using arithmetic operations and their properties 

2.2. Performing calculations with fractions using properties of arithmetic operations 

Chapter 3: Use of specific concepts and algorithms in various mathematical contexts  

Specific skills  Content 
3.1. Using the rules of calculation to perform operations on natural numbers and for divisibility 

3.2. Using algorithms to perform operations with ordinary fractions or decimals 

3.3. Determining perimeters, areas (square, rectangle) and volumes (cube, rectangular parallelepiped) and their expression in appropriate measurement units 

Chapter 4: Expressing information, conclusions and solutions for a given situation in the language specific to mathematics  

Specific skills  Content 
4.1. Expressing some properties related to comparisons, approximations, estimates, and natural number operations in mathematical language 

4.2. Using language specific of fractions/percentages in given situations 

4.3. Translating practical problems related to perimeters, areas, volumes, using the convenient conversion of units of measure, into specific language 

Chapter 5: Analyzing the mathematical characteristics of a given situation  

Specific skills  Content 
5.1. Analyzing given situations involving natural numbers to estimate or verify the validity of calculations 

5.2. Analyzing given situations involving fractions to estimate or verify the validity of some calculations 

Chapter 1: Identifying some data, quantities and mathematical relationships, in the context in which they appear  

Specific skills  Content 
1.1. Identifying specific notions of sets and the divisibility relation in ℕ 

1.2. Identifying ratios, proportions and directly or inversely proportional quantities 

1.3. Identifying the characteristics of whole numbers in various contexts 

1.4. Recognizing equivalent fractions, irreducible fractions, and ways of writing a rational number 

1.5. Recognizing flat geometric figures (straight lines, angles, circles, arcs of a circle) in given configurations 

1.6. Recognizing of elements of planar geometry associated with the notion of a triangle 

Chapter 2: The processing of quantitative, qualitative, structural mathematical data contained in various informational sources  

Specific skills  Content 
2.1. Highlighting, in examples, the relations of membership, inclusion, equality and criteria of divisibility by 2, 5, 10n, 3 and 9 in ℕ 

2.2. Quantitative processing of data using ratios and proportions to organize data 

2.3. Using integer operations to solve equations and inequations 

2.4. Applying rules of computation for rational numbers to solve equations of the type: x+a=b, x∙a=b, x:a=b (a≠0), ax + b = c, where a, b and c are rational numbers 

2.4. Applying rules of computation for rational numbers to solve equations of the type: x+a=b, x∙a=b, x:a=b (a≠0), ax + b = c, where a, b and c are rational numbers 

2.5. Recognizing the collinearity of some points, the fact that two angles are opposite at the apex, adjacent, complementary or supplementary and of the parallelism or perpendicularity of two lines 

2.6. Calculation of segment lengths, angle measures in the context of triangle geometry 

Chapter 3: Use of specific concepts and algorithms in various mathematical contexts  

Specific skills  Content 
3.1. Using appropriate ways of representing sets and determining GCD and LCM 

3.2. Applying specific methods of solving problems involving ratios, proportions and directly/inversely proportional quantities 

3.3. Applying the rules of calculation and using parentheses in performing operations with whole numbers 

3.4. Use properties of operations to compare and perform calculations with rational numbers 

3.5. The use of properties related to distances, lines, angles, circles for the realization of geometric constructions 

3.6. Using congruence criteria and properties of particular triangles to determine the characteristics of a geometric configuration 

Chapter 4: Expressing information, conclusions and solutions for a given situation in the language specific to mathematics  

Specific skills  Content 
4.1. Expressing concrete situations that can be described using sets and divisibility in ℕ 

4.2. Expressing in mathematical language the relationships and quantities that occur in problems with ratios, proportions and directly or inversely proportional quantities 

4.3. Writing the steps for solving the studied equations and inequalities in the set of integers 

4.4. Writing the stages of solving some problems, using operations in the set of rational numbers 

4.5. Expressing, through geometric representations or in specific mathematical language, notions related to straight lines, angles and circles 

4.6. Expressing in symbolic and figurative geometric language the characteristics of triangles and important lines in the triangle 

Chapter 5: Analyzing the mathematical characteristics of a given situation  

Specific skills  Content 
5.1. Analysis of given situations in the context of sets and divisibility in ℕ 

5.2. Analyzing practical situations using ratios, proportions and data collections 

5.3. Interpreting data from problems that are solved using whole numbers 

5.4. Determining effective methods in performing calculations with rational numbers 

5.5. Analyze numerical data sets or geometric representations to optimize calculations with segment lengths, distances, angle measures and arcs 

Chapter 6: Mathematical modeling of a given situation, by integrating acquisitions from different fields  

Specific skills  Content 
6.1. Translation, in mathematical language, of given situations using sets, set operations and divisibility in ℕ 

6.2. Mathematical modeling of a given situation involving ratios, proportions and directly or inversely proportional quantities 

6.3. Transposing, in algebraic language, a given situation, solving the obtained equation or inequality and interpreting the result 

6.4. Mathematical interpretation of practical problems using rational number operations 

6.5. Interpreting information contained in geometric representations to determine segment lengths, distances and angle/arc measures 

CHAPTER 1. NATURAL NUMBERS  

Specific skills  Content 
1.1. Operations with natural numbers 

1.2. Divisibility of natural numbers 

1.3. Common divisors, common multiples 

CHAPTER 2. THE SET OF RATIONAL NUMBERS  

Specific skills  Content 
2.1. Rational numbers 

2.2. Operations with rational numbers 

2.3. Equations in Q 

CHAPTER 3. RATIOS AND PROPORTIONS  

Specific skills  Content 
3.1. Ordinary fractions 

3.2. Proportion 

3.3. Statistical elements 

CHAPTER 4. INTEGERS  

Specific skills  Content 
4.1. Integers 

4.2. Operations with integers 

4.3. Equations 

CHAPTER 5. THE SET OF REAL NUMBERS  

Specific skills  Content 
5.1. The square root 

5.2. Real number 

5.3. Radicals calculation rules 

5.4. Operations with real numbers 

CHAPTER 6. ALGEBRAIC CALCULUS  

Specific skills  Content 
6.1. Calculations with real numbers represented by letters 

6.2. Decomposition into factors 

6.3. Equations and inequations 

CHAPTER 7. GEOMETRIC FIGURES  

Specific skills  Content 
7.1. Congruence of triangles 

7.2. Perpendicularity 

7.3. Area of the triangle 

7.4. Parallelism 

7.5. Properties of triangles 

7.6. Properties of the isosceles and equilateral triangle 

7.7. Properties of the right triangle 

CHAPTER 8. THE CIRCLE  

Specific skills  Content 
8.1. Elements in a circle 

8.2. Angles in a circle 

8.3. Regular polygons 

8.4. The length of the circle and the area of the disc 

CHAPTER 1. THE SET OF RATIONAL NUMBERS  

Specific skills  Content 
1.1. Rational number 

1.2. Operations with rational numbers 

1.3. Equations in Q 

CHAPTER 2. THE SET OF REAL NUMBERS  

Specific skills  Content 
5.1. The square root 

2.2. Real number 

2.3. Radicals calculation rules 

2.4. Operations with real numbers 

CHAPTER 3. ALGEBRAIC CALCULUS  

Specific skills  Content 
3.1. Calculations with real numbers represented by letters 

3.2. Decomposition into factors 

3.3. Equations and inequations 

CHAPTER 4. THE TRIANGLE  

Specific skills  Content 
4.1. Properties of triangles 

4.2. The isosceles triangle 

4.3. Right triangle 

4.4. Thales' theorem 

4.5. Similar triangles 

4.6. Properties of the isosceles and equilateral triangle 

CHAPTER 5. THE QUADRILATERAL  

Specific skills  Content 
5.1. Properties of quadrilaterals 

5.2. Parallelogram 

5.3. Trapezium 

CHAPTER 6. THE CIRCLE  

Specific skills  Content 
6.1. Elements in a circle 

6.2. Angles in a circle 

6.3. Regular polygons 

6.4. The length of the circle and the area of the disc 

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