Mathematics — Grade 4

Your child learns to capture the size of a flat figure as a number of unit squares: they cover the area with equal-sized squares or mentally cover it and count the squares. The curriculum also requires measuring or estimating areas with such units, as well as calculating the area and perimeter of squares, rectangles, and simple composite figures. The curriculum point does not specify a number range, so we do not give one here.

Children often count only the squares along the edge, overlook partial squares, or confuse area with perimeter. The reason: the area is a number of units inside the figure, while the perimeter is the length of its boundary. Anyone who counts side lengths instead of squares is measuring the perimeter, not the area.

In this section's worksheets, the covering tasks typically look like this:

• How many squares cover the rectangle: The child counts the unit squares.
• Area of a figure made of two rectangles: The child splits the figure and adds the partial areas.
• How many tiles are still missing: The child completes a partially covered area.
• Area by covering: right or wrong: The child checks whether a covering correctly fills the area.
• Area and one side: how long is the other: The child determines the other side length from the area and one side.

The child works with points in time and periods of time in simple everyday situations. They read clock times, figure out when something started, and calculate how long something lasted. The curriculum points on times with half and quarter hours, as well as hours and minutes, span several school years. For Grade 4, the focus is mainly on working with points in time and periods of time.

A typical mistake occurs when calculating across the full hour. For example, 10:50 plus 20 minutes is then written as 10:70, although 11:10 is meant. This often comes from thinking in the decimal system: an hour has 60 minutes, not 100. Similarly, 1 hour 30 minutes is sometimes read as 1.30 hours, although 1.5 hours or 90 minutes is meant.

Such tasks look, for example, like this:

• At what time did it start?
• Calculate the duration
• How many minutes have passed?
• How much longer one thing lasted than another
• Converting hours into minutes
• Daily schedule: put the times in order

There are also tick-box exercises such as Hours into minutes: choose the correct answer and Hours into minutes: true or false. For this topic, there are sample tasks for printable worksheets with solutions.

The curriculum points require presenting and solving simple combinatorial counting tasks. They do not name a number range for this. The tasks in this class work with small sets, where all possibilities can still be written out completely. What matters is that the child can justify the count and not just name a number.

A typical mistake: children forget possibilities because they do not proceed in a fixed order. For example, someone who has to combine every pair of trousers with every shirt easily overlooks a shirt with the second pair, or counts a combination twice because it is unclear whether the order matters. Without order, it is not noticed that something is missing.

Typical tasks in this area are:

• How many different pairs: true or false, or choosing the correct answer
• How many different combinations are possible and How many combinations from three kinds
• Write down all combinations: listing is the tool with which one counts completely
• How many pairs remain if one part breaks and How many more pairs after an additional part
• Known number of pairs: how many in the other set

As a suggestion of your own, not as a requirement: it helps to order the list by a fixed pattern, for example first all possibilities with the first part, then with the second. This makes it possible to check at the end whether anything is missing. The curriculum point on probability applies to the stage as a whole and is not practised specifically in the tasks of this class.

In 4th grade, children work with value tables in which a calculation rule is applied to numbers. Each number in the top row corresponds to a number in the bottom row. The child recognizes the rule from the given pairs and fills in the missing values. Particularly important here is the directly proportional relationship, for example when each number is always multiplied by the same factor, as with prices or quantities.

A typical mistake is guessing the rule from a single pair of numbers. For 3 → 12, both "plus 9" and "times 4" fit. Only a second pair, such as 5 → 20, shows that only "times 4" is correct. Often addition is used where multiplication would be needed. That is why it is worthwhile to check the rule you have found against all the given rows before filling in the blanks.

You will encounter these tasks on worksheets in the following forms:

• Fill in the table using the times rule: The rule is given, and the missing values are calculated.
• Value table: find the rule: The calculation rule is worked out from the given pairs.
• Which number went into the machine? From the result, you work backwards to the input number.
• Choose what comes out of the machine: For an input number, the matching result is found.
• Calculation program and A table that subtracts: Tables with a fixed sequence of operations.
• Correct the error in the table: An incorrect row is found and corrected.

Your child can read the number that belongs to a category from a table or a bar chart and calculate with these values. The curriculum points mention reading data from different forms of representation as well as interpreting column and bar charts and pictograms. These points describe the content for the whole stage, not only for Grade 4. For this topic, the curriculum points do not name a separate number range; the tasks work with the numbers that appear in the given table or chart.

A typical mistake: the child reads a number correctly, but from the wrong row or the wrong column. In a task such as "How many more according to the table," the child then calculates with the values of two categories that were not asked about. The difficulty often lies less in the calculation than in the matching: which number belongs to which category? A finger that moves along row by row can help with this. This is a tip from us and not a requirement of the curriculum.

Tasks on this topic take the following forms in this grade:

• How many more according to the table
• Bar chart: how many more
• Which category has the most
• The distance between the largest and the smallest value
• How many groups lie above the given number
• Difference between two rows: choose the correct answer or decide true or false

The tasks mainly require comparisons within one representation. The curriculum also mentions recognising manipulations in statistical representations, but this is not specifically included in the task formats offered here.

In Grade 4, the child carries out simple random experiments and repeats them. They record the results as absolute frequencies, that is, as the number of times something has occurred, and from these compare the chances of the events. This comparison is meant qualitatively, that is: greater, smaller, or equal. Exact probabilities as numbers are not required for this. For this learning point, the curriculum also does not name a separate number range.

A typical mistake is to look only at the number of one colour and not at its share of all the balls. If bag A contains 3 red and 5 blue balls, and bag B contains 2 red and 2 blue, the child often gets the impression that bag A offers a greater chance of red, because there are more red balls in it. What is overlooked is that in bag B the larger part of the balls is red. Another common mistake is to take a single result as certain. Repeated experiments help to recognise such distortions.

Typical tasks on the existing worksheets are:

• "Which chance is greater? Choose …": The child decides between two events.
• "Fill the bag: greater, smaller or equal chance": The child adds balls so that a given chance becomes greater, smaller or equal.
• "Correct the comparison of the chances": The child finds and corrects an incorrect comparison.
• "Did the character compare the chances correctly?": The child checks a character's statement and justifies their answer.
• "What do you most likely draw?": The child chooses the result with the greatest chance.
• "A bag with balls: what is more probable?": The child compares the probability of different draws from a bag.

The child learns to decide whether events are certain, possible, or impossible. This includes carrying out simple chance experiments such as coin tossing, rolling a die, or drawing from a bag, and saying which outcome is more likely to be expected. The curriculum does not require exact probabilities for this, but a qualitative description and a comparison, that is, without numerical values. The curriculum points for this area do not specify a particular numerical range.

People often confuse what possible means. A child may, for example, consider drawing a red ball from a bag containing only blue balls to be "possible," because one could simply "be unlucky." The correct view is: impossible means that it can never happen. Possible means that it can happen, but does not have to. How often a possible case actually occurs is a different question.

In class, the children encounter this classification in the task types that also appear on the worksheets:

• Fill the bag: Put balls in so that an event becomes certain, possible, or impossible.
• Certain, possible, or impossible: Assign statements to the matching category.
• True or false: Check a given classification.
• Correct it: Fix an incorrect classification.
• Choose: Select the appropriate classification from the given options.

For primary school, the curriculum also describes repeating simple chance experiments and presenting the results as absolute frequencies, for example in a tally chart. The worksheet tasks mentioned here mainly show the classification itself.

According to the curriculum, the child should write quantities with one or more units, interpret measurement specifications and carry out conversions. The named area units are km², ha, a, m², dm², cm² and mm². The curriculum points do not specify a separate number range for these conversions, so the difficulty depends on the numbers in the tasks.

A common mistake arises because 1 m = 10 dm: children then apply the factor 10 to areas as well and write 1 m² = 10 dm². The correct value is 1 m² = 100 dm². An area of 1 m by 1 m can be covered with 10 by 10 squares, each with a side length of 1 dm. Likewise, 1 ha = 100 a and 1 a = 100 m².

Suitable tasks in the offering of this area are:

• Convert to a larger area unit
• Convert to a smaller area unit
• Convert hectares to ares
• Convert ares to square metres

There is also the template “Convert to a smaller volume unit”. However, the cited curriculum points only mention area units.

In Grade 4, the child writes lengths in single-unit and multi-unit forms and converts between the units mm, cm, dm, m and km. A length can be written as, for example, 2 m 5 cm (multi-unit) or as 2.05 m (single-unit). For this, the child needs the relationships between the units, for example that 1 m equals 100 cm. The curriculum begins building the necessary ideas earlier; for Grade 4, the conversions and notations that this area practices are the most important.

A typical mistake lies in the direction of the conversion. When switching to a smaller unit, the number becomes larger: 3 m are 300 cm, not 0.3 cm. With multi-unit expressions, the decimal point is often placed incorrectly, for example when 2 m 5 cm is written as 2.5 m, even though it is 2.05 m. The cause is usually that the factors 10 and 100 between the units are not connected to an intuitive picture.

The worksheets in this area include three types of tasks: Converting to a smaller unit of length (e.g., 4 dm into cm), Converting to a larger unit of length (e.g., 750 m into km) and Expressing a length in one unit (e.g., writing a multi-unit length as a single number with one unit). As an aid, one can draw a step bar with mm, cm, dm, m and km and show each time how many steps one jumps. This is a suggestion for practice and not part of the curriculum requirements.

The child can determine the area of a rectangle by multiplying length and width. The child should also be able to explain why this formula works, for example by covering a rectangle with unit squares and counting them. The curriculum does not name a specific number range for this point; the concrete numbers are shown on the worksheets.

With rectangular areas, children often add instead of multiply, or confuse the perimeter with the area, because both are calculated with the same sides. With the missing side, many children struggle to see that the side being sought, together with the known side, must give exactly the given area. Mixed units of measurement, such as metres and centimetres in one task, also often lead to wrong results.

On the worksheets, the child meets three types of tasks:

• Area of a rectangle: length and width are given, the area is calculated.
• Missing side of a rectangle: the area and one side are given, the other side is sought.
• Area of a rectangle in everyday life: for example the size of a room floor or a flower bed, with a real-life context.

At home, it can help to measure rectangles in everyday life together and estimate the area before calculating. This is a suggestion of our own and not a requirement of the curriculum.

Your child works with points in time and time spans in Grade 4: they determine how many minutes lie between two clock times or how long something took, and they convert minutes and seconds into seconds. The curriculum points do not name a number range for this. The point on reading clock times with hours and minutes applies to a larger stage range, not only to this grade. The task templates for this grade mainly show calculating with time spans.

A typical mistake: minutes and seconds are written together like decimal numbers. For example, 2 minutes 15 seconds becomes the number 215 instead of 135 seconds, because the child calculates with tens instead of 60. It is similar with time spans that cross a full hour: anyone who calculates as in the decimal system from 10:50 to 11:15 easily arrives at a wrong result. The basis is always the same: one minute has 60 seconds, and one hour has 60 minutes.

The worksheets include three task templates for this, each with solutions for checking:

• Minutes and seconds into seconds: e.g., convert 3 minutes 20 seconds into seconds (200 seconds).
• How many minutes have passed? e.g., from 14:20 to 14:50 is 30 minutes that have passed.
• How long did it take? The start and end times are given; the duration is what is being sought.

Your child learns to model a variety of real-life situations: they read an everyday story, identify the important information, and set up the matching calculation. This also includes recognizing directly proportional relationships, for example that when the quantity doubles, the price also doubles, representing them in a table, and using them for calculations. The number range of this topic area extends to one million, and long division with a two-digit divisor is part of it. The curriculum itself does not name a specific number range for this topic, so for this grade I only describe what the available worksheet tasks show.

Typically, with multi-step problems, children stop after the first result or do not carry an intermediate number into the next step. The question is also often overlooked: for example, the total amount is asked for and not the price per item. With tasks that say "at most," people often round up as they would in everyday life, even though only complete sets count. A remainder of 3 is then turned into another set, even though it is not complete at all.

On the worksheets for this grade, you will find two types of tasks for this:

• Multi-step word problem (combining): several calculation steps lead to a single answer.
• How many full sets at most from the supply: a division in which only complete units count.

Practice tip: Have your child write down the intermediate results and read the question aloud again at the end. Solutions are available for the worksheets.

The child adds and subtracts multi-digit whole numbers in writing, that is, written one below the other in columns. For Grade 4, the curriculum names the number range up to 1,000,000. The curriculum point for the stage before (VS3) requires written calculation in the number range up to 1,000.

Typical errors arise mostly because place values are not observed:

• Places not aligned: The numbers are written offset, so that, for example, ones stand under tens. The result then has the wrong order of magnitude.
• Forgetting the carry: In 5,678 + 3,547, the carry from the tens is not written into the next column or is not added there.
• Subtracting the smaller number from the larger one: In 52 − 27, the child calculates 5 − 2 and 7 − 2, giving 35. When there are zeros in the minuend, such as 4,002 − 1,967, the regrouping across several places is often skipped.

The worksheets on this topic include the templates Adding in writing and Subtracting in writing. There, the child calculates tasks written one below the other in columns, and the solutions serve for self-checking. The curriculum point also names estimating results by rounding and approximation. A simple check is therefore the question: Does the result roughly match the rounded numbers?

The perimeter is the length of the boundary of a figure. According to the curriculum, this includes measuring or estimating the perimeter of plane figures and calculating the perimeter of squares and rectangles. The curriculum points do not specify a separate number range for this and refer to a larger section of primary school. For Grade 4, the tasks that are actually printed in this area are therefore the most important ones.

A typical mistake when a side is missing is that the child adds up the known sides instead of subtracting them from the total perimeter. With the perimeter of a polygon, one side is often overlooked, especially when the figure has more than four sides.

The worksheet presents the child with two types of tasks:

• Perimeter of a polygon: All side lengths are given, and the sum is required.
• Missing side from the perimeter: The perimeter and all but one side are given, and the missing side is calculated.

There are solutions for the worksheets, so that parents can follow the calculation steps.

Your child works with amounts of money such as €3.50 or €12.05. In doing so, they write quantities with multiple units, that is, in euros and cents, and can read and convert measurements correctly, for example €2.50 = 250 ct. The number range of 4th-grade mathematics lessons extends up to one million. The curriculum points themselves do not name a separate number range for money calculations.

A common mistake occurs with the decimal comma: an amount such as €3.5 is read as "3 euros and 5 cents" instead of 3 euros and 50 cents. Then sums and remaining amounts come out wrong. A similar problem arises when comparing prices: a child compares the total price of two packs of different sizes without checking how much each one contains.

Typical tasks in this area are:

• Which offer is cheaper? Two offers for the same goods are compared, for example for 1, 2 or 5 items. A table with the prices shows how the price rises with the quantity (direct proportionality).
• How much money is left over? The purchases are subtracted from the starting amount, and the change is calculated.

Printable worksheets with solutions are available for both types of task.

The Volksschule curriculum sets the goal of the number range up to 1,000,000: reading, writing, representing, decomposing, comparing, ordering and rounding numbers. The 4th-grade task templates practise above all comparing large numbers and thinking in place values, that is, the question of what value a digit has depending on its position.

A typical mistake arises with zeros. When a number contains zeros in the middle, these are easily forgotten when writing or reading it. 300 005 then becomes 3005, and 400 000 becomes 40 000, because the child does not correctly fill the position of the hundred thousands. When comparing, often only the first digit is looked at, even though the number of places decides. It helps to read digits with a place-value chart or with spaces as groups of three.

A task on this topic looks, for example, like this: numbers are compared using the symbols <, > or = (template "Comparing large numbers"). In "How many times as large? Place values", it is asked how often one number fits into another, for example How many times as large is 400 000 as 4 000? The worksheets for these templates are available to print, and solutions are included.

The curriculum states that arithmetic operations in the number range up to 1000 should be carried out flexibly using mental strategies (halbschriftlich), and that results should be estimated through rounding and estimation calculations. This applies to the entire stage and not only to Grade 4. For this grade, the task templates practised in this area are especially relevant: the child recognises when an addition or multiplication can be simplified by cleverly restructuring it.

A typical mistake occurs when a number is rounded and the correction is forgotten. For 398 + 57, some children calculate 400 + 57 = 457 and do not subtract the two extra again; the correct answer is 455. Something similar happens with multiplication: for 7 · 18 = 7 · 10 + 7 · 8, the second part is sometimes not multiplied by 7 but only added (7 · 10 + 8). The cause is usually that the child changes the number but loses track of what has been changed.

In practice, such a task might look like this: the child restructures calculations such as 99 + 143 or 25 · 16 so that they become easier, calculates afterwards, and compares the result with a rough estimate. Suitable practice problems with solutions are available as printable worksheets for the following templates:

• Adding cleverly: sums in which numbers can be completed to round values or easily rounded.
• Multiplying cleverly: products that can be broken down into simpler partial products.

The curriculum covers rounding numbers within the range up to 1,000,000. In Year 4, the tasks on this topic focus on rounding to the nearest thousand and rounding to the nearest ten thousand. Rounding also helps with estimation: you round the numbers first to estimate the approximate result of a written calculation.

A common mistake is to look at the digit in the rounding place itself or to take the wrong neighbouring place. What always matters is the digit directly to the right of the rounding place: if it is 5 or more, you round up; if it is 4 or less, you round down. Those who always round down or simply cut off the last digits will get a wrong answer for many numbers.

For example, a task might look like this:

• Rounding to the nearest thousand: 36 849 becomes 37 000, because the hundreds digit is 8. For 36 449, the hundreds digit is 4, so it is rounded down to 36 000.
• Rounding to the nearest ten thousand: 384 620 becomes 380 000, because the thousands digit is 4. For 385 000, the thousands digit is 5, so it is rounded up to 390 000.

The worksheets contain sample tasks with solutions that children can use to practise rounding.

In the number range up to 1,000,000, the child divides a multi-digit number by a two-digit number in written form, for example 4,872 ÷ 24. First, they estimate how often the divisor fits into the leading digits, and then they continue step by step until a remainder is left.

It is typical that the first digit of the result is estimated incorrectly, because the divisor is judged to be too large or too small. Then the remainder no longer fits the calculation. Often, a digit of the original number is also forgotten, meaning it is not brought down, or a remainder arises that is larger than the divisor.

Suitable exercises are the tasks on the worksheet "Dividing by a Two-Digit Number in Written Form": the child solves several divisions of this kind in writing, and the worksheets contain solutions for checking. As an additional supplement, for checking purposes one can practise estimation by rounding numbers and comparing the rough result with the exact one.

When estimating, the child rounds the numbers so that they are easy to calculate with, and thus obtains an approximate result. The curriculum names rounding and estimation calculations as a means of estimating results. For written calculations this is required in the number range up to 1,000,000, which is exactly the range this class works with (curriculum point VS4.2.1). For mental-written calculations in the number range 1000, the same strategy applies (VS3.2.1).

A typical mistake: numbers are cut off instead of rounded. For example, 48,972 rounded to the nearest ten thousand becomes 40,000 instead of 50,000. As a result, the estimate turns out significantly too low. Equally important is that an estimate is not the exact result. It serves to check whether the exact result is plausible.

In practice, the child works on tasks such as "estimate the sum": they round the individual addends to a suitable place value, add the rounded numbers, and then compare the result with the exact sum. The worksheets on this topic contain sample tasks with solutions that you can practise with together.

In Grade 4, children work with plans and maps. They enlarge and reduce plane figures, mainly with the help of grids, and they learn to read and draw simple plans (VS4.4.3). The scale connects a distance on the plan with the corresponding distance in reality. The curriculum entries give no specific number range for this skill.

The other curriculum entries on similar figures and rectangles drawn to scale describe a longer period. For this grade, only the part shown by the example tasks can be derived from them. A typical error is that the child measures the length on the map correctly but does not adjust the unit when converting. The child then gets centimeters even though meters or kilometers are asked for. A second common mistake concerns the direction of calculation: some children divide by the scale where they should multiply, or the other way round. Both arise when the scale is read only as a number and not as a ratio between map and reality.

One task type on this topic is distance on the map and in reality. The worksheets show example tasks with solutions for this, for instance:

• A distance on the map is measured, and the real distance is calculated using the given scale.
• A real distance is given, and the length on the map is to be found.
• The result is converted into a suitable unit, such as from centimeters into meters or kilometers.

The child can determine a fraction of a quantity or size. The curriculum specifically names the denominators 2, 4 and 8 for this. It also includes reading and writing fraction notation. The curriculum does not specify in more detail which numerical sizes come up at this point.

A typical mistake: the child divides only by the denominator and forgets the numerator. For three quarters of 20, it calculates 20 : 4 = 5 and stops there, even though that would only be one quarter. The task has two steps, and the second one is easily overlooked.

In class, this skill appears as the task "Calculating a fraction of a number". The worksheets for this area contain sample tasks with solutions for printing, so that at home you can follow the solution steps and check the results. A tip for home: the child can say the steps out loud, first dividing by the denominator and then multiplying by the numerator.

The 4th-grade curriculum requires students to write quantities with one or several unit names and to carry out conversions. The tasks in this area mainly print conversions into a smaller mass unit, for example from kilograms to grams or from tonnes to kilograms. The curriculum does not name a separate number range for masses; the numbers in this math area reach up to one million in 4th grade.

A typical mistake concerns the direction: because a smaller unit is needed to describe the same weight, the number becomes larger. Someone who divides by 1000 instead turns 3 kg into 0.003 g. It helps to picture that one kilogram consists of a thousand grams. For 3 kg, you therefore need three times a thousand grams.

A typical task looks like this:

• Convert 4 kg into grams. (Solution: 4000 g)
• Convert 2 t into kilograms. (Solution: 2000 kg)

As a suggestion of our own, not a curriculum requirement: Children can also consider whether 2500 g is more or less than 2 kg.

The child reads and writes fractions with small denominators, especially 2, 4 and 8, for example 1/4 or 5/8. The fraction stands for a part of a whole. The sample tasks in this area in Grade 4 mainly practise the fraction of a quantity: a/b of the whole.

A common mistake is that numerator and denominator get mixed up. For 3/4 of 20, the child then divides 20 by 3 instead of by 4, because they take the numbers in the fraction separately. The denominator, however, indicates into how many equally sized parts the whole is divided, and the numerator indicates how many of these parts are meant.

A typical task is, for example: Of 24 sweets, 3/8 are red. How many are red? The child works in two steps: 24 : 8 = 3 (one eighth of the sweets), then 3 · 3 = 9 red sweets. This is how fractions of quantities are determined.

In Grade 4, children should read, write, represent, order and round numbers up to 1,000,000. On the number line, this means they mark a number as a point and, conversely, read the number from a marked point. By the end of Grade 3, numbers up to 1,000 were broken down, compared and rounded; the larger number range is added in Grade 4.

A typical mistake arises when children count the tick marks instead of paying attention to the value of the steps. If there are several ticks between two labelled numbers, each step has a value other than 1. If they then simply keep counting, they end up at a wrong number. This happens especially often when jumping over a ten, for example from 47 past 50, because the ten is overlooked as an intermediate stop.

A task on the topic "jumping across tens on the number line" could look like this, for example:

• The arrow starts at 47. Where does it land after a jump of +5? (Solution: 52, with the intermediate stop at 50.)
• Which number lies exactly between 60 and 70 if the number line is labelled in steps of ten?

The worksheets on this topic are printable and include solutions, so you can use the tasks directly at home or in the classroom.

In Grade 4, the child learns to write quantities in standard units and to perform conversions. Tasks in this area require a step into a smaller volume unit: for example, how many milliliters 3 ℓ makes. The child should understand that one liter consists of a thousand milliliters and that the number therefore becomes larger.

A typical mistake is to calculate with 10 or 100 instead of 1000, because the child transfers calculating in the base-ten system to the unit. With decimal numbers, moving the decimal point is added to this: 1.5 ℓ then wrongly becomes 15 mℓ instead of 1500 mℓ. Here it helps to picture the amount: 1.5 liters is more than one liter carton and must come to clearly more than 1000 mℓ.

A task on this topic might look like this: "How many milliliters are 2 ℓ?" or "Convert 0.5 ℓ into mℓ." The template in this area is "Convert into a smaller volume unit." At home, you can use a liter milk carton and a small measuring cup as a help to make the size relationships clear.

The child can multiply multi-digit numbers in columns in writing. The curriculum names for this the written multiplication with a one- or two-digit multiplier in the number range up to 1,000,000. This specification describes the entire curriculum section and not only the 4th grade. For this grade, the worksheets show which tasks actually occur. This also includes estimating the result by rounding and approximating.

A typical mistake arises with place values. When the child multiplies by the tens digit, the partial result must be shifted one place to the left, otherwise the order of magnitude is wrong. Likewise, the carry is sometimes missing or is overlooked when adding the partial products. The individual calculation steps are then often correct, but the overall result is not. A short estimate before calculating helps to notice gross errors.

On the worksheets, the template "Multiplying multi-digit numbers in writing" fits this. The tasks are arranged one below the other in columns, for example 348 × 6 or 245 × 13. A sensible sequence is:

• first estimate roughly, for example 350 × 6 ≈ 2,100,
• then calculate exactly in columns,
• finally compare with the solutions.

The child recognizes, in word problems, when two quantities are directly proportional, such as number and price. It represents this relationship in a table and uses it for calculations. A central step is determining the value for one unit: if 4 notebooks cost 8 euros, one notebook costs 2 euros.

The curriculum point does not name a separate number range. In the mathematics area of the 4th grade overall, the focus is on numbers up to one million.

A typical mistake: the child continues calculating with the total amount instead of first dividing by the number of units, or multiplies where it should divide. Often it also stops at the given quantity and does not arrive at the value for one. The task requires two steps, and it is not always clear which operation is needed in the first step.

Suitable exercises can be found in the worksheets on this topic, which are available with solutions for printing. There are tasks of the form „What is it for one?“ The child sees a value for several units and works out from it the value for one unit.

In grade 4, the child works with points in time and time spans and applies units in word problems. When calculating with calendars, this means determining the time between two dates from two date entries. The curriculum does not specify a separate number range for this topic. We therefore describe here only what the tasks of this grade actually require: the number of days between two dates.

Mistakes often arise when a time span crosses the end of a month. Months have different numbers of days (28, 29, 30 or 31), and the child often calculates as if every month had the same number of days. Confusion also arises when it is unclear whether the starting day or the ending day is counted. A tip from practice (not from the curriculum): Let the child trace the calendar with a finger instead of only calculating in their head.

A typical task is: How many days is that? For example: How many days are there between March 3rd and March 15th? You can find such tasks as a worksheet with solutions in the Grade 4 Mathematics section.

The child learns to describe the position of line segments in the plane. Two line segments are parallel if they have the same direction and never meet. They are perpendicular if they form a right angle. This also includes drawing right angles with a set square. The curriculum also mentions squares and rectangles. It describes this content for a multi-year section, not only for the 4th grade. There are no number ranges here, because the focus is on position and shape.

A typical mistake: line segments are judged by eye. On squared paper, slanted lines often quickly look horizontal or vertical, or an angle that is almost a right angle is taken to be a right angle. It helps to count the squares: a vertical line segment goes one square to the right and then one square up. Parallel line segments have the same steps in both directions.

The worksheets in this area contain the task „Parallel oder senkrecht?“ (“Parallel or perpendicular?”). There, the child decides, for line segments on a grid, which position they have and justifies the answer. To check, the child can measure again or redraw with a set square.

The child learns to tell apart three straight objects in the plane. The curriculum points do not name a number range for this, because the topic is about shapes and their position, not about numbers. The requirement is to describe positional relationships of line segments in the plane.

A typical mistake is confusing a ray with a line segment, because both begin at a point. Likewise, a straight line is often called a line segment, because only a piece of it is visible on the sheet. The reason: a drawing is always limited, but the terms describe how the object continues beyond the edge of the paper.

• Line segment: has two fixed endpoints and a definite length.
• Ray: has a starting point and continues without limit in one direction.
• Straight line: has no endpoint and continues without limit in both directions.

The task template Line segment, ray or straight line? asks which of these objects is shown. The child must choose a term for it and justify the choice. The available tasks on this topic do not show whether drawing right angles, squares and rectangles with a set square is also planned for this class. This description is therefore limited to distinguishing the three objects.

In Grade 4, your child reflects individual points across a straight line. The mirror image lies on the other side of the line, on the same perpendicular to the line, and at the same distance as the original point. If you connect the reflected points, you get a figure that matches the original figure.

Overall, the curriculum describes that plane figures are examined, described and compared, especially symmetrical objects, and that axially symmetric figures are recognised and constructed. For Grade 4, the tasks in this area mainly show reflecting points across a straight line.

A typical mistake: the mirror image is placed on the same side of the line as the original point, or it lies on the other side but at a different distance. This often happens when drawing by eye instead of counting how far the point is from the line.

A typical task shows a straight line and a few points beside it. Your child draws the mirror image for each point and connects the points to form a figure. The task is called Reflect a point across a straight line in the offer, and solutions are included.

The child recognizes geometric solids by their properties and can describe and compare them. This includes whether a solid has flat or round faces, whether it has corners, edges or a point, and whether it is symmetrical. For this topic the curriculum does not specify a number range, because it is about shapes and not about calculating.

Solids that look similar are often confused, for example cones and pyramids, because both have a point, or cylinders and prisms, because both have identically shaped base and top faces. The child then often focuses on just one feature, for example the point or the base, instead of checking all properties. It helps to ask: Which faces are flat, which are round, and how many corners does the solid have?

A typical task is the template "Which solid is this?", in which the child identifies a solid based on a description or illustration. The printable worksheets with solutions are suitable for practice. The curriculum also calls for working with solids in a playful and systematic way, especially with symmetrical objects. The curriculum point on surface areas and volumes of prisms and pyramids applies to the whole area and is not practiced in the tasks presented here.

The child learns to break a flat figure made up of rectangles into simpler parts. They calculate the area of each sub-rectangle and add the results. The curriculum requires calculating the area of squares and rectangles as well as simple figures composed of these. The curriculum items U1.3.2 and U3.3.1 describe the content over a longer period. Which number range actually occurs in Grade 4 is shown by the sample tasks.

It is typical for children to confuse perimeter with area: they add the side lengths even though the question asks for the area. It also often happens that a part is forgotten or counted twice when decomposing the figure. The figure looks like a single surface, but the calculation requires two separate steps: first calculate each partial area, then add the results.

A task on this topic can be found in the worksheet „Flächeninhalt einer L-Figur“. There, an L-shaped figure with given measurements is provided. The child divides it into rectangles, calculates each area, and states the total area. The solutions on the worksheet help to follow the calculation steps.

A net is the flat form of a solid: you cut the edges of a cube and unfold it. The child learns to imagine how a flat figure looks when folded together. The curriculum for primary school as a whole states that simple solid models and nets are examined, matched, and created. For the 4th grade, the task template for this area mainly shows examining: Is a drawn figure a cube net?

A typical mistake: the child counts six squares and therefore considers the figure a net. What matters, however, is whether, when folded, each of the six faces is covered exactly once. If two squares land on the same face when folded, another face is left missing, even if the number is correct. Anyone who only looks at the appearance of the figure instead of at the folding easily overlooks this difference.

In practice, it comes down to tasks like "Is this a cube net?": a figure made of squares is shown, and the child decides, with a short justification, whether it can be folded into a cube. As an aid, the figure can be cut out and actually folded. The curriculum point on cuboids with formulas for surface area and volume (U1.3.3) extends beyond the 4th grade and is not described here as a requirement for this grade.