Ukraine Mathematics Curriculum (4th Grade)

This outlines the mathematics curriculum for 4th grade in Ukraine, based on the Ministry of Education's guidelines.

Numbers, Actions with Numbers, and Quantities:

• Numbering: Students will work with numbers up to one million, learning to read, write, compare, and order them. They will also understand place value and decompose numbers into different place values.
• Arithmetic Operations: Students will perform addition, subtraction, multiplication, and division with multi-digit numbers, including division with remainders. They will develop fluency in multiplication and division facts and learn strategies for mental and written calculations. Emphasis is placed on understanding the relationship between operations and checking the correctness of calculations.
• Fractions: Students will be introduced to the concept of fractions, learning to read, write, and compare fractions with the same denominators. They will also learn to find a fraction of a number and the value of its fraction.
• Measurements and Units: Students will work with units of length (millimeter, centimeter, decimeter, meter, kilometer), mass (gram, kilogram, centner, ton), capacity (liter), and time (day, week, hour, minute, second, month, year, century). They will learn to convert between units, perform arithmetic operations with named numbers, and solve practical problems involving measurements.
• Interrelated Quantities: Students will explore the relationships between quantities in various contexts, such as movement (path, speed, and time) and purchase and sale situations. They will use formulas to find unknown quantities and predict expected results.

Expressions, Equations, and Inequalities:

• Numerical and Algebraic Expressions: Students will learn to read, write, and evaluate numerical and algebraic expressions, applying the order of operations.
• Equations and Inequalities: Students will solve equations with one variable and understand that inequalities with a variable can have one, several, or a multitude of solutions. They will also explore inequalities that have no solutions.

Geometric Shapes:

• Plane Figures: Students will classify and recognize geometric figures such as rectangles, squares, triangles, circles, and circular disks. They will learn about angles and their types (straight, acute, obtuse). They will also calculate the perimeter and area of rectangles and squares.
• Spatial Figures: Students will be introduced to three-dimensional shapes such as cones, cylinders, pyramids, balls, and rectangular parallelepipeds (cubes).

Mathematical Problems and Studies:

• Problem Solving: Students will solve simple and complex word problems, including problems involving fractions, geometric content, and real-world situations. They will develop problem-solving strategies, such as creating auxiliary models and planning solutions.
• Mathematical Investigations: Students will conduct elementary studies of mathematical patterns and dependencies, developing their ability to analyze and generalize.

Data Handling:

• Data Representation and Interpretation: Students will read and interpret data presented in tables and line graphs. They will also learn to create line graphs and summarize data.

Extra Topics:

The curriculum also includes extra topics such as rational computational techniques, specific multiplication and division strategies, solving equations and inequalities with variables, operations with composite named numbers, and more complex problem-solving scenarios.