Mathematics — Grade 4 of Primary School

In 4th grade, children consolidate flexible addition within the 100 number range with regrouping (bridging tens). To do this, they use reliable mental or semi-written strategies without having to rely on column addition. Typical methods include decomposing the second addend (first bridging to the next ten, then adding the remainder) or calculating step-by-step in tens and ones.

Common mistakes occur when the regrouping is lost during mental calculation: children add the ones, but forget to add the newly formed ten to the tens place. In a problem like 47 + 28, for example, the result might be calculated as 65 instead of 75 because they calculate 40 + 20 and 7 + 8, but overlook the extra ten.

In the exercises, children encounter a wide variety of task formats:

• Simple calculations such as Addition within 100 with regrouping or How much is needed to reach the next ten.
• Comparisons and equations, such as Balancing both sides or Which sum is greater.
• Error analysis and checking, such as Check the result and find the mistake as well as True or false.
• Word problems, including Word problem with an extra number or problems with an unknown initial quantity.

In 4th grade, children master mental division within the number range up to 100. They understand division as the inverse operation of multiplication and derive division problems directly from the familiar core and basic multiplication facts.

Children often find it difficult to recall the matching multiplication fact as a calculation aid—especially when dividends are close to each other (such as 54 and 56). Another typical mistake is solving word problems mechanically without checking whether the number is shared equally or which number in the text is actually needed for the calculation.

Typical exercise formats reinforce this skill in different ways:

• Pure arithmetic problems on division using multiplication facts, as well as tables where the appropriate divisor must be found.
• Spot-the-mistake tasks where incorrect calculations are identified and corrected.
• Practical word problems involving sharing and grouping, such as determining package sizes or sorting with superfluous information in the problem text.

In 4th grade, children have mastered the multiplication tables up to 100 by heart. Not only do they solve simple multiplication problems directly in their heads, but they also understand the connections between the four basic arithmetic operations: they reliably derive inverse operations, recognize functional relationships such as between quantity and price, and use this conceptual understanding of operations as a foundation for written methods and solving word problems.

Difficulties often arise when tasks deviate from the familiar format. In missing-number problems, children often divide or add hastily instead of determining the missing factor deliberately using the multiplication sequence. Errors also easily occur when comparing two results if children calculate both multiplication problems correctly, but then determine the difference between the products inaccurately.

Typical task formats require a flexible application of the multiplication facts:

• Solving equations with a missing factor or determining how many times one number goes into another.
• Comparing results and determining which product is greater and by how much.
• Targeted checking of given calculations and spotting arithmetic errors, as well as handling problems with an extraneous number.

In Grade 4, children can reliably subtract within the number range up to 100 mentally or in manageable partial steps. In doing so, they use flexible strategies, such as subtracting tens and ones step by step. Standard written column subtraction is not intended for this number range here, as the focus is on understanding calculation strategies and number relationships.

Typical errors often occur when crossing tens: children then incorrectly subtract the smaller digit from the larger one (such as 52 − 7 = 55 instead of 45) or, in multi-step problems, forget which intermediate value remained after the first step. Confusing adding and taking away in word problems also frequently leads to incorrect results.

In the exercises, children work on a variety of task formats:

• Reliably carrying out two subtractions in succession or checking given calculations and finding errors.
• Solving word problems in which items are taken away or where they must determine how many there were at the beginning.
• Working on problems that contain an unnecessary number in order to selectively identify the relevant values for subtraction.

In 4th grade, children solve word problems involving euros and cents. In doing so, they recognize functional relationships such as the connection between quantity and price: If a notebook costs a certain amount, they can reliably calculate the total price for several notebooks. In addition, they determine exactly how much money is left over after a purchase or what amount is still needed to reach a specific total.

Common mistakes occur when crossing the decimal point between euros and cents or when calculating change. Children sometimes subtract amounts place by place incorrectly, forget to regroup from cents to whole euros, or do not accurately estimate whether the available money is actually enough for the planned purchase.

Typical task formats include the following exercises:

• Shopping and Change as well as How Much Is Still Missing: Completing missing amounts or calculating change.
• How Much Do Multiple Items Cost: Determining the price for a larger quantity of goods.
• Is There Enough Money and Which Coins to Pay With: Comparing amounts and selecting the appropriate coins and banknotes.

In Grade 4, children consolidate their understanding of addition within the number range up to 100. They perform this calculation reliably in their heads and skillfully use relationships between numbers to flexibly combine multiple values.

Difficulties often arise when multiple steps must be managed at once. When adding more than two numbers together, intermediate results are sometimes forgotten or regroupings across tens are carried out inaccurately. Reading larger steps on scales also occasionally leads to counting errors.

Typical exercise formats for this area include:

• Three addends at once: Skillfully adding three numbers together within the range up to 100.
• Addition on the number line: Following or drawing jumps and intermediate steps on the number line.
• Which problem has a different result: Comparing multiple calculations and finding the differing result.
• Fill in the result table: Systematically adding rows and columns and entering the sums.

In Grade 4, children grasp the mathematical core of short word problems within the number range from 100 to 1000. They translate everyday situations—often involving money, time intervals, or lengths—into the appropriate basic arithmetic operations and explain each step along the way to the result.

Often, signal words lead to hasty conclusions: for example, if a child reads the word together, they often automatically add, even though the context of the text requires subtraction. Determining an unknown initial value also leads to errors if children do not work backward through the chronological sequence of the story.

Typical task formats require either direct calculation or the targeted selection of the solution path:

• Which calculation solves the problem: From several given mathematical expressions, children choose the one that correctly represents the described situation.
• How many are left or were there at the beginning: Children determine a final quantity after a change, or work backward from an intermediate state to the original starting amount.

In Grade 4, children explore plane figures and determine the perimeter of a rectangle directly from given side lengths. They add all four sides or double both the length and width and add them together. Besides simply finding the perimeter, they also learn to think backwards: if the total perimeter and one side length are known, they determine the missing side of the rectangle.

A common mistake arises from confusing perimeter and area: children multiply the two known side lengths instead of adding all four sides together, or they only add length plus width and forget the opposite sides.

Typical task formats look like this:

• Perimeter of a rectangle: Two side lengths are given, and children calculate the total boundary of the rectangle.
• Missing side of a rectangle: The perimeter and one side are given; the other side length must be calculated.
• Which figure has the larger perimeter: Two given figures are compared mathematically to decide which figure has the longer boundary.

In Year 4, children solve word problems involving time by accurately calculating time intervals on a calendar. They determine the number of days between two given dates and calculate which day of the week a future or past date falls on.

A typical error occurs when counting days: often, the start date is mistakenly included, or the change of month is calculated inaccurately because months have varying numbers of days. Children also easily get confused when counting forward through the days of the week in a rhythm of seven, especially when crossing into a new month.

In the exercises, children work on specific word problems in two typical formats:

• How many days between two dates: Given two calendar dates, children calculate the exact number of days between them.
• Which day of the week will it be: Starting from a known day of the week and date, children determine the day of the week for another date.

In Grade 4, children consolidate basic arithmetic laws and intentionally use them to simplify calculations. Within the number range up to 100, they realize that addends can be rearranged or grouped conveniently in any order. They discover that different arithmetic expressions can have the same value and use this equivalence to make calculations easier.

A typical mistake occurs when children stubbornly work through problems from left to right instead of first looking at the expression as a whole. In doing so, they overlook matching pairs of numbers that add up to round tens, or they incorrectly apply commutative properties to other arithmetic operations.

In the exercises, children mainly encounter two types of tasks:

• Choose the convenient order: Rearranging and grouping numbers in an addition problem so that intermediate steps are easy to calculate mentally.
• Compare the two sums: Looking at two different expressions and recognizing, without lengthy calculation, whether and why they yield the same result.

In 4th grade, children compare and order different measurements, such as lengths and masses. They grasp properties such as lighter or longer and can not only determine an order, but also find specific differences between two objects.

Children often mix up the sequence when ordering, mistakenly starting with the heaviest instead of the lightest object. When determining differences, they also often forget to align both quantities to the same baseline or unit of measurement before comparing.

In practice, typical tasks look like this:

• Order from lightest: Several weights are compared with one another and written down in sequence.
• How much longer is the ribbon: Two ribbons of different lengths are compared side by side to determine the exact difference.

In 4th grade, children explore 2D shapes and calculate the perimeter of a square directly from its side lengths. They use the property that all four sides are equal in length: they either add the four lengths together or multiply one side length by 4. Conversely, they use division to determine the length of a square's side when the total perimeter is given.

Children often confuse perimeter with area. For example, they might multiply two side lengths together instead of adding all four sides along the outer edge, or they might forget two of the four sides when adding.

Typical task formats include:

• Perimeter of a square: A side length is given (e.g., 6 cm), and the child calculates the total perimeter.
• Square side from the perimeter: The total perimeter is known (e.g., 24 cm), and the child divides by 4 to find the length of a single side of the square.

In 4th grade, children determine the perimeter of plane figures directly from the lengths of their boundary lines. For a triangle, they add the three individual side lengths. They understand the perimeter as the total distance once around the figure and use addition as well as subtraction to calculate with these length measurements.

Children often forget one of the three sides when adding or confuse perimeter with area. In inverse problems, it is also frequently overlooked that both known sides must be subtracted from the total perimeter to find the remaining third side.

Typical exercises use templates such as Perimeter of a Triangle, where all three sides are given and must be added together. In tasks like Third Side of a Triangle, the total perimeter is given along with two side lengths, so children determine the missing side length through calculation.

In this area, children consolidate their orientation in the number range up to 1000. They confidently compare three-digit numbers with each other, arrange several values in the correct order from smallest to largest, and precisely determine how much greater one number is than another.

Common mistakes occur when children confuse place values. For example, if a number has a higher digit in the ones or tens place than the comparison number (such as with 438 and 483), it is hastily classified as the larger number, instead of systematically comparing the hundreds and tens places from left to right.

In the exercises, the children work on two typical task formats:

• Order five numbers: Five unordered numbers up to 1000 are written down sorted by size.
• How much greater — Numbers up to 1000: The children determine the exact calculated difference between two three-digit numbers.

In Grade 4, children use tools such as rulers or tape measures to determine lengths accurately. They know the units millimeter (mm), centimeter (cm), and meter (m) and can relate them to one another. Specifically, they convert mixed length measurements into a single, smaller unit.

Mistakes frequently occur due to the different conversion factors: while 1 meter equals exactly 100 centimeters, there are only steps of ten from centimeters to millimeters (1 cm = 10 mm). Children occasionally forget these place-value zeros or mistakenly add only a single zero for single-digit centimeter amounts when converting meters to centimeters.

Typical practice exercises require converting two-part measurements into a target unit:

• Converting meters and centimeters to centimeters, such as 2 m 45 cm to 245 cm,
• Converting centimeters and millimeters to millimeters, such as 7 cm 3 mm to 73 mm.

In 4th grade, children deepen their understanding of the measurement of time. They know the standard units second (s), minute (min), and hour (h) and relate them to one another. Specifically, they convert times from hours to minutes and determine the exact duration between a start and an end time, including in word problems.

A typical mistake arises from the familiar base-ten system: when converting between units, children mistakenly calculate using the number 100 instead of 60. For a calculation such as from 14:45 to 15:15, a decimal carryover is often attempted instead of adding the 15 minutes to the full hour and the remaining 15 minutes together.

Typical task formats require either direct conversion or determining intervals:

• Converting hours to minutes: Stating times such as 3 h or mixed quantities in minutes.
• Calculating time duration: Determining the interval between two times, such as departure and arrival times in a word problem.

In Grade 4, children independently analyze given tables. They specifically extract numerical values from the display to draw concrete conclusions: they determine which category occurs the most or the least, and calculate by subtraction how many more units belong to one specific area than to another.

When comparing, children frequently read inaccurately from the wrong row or column when multiple categories are placed next to each other. Another typical mistake occurs with questions like "How many more?": instead of determining the calculated difference between two table entries, children often just state the higher table value itself.

In the exercises, children work on tasks such as Which category has the most, where they must quickly identify the peak value. In templates like How many more according to the table, they compare two specific categories with each other and determine the difference between the two numerical values.

In 4th grade, children consciously use the equals sign as a symbol of balance on both sides. They recognize that both sides of an equation must have the same value, and they specifically determine a missing addend shown as an empty box.

Children often mistakenly understand the equals sign merely as an instruction to calculate the result. If the box is in the middle of the problem, some mistakenly simply add the two visible numbers instead of determining the difference from the total value or establishing equality.

Typical task formats include:

• Missing addend (placeholder problem): An addition problem contains an empty box into which the appropriate number must be entered (for example, as an incomplete sum).
• Insert the symbol between sum and number: The children compare an addition expression with a fixed number and insert the appropriate relational symbol.

In this area, children grasp the structure of the decimal place value system in the number range up to 1000. They understand the interplay between ones, tens, and hundreds places, and reliably connect spoken or written language with the appropriate numerical representation.

Common errors arise from the German way of speaking two-digit numbers, where the ones are named before the tens. With words like "dreihundertvierundfünfzig" (three hundred fifty-four), children often reverse the order of the digits and write, for example, 345 instead of 354. The zero as a placeholder in the tens place (as in "vierhundertsieben" for 407) is also occasionally forgotten when writing down the number.

Typical task formats support targeted practice of this conversion:

• Write the number in digits: A number word like "sechshundertachtzehn" (six hundred eighteen) is converted into the numerical form 618.
• Read the number in words: A given number like 802 is read aloud or comprehended as a number word.

In 4th grade, children match drawn plane figures to their correct mathematical terms. They examine geometric shapes based on their properties and describe relationships between them, such as the connection between a square and a rectangle. In addition, they reliably discover shapes in their environment and identify sub-figures within more complex drawings.

Children often find it difficult to recognize figures when they are rotated or overlap with other shapes. In counting tasks, they often overlook larger triangles composed of several smaller sub-triangles because they focus their attention only on the smallest individual units.

In typical tasks, students identify individual shapes directly, for example with questions such as What is the name of the drawn figure? In search tasks like How many triangles are in the picture?, they systematically count how often a specific shape appears in an overall drawing.

In Grade 4, children use approximate values to quickly check the plausibility of calculation results. They appropriately round monetary amounts to the nearest tens or hundreds, perform rough estimates, and use familiar benchmark objects as aids to realistically assess volumes and sizes in everyday life.

However, children often still try to calculate cent amounts exactly in their heads instead of rounding up generously. When estimating space or containers, they often lack a connection to known measurements, leading to results that are impractical in reality.

Typical practice tasks demand precisely this forward-thinking approach: In Estimating costs by rounding up, children determine whether pocket money is sufficient for a purchase by deliberately rounding up. In tasks such as Does it fit inside, they compare given measurements with everyday objects to realistically assess capacity.

Children master the basic addition facts up to 20 from memory. With this skill, they add single-digit numbers or solve problems such as 12 + 5, which do not involve bridging through ten. Number bonds and finding missing numbers up to 10 are also part of this established foundation in mental arithmetic.

Difficulties often arise when children still rely on counting rather than recalling problem patterns or known number bonds. Typical mistakes occur when counting on fingers inaccurately or through an off-by-one error when the starting number is mistakenly included in the count.

In class and on worksheets, children work on classic task formats to practice this:

• Addition up to 20: Straightforward arithmetic problems such as 4 + 3 or 13 + 4, which are solved without bridging through ten.
• Making ten: Missing addend problems to the number 10, designed to quickly recall number bonds from memory.

In this area, children understand the structure of three-digit numbers within the range up to 1000. They use the decimal place value system to confidently decompose numbers and determine how many hundreds or full tens are contained in a given number.

Children often confuse individual place values or overlook the value of a digit in its respective position. A typical source of error, for example, is asking for the full tens: with a number like 340, often only the digit 4 in the tens place is mentioned, instead of recognizing that the entire number consists of 34 full tens.

In typical task formats, children work on concrete decompositions:

• How many full tens: They determine how many times the value 10 is fully contained in a three-digit number.
• Decompose the number into hundreds and remainder: A number is divided appropriately, for example into full hundreds and the remaining amount.

Children discover the underlying pattern in a sequence and continue it. They determine the fixed interval between consecutive values and apply this step repeatedly—both forwards and backwards. In these exercises, children work within the number range up to 1,000.

Difficulties frequently arise when crossing tens and hundreds boundaries, especially when counting backwards. For example, when counting in steps of 20 or 50 across a hundreds boundary, children easily lose track of the place value system, skip numbers, or choose the wrong hundreds.

In the exercises under Count on in equal steps, children work with given number sequences. They first determine the step size from the initial numbers (such as 450, 475, 500 ...) and then independently continue the sequence with the correct next numbers.

In Grade 4, children use familiar basic addition facts to modify larger numbers mentally. They add and subtract exact multiples of 10 and 100, transferring known basic facts to analogous calculations in the numbers up to one million. In this way, a simple problem like 3 + 4 = 7 easily becomes a step like 300 + 400 = 700 or counting on from a large number.

Children often get confused with place value: they accidentally change the tens place instead of the hundreds place, or, when dealing with multiple zeros, forget which digit is actually being calculated. Regrouping over tens or hundreds also leads to mistakes when zeros are simply appended mechanically rather than considering place value.

Typical exercises run under task formats such as jumping by whole hundreds. In these, children start from a given number and jump forward or backward in steady steps of hundreds to consolidate confidence in flexible mental arithmetic.

Children use their knowledge of basic multiplication facts and apply it to working with tens. They multiply numbers under 20 by 10 and confidently calculate problems like 7 · 10 = 70 or 14 · 10 = 140 mentally. In doing so, they recognize the mathematical pattern that the place value of the initial number shifts one place to the left.

Often, children merely memorize the mechanical rule of "just adding a zero." For problems above 10, this can easily lead to uncertainty or confusion, such as when 14 · 10 is mistakenly understood as addition and calculated as 24. It is therefore crucial to understand that ones become tens and tens grow into hundreds.

Typical problems in the area of Multiplying by 10 consist of direct calculations such as 12 · 10 or 18 · 10, which practice the fast and automated conversion of basic numbers into the corresponding ten-value.

In 4th grade, children work on word problems with numbers ranging from 100 to 1000. In doing so, they learn to understand the context thoroughly and decide which numerical data are needed for the arithmetic operations and which are irrelevant to the actual question.

A typical mistake occurs when children only skim texts superficially and blindly calculate with all the numbers that appear. Often, the largest number is automatically combined with a smaller number without checking whether these values are logically related at all.

In the exercises under Which information is needed, children read short word problems that contain additional or unimportant numbers. The task is to identify the information necessary for the solution step and deliberately leave out unimportant details.

In 4th grade, children deepen their understanding of weights and relate the appropriate standard units to one another. They weigh objects properly using a scale and learn to convert measurements from one unit to another – especially when converting between kilograms (kg) and decagrams (dag).

Typical mistakes often arise from confusing conversion factors: since weight calculations usually involve a factor of 1000 (such as from kilograms to grams), children often forget that 1 kilogram equals exactly 100 decagrams. When converting, an extra zero is then mistakenly added or omitted.

In the exercises, children work on specific math problems: they convert given kilogram values into decagrams (for example, 3 kg = 300 dag) or, conversely, determine how many full kilograms a given number of decagrams represents.

In 4th grade, children use the clock as a measuring tool to accurately tell the time. They can read the exact time on both analog dials and digital displays and use it to calculate intervals of time.

Errors often occur when the hour hand is just before the next number. For example, if the clock shows 11:50, many children mistakenly interpret the hour hand as pointing to 12 already and read it as 12:50. Accurately converting between the 12-hour display and the 24-hour format for the afternoon also occasionally causes difficulties.

Typical tasks from the Telling the time template show analog clock faces with hour and minute hands. The children read the displayed time and write down the corresponding time in numbers or fill in the matching digital notation for morning and afternoon.

By the end of elementary school, children deliberately make use of the relationships between the basic arithmetic operations. In this area, within the number range up to 100, they apply subtraction as an inverse operation to independently check the result of an addition.

Often, children do not make calculation errors during the actual addition, but rather choose the wrong numbers for the check. Instead of using the calculated total as the starting point for the subtraction problem, they might, for example, subtract the two addends from each other or add the result again.

Typical tasks from the template Check addition using subtraction prompt children to solve a given addition problem and write down the corresponding inverse operation directly next to it. For instance, an equation like 43 + 28 = 71 is checked by forming the problem 71 − 28 = 43.

In Grade 4, children learn to assess random events with linguistic and logical precision. They systematically use the basic terms certain, possible, and impossible to make statements about draws or game situations.

Children often confuse possible with certain as soon as an event seems very likely—such as when a bag contains almost exclusively red marbles. Another typical mistake is placing one's own wishful thinking or personal experiences of luck above mathematical reality.

In the exercises of the template Certain, possible, or impossible, children assign given situations to these three terms. For example, they assess how certain it is to draw a specific marble from an urn or roll certain numbers on a die.

In 4th grade, children master the use of standard units of length: millimeters (mm), centimeters (cm), meters (m), and kilometers (km). They can represent the same length in different ways and relate them to one another—for example, as a decimal (2.5 km), in whole meters (2500 m), or in mixed notation (2 km 500 m).

A typical error occurs when children add values with different units directly without converting them first. As a result, 2 km + 300 m mistakenly turns into a calculation like 2 + 300 = 302, because the conversion factor (1 km = 1000 m) is overlooked during the calculation.

Typical problems therefore require adding lengths given in different representations. Children first convert the addends into a common unit or notation and then calculate the total result.

In this grade level, children reliably identify the predecessor and the successor of a given number in the number range up to 1000. They use their understanding of the number sequence to name the immediately adjacent numbers (that is, number minus 1 and number plus 1) and connect them through calculation.

Difficulties arise primarily when crossing tens and hundreds boundaries. For the predecessor of round hundreds such as 400, children occasionally write 409 instead of 399 by mistake, or in their haste they confuse the directions of predecessor and successor.

Typical exercises use the format sum of successor and predecessor. Here, children first determine both neighboring numbers for a given number and then add them together, for example for the number 250 via the calculation 249 + 251 = 500.

In Grade 4, children consolidate their understanding of standard units of length (mm, cm, m, km). In doing so, they learn the relationship between the units: 1 km equals exactly 1000 m. Children can break down mixed measurements of kilometers and meters and express them entirely as a meter value.

A typical mistake often occurs due to missing zeros in one- or two-digit meter values: if a task specifies 3 km 45 m, children often mistakenly calculate this as 345 m instead of 3045 m. The reason is that the three-digit nature of the thousands place is overlooked when simply joining the digits together.

In the practice exercises, children convert mixed notations step by step. A typical task is, for example: Convert: 2 km 350 m = ___ m.

In Grade 4, children work on multi-step word problems in the number range from 100 to 1,000. They understand functional relationships such as simple direct proportion (for example: If 3 items cost this much, how much do 6 items cost?) and assign the appropriate basic arithmetic operations to the individual steps of the practical situation.

Typical difficulties arise when children prematurely pick out individual numbers from the problem and calculate them without understanding the entire situation. Often, a necessary intermediate step is overlooked, or the connection between the intermediate result and the actual question is lost.

In the practice exercises (Template Multi-step word problem (combining)), children read a short everyday situation. They structure the solution path into clear steps, perform the calculations within the number range up to 1,000, and combine the intermediate results into a final answer.

In 4th grade, children learn to compare the probability of two events based on data. In simple chance experiments, they estimate which outcome is more likely to occur and use appropriate terms such as "is more likely than" or "has a greater chance than".

Children are often still guided by personal wishful thinking or favorite colors instead of counting the actual number of elements present. Another typical mistake is to pay attention only to the presence of a feature, rather than directly comparing the specific quantities of the two possibilities.

In the exercises for the template What are you most likely to draw, children look at a container with different colored balls, for example. They count the respective colors and determine which ball is most likely to be drawn in a blind draw.

In this area, children solve addition problems with three-digit numbers within the number range up to 1000. They use mental or semi-written calculation strategies. Standard column addition with regrouping is explicitly not required here; instead, children break down the numbers step by step, such as into hundreds, tens, and ones.

A typical error occurs when place values are confused with one another. For example, children might mistakenly add tens to hundreds or overlook a zero as a placeholder in a number like 405. Even when there is no regrouping, an inaccurate alignment of the place values quickly leads to an incorrect total.

Typical task formats such as Adding three-digit numbers (without regrouping) present direct calculations like 342 + 125 or 514 + 230. Children solve these tasks written horizontally and calculate the sum place by place in their heads or with just a few intermediate steps.

In 4th grade, children solidify their understanding of everyday simple fractions as part of a whole. They grasp what terms like half a meter (1/2 m), a quarter of a liter (1/4 l), or three-quarters of an hour mean, and use these fractions in connection with familiar units of measurement.

Difficulties often arise when children confuse fractions with fixed quantities instead of viewing them as a portion of a whole. For instance, a quarter of a liter is sometimes misunderstood as four liters, or children overlook that three-quarters of an hour consists of three quarters of a full hour.

Typical task formats under the topic Part of a Whole (Half and Quarter) ask children to identify and draw parts such as a half or a quarter in given shapes or in context problems involving measurements. For example, they determine the missing parts or calculate specific fractions of known quantities.

In Grade 4, children understand functional relationships using a fixed calculation rule. They apply a given multiplication rule to given values to determine the corresponding target values step by step and enter them directly into an input-output table.

Children often confuse the direction of the mapping or habitually apply an addition rule instead of the required multiplication rule. When some values are already given, some children also find it difficult to consistently apply the multiplication rule to each row or column instead of simply skip-counting in fixed intervals.

In the exercises under Fill in the table according to the multiplication rule, a table with given starting numbers is provided. Children multiply each of these by the given factor and enter the correct result into the corresponding blank space.

At the end of primary school, children deliberately check given calculations within the number range up to 100 for accuracy. They recalculate the problems independently, identify incorrect results, and replace them with the correct calculation result.

Typical errors often occur in problems involving crossing the tens boundary: children miscalculate by exactly one ten or forget to correctly add or subtract the ones in intermediate steps. Sometimes, an incorrect intermediate result is simply accepted without checking.

In the exercises for the template Correct the wrong result, children see completed arithmetic problems with an incorrect result. Their task is to identify the error, perform the calculation correctly again, and enter the right result.

In Grade 4, children use the ruler as a precise drawing tool. They confidently draw straight line segments and closed polygons on a square grid structure (the familiar grid paper pattern) to accurately represent geometric shapes according to specified measurements.

Often, the ruler slips while guiding the pencil, or children mistakenly start measuring from the outer edge of the ruler instead of the zero mark. Inaccurately following the grid lines also causes right angles to become skewed and opposite sides to no longer be exactly the same length.

Typical tasks ask them to: Draw a rectangle with the given sides. In doing so, children read the centimeter measurements for length and width, align the ruler precisely with the grid, and complete the shape with neat corners and straight edges.

In Grade 4, children determine the total number of possible combinations for simple combinatorial problems. They no longer experiment completely aimlessly, but instead capture all cases through a systematic approach. In doing so, they use tools such as sketches, tree diagrams, or tables to record all options in an orderly fashion and ensure that no variant is missed.

Typically, children often start writing down individual ideas in an unstructured way. As a result, they quickly lose track: some combinations are counted twice, while others are forgotten entirely. The main difficulty lies in maintaining a consistent organizing principle—such as keeping one property fixed first and then varying the others step by step.

Typical exercises are based on the question "How many different combinations are possible?". For example, children determine in how many ways different items of clothing like T-shirts and trousers can be combined, or how many different two-colored flags can be created from a given selection of colors.

In Grade 4, children consolidate their use of the standard units milliliter (ml) and liter (l). They know how these units relate to each other (1 l = 1000 ml) and can measure liquid amounts using measuring cups or suitable tools and divide them mathematically.

A typical error often occurs when calculating with different units: children add or divide numerical values without first converting all values into the same unit. For example, they add liters and milliliters directly together instead of converting everything to milliliters first.

In practical word problems such as How many bottles does the juice fill, children determine how many times a smaller quantity (for example, a bottle with 250 ml or 500 ml) fits into a larger volume (such as 2 liters of juice).

In 4th grade, children recognize and describe rules in arithmetic patterns and use these structures systematically. They examine continuous number sequences, discover the underlying calculation rule, and continue the sequence independently.

Children often only pay attention to the difference between the first two numbers and apply it too quickly to the entire sequence. Alternating operations (such as alternating addition and subtraction) or growing differences are then easily overlooked because not all given elements of the chain are checked.

Typical exercise formats like Continue the number pattern encourage children to analyze number sequences carefully. Children determine the respective step size and fill in the missing numbers correctly in the sequence.

In Grade 4, children master the standard algorithm for addition with confidence. They add three-digit numbers in columns, describe the individual calculation steps, and carry out the algorithm quickly and reliably.

A typical stumbling block involves carrying: when adding units or tens column by column and the sum reaches or exceeds 10, children sometimes forget to write down the carried digit in the next column or fail to include it in the following step.

Typical practice tasks consist of adding two vertically arranged three-digit numbers digit by digit from right to left and writing the total result below the calculation line.

In Grade 4, children learn the basic principle of measuring area: they determine the area of a plane figure by covering it completely and without overlaps using unit squares of equal size. Instead of abstract formulas, children use repeated counting or clever grouping of grid squares to measure areas and compare them with one another.

Children often confuse area with perimeter. Instead of filling the entire area with squares or counting all the inner grid squares, they mistakenly count only the edges of the squares along the outer boundary. Another common source of error is inaccurate tiling, where gaps are left or squares are counted twice.

In the exercises of the template How Many Squares Cover the Rectangle, children see given rectangles on a grid. They count the unit squares contained inside or determine the total number using rows and columns to state the exact area in grid squares.

In 4th grade, children record data in a structured way using tables and bar charts. They specifically extract values from these representations and use them to calculate total amounts across rows or columns.

Children often slip into the wrong row or column when reading a table and assign numbers to the wrong category. With charts, the scale of the axes is also frequently overlooked, leading them to count simple tick marks instead of reading the actual numerical value on the axis.

Typical task formats such as How many in total in the table require children to evaluate given entries and fill in missing totals using written or mental addition strategies.

By the end of 4th grade, children can accurately describe geometric solids and plane figures based on their characteristics and distinguish between them. They use the correct technical terms for this and also recognize typical shapes in everyday objects.

Children often still confuse three-dimensional solids with plane figures, for example, by calling a sphere a circle or a cuboid simply a rectangle. Distinguishing between similar solids, such as a cube and a cuboid, can also be difficult if the faces are not carefully counted and compared.

In typical exercises such as What is the name of this solid?, children look at an image of a three-dimensional shape and assign it the correct mathematical name.