Mathematics — Grade 3 of primary school

In Grade 3, a child adds two-digit numbers mentally up to 100 in situations where the sum of the ones crosses into the next ten (e.g., 38 + 25). At this stage, using written column algorithms is not required. The student uses their own convenient strategies: making the next ten, breaking addends into tens and ones, or directly providing the result, writing down only auxiliary partial results if needed.

A typical mistake in such calculations is omitting the newly formed ten—the child adds the ones correctly, but forgets to add the extra 10 to the sum of the tens (for example, giving the result of 27 + 15 as 32 instead of 42). Another difficulty is losing track mentally when breaking down the second addend, especially when an intermediate step, such as writing down the complement to the next ten, is missing.

Tasks that practice this skill take various forms:

• mental calculations and filling in the blanks, e.g., how much is missing to the next ten, how much is missing to the target, or finding the unknown start,
• comparing values and verifying correctness, such as balancing both sides, true or false tasks, and check the result and find the mistake,
• practical word problems (including those with extraneous information), as well as identifying rules in number patterns or performing two consecutive operations.

In 3rd grade, children subtract two-digit numbers up to 100 mentally or by writing down intermediate steps (for example, by subtracting the tens first and then the ones: 54 – 23 = 54 – 20 – 3 = 31). At this stage, standard written column algorithms are not yet required—students are free to choose their own calculation strategies that make sense to them.

A common mistake occurs in problems that involve crossing the tens threshold (e.g., 52 – 18). Instead of correctly breaking down the subtrahend, children often subtract the smaller ones digit from the larger one (calculating 8 – 2 instead of subtracting 8 from 52), leading to an incorrect answer of 46 instead of 34.

Tasks that practice this skill include both straightforward calculations within 100 and word problems. Children perform two subtractions in a row, solve "increased and decreased" change problems, find a missing starting number, and analyze worked-out calculations to spot errors and check the accuracy of the result.

In 3rd grade, children perform mental division within the multiplication table (up to 100). They learn to see division as the inverse operation of multiplication and can justify the correctness of a result by multiplying the quotient by the divisor. At this educational stage, long division and division with remainders are not yet required of the student.

A common problem is confusing the roles of numbers in division or struggling to identify the missing divisor in fill-in-the-blank equations (e.g., 42 : [ ] = 7). Children who have not yet memorized multiplication facts often try to repeatedly subtract numbers instead of immediately recalling the relevant multiplication fact. Sometimes, they also write down the result without attempting to check it using multiplication, which makes it harder to catch their own mistakes.

Exercises targeting this skill include direct mental math, finding errors in written calculations, and practical real-life situations. For example, the child determines how many packages will be made after packing items, divides items into equal parts, compares which division yields more per person, or solves word problems where they must first filter out unnecessary numbers.

In Grade 3, a child masters mental multiplication up to 100 and multiplying numbers less than 20 by 10. The student efficiently uses operation and relation symbols, can calculate a product, and can also solve a simple equation with an unknown written as a blank box, finding the missing factor.

A typical problem at this stage is confusing multiplication with addition (for example, giving the result 4 · 4 = 8 instead of 16) and difficulty with reversing operations when determining which number should go in the box: ___ · 7 = 42. Mistakes also often stem from mechanical guessing instead of using known helper facts.

The tasks in this section practice computational fluency in varied ways. Children solve traditional multiplication problems up to 100, fill in missing factors, check the accuracy of completed calculations by finding errors, and compare the results of operations by determining how much greater one product is than another.

In the 3rd grade, a child mentally adds numbers proficiently within the range up to 100. They can add a single-digit number, whole tens (for example, 10, 20, or 40), and other two-digit numbers to any number, using partial notation and number decomposition. At this stage, column addition algorithms are not yet required—the key is to develop flexible mental strategies.

A common problem is regrouping over the tens boundary. Children get confused when adding ones creates a new ten (e.g., in operations like 47 + 8 or 38 + 25)—sometimes they add only the tens together, forgetting to include the new ten formed from the sum of the ones.

Exercises reinforcing this skill involve various forms of notation. The student will encounter tasks such as:

• addition on a number line, which helps visualize jumps by tens and ones,
• adding three addends at once (within 100), which encourages combining numbers into convenient whole tens,
• completing result tables and identifying which operation has a different result from the others.

In Grade 3, a child navigates shopping situations up to 100 PLN with ease. They recognize banknotes and coins, convert zlotys to groszy without difficulty, and can assess the purchasing power of money. In practice, this means being able to easily add the prices of several products, multiply the cost of a single item by the number of units, and subtract the spent amount from an available budget.

The most common difficulty is handling both zlotys and groszy at the same time when calculating change, especially when needing to "break" 1 PLN into 100 gr. Children also sometimes struggle with choosing the exact cash—instead of picking a specific set of coins and banknotes that equals a given price, they focus only on adding up values without considering the available denominations.

The exercises in this section are based on practical, everyday scenarios. The child solves tasks such as:

• Is there enough money? and How much more is needed?—comparing the wallet's contents with the shelf price;
• Shopping and change—calculating how much the cashier needs to return after paying with a banknote;
• How much for several items?—simple calculations combining shopping with multiplication;
• Which coins to pay with?—selecting the correct coins needed to settle a bill.

At this stage, the student performs simple mental calculations within 20. They add single-digit numbers to each other (e.g., 4 + 5) or add a single-digit number to a two-digit number so that the sum does not cross the next ten (e.g., 12 + 5 = 17). The child solves all these operations mentally, without using written vertical addition.

A typical problem is confusing place values when adding to a teen number. Sometimes, a child adds the ones digit to the tens place instead of the ones place, giving an incorrect result (for example, calculating 13 + 4 as 53 instead of 17). Another common difficulty is automatically counting on fingers by ones instead of noticing the simple fact that it is enough to add just the ones: 3 + 4, while the ten remains unchanged.

Exercises from the Addition within 20 template take the form of short, one-line mathematical operations to complete mentally, such as 11 + 6, 14 + 3, or 5 + 4. These tasks reinforce arithmetic fluency, which serves as a foundation for later calculations with larger numbers.

In third grade, a child efficiently compares quantities and orders numbers up to 100. They can determine which value is smaller or greater and correctly use relation symbols: <, =, and >. At the same time, they understand place value in a two-digit number, knowing that the tens digit determines the size first, followed by the ones digit.

The most common issue at this stage is confusing the direction of the less than and greater than signs, especially when numbers consist of the same digits written in a different order (for example, 37 and 73). Children also sometimes struggle to compare quantities when simple addition or subtraction must be performed first, focusing only on a single digit rather than the entire result.

In practice, tasks involve inserting the correct symbol between two numbers or calculation results (the templates Comparing numbers up to 100 and Insert the sign: <, > or =). Students also solve open-ended exercises where they look for missing digits that satisfy a given condition, identify even numbers lying between two values, or analyze simple real-life situations, such as determining which group scored the fewest points.

In grade 3, children analyze the content of a simple word problem, extract data, and independently choose a solution strategy. They write down the situation using a single mathematical operation, an equation with a blank box, or an auxiliary drawing, arriving at the correct result.

A common mistake at this stage is mechanically combining the given numbers using the first operation that comes to mind, without understanding the relationships in the text. Children confuse situations where they need to calculate the initial state with situations where they are looking for the remainder—for example, they add numbers in a problem asking how many are left, or subtract instead of reversing the operation to determine the starting amount.

Problems that practice this skill come in several variations:

• calculating the initial state (How many were there at the beginning),
• determining the remainder after some elements are removed (Simple word problem — how many are left),
• identifying the correct mathematical notation that leads to the result, including addition situations (Which operation solves the problem and Which operation solves the problem (altogether)).

By the end of grade 3, a child can fluently tell time both from a traditional analog clock face and from a 24-hour electronic display. They recognize morning and afternoon hours, matching, for example, the position of the clock hands with digital representations like 15:30 or 21:45. When reading the time, they use units of time such as the hour and minute, and they can also navigate a clock face with Roman numerals up to XII.

The most common difficulty is confusing the roles of the hour and minute hands, especially when the longer hand approaches the next full hour. Children then often mistakenly read the hour ahead, for example interpreting ten to three as 3:50 instead of 2:50. Converting afternoon hours into the 24-hour format can also be tricky, as it requires quickly adding 12 to the number shown on the clock face.

In tasks from the Reading a clock template, the student is usually given a drawing of an analog clock face and is asked to write the indicated time in digital format or match the correct morning and afternoon time.

In Grade 3, a child measures the sides of a shape using a ruler or uses given dimensions to calculate the perimeter of a rectangle. They understand that opposite sides are equal in length and add the four values together, performing calculations with results up to 100.

A common mistake at this stage is adding only two different sides (length and width) instead of all four. Students forget that a rectangle has two pairs of equal sides, resulting in them giving half of the actual perimeter.

Tasks that practice this skill include:

• calculating the perimeter of a rectangle based on a drawing or given dimensions,
• finding the length of a missing side when the perimeter and one of the shape's dimensions are known,
• comparing perimeters and identifying which shape has a larger perimeter.

In grade 3, a child uses a calendar proficiently and performs practical calculations related to the passage of time. The student can correctly write the current date or their birthday using Arabic numerals and Roman numerals (at least up to XII when denoting months). They understand the division of a year into months, weeks, and days, and can also associate a specific date with the correct day of the week.

A common mistake at this stage is failing to take into account the varying number of days in different months (e.g., assuming that every month has 30 days) or getting lost when crossing the boundary between months while counting days. Children also sometimes have difficulty correctly determining a time interval, confusing the number of elapsed days with the day's date on the calendar and unnecessarily including the starting day.

Exercises in this area are based on practical word problems and working with a calendar page. The tasks take the form of questions about how many days pass between two dates (e.g., how many days are left until the end of the holidays) and which day of the week it will be after a specified number of days has elapsed from a given day.

In Grade 3, a child measures the sides of shapes using a ruler and calculates the perimeter of a square by adding four equal lengths or multiplying the length of one side by 4. They also perform the reverse operation: dividing a given perimeter by 4 to determine how long a single side is. All calculations are within the range of numbers up to 100.

The most common mistake is confusing a square with a rectangle with unequal sides and adding only two dimensions together instead of four. Children also sometimes forget that all sides of a square have the same length, which causes them to look for extra data on the drawing instead of multiplying the known dimension by 4.

Tasks for independent practice take two forms:

• Perimeter of a square – the student is given the side length (e.g., 6 cm) and calculates the sum of all four sides (4 · 6 cm = 24 cm).
• Side of a square from the perimeter – the student is given the total perimeter (e.g., 32 cm) and uses division to calculate the length of one side (32 cm : 4 = 8 cm).

In Grade 3, a child skillfully measures the side lengths of a triangle using a ruler and calculates its perimeter by adding up the lengths of all three segments. They work with whole numbers, performing addition and subtraction up to 100.

The most common mistake is skipping one of the sides during addition or treating the triangle like a quadrilateral, where students attempt to add only two values. The reverse situation also poses a challenge: when the perimeter and two sides are known, the child sometimes struggles to correctly subtract their sum from the perimeter to determine the missing length.

On the worksheets, the student encounters two main types of exercises:

• Perimeter of a triangle – the task involves measuring a drawn shape or adding three given numbers to write down the full perimeter;
• The third side of a triangle – a fill-in-the-blank exercise in which, based on a given perimeter and two known sides, the child calculates the length of the third side.

In grade 3, a child can find the missing number hidden in the blank box of an equation. In this unit, the student focuses on addition and determining the missing addend using the equals sign and mastered mental math strategies. They understand that an equation with a box requires balancing both sides of the equals sign.

A typical mistake at this stage is mechanically adding all visible numbers together instead of looking for the missing part of the sum. For example, upon seeing an addition sign, a child might add the given addend to the final result, ignoring the relationship between the parts and the whole.

Printable worksheets generated from the template Box equations (missing addend) take the form of simple equations, such as [] + 15 = 40 or 23 + [] = 50. The student's task is to write the correct number in the blank box to complete the sum.

In Grade 3, a child efficiently compares three-digit numbers up to 1000. They can indicate which one is smaller or larger, correctly recording this relationship using the symbols <, =, and >. They also arrange sets of numbers in ascending order (from smallest to largest) or descending order and understand phrases indicating a difference in value, such as how much greater or how much smaller.

A common difficulty at this stage is comparing numbers with similar digits, especially when they differ by the tens digit rather than the hundreds (for example, 438 and 483). Children can also be confused by the direction of comparison symbols or confuse ascending with descending order, arranging numbers in the opposite order of what the instructions require.

In practice, exercises involve working with specific tasks:

• Order five numbers — the student arranges a given set of five three-digit numbers in the correct order, from smallest to largest or vice versa;
• How much greater — numbers up to 1000 — the child compares two values and accurately calculates the difference between them.

In Grade 3, children learn the basic Roman numerals (I, V, X) and learn to read and write numbers from I to XII. This skill allows third-graders to easily read the time on a traditional clock face with hands, as well as correctly read and write months in a calendar or a date.

The most common difficulty at this stage is confusing the rules of adding and subtracting numerals depending on their order. Children often mix up the number IV (4) with the number VI (6) and IX (9) with XI (11), forgetting that a smaller numeral placed before a larger one means subtraction, while one placed after it means addition.

Exercises in the Roman Numerals (I-XII) template involve converting traditional Arabic numerals to their Roman equivalents and vice versa. Children match equal values, fill in missing symbols in number sequences, or tell time on clocks with Roman numeral dials.

In grade 3, children perform practical clock calculations using units of time such as the hour and the minute. Students can convert full hours into minutes (remembering that one hour is 60 minutes) and determine how much time has passed between two given points in time using the 24-hour system.

The most common mistake at this stage is intuitively treating the passage of time like a standard base-10 decimal system. Children often assume that an hour has 100 minutes, which leads to errors when adding and subtracting—for example, writing 14:60 instead of 15:00 after 14:50, or making mistakes when subtracting minutes mentally.

Exercises that practice this skill are based on everyday situations and come in two main forms:

• Convert hours to minutes – the child converts a simple duration of time, for example, calculating how many minutes are in 2 or 3 hours;
• Clock calculations — duration – the student checks the start and end times of an activity (e.g., a lesson, a movie, or a trip) and calculates how many hours and minutes it lasted.

In 3rd grade, children move comfortably within the range of numbers from zero to 1000. They can read a written three-digit number, as well as write a number given in words using digits. At the same time, they understand the structure of decimal notation: they can point out which digit represents hundreds, which represents tens, and which represents ones, and explain their meaning.

The most common difficulty at this stage is writing numbers that contain a zero in the tens or ones place. Children often drop the zero, for example writing the number six hundred five as 65 instead of 605, or conversely—they add unnecessary zeros, creating a phonetic notation, e.g., 6005.

In practice, the exercises involve converting word form into standard numerical form and vice versa. In tasks such as Write the number in digits, the child converts text (e.g., four hundred twenty-eight) into 428, while in the exercise Write the number in words, they write out the full name of the displayed three-digit number.

In Grade 3, a child analyzes the content of a word problem and devises their own strategy to solve it. Performing a single calculation is not enough here—the student must realize that several connected steps lead to the final answer. They record their solution using successive operations, an auxiliary drawing, or a missing-number equation.

The most common mistake at this stage is stopping after the first calculation. The child performs one operation using the numbers directly given in the text and immediately treats the resulting number as the final answer, losing track of the meaning of the final question.

In practice, these tasks involve analyzing multi-step situations where the result of the first step is essential for carrying out the next. In the worksheets, the exercise takes the form of matching tasks, in which the student matches the problem's text and individual stages with the correct sequence of calculations.

By the end of Grade 3, a child can easily recognize and distinguish basic plane figures: rectangle, square, triangle, and circle. The student identifies them in individual drawings, as well as finds them in their immediate environment and on the faces of three-dimensional solids.

A common problem at this stage is recognizing shapes that are rotated or hidden inside more complex compositions. Children often confuse a square resting on a vertex with a separate shape or miss smaller triangles that overlap and together form a larger shape.

In practice, tasks involve providing the correct name of a drawn figure (e.g., What is the name of the drawn figure?) or carefully counting specific shapes in a complex image, for example, in tasks such as How many triangles are in the drawing?.

In Grade 3, children perform simple calculations with larger numbers, working with three-digit values mentally (for example, of the type 250 + 50 or 180 – 30). Students use their own convenient calculation strategies and may write down intermediate results if necessary. At this stage, formal written algorithms (column addition and subtraction) are not yet required.

The most common problem with such calculations is confusing place values—for example, adding tens to hundreds (an incorrect result of 250 + 50 = 750 instead of 300) or losing whole tens when rounding up to the next hundred.

The tasks in this section are based on the template Adding three-digit numbers (without regrouping). Children solve simple problems presented as horizontal equations, practicing fluent manipulation of whole tens and hundreds without the need to set up vertical columns.

In 3rd grade, a child works confidently with three-digit numbers up to 1000. They can identify what each digit in a number represents and easily distinguish between the ones, tens, and hundreds places. For example, they understand that the digit 4 in the number 425 means four hundred (four hundreds), not just four.

A common mistake at this stage is confusing the tens digit itself with the total number of whole tens in the entire number. When seeing 350, children often state that there are only 5 tens, forgetting that 3 hundreds contain 30 tens. A zero in the middle of a number (e.g., in 408) also presents a challenge, where the absence of tens is sometimes overlooked, leading to an incorrect reading of the remaining digits' values.

On the worksheets, the exercises are based on specific tasks that develop this skill:

• Decompose the number into hundreds and the remainder — the student breaks down a three-digit number, separating whole hundreds from the remaining tens and ones (e.g., 542 is 500 and 42).
• How many whole tens — the child determines how many tens are contained in the entire given number, looking at it as a whole rather than just focusing on a single digit.

In grade 3, children are introduced intuitively to fractions by dividing concrete objects and shapes. They learn to divide a whole—such as a sheet of paper, a circle, or a chocolate bar—into two equal parts (halves) and into four equal parts (quarters). In addition to the division itself, children practice using the correct vocabulary, becoming comfortable with terms such as half, fourth part, quarter, as well as the phrase two and a half.

The most common mistake at this stage is overlooking the requirement of equal parts. Children often divide a shape with two arbitrary lines into four pieces and call each of them a "quarter," even if they differ in size. Another difficulty is confusing the terms: calling one of four parts a "half" or vice versa.

In tasks from the template Part of a whole (halves and quarters), children most often work with illustrations of geometric shapes or everyday objects. The instructions may ask them, for example, to color in a half or a quarter of a drawn shape, identify shapes divided into equal parts, or draw the missing half to complete a symmetrical whole.

By the end of grade 3, a child can easily continue a number sequence up to 1,000 by adding or subtracting a constant value. They count not only by 1, but also in larger steps—for example, by 2, 5, or 10—starting from any number, including odd numbers or numbers that are not multiples of ten.

Crossing the tens and hundreds thresholds when counting backwards poses the greatest challenge for children. A typical mistake occurs at points such as counting down by 10 from 304—students lose track of the digits in the hundreds or tens place and, instead of 294, write, for example, 204 or 394.

In tasks from the Count on by a constant step template, the child receives a sequence of several starting numbers and writes the next ones according to the discovered rule, or fills in missing links in increasing and decreasing number chains.

In 3rd grade, children perform calculations involving two operations with two-digit numbers (as well as in simple examples with larger numbers, such as 250 + 50). Students use their own convenient mental calculation strategies, and if needed, write down intermediate results below or next to the problem they are solving. At this stage, standard written column methods are not required.

The most common problem is mechanically solving the expression from left to right without paying attention to the operational signs. When a child sees an expression where the second operation takes precedence, they may disregard the correct rule and calculate everything sequentially. Holding the result of the first step in working memory while carrying out the second can also be challenging, which is why allowing students to write down intermediate results is so important.

Exercises from the Order of operations (two operations) template take the form of single numerical problems. The student's task is to determine which step to perform first, optionally write down the intermediate result, and provide the final result of the entire expression.

In 3rd grade, children perform mental calculations with larger numbers, adding and subtracting whole tens and hundreds (e.g., 20, 70, 300, or 500) to and from a given number. At this stage, column addition and subtraction methods are not yet used – the student relies on efficient mental math and, where helpful, partial written steps.

A common mistake is losing track of place value, for example, adding hundreds to the tens digit instead of the hundreds digit. Children also sometimes write an incorrect number of zeros in the answer, confusing the addition of tens with the addition of hundreds (e.g., treating the addition of 200 like the addition of 20).

In practice, children solve tasks that involve moving along a number line or completing simple equations, such as in the Jump by whole hundreds template, where they add or subtract whole hundreds to or from a given multi-digit number.

In 3rd grade, children intuitively use the properties of addition and multiplication to make mental calculations easier. Instead of calculating numbers sequentially from left to right, they notice connections between them and group them into convenient pairs, for example, by rounding addends up to full tens.

A common mistake is mechanically applying this flexibility to subtraction or division. Children try to change the order of numbers in operations like 15 − 7 or 20 : 4, forgetting that the order can only be rearranged freely in addition and multiplication.

In tasks from the Choose a convenient order template, the student is given a longer calculation and tasked with pairing the appropriate numbers. For example, when adding several numbers, they look for those that yield a round number, write them next to each other, and only then calculate the final sum.

In Grade 3, children perform mental multiplication by 10 for single-digit numbers and two-digit numbers less than 20 (from 1 to 19). Instead of tedious repeated addition, the student notices and applies a simple rule: multiplying an integer by 10 means appending a zero to the right of it (for example, 14 · 10 = 140).

A typical mistake at this stage is confusing multiplying by 10 with adding 10 (e.g., writing the result 13 · 10 = 23 instead of 130). It also happens that children drop the units digit of the number being multiplied or incorrectly combine digits for teen numbers (e.g., writing 15 · 10 = 1500, adding too many zeros).

Tasks from the Multiplying by 10 template involve directly entering the result of the mental calculation or filling in the missing number in an equation (written in the form of a blank box, e.g., 16 · 10 = … or … · 10 = 170).

In grade 3, a child multiplies two-digit numbers by 2, relying on mental math strategies rather than written algorithms. The student breaks down the number into tens and ones and doubles each part separately. According to the curriculum, they can give the result directly from memory or—if needed—write down partial results (for example, for the calculation 24 · 2, they write down 40 and 8, which gives 48).

The most common problem arises in examples that involve regrouping (e.g., 37 · 2). Children correctly multiply the tens (30 · 2 = 60) and the ones (7 · 2 = 14), but get confused during the final mental addition of these values or forget to add the extra ten resulting from doubling the ones.

Tasks from the template Multiplying a two-digit number by 2 come in the form of individual arithmetic problems (e.g., 18 · 2 or 43 · 2), where the student independently chooses a convenient method to reach the result and writes down the final number.

In 3rd grade, a child efficiently converts amounts of money, changing whole zlotys into groszy up to 100 zł. The student relies on a key financial relationship: 1 zł = 100 gr. Thanks to this, they can quickly determine how many groszy are in coins or banknotes of denominations such as 2 zł, 5 zł, or whole tens of zlotys.

The most common mistake at this stage is adding a single zero instead of two zeros, which results from confusing the conversion of monetary units with regular multiplication by 10 (for example, writing that 4 zł is 40 gr). Sometimes, intuitively understanding that the same value requires a much larger number when switching to a smaller denomination also poses a difficulty.

Tasks from the template Converting zlotys to groszy involve completing equations where an amount in zlotys is given, and the student must enter the correct number of groszy (e.g., 7 zł = … gr). In this way, the child practices the computational automaticity necessary for everyday shopping and giving change.

In Grade 3, the child analyzes the content of simple and multi-step word problems to identify only those numbers that lead to answering the given question. The student develops their own solution strategy and presents it using a written mathematical operation, an equation with a box (placeholder), or a supporting drawing.

A common mistake made by children at this stage is mechanically performing operations on all the numbers that appear in the text. Upon seeing several values, the student tries to add or multiply them without reflection, without checking whether each of them is actually related to the final question.

The tasks from the Which data is needed template contain short stories with intentionally added distracting information. The child's task is to identify or underline only the numerical data necessary to perform the calculations, and then write down the correct operation.

In Grade 3, a child can compare two numbers and precisely calculate the difference between them within the range up to 1000. They understand phrases such as how much greater and can choose the correct operation—subtraction—to determine how much one value exceeds another.

A common mistake children make at this stage is automatically adding the numbers when they see the word greater. Instead of calculating the difference between the given quantities, they sum them up, confusing the question how much more with the instruction to increase a number by a given value.

Exercises from the How much more template involve comparing two numbers and writing down the operation that calculates the difference. The child compares the given quantities and indicates by how many units the first number exceeds the second.

In Grade 3, children learn the basic units of mass—gram, decagram, kilogram, and ton—and the relationships between them. At this stage, students primarily practice converting larger units into smaller ones, smoothly converting whole kilograms into decagrams based on the knowledge that 1 kg = 100 dag.

The most common mistake is confusing the number of zeros when converting units. Children often instinctively add only one zero (as when converting to tens) and write that 1 kg is 10 dag, instead of multiplying the number of kilograms by 100. They also find it difficult to intuitively distinguish when the result should be a larger or a smaller number.

Tasks from the template Converting kilograms to decagrams involve completing mathematical equations. The child is given a mass in whole kilograms (e.g., 4 kg, 7 kg) and tasked with entering the correct number of decagrams (400 dag, 700 dag).

In Grade 3, a child begins to consciously check their own calculations, using the relationships between operations. The student understands that addition and subtraction, as well as multiplication and division, are inverse operations. By the end of Grades 1–3, they can recall multiplication and division facts from memory and skillfully check division using multiplication as well as addition using subtraction.

A typical mistake at this stage is mechanically copying numbers without understanding their role in the operation. Children often subtract the wrong number from the sum or, when checking division, perform division again instead of multiplication. Sometimes, a student might write down a correct checking pattern "from memory" without noticing that their original result was incorrect.

Tasks that practice this skill most often involve performing addition and then writing a checking operation next to it using the template: sum minus one addend equals the other addend. This allows the child to independently verify the accuracy of their result and build confidence in their calculations.

In Grade 3, children use ordinal numbers to precisely determine the position of a given element in an ordered sequence. By the end of this educational stage, the student can identify the order of objects within the range of three-digit numbers, connecting the concept of an ordinal number (e.g., one hundredth, one hundred twenty-fifth) with its position in a sequence counted from the beginning.

A common mistake children make is confusing ordinal numbers with cardinal numbers—for example, answering how many objects they see instead of identifying which position a given element holds. Another difficulty lies in establishing the correct starting point and skipping the first element when counting (counting from zero instead of the first position).

In tasks of the type Which in line from the beginning, the student analyzes a sequence of objects or numbered positions and is tasked with identifying a specific element by always counting from the left or from the beginning of the line, and then writing down or selecting its correct ordinal number.

By the end of grades 1–3, a child navigates the number line up to 1000 smoothly, counting forward and backward by 1. In practice, this means accurately identifying the predecessor (the number that is 1 less) and the successor (the number that is 1 greater) for any given natural number.

Difficulties most often arise when crossing tens and hundreds boundaries. Children easily identify the neighbors of 456, but they make mistakes with round tens or hundreds—for example, mistakenly giving 209 instead of 299 as the predecessor of 300, losing track of the correct digit order when counting backward.

Tasks testing this skill combine knowledge of number order with addition. In the Sum of the successor and predecessor template, the student is given a single starting number, must independently determine both of its neighbors, and then calculate their sum.

In Grade 3, a child can not only solve ready-made tasks, but also independently create word problems and puzzles using given numbers. The student connects a real-life situation with a specific mathematical operation, choosing suitable content and formulating a clear question that leads to the solution.

A common difficulty at this stage is that the child only tells a story without posing a final question. It also happens that the student makes up a story where they immediately state the result—meaning it is no longer a problem to solve—or combines numbers in a way that makes no sense for the chosen situation.

In practice, using the template Create a word problem for the given numbers, the student receives a set of numerical data (for example, two numbers) and is tasked with inventing the story, writing a matching question, setting up the correct mathematical operation, and providing the final answer.

In grade 3, a child is able to skillfully use a ruler to draw straight line segments and connected broken lines. The student uses this skill to construct the sides of basic geometric shapes, such as rectangles and squares.

A common problem at this stage is the ruler slipping while drawing with the pencil, which leads to crooked lines or imprecise corners. Children also sometimes start drawing from the edge of the ruler instead of the zero mark on the centimeter scale, causing the drawn sides to have the wrong length.

Practical tasks most often involve drawing a shape with specific dimensions—for example, a rectangle with given side lengths. The child must measure out the appropriate segments, carefully draw straight lines, and connect them at right angles.

In grade 3, a child can measure liquids and use the concepts of a liter and a half-liter. They understand the basic relationship that one liter holds exactly two half-liter containers and can apply this knowledge to simple mental calculations.

The most common mistake at this stage is confusing the number of bottles with the actual number of liters. Children often automatically divide or multiply the given values, forgetting that two half-liter bottles together make only one full liter of liquid, not two.

In tasks such as How Many Bottles Will the Juice Fill, the student solves practical word problems. For example, they calculate how many half-liter bottles are needed to pour out a specific number of liters of juice, or how many liters of a drink are contained in several such bottles.

In 3rd grade, a child can analyze a given sequence of numbers, determine the repeating pattern, and fill in the subsequent missing values. The task involves quickly identifying by how much adjacent numbers increase or decrease, which requires proficient mental addition and subtraction.

The most common mistake students make is focusing solely on the difference between the first two terms of the sequence without checking the subsequent steps. Children also often confuse the direction of change—instead of consistently subtracting a constant value in a decreasing sequence, they begin adding it back, losing track of the previously discovered rule.

Exercises from the Continue the Number Pattern template take the form of rows of numbers with empty spaces at the end or in the middle of the series (e.g., 12, 16, 20, ..., ...). The student's task is to write in the missing numbers according to the discovered rule.

In Grade 3, a child proficiently uses the concepts of vertical, horizontal, and diagonal (slanted) in relation to shapes, lines, and objects in space or on a sheet of paper. They can confidently indicate the orientation of an element and independently draw a straight line running in a specified direction.

The most common difficulty at this stage is confusing vertical lines with horizontal ones. Children also sometimes describe any line drawn at a slight angle as curved, rather than recognizing and naming its slanted, or diagonal, orientation.

Tasks from the template Vertical, Horizontal, or Diagonal involve analyzing drawings of line segments, arrows, or everyday objects. The student identifies their orientation by choosing the correct name for the direction, or draws lines according to the given instructions.

In 3rd grade, a child can identify a longer or shorter object and precisely determine the difference between them. Instead of relying solely on visual judgment, the student compares two numerical values representing length and, using subtraction, determines by how much one quantity exceeds the other.

A common difficulty at this stage is confusing the question how much longer with asking what the length of the longer object is. Children also sometimes struggle to set up the calculation correctly and, instead of subtracting the smaller value from the larger one, try to add the two numbers together.

In tasks such as How Much Longer Is the Ribbon, the student analyzes illustrations or numerical data showing two strips, ribbons, or line segments. Their goal is to read both measurements, write down the appropriate subtraction, and state the exact difference in length.