Mathematics — Grade 3

The child reads and shows times in hours and minutes, including half hours and quarter hours. It works with points in time ("When does it start?") and durations ("How long does it take?") in simple everyday situations. The curriculum points describe a period spanning several school years. For Grade 3, the printed tasks mainly show how hours and minutes are related and how to calculate durations with them.

A typical mistake: minutes are treated like tens and ones, as if they were in the base-ten system. Then, for example, "1 hour 45 minutes plus 30 minutes" becomes "1 hour 75 minutes" instead of "2 hours 15 minutes". Similarly, the idea arises that an hour has 100 minutes. The reason is that time is counted in a base-sixty system and not in the base-ten system like the numbers the child is otherwise used to.

In class, the child encounters tasks such as:

• At what time did it start?
• Calculate the duration
• How many minutes have passed?
• Convert hours into minutes (also as a "true or false" choice or "choose the correct answer")
• Daily schedule: put the times in order
• How much longer one lasted than the other

The child represents simple counting tasks and solves them by finding and counting all the possibilities, for example when they need to know how many different pairs can be formed from two sets. For this skill, the curriculum points do not name a separate number range. They describe the level for primary school as a whole. In Grade 3, the tasks in this area mainly show the task types listed below.

Children often do not work systematically. They write down combinations in no particular order, and then one possibility is missing or the same one appears twice. A fixed order helps: one part stays the same, and the other is changed in turn. This way, when writing things down, you can see immediately whether something is missing.

In practice, the child encounters tasks such as these:

• How many different combinations are possible?
• How many combinations are there from three kinds?
• Write down all the combinations, for example in a list or table.
• How many different pairs: true or false?
• How many different pairs: choose the correct answer?
• How many pairs remain if one part breaks?
• How many more pairs are there after one additional part?
• Known number of pairs: how many parts does the other set have?

The curriculum points also connect counting possibilities with the qualitative comparison of the probabilities of everyday events. Anyone who knows the possibilities completely can more easily describe whether something is more likely or less likely.

The child calculates the perimeter of a square, that is, the length of its edge. The curriculum requires measuring or estimating the perimeter of plane figures and calculating the perimeter of squares and rectangles. In this grade, work is done in the number range up to 1000.

A typical mistake is adding only two or three sides because one side gets overlooked. Just as often, perimeter and area are confused, and side times side is calculated. It helps to trace the edge side by side and name each side while adding.

The tasks in this area on the perimeter of a square look like this:

• Perimeter of a square: direct calculation from the given side length.
• Perimeter of a square on grid paper: The perimeter is determined from a figure on grid paper.
• Side of a square from the perimeter: The calculation runs backwards, from a given perimeter to the side length.
• By how much do the perimeters differ: Two perimeters are compared.
• find the error, right or wrong, choose the correct answer: Calculated solutions are checked or chosen from multiple-choice answers.

The curriculum point also mentions rectangles. However, this area has no separate templates for them; the tasks here revolve around squares.

The curriculum points describe this area across several school years and name tables, column and bar charts, as well as pictograms. This page only covers what the 3rd grade tasks show: reading and comparing values from tables and column charts. The numbers lie within the number range up to 1000, which the class works with overall. For this topic, the curriculum points do not name a separate number range.

A typical mistake is, when asked "How many more?", to name only one of the two values or to add the two values instead of subtracting. Often the child finds the right row or column but then does not consider how the two values relate to each other. It helps to first name both values aloud for each task and then ask what the question actually requires.

Tasks on this topic look like this in practice:

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

Within the number range up to 1000, the child breaks a number down into hundreds, tens and ones. For example, for 375 the child says: 3 hundreds, 7 tens and 5 ones. This includes reading numbers from blocks, representing numbers with blocks, and reading and writing them correctly.

A typical mistake happens when the digits are not read according to their place value. For 205, the zero is overlooked and the number is written as 25, or for 352 the 5 is taken as the number of tens. This happens because the digits are read as individual numbers rather than as a bundle of hundreds, tens and ones.

On the worksheet, place value appears in tasks such as:

• Form the number from hundreds, tens and ones
• Split the number into hundreds and the remainder
• How many full tens, for example: How many full tens are in 468? (46)
• How many ones in total
• Read the number from the blocks
• Place value: how many full tens and Place value: true or false, for example: 375 has 3 tens. (false)

In the number range up to 1000, the child writes numbers one under another so that ones stand under ones, tens under tens and hundreds under hundreds. It then calculates from right to left. The curriculum point names for this written addition and subtraction as well as multiplication by a one-digit multiplier and division by a one-digit divisor. For multiplication and division there are currently no task templates in this range. The tasks show addition and subtraction with three-digit numbers.

The error with carrying over is typical. For 468 + 357, 8 + 7 = 15 is written correctly, but the carried 1 in the tens column is then forgotten. When subtracting, the child often subtracts the smaller digit from the larger one, for example with 532 − 268 in the ones column 2 − 8 = 6, instead of borrowing a ten from the neighbouring column. A second common error: after borrowing a ten, the digit in the tens column is not reduced by one.

Typical tasks in this area are:

• Add three-digit numbers in writing
• Add three numbers in writing
• Written addition step by step
• Written subtraction up to 1000
• Choose the result of the written subtraction
• Correct the error in the written subtraction
• Missing addend in written addition

The child can say, in simple random experiments such as drawing from a bag, which outcome is more likely, less likely, or equally likely. To do this, it first relies on an intuitive feeling for "likely" and simply counts the possible outcomes. The curriculum does not specify a separate number range for this skill. The focus is on qualitative comparison, not on precisely calculating proportions.

A typical mistake: the child compares only the number of one colour and overlooks the total number. If the first bag contains 3 red balls out of 4 balls and the second contains 5 red balls out of 12 balls, the first bag has the greater chance of red, even though the second contains more red balls. The child therefore has to take into account how many balls are in the bag altogether.

Tasks on this look, for example, like this:

• Which chance is greater? The child chooses between two events.
• Fill the bag: It puts balls in so that one chance is greater, smaller, or equally large.
• A bag with balls: It decides which outcome is more likely.
• Which do you most likely draw? It names the colour that can most likely be expected.
• Improve the comparison of the chances and Did the character compare the chances correctly? The child checks someone else's reasoning and finds where it is wrong.

In Grade 3, the child calculates within the number range up to 1000. They should compare numbers in this range, that is, determine which number is greater or smaller, and order them, that is, arrange several numbers in sequence.

A typical mistake: the child looks only at the last digit. Then they consider 385 to be greater than 412, because 5 is more than 2. The reason is that the digits are treated like individual numbers instead of as hundreds, tens and ones. It helps to first compare the hundreds, then the tens if they are equal, and finally the ones. This shows that 412 is greater, because it has 4 hundreds and 385 has only 3.

On the worksheets, the child mainly encounters these task types:

• Which number is the largest? Several numbers are given, and the child circles or names the largest one.
• Order numbers up to 1000 from the smallest The child sorts a row of numbers from the smallest to the largest value.
• Insert the sign: numbers up to 1000 The matching comparison sign is written between two numbers.

The worksheets are available to print, and for every task there is a solution so that the answers can be checked together.

The child learns to recognize, name, describe, and compare flat shapes based on simple features. This concerns properties such as corners and sides, not numbers. The curriculum points therefore do not name a number range.

A typical mistake: The child names a shape based on how it looks in its current position. A rotated square may then be called a "rhombus" or a "rectangle", even though it is a square. Similarly, every shape with four corners is often named a "square". This happens when the child looks at the overall picture and not at the corners and sides.

For Grade 3, the task templates in this area show what is practiced:

• What is the name of the drawn shape? The child names a drawn shape.
• What is the name of this rotated shape? The child recognizes the same shape in a rotated position.
• How many triangles are in the picture? The child finds triangles in a composite picture.
• Is this the shape? True or false The child checks whether a name matches the shape.
• What is the name of this shape? Choose The child chooses the correct name from several options.
• Correct the name of the drawn shape The child corrects an incorrect name.

The curriculum also mentions symmetrical objects. However, there is no separate task for this among the task templates available here.

The curriculum requires children to be able to read and write numbers up to 1000. In Grade 3, this shows mainly in the child's ability to write a number like 472 as a sequence of digits, to translate the word form "four hundred and seventy-two" into digits, and vice versa.

A typical mistake occurs with zero in the middle. The child writes "two hundred and five" as 25 or as 2005. The reason: the word contains no tens, and the child often writes down only what they hear. It is therefore helpful to name the places explicitly: hundreds, tens, ones, even when a ten is missing.

The worksheets for this grade include matching tasks:

• Write the number in digits: The number is given in words and must be written in digits.
• Read the number in words: The digit number is converted into words.
• Zero in the middle: correct the way the number is written: The missing zero is added.
• Correct the error in writing the number and Is this way of writing the number correct?: Incorrect written forms are identified and corrected.
• Choose the correct way to write the number in digits: The correct form is selected from several written versions.

In Grade 3, the child estimates quantities and results in everyday life using ideas about approximate sizes, and assigns the appropriate unit of measurement. The numbers lie within the number range up to 1000. The curriculum describes estimating for many units of measurement (for example kg, m, ℓ or min). In this area, in Grade 3, Euro amounts and sums are primarily in the foreground.

A typical mistake occurs when rounding: the number 38 is cut down to 30 instead of rounded up to 40, so the overall result turns out too low. In addition, the unit of measurement is often missing when writing down the result, for example "42" instead of "42 €".

Typical tasks in this area are:

• Estimate a sum: round to the nearest ten
• Estimate a difference: round to the nearest ten
• Estimate costs by rounding up
• About how much do we pay together
• Does it fit in
• Find prices that match the estimate

The printable worksheets in this area include solutions, so the estimate can be compared with the exact calculation.

The child adds within the number range up to 1000 and skilfully breaks numbers apart, for example 298 + 415 as 300 + 415 minus 2. It also estimates results by rounding and approximating: 298 + 415 is roughly 300 + 400, so just over 700.

A common mistake when writing numbers in columns is that the ones, tens and hundreds are not lined up properly. Carrying is also forgotten when the sum of a column is greater than 9. The result then often looks plausible even though it is wrong. Estimation helps here: a result like 543 for 298 + 415 is obviously too small.

This class mainly practises addition tasks. The available task templates are:

• Add three-digit numbers (without carrying)
• Addition up to 1000: three addends
• Addition up to 1000: true or false
• Addition up to 1000: correct the wrong result
• Addition up to 1000: choose the correct result
• Find two numbers with the given sum

The templates for true or false and correct the wrong result are well suited to checking results. Differences (subtraction) are part of the skill, but are not available here as a separate task template.

In Grade 3, children work with the weight units kilogram (kg) and gram (g). They know that 1 kg = 1000 g, and they can convert weight measurements from kilograms into grams. The tasks in this area stay within the number range up to 1000.

A typical mistake arises because children transfer the conversion between centimetres and metres. There, 100 cm = 1 m, and so some children also calculate 1 kg = 100 g. As a result, conversions and complements are calculated incorrectly. A good reference point is to picture a 1 kg package of flour: it contains one thousand grams, not one hundred.

In class, children mainly encounter these types of tasks:

• Converting kilograms into smaller units, as well as tasks with true or false or with choosing the correct answer, in which conversions are checked
• How many grams are missing up to a kilogram and How much is missing up to a full kilogram, in which children add the remainder up to 1000 g to a given part
• How many portions the package is enough for, a word problem in which weight measurements from everyday life are applied

The child reads the time from a clock face: the hours on a dial numbered 1 to 12, and the minutes from 0 to 59. The curriculum describes this goal for the whole stage, from full hours through half hours and quarter hours to times with minutes. For this class, that mainly means the child can tell the short hour hand from the long minute hand and can read minutes on the clock face.

A typical mistake is confusing the two hands, for example when the child reads the long hand as the hour. The expression "halb drei" (half three) also often causes confusion: it means 2:30, not 3:30. The child may then see the hands correctly and still name the wrong time, because the way of speaking does not match.

The worksheets on this topic come in different task types, each with solutions:

• Read the clock: The child reads the time shown on the clock.
• Read the clock: which time does the clock face show: The child determines the time that the clock face shows.
• Read the clock: true or false: A given reading is judged as true or false.
• Correct the mistake when reading the clock: An incorrect reading is corrected.
• How many minutes until the full hour: The child counts the minutes until the next full hour.
• Which clock shows the earlier time: The child compares two clocks and chooses the earlier time.

The child connects the unit of measurement liter (ℓ) with real containers and bottles. It can state how much a container holds, interpret size information and write down results with ℓ. The curriculum point for this stage also covers relationships between units and conversions, for example milliliters (mℓ). In this grade's tasks, this shows up mainly when working with liters and half-liters.

A typical mistake is judging by shape: a tall, narrow glass seems bigger even though it holds less. Half-liter bottles are also often added up incorrectly, for example when a child does not recognize two bottles as one liter. Then the result is wrong, even though the calculation looks right.

In class, the child encounters tasks like these, which are available as printable worksheets with solutions:

• How many liters do that many half-liter bottles make?
• How many bottles does the juice fill?
• Capacity: true or false?
• Capacity: Which number of bottles fits?
• How much more does one container hold than the other?
• How many liters are still missing to fill it up?

In Grade 3, the child works within the number range up to 1000 and calculates mentally in partial steps, meaning with intermediate steps rather than only by writing numbers one under the other. When doubling a two-digit number, the task is broken down into tens and ones: for 34 · 2, the child calculates 30 · 2 = 60 and 4 · 2 = 8 and adds the partial results to get 68. In addition, the child should be able to estimate results by rounding and approximating, for example, that 38 · 2 is about 80.

A typical mistake occurs when adding the partial results. If the ones step gives more than 9, such as 7 · 2 = 14, often only the 4 is written down and the ten is forgotten. Then 74 becomes 64. Estimation helps to notice such errors: with rounded numbers (37 becomes 40, so 40 · 2 = 80), one can see whether the result is in the correct order of magnitude.

The worksheets on this topic contain the following types of tasks:

• Two-digit number times 2: direct calculation tasks such as 46 · 2.
• Multiplying by 2: choosing the correct result and Multiplying by 2: true or false: The child checks given results and recognizes errors such as the forgotten ten.
• Which number doubled gives this: the reverse, for example "Which number times 2 gives 58?"
• How much more after doubling both numbers: two numbers are doubled and the child compares the results.

The third-grade curriculum requires that children mathematically model a variety of real-world situations. In this grade, this is done with numbers in the number range up to 1000. An important part of this is picking out from a text the information that is actually needed for the calculation.

A typical mistake: many children calculate with all the numbers that appear in the text, because every number sounds important. For example, a price is added that does not count at all for the question being asked. When practising, it helps to read the question aloud first and then consider which numbers are needed for it.

There are worksheets with solutions on this topic. They contain, among others, these task types:

• Which information is needed
• Subtract two of the three numbers given
• One superfluous piece of information: choose the correct answer
• One superfluous piece of information: true or false
• Two steps and one number too many

In some tasks, the child decides which numbers they need. In others, they have to recognise a superfluous piece of information and still solve the task correctly, in some cases in two steps.

Your child learns to sort everyday events into three groups: certain (always happens), possible (may happen, but doesn't have to) and impossible (cannot happen). This is a verbal judgement of how likely something is, not a matter of numbers or percentages.

A typical mistake is confusing possible with certain or with impossible. An event that rarely occurs is then called impossible, or an event that is very likely is called certain. A helpful question is: could it turn out differently? If yes, it is not certain. If it cannot turn out any other way, it is impossible.

In the tasks of this class, this appears mainly in the following forms:

• Fill the bag: Your child places balls in a bag so that a draw is certain, possible or impossible.
• Certain, possible or impossible? Your child assigns statements about an event to one of these three groups.
• True or false: Your child checks whether a given classification is correct.
• Correct it: Your child corrects a wrong classification.
• Choose: Your child selects the appropriate classification from among the answers.

The curriculum for primary school also describes simple random experiments that are repeated and represented by their frequencies. The worksheets in this class show only the sorting and comparing part of this.

The child learns to write a length in two ways: single-unit in just one unit (235 cm) and multi-unit with two units (2 m 35 cm). The child recognizes that both notations describe the same length and uses the relationship 1 m = 100 cm for this. The curriculum requires writing quantities with the appropriate unit of measurement and applying relationships between units of measurement. The numbers stay within the number range up to 1000.

A typical mistake is treating the two units like two separate numbers. 2 m 35 cm then becomes something like "2.35 m" or "2 and 35", because the child does not see the centimeters as part of a meter. The same thing happens when adding: for 2 m 70 cm + 1 m 40 cm, children often add the meters (3) and the centimeters (110) separately and write "3 m 110 cm". The correct answer is 4 m 10 cm, because 110 cm = 1 m 10 cm. The error usually lies in not paying attention to the unit, not in the calculation itself.

In this class, tasks about lengths mainly appear in the following forms:

• Adding lengths written in different notations: The child calculates with lengths where one is given in single-unit and the other in multi-unit notation.
• Two length values together: right or wrong: The child checks whether a given calculation is correct.
• Two length values together: choose the right answer: The child recognizes the correct solution among several options.
• How many whole meters is that: The child determines how many full meters are contained in a length given in cm.
• How much longer one is than the other: The child compares two lengths and determines the difference.

In Grade 3, children learn that 1 km = 1000 m and convert back and forth between the two units. This belongs to the number range up to 1000, which the class works with throughout. The child should therefore be able to translate a statement such as "3 km" into metres, and, given a metre value, recognise how many full kilometres it contains.

A typical mistake is to carry over the conversion between metres and centimetres (1 m = 100 cm) to kilometres and calculate with 100 instead of 1000. Then "2 km" wrongly becomes "200 m". The reason: the number 100 is strongly anchored in the area of metres and centimetres and is adopted unconsciously. It helps to briefly ask yourself with every conversion whether a kilometre has more or fewer metres than a metre has centimetres.

Tasks on this topic look like this:

• Convert kilometres and metres into metres: Statements such as "4 km" or "4 km 250 m" are written completely in metres.
• Kilometres into metres: right or wrong: A conversion is given and the child checks whether it is correct.
• How many full kilometres is that: A metre value is grouped into full kilometres.
• How much is missing to the full kilometre: For a metre value, the child adds what is still missing to reach 1 km or to the next full kilometre.
• Kilometres into metres: choose the right answer: The matching conversion is selected from several options.

This topic does not involve a number range. It is about the position of lines on the sheet. The child should describe a line as horizontal if it runs from left to right, as vertical if it stands from top to bottom and is at a right angle to the horizontal line, and as oblique if it is neither of these.

A typical mistake arises because the name refers to the sheet and not to the line itself. If a child turns the sheet, a horizontal line suddenly becomes a vertical one. Lines that are only slightly tilted are also often named as horizontal or vertical, even though they are oblique. It helps to always check the line against the edge of the sheet or a table edge.

In the tasks of this area, the topic appears in the following forms:

• Vertical, horizontal or oblique: The child assigns a drawn line to one of these three names.
• Vertical, horizontal or oblique? True or false: The child checks whether a statement about a line is correct.
• Correct: vertical, horizontal or oblique: The child corrects an incorrect name.
• What kind of line is this? Choose: The child chooses the matching name from several options.
• Draw a line: vertical, horizontal or oblique: The child draws a line with a given position.

The curriculum also links this topic to drawing right angles, squares and rectangles with a set square. The tasks in this area mainly show the drawing of lines for this purpose.

Your child can read quantities from tally marks and tables and determine the total from them. It can also complete a table when the sum is known, and understand what a pictogram shows when one picture stands for several things. The curriculum points do not name a separate number range for this topic. The tasks for it work with counting and adding quantities from tables and pictures.

A typical mistake: the child reads only one row or only one column of the table and therefore arrives at a total that is too small. With pictograms, it counts the pictures and forgets that one picture means several things. With tally marks, the strokes are grouped incorrectly when the groups of five are not recognised cleanly. This usually happens because the representation is looked at only as a picture and not as information about quantities.

Typical tasks in this area are:

• How many in total in the table: The child forms the total from all rows.
• Pictogram: one picture stands for several: The child works out the quantity from the pictures and the value of one picture.
• The missing row when the sum is known: The child fills in the missing quantity.
• Total from the table: choose the correct answer: The child selects the correct total from several answers.
• Total from the table: true or false: The child checks whether a statement about the table is correct.

Drawing column and bar charts is mentioned in the curriculum points. For this topic, however, there is no task template for it in this area.

The child learns to state a length in one unit and convert it into another unit of length. The curriculum names units such as km, m, dm, cm and mm for this. The numbers stay within the number range up to 1000, which this area uses overall. For example: 2 m are 200 cm, and 350 cm are 3 m and 50 cm.

A typical mistake is to change only the unit and leave the number as it is, for instance 2 m = 2 cm. Children just as often confuse the direction: when converting to a smaller unit the number gets bigger, and when converting to a larger unit it gets smaller. This usually stems from the child remembering only a calculation rule such as "times 10" without knowing how many small units fit into a large one (1 m has 100 cm).

The worksheets for this area include three types of tasks:

• Converting to a smaller unit of length, for example 4 m into cm.
• Converting to a larger unit of length, for example 500 cm into m.
• Stating a length in a unit, where a length has to be written in the requested unit.

The solutions are included with the printable worksheets so that parents can check the results.

In Grade 3, the child learns to read and show times in hours and minutes and works with time spans in word problems. The curriculum does not name a separate number range for this. Calculating with points in time and time spans goes beyond Grade 3. Only the part that the tasks of this grade show is described here.

It is typical that children treat the clock like our base-ten system. If they write 1 hour and 45 minutes plus 30 minutes as "1 h 75 min", or calculate 2:30 minus 1:45 like a decimal number, a wrong result comes out. The reason: an hour has 60 minutes, a minute has 60 seconds. When working with time, the child must think in steps of 60.

Tasks on this topic in Grade 3 look something like this:

• Converting minutes and seconds into seconds, for example 2 min 15 s = 135 s
• How many minutes have passed?
• How long did it take?

In grade 3, children model a variety of real-world situations in the number range up to 1000. This means they work out from a text which pieces of information are important, which arithmetic operations are needed, and in what order to proceed. The curriculum point on proportional relationships belongs to a later level target and is not assumed in this grade.

It is typical that children stop after the first calculation step or confuse an intermediate result with a piece of information from the text. If, for example, they are asked how much money remains after two purchases, the child often only calculates the first price or takes the sum instead of the remaining amount. The reason usually lies in the fact that the text is not read as a sequence, but as a collection of numbers that are somehow linked together.

On the worksheets, such tasks appear in two forms:

• Multi-step word problem (combining): Several pieces of information are combined into one result, for example by first forming partial sums and then continuing to calculate.
• How many sets at most from the supply: The question asks how many complete sets can be made from an existing supply. The child must relate the supply and the quantity per set to each other and take into account that only whole sets count.

Within the number range up to 1000, the child can carry out additions and subtractions in written form. In doing so, it writes the numbers one below the other so that ones are under ones, tens under tens, and hundreds under hundreds, and it calculates column by column from right to left. If a column results in more than 9 (carry-over), or if during subtraction a place value must be "borrowed" from the tens, this is explicitly noted.

A typical mistake is that the numbers are not lined up neatly one below the other. Then ones get combined with tens, and the result no longer matches the place-value notation. In subtraction, the following often happens: the child subtracts the smaller digit from the larger one in every column, regardless of which number is on top. From 52 − 37, this then becomes 25 instead of 15. A zero in the tens place is especially difficult, for example in 305 − 128, because borrowing must then be done across several places. Often the carry-over or the borrowing is forgotten in such cases.

A task on this topic consists of a calculation within the number range up to 1000, set one below the other. On the worksheets, you will find the templates "Addition in Written Form" and "Subtraction in Written Form", each with solutions. When practising, it helps to solve tasks step by step and to say the calculation in each column aloud.

In Grade 3, children learn to round numbers within the number range up to 1000. They decide whether a number is closer to the next full ten or the next full hundred, and write down the rounded result.

A typical mistake is simply cutting off the last digits. For example, 347 then becomes 340 instead of 350 (rounding to the nearest ten), and 851 becomes 800 instead of 900 (rounding to the nearest hundred). The reason: the child only sees the digits that drop away and overlooks that the digit to the right of the rounding place decides whether to round up or down. It helps to deliberately look at this neighbouring digit.

The tasks on the worksheets follow two templates:

• Rounding to the nearest ten, for example 347 → 350
• Rounding to the nearest hundred, for example 851 → 900

Solutions are provided for the worksheets, so parents can check the results directly.

The child can add up the side lengths of a figure to determine its perimeter. For squares and rectangles this means calculating the perimeter, and for other figures it means measuring or estimating it. The numbers stay within the number range up to 1000, as intended for this school level.

A typical mistake is counting only two of the four sides of a rectangle or forgetting one side. Another common error when finding the missing side: the child adds the known sides instead of subtracting them from the total perimeter. This often happens because the perimeter as the length of the whole boundary is not yet clear enough and gets confused with area.

The tasks for this topic are available as printable worksheets with solutions. They usually appear in two forms:

• Perimeter of a polygon: The side lengths are given, and the perimeter is to be found.
• Missing side from the perimeter: The perimeter and the other sides are given, and the last side length is to be found.

In Grade 3, your child works with numbers up to 1000 not only by following a fixed procedure, but by choosing a method that suits the task. They break numbers apart, calculate with easy intermediate steps, and check the result with an estimate, that is, by rounding to approximate values.

A typical mistake happens when a number is split up but only one part is carried on. For 8 · 25, for example, 25 = 20 + 5 can turn into the calculation 8 · 20 + 5 instead of 8 · 20 + 8 · 5. The child then forgets the second part. It helps to write down the intermediate results deliberately and compare them with the rounded result at the end.

On the worksheets, the tasks usually appear under the headings „Geschickt addieren“ and „Geschickt multiplizieren“, each with solutions. Your child can first think about which breakdown or order of steps simplifies the calculation, and then check the solution by comparing it with the estimate.

Children in Year 3 learn to estimate a result by rounding, within the number range up to 1000. To do this, the numbers are first rounded to tens or hundreds, and then the calculation is done with the rounded numbers. The curriculum describes this for addition and multiplication: results should be estimated by rounding and by estimation calculations.

A typical mistake is choosing the wrong place value when rounding, for example rounding 387 to 380 instead of 400. Then the estimate does not match the exact calculation, and the child believes they made a calculation error. Often the cause is that place value is not yet secure. A second mistake: the estimation calculation is understood as an exact result, even though it is only meant to give the approximate size.

A task could look like this: Estimate 487 + 329. You round 487 to 500 and 329 to 300 and get about 800. Then the exact calculation is done (816) and compared with the estimate. The available task template for this is called "Summe überschlagen" (Estimate the sum); the worksheets are printable with solutions. For multiplications, no separate templates are listed for this range.

The curriculum point describes the number range up to 1000 for the level as a whole. In Grade 3, the worksheet mainly focuses on this type of task: multiplying a single-digit number by a multiple of ten, for example 4 × 60 = 240. The child thinks: 4 × 6 tens are 24 tens, so 240.

A typical mistake is to leave out the zero and write 3 × 40 = 12. This happens because the child only calculates with the digits and forgets that the 4 here stands for 4 tens. It helps to imagine 3 packs with 40 pencils each, or to lay them out with tens rods: then you can see that the result is more than 12 ones, namely 12 tens, so 120.

The tasks on the worksheet Multiplying with multiples of ten are short calculations such as 3 × 40, 5 × 20 or 2 × 70, each with solutions. As a check, the child can estimate the result: 5 × 20 must be roughly 100, because 5 × 20 is exactly 100. This way you quickly notice when a zero is missing.

Your child learns to convert quantities of mass from a larger unit into a smaller one, for example from kilograms into grams. To do this, the child connects the units with concrete ideas, such as 1 kg as a bag of flour, and uses the relationships between the units. The numbers stay within the number range up to 1000.

A typical mistake is confusing the direction of the conversion: 3 kg then becomes 3 g instead of 3000 g. This often happens because the child does not consider that a smaller unit fits more of them into the same amount. Another common mistake is calculating with 100 for kg and g, because this is the case for decagrams (dag) and kg (1 kg = 100 dag).

A task of this type is, for example: Convert 4 kg into grams. The printable worksheets with solutions for this class include the task template "Converting into a smaller unit of mass" for this purpose. A good way to check the answer is to ask whether the result means more or fewer grams than the starting amount in kilograms.

In the number range up to 1000, the child can multiply a multi-digit number by a single-digit number in written form, for example 213 × 4. The calculation is written one number below the other, and the child works through the ones, the tens and the hundreds one after another.

A typical mistake occurs with carrying. If, for example, 3 × 4 = 12, the 12 is sometimes written entirely under the ones instead of writing down the 2 and adding the 1 to the tens. This usually happens because the place value is not yet being reliably taken into account: the ten from one place belongs to the next place.

A task in this area usually requires exactly this procedure:

• Write the task one number below the other.
• First multiply the ones and note down the carry.
• Then multiply the tens and hundreds and add the carry each time.

The printable worksheets for this area include the task template "Multiply a multi-digit number by a single-digit number in written form", each with solutions.

The curriculum requires that quantities such as litres (ℓ) and millilitres (mℓ) are linked to suitable mental images, written correctly and converted. The child should therefore understand quantity specifications, use the relationships between units and carry out conversions. This area works within the number range up to 1000.

A typical mistake when converting to the smaller unit is multiplying by the wrong number. Then, for example, 2 ℓ becomes only 200 mℓ, because the number 100 from other units stays in mind. Another stumbling block arises with multi-part quantities, such as 2 ℓ 50 mℓ, when the notation is confused with decimal notation.

• Mental image as an aid: A litre is an amount roughly equal to a large milk carton. The child can use this to check whether a conversion is plausible.
• Check: The number in millilitres must be clearly larger than the number in litres, and in fact a thousand times as large.

Tasks of this kind are in the template "Converting into a smaller volume unit". There, a quantity given in litres is converted into a smaller unit, for example into millilitres. The worksheets contain solutions that parents and teachers can use to check the results.

In grade 3, the child performs written division within the number range up to 1000 by a one-digit number. They divide place by place from left to right, write down each digit of the result, and carry on with the remainder. If the division does not come out evenly, a remainder is left that is smaller than the divisor.

The curriculum for primary school as a whole also covers larger number ranges and two-digit divisors. That belongs to a later learning unit and is not meant for this grade.

A typical mistake occurs when the first digit is smaller than the divisor, for example 3 hundreds divided by 4. The child then overlooks that the hundreds must be exchanged for tens and does not write a zero in the tens place. For 824 : 4, this produces 26 instead of 206. Counters or place-value strips are useful for practice, as they make the place values visible before the exchange.

The worksheets on the topic Dividing by a one-digit number in writing offer sample tasks in the number range up to 1000 for printing, each with solutions.

Your child can describe how two line segments in the plane are positioned relative to each other. Parallel means: the segments run side by side and would never meet. Perpendicular means: they meet at a right angle. The curriculum points do not specify a number range for this. It is about position and direction, not about calculating with large numbers.

A common mistake: the child judges the position only by eye. Horizontal and vertical segments are easy to notice. With slanted segments on a grid, it becomes harder. Two segments that each go two squares to the right and one up, or one to the right and two down, are perpendicular to each other, even though at first glance they do not look that way. Another misconception: two segments that do not touch are automatically called parallel, even if they point in different directions.

A typical task is "Parallel or perpendicular?" Here, the child decides for several pairs of segments on a grid which position applies. The printable worksheets include solutions with which you can check your child's answers. The curriculum also covers drawing right angles with a set square. For this part, there is currently no dedicated task template for Grade 3 in this area.

The curriculum covers basic geometric objects in the plane. The child is to work with the line segment, the ray, and the line, and describe how line segments lie relative to one another in the plane. In this grade, that mainly means: the child recognizes the three figures and names them correctly.

• Line segment: has two endpoints and has a measurable length.
• Ray: has a starting point and continues from there in one direction without end.
• Line: has no beginning and no end and continues in both directions without end.

A typical mistake: a line is drawn as a short stroke that ends at the edge of the paper, and is therefore named as a line segment. The child treats the edge of the paper like an endpoint. Conversely, a ray is often drawn with arrows at both ends, so that it looks like a line. This usually rests on the idea that the drawn piece is what counts, and not the direction and the starting point.

In this area there are worksheets using the template "Line segment, ray or line?". Here the child decides, based on a drawing or description, which figure is meant. The curriculum point also mentions drawing right angles, squares and rectangles with a set square. This area does not provide a separate template for these drawing tasks.

Your child examines plane figures and solids for their properties, works playfully and systematically with symmetrical objects, and recognizes figures with axial symmetry. The curriculum points describe this across several school years. In this grade, the task template shows concretely what is practiced: reflecting a point across a straight line.

A typical mistake is that the point is placed on the other side, but not at the correct distance from the line. Sometimes it is also shifted parallel to the line instead of perpendicular to it. This often happens because "reflecting" sounds in everyday language like "moving." It helps to count the distance of the point to the line and then mark the same number of squares on the other side, always at right angles to the line.

A typical task looks like this:

• A straight line and a point on one side are given, for example on squared paper.
• The child places the mirror point on the other side of the line, at the same distance.
• If several points are reflected and connected, a figure emerges whose two halves are identical.

The worksheets on this topic contain solutions that you can use to check your child's results.

The child examines solids more closely, describes them and compares them with one another. In doing so, they pay attention to properties such as flat or curved surfaces, corners, edges and tips. They work playfully and purposefully with solids, especially symmetrical objects, and can thus distinguish prisms, pyramids, cylinders, cones and spheres from one another.

It is typical for children to judge a solid by its position or by a familiar object. A cylinder lying on its side quickly looks like a roll, and a sphere is sometimes confused with a cylinder because both are round. Cones and pyramids both have a tip and are therefore often given the same name. It helps to look at the faces: are they flat or curved, and how many are there?

One task of this kind is "Which solid is this?" The child is given a solid or a description and names it. At home, packaging, tins or balls can be used for this, and you can work together to explain why a solid fits a particular name. The curriculum item also mentions determining the surface areas and volumes of right prisms and pyramids. However, the only task type provided for this in this area is "Which solid is this?"