Mathematics — Grade 5

In the number range up to 100, children calculate additions where the ones add up to more than 10, for example 18 + 14. They can show their method of calculation, for instance with the number line: from 18 they first count on 2 to reach 20, then add 12 more, giving 32. The curriculum describes this step for the whole number range up to 100, a stage that extends over several school years.

A typical mistake: the ones are added, but the ten is not carried over. For 18 + 14, 8 + 4 does give 12, and some children write down the 2, forget the 1, and calculate 1 + 1 = 2 for the tens. The result then reads 22 instead of 32. The reason is that the 12 ones also contain a ten, which must be made visible. If it is not recorded, it gets lost.

On the worksheet, this step appears in tasks such as:

• Addition in the number range up to 100 with crossing the tens
• Complete to the next ten and continue calculating
• Addition up to 100 with crossing the tens: choose the result
• Addition up to 100: check the result, find the error

The child can determine the area of a figure by counting how many unit squares, for example grid squares or square metres, cover it. They use this to compare areas of rectangles and composite figures, for instance by covering two rectangles of different sizes with squares. The curriculum points do not specify a number range, so none is given here.

It is typical for children to add side lengths or count only the squares along the edge instead of covering the whole area. The outline of a figure (its perimeter) and its area get confused, even though they are two different quantities. For this reason, a long, narrow figure may seem larger even though it covers fewer squares.

The worksheets at this level include, among others, the following task types:

• Rectangle area: How many squares cover it?
• Area on a grid: How many squares cover the figure?
• Area of a figure made of two rectangles
• Area with tiles: How many two-by-one tiles are needed, or how many tiles are still missing?
• Area by covering: Choose the correct answer or distinguish between true and false.
• Area of two figures: How much larger is one of them?
• Area and one side: How long is the other side?
• Draw a rectangle with the given area.
• Area: Correct someone else's result.

The curriculum points apply across several school years. In this 5th grade, the tasks mainly focus on division within the number range up to 100. The child understands division as the inverse of multiplication: if 4 · 7 = 28 holds, then 28 : 7 = 4 also holds. It can explain the connection to addition, for example 28 = 7 + 7 + 7 + 7, and can read and use the symbol ":" as well as the word "durch" (meaning "divided by"). In doing so, it also uses relationships between the small multiplication table and the multiples-of-ten multiplication table, for example that 6 · 10 = 60 also gives 60 : 6 = 10.

A typical mistake is swapping the two numbers. For 28 : 7, a child might then calculate 7 : 28 or see the wrong number as the divisor. This often happens when division is treated only as a result to be memorised, rather than as the inverse task of multiplication. It is therefore helpful to always think of the matching multiplication problem for every division task.

The worksheets on this topic include, among others, the following task types:

• Division within the multiplication table (up to 100): determine results directly from the multiplication table.
• Which number was divided by (division table): work out the divisor from a table.
• Missing divisor: choose the number: find the missing number in a division task.
• Divided within the multiplication table: choose the result: select the correct answer from several options.
• Division: check and find the error: check a given calculation.
• Division with an unnecessary number: recognise which piece of information is not needed for the task.
• Share evenly, Divide into equal parts, Division: how many packets result, Division: how many in one row, Division: which sharing gives more per person?: apply division in real-life situations.

Printable worksheets with solutions are available for every topic.

The child knows the products of the small multiplication table, i.e. all multiplications with factors from 1 to 10 up to 10 · 10 = 100. The curriculum additionally names the products with the factors 2, 5 and 10, as well as breaking a product down into factors, for example 36 = 6 · 6 = 4 · 9.

It is also important that the child uses relationships between products instead of memorising every result individually. For example, 6 · 8 is 8 larger than 5 · 8, and 8 · 3 gives the same as 3 · 8. In a dot array, the child recognises that 6 · 4 is a doubling of 3 · 4.

A typical mistake occurs when a product is retrieved only from memory. If the memory is uncertain, a neighbouring result is often taken, for example 42 instead of 48 for 6 · 8, because the task 6 · 7 is confused. Anyone who does not use the relationships between products has no way of working out the correct result themselves.

Tasks on this topic:

• Multiplication table (up to 100)
• Missing factor (small multiplication table) and Missing factor: choose the number
• Multiplication table: choose the result
• Multiplication: how many dots in the dot array
• Multiplication: which product is larger, by how much?
• Multiplication: check and find errors
• Multiplication as addition: how many times taken
• Multiplication: equal-sized groups in total
• Multiplication with a superfluous number

The child learns to write down possibilities in an organised way rather than at random, so that nothing is forgotten or counted twice. The curriculum points describe a period of several school years. The examples range from forming pairs, through numbers made from the digits 1, 2, 3, to letter sequences such as ADEN. In Year 5, the task templates mainly show pairs and sets from a small selection.

Often the possibilities are simply written down as they come to mind. Then one combination is missing, or the same one appears twice. With pairs, the order does not matter: "Anna and Ben" is the same pair as "Ben and Anna" and is counted only once. A plan helps: first write down all the possibilities with the first part, then with the next.

Typical tasks are:

• How many different pairs: true or false. A given number is checked.
• How many different pairs: choose the correct answer.
• Combinations: how many different sets are there? Or how many sets from three kinds?
• Write down all the combinations: The list must be complete and without duplicates.
• Combinations: how many pairs are left over, or how many more pairs with one piece?
• Known number of pairs: how many pairs are there in the other set?

Your child learns to multiply numbers under 20 by 10, for example 7 · 10 = 70 or 13 · 10 = 130. In doing so, they use the connection to the basic multiplication facts: 7 · 1 is 7, so 7 · 10 is 7 tens, that is 70. This very relationship between the basic multiplication facts and the multiplication of tens is what the Lehrplan 21 calls for.

A typical mistake with two-digit numbers is that the zero is added at the front instead of at the back, so that 13 · 10 is written as 103. Sometimes the zero is left out altogether (13 · 10 = 13). This is usually because the zero was learned as a mere add-on, without it being clear that every digit shifts one place to the left.

In the worksheets for this class, you will find among others:

• Multiplying by 10: basic tasks with numbers under 20.
• Multiplying by 10: a superfluous piece of information: tasks with additional information that is not needed for the calculation.
• Tens: how many full tens fit in?: Here the reverse operation becomes visible, for example 70 : 10 = 7.
• Ten times ten, that is two places further: Here 10 · 10 = 100 is examined.
• Multiplying by 10: choosing the correct result, true or false and a chain of changes: tasks in which results are checked or several multiplications are carried out one after another.

In Grade 5, the child takes numbers from tables and bar charts and uses them to answer questions. They compare two rows or bars, determine the difference, count how many values are above a certain number, and find the category with the largest value. The curriculum points do not specify a separate number range for this grade. Their examples come from everyday life, such as school routes or pets.

A typical mistake: the child reads the wrong row or bar, especially when the table contains many numbers. For the question "How much more?", sometimes only one of the two values is given or the calculation is done in the wrong direction. In bar charts, the scale is often misread when a bar ends between two marks. For "true or false" statements, a statement is often accepted without checking it against the numbers.

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

• Table: how much more according to the table?
• Table: difference between the largest and smallest value
• Table: how many groups are above the number?
• Table: which category has the most?
• Bar chart: how many more?
• Difference between two rows: choose the correct answer
• Difference between two rows: true or false

Your child can determine the perimeter of a rectangle by adding up all four sides. In doing so, they use the fact that opposite sides are equal in length. From the perimeter and one known side, they can also calculate the missing side length. Drawing a rectangle with a given perimeter is also part of this.

A typical mistake is confusing perimeter and area: instead of walking along the edge, the squares inside are counted. Another common mistake is adding only the length and width and forgetting the opposite sides. The result then becomes too small, because only two of the four sides were included. It helps to trace the sides once all the way around the figure with a finger while counting.

In class, your child will encounter the following types of tasks:

• Perimeter of a rectangle
• Missing rectangle side from the perimeter
• Perimeter: which figure has the greater perimeter?
• Perimeter of a rectangle on squared paper
• Perimeter of the rectangle: true or false
• Draw a rectangle with the given perimeter
• Perimeter of the rectangle: choose the correct result

Your child learns to read the digits of a number up to 1'000 by their place value. The digit on the far right stands for the ones, the middle one for the tens, and the one on the left for the hundreds. For the number 257 this means: 2 hundreds, 5 tens and 7 ones. The curriculum shows this with materials: 2 hundreds blocks, 5 tens rods and 7 ones cubes together make 257.

A typical mistake happens when the digits are read only as single numbers, without their place value. Then 257 is read as 2, 5 and 7, without it being clear what each digit stands for. The zero in the middle is also often forgotten: 307 is then written or read as 37. The zero shows that there are no tens in this place. It is easily overlooked because at first glance it seems to have no value.

In this class, the tasks involve three-digit numbers. The worksheets with solutions include, for example:

• Composing a number from hundreds, tens and ones
• Breaking a number down into hundreds and the remainder
• Reading the number from the blocks
• How many full tens does the number have? How many ones in total?
• Judging statements about place value as true or false

The child counts in full hundreds such as 200, 300 or 700. It adds them to a number or takes them away from it, writes down the calculation steps, and checks whether the result is correct. The curriculum points do not name a specific number range. The task templates for this topic work with full hundreds.

A typical mistake: the child calculates 470 + 100 and writes 480. It treats the hundreds like tens and changes only the tens digit. It helps to look deliberately at the hundreds digit: One hundred more means the hundreds digit goes up by one.

In practice, these task types occur:

• Jump by full hundreds: starting from the initial value, jump forwards or backwards by full hundreds.
• Jump by full hundreds: two jumps in a row: carry out two jumps one after the other and write down the result.
• Subtract full hundreds: take full hundreds away from a number.
• How many hundreds were added: determine from the start and end values how many hundreds have been added.
• How much is missing so that both sides are equal: add on until both sides are equally large.
• Jump by full hundreds: choose the correct result and Full hundreds: find the mistake: compare results and check whether they are correct.

In 5th grade, the main focus is that your child divides a whole into two or four equal parts and recognises and names halves and quarters. Typical representations are squares, rectangles and circles that are folded or shaded, as well as sets of objects. The curriculum points on this topic are spread across several school years. What is specifically expected for this grade is shown in the task templates.

A common mistake: the child divides a figure into four parts that are not equal in size, and still counts off one quarter. The reason is that it pays attention to the number of parts and not to whether they are equal in size. Another typical mistake arises with the denominators: because 4 is greater than 2, the child thinks a quarter is more than a half. With sets, a single object is sometimes regarded as "one quarter" instead of as part of the whole set.

Tasks on this topic look, for example, like this:

• Part of a whole (half and quarter): The child determines which fraction of a folded or shaded figure is shown.
• How many are there in total if one part is …? Starting from a fraction, the child determines the total quantity.
• Fraction of a set: How many are one part? The child calculates a fraction of a set.
• Choose how many make up the fraction of the set: The child selects the correct number from the answer options.
• Part of a set: find the mistake: The child recognises where an incorrect division has been made.
• Invent sets for the same division: The child looks for different sets that can be divided in the same way.
• How many parts remain unshaded: true or false: The child checks statements about the fractions of a figure.

The curriculum points additionally mention sequences of fractions such as ½, ¼, ⅛ as well as fractions with other denominators such as 3, 5, 6, 8 and 10. These belong to the overall curriculum area and are not specifically listed in the task templates for this grade.

The Lehrplan 21 states for this area: children can write down their calculation steps when adding and subtracting, add and subtract in writing, and check their results. The tasks in this area work with numbers up to 1000. Your child writes the numbers one below the other and calculates place by place, from right to left.

A typical mistake when subtracting in writing: your child subtracts the smaller digit from the larger one within a column, even when the smaller number is on top. This usually happens because the place values get lost during the calculation, for example when "borrowing" something from the tens or hundreds. When adding, the carry often gets lost, that is, the tens or hundreds digit that belongs in the next column.

On the worksheets, children practise this with tasks such as:

• Add three-digit numbers in writing and Written addition step by step, including with three numbers
• Written subtraction up to 1000
• Written subtraction: correct the errors, where a wrong calculation method must be found and corrected
• Missing addend in written addition, where a number has to be found
• Written subtraction: choose the result and Written addition, three-digit: choose the result, where the correct result must be selected from several solutions

Each worksheet comes with solutions that you can use to check your child's results.

Your child identifies the vertices, edges and faces of prisms and pyramids. The curriculum uses the terms point, vertex (corner), edge and face for this area. The curriculum does not specify a number range for this area, so the tasks focus on the solids themselves and not on large numbers.

A typical mistake: in a picture, only the visible edges at the front are counted, and the hidden edges on the back are missed. With pyramids, it is often overlooked that the apex is only a single vertex and that the edges of the base count in addition to the lateral edges.

In this class, the worksheets print these task types:

• From the picture: Count the vertices, edges or faces of a depicted solid.
• Choose or determine the number: For a prism and a pyramid, state the appropriate number of vertices, edges or faces.
• Base from the number of edges: From the number of edges, work out which base belongs to the prism or the pyramid.

The child lays out amounts of money with coins and notes and calculates with them. The curriculum describes several number ranges for this: laying out amounts up to 20 francs, adding and subtracting them; laying out whole franc amounts up to 100 francs with coins and notes; and forming and calculating amounts with francs and centimes, for example 25 Fr. 60 Rp. + 14 Fr. 30 Rp. These details apply to the grade level as a whole. Which numbers actually appear in Year 5 is shown by the task examples in this area.

A typical mistake arises when calculating with francs and centimes. The child adds the franc parts and the centime parts separately and forgets that 100 centimes make one franc. So for 60 Rp. + 50 Rp., the result is 1 Fr. 10 Rp., not 1 Fr. 100 Rp. It is similar with change: whoever does not first clarify which amount was given and which price was paid easily calculates in the wrong direction. The task "Change: find the mistake" practises exactly these points.

Typical tasks in the area of money are:

• Money in the picture: how much is it? The child counts together the coins and notes shown.
• Coins: which coins to pay with? The child looks for suitable coins and notes for an amount.
• Shopping: what do several items cost? The child calculates the price of several identical items.
• Shopping: is the money enough? and Money: how much is still missing for the purchase compare money and price.
• Purchase and change and Change: choose the right amount practise working out the change to be returned.

The child solves a short word problem using addition or subtraction. It recognises what happens in the story, chooses the appropriate operation, and interprets the result again in context, for example "18 children" rather than just "18". The curriculum points give numbers up to 20 as an example, such as 12 + 8 on the playground. This number range applies to the stage as a whole and not specifically to Year 5. The task templates for this class do not specify a number range.

It is typical for a child to choose the operation based on individual keywords instead of understanding the story, or to calculate with all the numbers in the text. The curriculum therefore explicitly requires that the child distinguishes essential from non-essential information. For "A book is 5 cm thick, has 75 pages and is free of charge", only the question about the price is decisive. For the question "How many were there at the beginning?", many children wrongly use subtraction, although the starting amount is being sought and therefore must be added.

A task on this topic looks, for example, like this:

• Simple word problem: how many are left
• Real-life problem: how many were there at the beginning
• Choosing the operation: subtraction (taken away) or addition (together)
• Word problem with a superfluous number: how many are left
• Real-life problem: choose the correct result

Multiplication in word problems is also mentioned in the curriculum, but it is not provided as a separate form in the task templates for this topic.

Plane shapes are flat figures such as circle, triangle, rectangle and square. The child learns to name these figures and to tell them apart from one another. The curriculum points do not specify a number range for this and describe the skill across several school years. What is practised concretely in this class is shown by the task templates. The points also include tracing and drawing these figures; here, however, recognition is the main focus.

Typically, a child does not recognise a figure in an unfamiliar position: a rotated triangle or rectangle then looks like a different shape. Overlapping figures are also difficult. When two triangles lie inside each other, often only the clearly visible one is counted, and the hidden one is left out. In addition, figure names are sometimes mixed up or derived from memory rather than from the shape.

In the tasks, this shows up as follows:

• What is the name of the drawn figure? The child determines the name of a figure shown.
• What is the name of this rotated figure? The figure is rotated and must still be recognised.
• Figures in the picture: how many triangles? The child counts triangles in a picture with overlapping figures.
• Plane figures: true or false The child checks statements about figures as true or false.
• What is this figure called? Choose The child chooses the matching name from several options.
• Plane figures: correct the name of the figure The child finds incorrect names and corrects them.

The Lehrplan 21 sets the goal for this topic that pupils can read and write natural numbers up to 100 and up to 1'000. In Year 5, the tasks mainly focus on converting between number words and digit notation, for example with dreihundertfünf and 305.

A typical mistake concerns the zero in the middle. When people hear "dreihundertfünf", they often write 35, because there is no zero in the word and the tens place is left empty. The order of the digits also sometimes gets mixed up when number words are simply written down in sequence, without paying attention to hundreds, tens and ones.

The worksheets for this class contain tasks such as:

• Write the number in digits.
• Read the number in words.
• Zero in the middle: correct the way the number is written.
• Number words: correct mistakes, choose the digit notation, or decide whether statements are true or false.

The Lehrplan 21 requires that lengths, weights, volumes and contents are estimated and compared with suitable reference quantities. It also mentions converting into neighbouring units, for example 2'000 g = 2 kg. These goals apply to the whole cycle and not only to Grade 5. In this grade, the worksheets mainly show how to calculate with money in everyday life: numbers are rounded to the nearest ten, and so a rough sum or difference quickly emerges.

A typical mistake: children round only one number, or round all numbers in the same direction, for example always down. Then the estimate turns out significantly too low. It is also often unclear whether 45 is rounded to 40 or to 50. It helps to ask whether the estimate is close to the exact result, rather than whether it is exactly correct.

A task might look like this: A bike costs 48 Fr., a helmet 23 Fr. About how much do we pay together? The child rounds 48 up to 50 and 23 to 20 and gets about 70 Fr. The worksheets contain matching tasks for this:

• Estimate costs by rounding up
• Estimate a sum: round to the nearest ten
• Estimate a difference: round to the nearest ten
• Roughly how much do we pay together
• Estimate: does the result fit
• Find prices that match the estimate

The children learn to tell the time on a clock face and on a digital display. The curriculum names the goal of telling the time to the half hour. These curriculum points describe a stage that extends over several school years. What is practised concretely in Year 5 is shown by the task types on this page.

Two mistakes often happen. First, children count the numbers on the clock face instead of minutes: if the minute hand points to the 3, it is 15 minutes, not 3. Second, the word "halb" is tricky. "Halb sechs" means 5.30, not 6.30. Anyone who takes the expression literally reads the hour wrongly.

The worksheets on this page include, among others, the following task types:

• Reading the clock: true or false
• Clock: correct the reading errors
• Read the clock
• Clock: how many minutes until the full hour?
• Clock: which one shows the earlier time?
• Reading the clock: which time does the clock face show

Your child can measure and compare the contents of containers using a cup. In doing so, they use the units of capacity litre (l) and decilitre (dl) and orient themselves to the reference quantity 1 l. The curriculum does not specify a separate number range for capacity. The tasks in this class work with litres and half-litre bottles.

A typical mistake is judging containers by their height or shape. A tall, narrow glass looks bigger than a low, wide one, even if it holds less. A second mistake concerns counting: someone who counts four half-litre bottles as four litres overlooks that two halves together make one litre. Similarly, the relationship between decilitres and litres can be confused, because 10 dl make 1 l.

A task on this topic looks, for example, like this:

• Measuring jug: How much water is in the jug? The task asks for millilitres, although the curriculum extract mentions litres and decilitres.
• Capacity, how much is missing until it is full? A container is partly filled, and the child calculates the remaining amount.
• Capacity, how many litres from half-litre bottles? The child calculates with bottles of the same size.
• Capacity, right or wrong? The child checks statements about contents.
• Capacity, how many bottles does the juice fill? The child determines how often a bottle can be filled.
• Capacity, choosing the right number of bottles: The child decides which number of bottles fits.
• Capacity, how much more does a container hold? The child compares two containers.

The curriculum points require counting forwards and backwards in equal steps. They describe this across several levels: in steps of 2 up to 20, in steps of 1, 2, 5 and 10 up to 100, and in steps of 1, 2, 10 and 100 up to 1000. The task templates for this class show work with equal steps, without a specific number range being set.

A typical mistake happens when counting the steps. If a child counts in steps of 2 from 4 up to 16, they often count 4 as the first step too. Then they arrive at 7 steps instead of 6. A second common mistake occurs when crossing a ten: with steps of 5 starting from 47, they often go to 52, then 62 instead of 57.

The tasks in this class take the following forms:

• Continue counting in the same step: A sequence is continued by the same step.
• Count backwards in equal steps: The sequence is continued in descending order.
• Counting on: how many times must you count?: The child determines how many steps lead from one number to another.
• Counting in steps: choose the next number: From several options, the correct next number is chosen.
• How many times added: choose the number: The steps are thought of as repeated addition.
• Counting in steps: correct the wrong number: A sequence with an error is recognised and corrected.

In grade 5, the child multiplies two-digit numbers by 2, for example 37 · 2 or 58 · 2. For this, the child may write down their own calculation methods or calculate in their head. The curriculum describes the ability to multiply numbers, for the level as a whole, with larger numbers. This page only describes the part that the tasks for this grade cover.

A typical mistake happens when doubling the ones creates a ten. For 37 · 2, 7 · 2 = 14. The 4 is written down, but the ten is forgotten and not added to the tens. This gives 64 instead of 74. It helps to deliberately add the ten to the tens place.

The worksheet on this topic includes, among others, these task types:

• Two-digit number times 2: The child works out the task independently.
• Multiplying by 2: right or wrong: The child checks whether a given result is correct.
• Multiplying by 2: choose the correct result: The child chooses the correct solution from several options.
• Doubling: which number doubled gives this?: The child works backwards and finds the number which, when doubled, gives a given result.
• Doubling: how much more after doubling both?: The child doubles two numbers and compares how much greater the result is.

The child can compare objects by a size, above all by length and weight, and describe the difference in words: "B is longer than A", "C is the longest". The comparative and superlative forms longer, the longest, bigger, the biggest are used for this. Which number range applies is not stated in the information on this area.

A typical mistake is to estimate instead of compare. A bent or crumpled string often looks shorter than a straight one, even though it is the same length. The child then judges by appearance rather than by comparison. Often, for "How much longer?", the length of one object is given instead of the difference between the two.

The tasks in this area take the following forms:

• Compare lengths: which one is the longest?
• Compare lengths: how much longer is the ribbon?
• How much longer: true or false
• How much longer: choose the correct answer
• Mass: order from the lightest

Comparisons of area and volume are part of the curriculum but do not occur in the printed tasks in this area. As an idea for home, you can place objects side by side and ask together which is the longest and how much longer it is than the next one.

The child learns to connect basic operations and equations with a placeholder to a story, a picture, or an action. The curriculum gives as examples 5 · 8, which can be shown as five houses with eight bricks each, and 28 + _ = 50, which can be understood as a bus with 50 seats, of which 28 are occupied. The curriculum does not name a specific number range for Grade 5 at this point; the examples only show the type of tasks.

A typical mistake is that the story and the calculation do not match. For example, for "five houses with eight bricks each," the child writes the calculation 5 + 8, because it adds the numbers instead of thinking about what happens in the story. With equations containing a placeholder, there is often no explanation of what the symbol _ means in the story. The error usually lies in choosing the operation based on the numbers rather than on what is happening.

In class, this skill appears in tasks such as:

• Make up a task with the given result
• Make up a task for these numbers
• Which answer fits the task you made up?
• Does this answer fit the task? and Correct the answer under the task

The printable worksheets on this topic contain such tasks with solutions, so you as a parent can compare your child's story with the calculation.

Your child learns to classify statements about chance. An event is certain if it always happens, impossible if it can never happen, and possible if it can happen but does not have to. The Lehrplan 21 names the terms (un)likely, (im)possible and certain for this. It does not name a numerical range; the focus is on understanding and correctly using the words.

A typical mistake is to judge by feeling rather than by the situation. If something happens often, children quickly consider it certain. Or they consider a rare possibility to be impossible. For example, in a bag with only red marbles, a blue marble is impossible. In a bag with many marbles in different colours, a rare colour is only possible, not impossible.

The tasks in this area work with the following templates:

• Fill the bag: certain, possible or impossible – place marbles in a bag so that a particular draw is certain, possible or impossible.
• Certain, possible or impossible – match events to the appropriate terms.
• Correct it: certain, possible or impossible – find an incorrect classification and fix it.
• Certain, possible or impossible? True or false – check statements about events.
• Certain, possible or impossible? Choose – select the appropriate classification from given options.

The templates use the terms certain, possible and impossible. The terms likely and unlikely, which are also named in the Lehrplan, do not appear in these templates.

The child learns to understand lengths given in two units, for example 2 m 40 cm or 3 cm 5 mm. The curriculum describes for the whole stage that lengths up to 1 m are estimated, measured and added (e.g. 15 cm + 35 cm). In this class, the worksheets mainly show that lengths in different notations are recognised, compared, and added or subtracted.

A typical confusion is with decimal numbers: 1 m 5 cm is read as 1.5 m, although it is 1.05 m. When adding, an error often occurs with carrying over. For 1 m 60 cm + 1 m 50 cm, it is 110 cm, so 1 m 10 cm is added, giving a total of 3 m 10 cm. Many children instead write 2 m 110 cm.

Typical tasks on the worksheets are:

• Adding lengths in different notations
• Lengths in two notations: choose the result
• Two length values together: true or false
• Lengths in two notations: how much longer?
• Metres: how many full metres?

The child can name the neighbouring numbers of a given number and count forwards and backwards from any number. The curriculum points on which this topic builds mention the number range up to 20 and up to 100. They thus describe a learning path spanning several school years. For Year 5, the task templates show what is practised concretely.

A typical mistake: the child names the number that is 1 larger when asked for "1 less", because the direction is reversed while counting. A number line often helps: the predecessor lies to the left of the number, the successor to the right.

Typical tasks are "Which number is 1 less?" and "Which number is 1 more?". In addition, there are tasks in which the successor and predecessor are added, for example for 7: 6 + 8 = 14. Further tasks require choosing the correct answer or deciding whether a statement is "true or false". The templates do not name a number range. Which numbers occur is shown by the respective worksheet.

In the Lehrplan 21 the kilometre is named as a reference unit: the child should be able to orient themselves by 1 km and name and use the units km, dm and mm. The curriculum point does not set a number range for the kilometre. In Year 5, the task templates show what is practised concretely: converting kilometres and metres into metres, for example writing 2 km 300 m as 2300 m.

A typical mistake often happens here: the child writes 2 km as 200 m. They then calculate with the number 100, which they know from centimetres and decimetres, instead of 1000. Even when a number with a decimal comma or zeros is involved in the conversion, place values are easily shifted. It helps to become aware that 1 km consists of 1000 m.

A task on this topic might look like this, for example:

• Converting kilometres and metres into metres: Write the length only in metres.
• Kilometres into metres, choose the correct answer: From several options, select the matching one.
• Kilometres into metres, true or false: A conversion is given and must be judged.
• Kilometres: how many full kilometres? Determine how many whole kilometres are contained in a length.
• Kilometres: how much is missing to the full kilometre? Determine how many metres are still missing until the next full kilometre.

As an additional suggestion, not part of the requirements: a familiar route to school that is about one kilometre long can help children imagine the size of 1 km.

The child names the bodies cube, cuboid, sphere, cylinder and pyramid and recognises them in the environment and in pictures. It understands and uses the terms point, corner, edge and face, and can formulate relationships, such as that the faces of a cuboid are rectangles. Since this is about shapes and not numbers, there is no number range that would need to be specified.

Sphere and circle are often confused: a sphere looks like a circle in a picture, but a circle is flat, while a sphere is a solid body. A cuboid is also often called a cube, although not all of its edges are the same length. The reason is usually that only the outline shape is considered and not features such as corners, edges and faces.

Typical tasks for this are:

• What is this body called? The child names a body that is shown.
• Which body is this? True or false The child checks whether a name matches the body.
• Which body is this? Choose The child chooses the matching name from several options.
• Correct the name of the body The child corrects an incorrect name.
• Find an object in the shape of the body The child looks for an object that has the shape of the body.

The child learns to record and evaluate numbers from counts and surveys in a clear way: they note quantities in tally lists or tables and can display them graphically. The curriculum points describe this across several school years and do not specify a fixed number range. In Grade 5, the worksheets mainly focus on tasks in which the total is determined from tables and pictograms.

A typical mistake occurs with pictograms: one picture stands for several units, for example for five children. Anyone who simply counts the pictures gets a wrong total, because they treat each picture as a single unit. With tables, a row is often forgotten, or if a row is missing, all the values are simply added instead of subtracting the other rows from the known total.

The worksheets on this topic include, among others, these types of tasks:

• Table: how many in total? The child adds the values in a table.
• Pictogram: one picture stands for several The child converts the pictures into quantities.
• The missing row when the total is known The child completes a row whose value results from the total.
• Total from the table: choose the correct answer The matching total is selected from several options.
• Total from the table: true or false The child checks whether a given total is correct.

All worksheets are printable and come with solutions, so that parents can check the answers themselves.

In Year 5, children convert area units between neighbouring units, for example hectares into ares, ares into square metres, or square metres into square decimetres. For volume, the focus in this year is mainly on converting into a smaller unit, for example from cubic decimetres into cubic centimetres. This also includes comparing quantities, such as which of two given values is larger, and estimating with the help of familiar reference quantities like 1 dm² or 1 cm³.

A typical mistake arises when children carry over the conversion factor from length. Because 1 dm = 10 cm, they also calculate 1 dm² = 10 cm², although it is 100 cm². The same thing happens with volume: instead of 1 dm³ = 1000 cm³, they often calculate with 100. The reason is that for areas and volumes, the lengths change in two or all three directions respectively. It helps to imagine the unit as a square or a cube.

On the worksheets, this appears in tasks such as »Converting into a larger area unit«, »Converting into a smaller area unit«, »Converting hectares into ares«, »Converting ares into square metres« and »Converting into a smaller volume unit«. Additionally, there are »Area units: comparing quantities«, »Area units: choose the conversion« and »Area units: true or false«. The solutions are included. At home, you can ask your child why a conversion gives 100 and not 10.

In grade 5, children calculate with fractions whose denominators differ, for example ½ + ¼. To do this, the fractions are first brought to a common denominator, that is, expanded, and then the numerators are added or subtracted. The curriculum describes this area over several school years and names the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50 and 100. It also requires representing sums and differences with suitable models, such as the circle or rectangle model.

A typical mistake is adding the numerators and denominators directly: ½ + ¼ is then wrongly written as 2/6. A second common mistake: the child makes the denominators the same but forgets to expand the numerator by the same number. For this reason, it is worth consciously checking both parts of the expansion when rechecking the calculation.

You will find suitable tasks on the worksheets, for example under:

• Adding fractions with different denominators
• Subtracting fractions with different denominators
• Adding fractions with unlike denominators: word problem
• Fractions with unlike denominators: numerators after making the denominators the same
• Fractions with unlike denominators: true or false

The child can add and subtract decimal numbers, for example 30.8 + 5.6. The Lehrplan 21 specifies numbers with up to five digits in total (30.8 has three). This specification applies to the whole cycle and not only to Grade 5. The child may calculate in their head or write down their own methods on paper, such as splitting the number into several addends or showing the method on a number line. The curriculum also requires that such methods be presented, compared with others and understood.

A common mistake occurs with alignment: the digits are written down from the right instead of aligning the places at the decimal point. For 4.5 + 0.38, the 5 (tenths) then sits above the 8 (hundredths) instead of above the 3 (also tenths). When subtracting, it often helps to fill missing places with a zero, for example writing 2.3 as 2.30. This is a practice tip and not a requirement of the curriculum.

The worksheets in this area include the following task types:

• Adding decimal numbers and subtracting decimal numbers: calculations to solve
• Adding measurements with decimal numbers: adding length or weight values together
• missing addend and missing subtrahend: finding the missing number in an equation
• true or false and choose the result: checking finished results or choosing the correct one

The curriculum also mentions that basic operations can be carried out with a calculator. There is no separate task template for this point in this area.

The child can calculate the volume of cuboids. This also includes building cuboids from a given number of cubes and dividing cuboids into a specific number of smaller cuboids. The curriculum does not specify a fixed number range for this point.

A typical mistake is that children multiply only two edges or add the edge lengths. This is understandable, because they are used to working with two quantities from area and perimeter calculations. The unit is also often wrong: instead of cm³, children simply write cm or confuse volume with surface area.

The worksheets on this topic are printable and include solutions. Typical tasks are:

• Volume from unit cubes: counting the cubes before using a formula.
• Volume of a cube and Volume of a cuboid: direct calculation with given edges.
• Volume of a cuboid: missing edge: deducing an unknown edge from the volume.
• Volume: edges k times as long: investigating how the volume changes when all edges are, for example, doubled.
• Volume of a cuboid: comparing two boxes and Word problem (box): applying volume in everyday contexts.
• Volume of a cuboid: true or false and choose the result: checking statements or selecting the correct solution.
• Volume of a solid made of two cuboids: a composite solid is divided into partial cuboids.

In 5th grade, the children convert lengths between neighbouring units of measurement: metres, centimetres and millimetres. They write a length in a different unit, for example 1 m = 100 cm, and add lengths given in two units, such as 3 cm 5 mm + 2 cm 7 mm. The curriculum points do not name a fixed number limit, but give examples like these.

The link between units based on ten is often missing: 1 cm has 10 mm, 1 m has 100 cm. It is typical to calculate with the wrong number, for example 4 m = 40 cm. When adding 3 cm 5 mm + 2 cm 7 mm, the units are often added separately, so that 5 cm 12 mm results, instead of converting the 10 mm into 1 cm. Behind this is often the fact that the units of measurement are read like separate numbers, without seeing their relationship to each other.

The worksheets on this topic contain the following task types:

• Convert into a larger or smaller unit of length
• Add lengths given in two units
• Choose the converted value
• Compare units of length
• State a length in one unit
• Length in one unit: true or false

The curriculum points also name estimating lengths and the relation of the prefixes kilo, deci, centi and milli to powers of ten. These contents belong to the learning goal, but are not specifically practised in the task types of this area.

In 5th grade the child learns to determine the mean (arithmetic mean) of a data set: all values are added together and the sum is divided by the number of values. In the same data sets, the maximum and minimum are also determined. The curriculum does not specify a particular number range for the mean. Which numbers actually appear is shown by the sample tasks for this topic.

A typical mistake is dividing the sum by the wrong number, for example by the number of different values instead of the number of all entries when values repeat. It also happens that one value is forgotten when adding. The mean is often confused with the maximum, the minimum, or the value in the middle of the ordered series. When working with a bar chart, reading a bar height incorrectly can already lead to a wrong result.

In class, the child encounters the following task types, for which printable worksheets with solutions are available:

• Calculate the mean: The mean is determined from a series of numbers.
• The mean in everyday life: A mean is calculated from an everyday situation and interpreted in its context.
• Mean from a bar chart: The values are read from the bars and the mean is determined from them.
• Mean: choose the result: The matching result is chosen from given answers.
• Mean from the chart: choose the value: In the chart, the value that matches the mean is chosen.

The curriculum points describe a level that spans several school years. For Year 5, it is therefore mainly the task templates that show what is required. The children calculate the area of squares and rectangles. The curriculum points do not name a specific number range, so here we only describe the activity: multiplying side lengths and stating the area in square units.

A common mistake is confusing perimeter and area. Anyone who adds all the sides measures the border and not the area. Something similar often happens with the missing side: the known side is added to the area or multiplied by it, instead of working out which number, multiplied by the known side, gives the given area. It helps to count the squares of the area on a grid and so see why multiplication works.

Typical tasks in this area are:

• Calculating the area of a rectangle
• Comparing two areas
• Area of a rectangle in everyday life, for example for a table or a sheet of paper
• Judging statements about area as true or false
• Calculating shapes with a cut-out corner
• Missing rectangle side: first choose which side is sought, then calculate
• Determining a missing rectangle side from the area
• Investigating how the area changes when one side becomes k times as long
• Determining the side of a square from its area

In 5th grade, the child works with time measurements in hours, minutes and seconds and calculates with these quantities. This includes converting times into the neighbouring unit, for example 2 min 30 s into seconds. The curriculum does not name a specific number range for this level, so the numbers follow the worksheets.

A typical mistake arises from the decimal system, which the child already knows from calculating with francs and metres. Thus 2 min 30 s is sometimes written as 2.30 min, or calculations are done as if one minute had 100 seconds. With clock times, it is often overlooked that one hour has 60 minutes: anyone who subtracts the hours and the minutes separately for 10:50 to 11:10 arrives at a wrong result.

Typical tasks in this area are:

• Word problem on duration: How long did it take?
• Minutes and seconds into seconds: Convert, for example 3 min 15 s into seconds.
• Clock time: How many minutes have passed between two clock times?
• Comparing durations: Which time span is longer?
• Choosing a time span: How many minutes have passed? The matching answer is selected.
• Minutes and seconds right or wrong: Is the statement correct?

Your child learns to recognise the rule in a number sequence and to determine the next terms. The focus is on sequences where the same number is always added or multiplied by the same number, as well as sequences with a fixed step, where the question asks for the first term, a particular term, or a selected term. Pattern figures also belong here: students describe how many squares figure n has. The curriculum also mentions non-linear sequences such as 1, 4, 9, 16 or 1, 3, 6, 10, 15. These do not appear in the task templates for this grade.

It is typical that children add when working with multiplicative sequences, instead of multiplying. For 3, 6, 12, 24, they may then write 3, 6, 9, 12 and not notice that the number doubles. A second common mistake arises when asked which term it is: if counting of the first term starts with 0 or with 1, the answer is shifted by one. With pattern figures, children often consider only the newly added number or only the last figure, instead of determining the total number of squares for figure n.

Typical tasks are:

• Recognise the rule and continue the sequence: The rule is found from the first terms and the sequence is continued.
• Sequence: always add the same amount and Sequence: always multiply by the same number: The rule is either given or must be found.
• Sequence with a fixed step: The question asks for the first term, for which term it is, or for a selected term.
• Sequence with a fixed step: true or false: The child checks whether a given sequence follows the rule.
• Pattern figures: how many squares in figure n: The child describes the number of squares in a figure using numbers.

The child can recognise, from a word problem, which basic operation is meant, and set up the calculation with a placeholder. The examples in the curriculum work with sums of money such as 36 Fr., 23 Fr. and 125 Fr. This also includes the inverse operation: if 23 Fr. of the 36 Fr. has been saved, one asks how much is still missing and calculates 36 Fr. minus 23 Fr.

A typical mistake occurs when the child only picks the numbers out of the text and chooses the operation by feel, for example adding 36 Fr. and 23 Fr., even though the question asks for the missing amount. A second mistake: the child works out a term but cannot say what the number means. For 125 Fr. + 4 Fr. + 4 Fr. + 4 Fr. − 34 Fr., the result is the amount of savings, and interpreting this result is part of the task. It helps to check the result against the text.

On the worksheet, this skill appears in the following task types:

• Multi-step word problem (summarising): several steps from a story are combined into one term.
• Supplies and portions: how many portions at most: the child determines how many complete portions can be made from a supply.
• Supplies and portions: choose the number: the child chooses the appropriate number from given options.
• Word problem, three days: choose the result: the correct result is chosen from several solutions.
• Word problem, three days: true or false: the child checks statements about the story and justifies the decision with a calculation.

The child calculates with fractions that have the same denominator, for example 2/5 + 1/5 = 3/5 or 4/6 - 1/6 = 3/6. The denominator stays the same because all parts are equally sized; only the numerators are combined. The curriculum names the rectangle model for this area and denominators such as 2, 3, 4, 5, 6, 8, 10, 20, 50 and 100. However, this information applies to a longer stage and not only to Year 5. The tasks for this grade mainly show adding and subtracting with the same denominator, even when the sum is greater than 1.

Children often also add the denominators, for example 1/4 + 1/4 = 2/8 instead of 2/4. They then treat numerator and denominator the same way, even though the denominator only indicates how many equal parts the whole is divided into. It also becomes difficult when subtracting from a whole, for example 1 - 3/5: the child must recognise the whole as 5/5 so that they can continue calculating.

The worksheet on this topic includes, among others, these task types:

• Adding and subtracting fractions with the same denominator
• Fractions with the same denominator: sum greater than 1
• Fractions with the same denominator: missing numerator
• Fractions: how much is missing to the whole?
• Subtracting fractions: taking away from the whole
• Fractions with the same denominator: comparing sums

The solutions are given alongside each task, so you can go through the exercises well with your child.

In Year 5, children round decimal numbers to a given place value: to tenths and to hundredths. For example, 1.745 rounded to tenths becomes 1.7, because the digit after the tenths place is a 4 and so the number is rounded down. The curriculum point applies to the whole stage and also mentions rounding whole numbers. For Year 5, the tasks in this area show rounding decimal numbers to tenths and hundredths.

It is typical for children to simply cut off the digits instead of rounding. For instance, 1.78 rounded to tenths then becomes 1.7 instead of 1.8, although the 8 after the tenths place decides that the number is rounded up. Carrying over is also difficult: 1.96 rounded to tenths gives 2.0. Many children forget that the 9 increases the tenths and thereby creates a units digit.

The tasks on the worksheets appear in four forms:

• Rounding to tenths: Decimal numbers are rounded to one decimal place.
• Rounding to hundredths: Decimal numbers are rounded to two decimal places.
• Rounding to tenths: choose the result: The correct answer is selected from several options.
• Rounding to tenths: true or false: A given rounding is judged as true or false.

The learning objective describes figures with a given perimeter. As an example, it names triangles that are made with 5, 6 or 7 matchsticks. The tasks on this topic in Year 5 focus on side lengths: the child checks whether three lengths form a triangle, and looks for possible lengths for a missing side.

It is typical for children to think that any combination of three lengths forms a triangle. With lengths such as 2 cm, 3 cm and 6 cm, this does not work: the two short sides together do not reach the long side, so the figure does not close. The reason usually lies in the fact that only the total length is in mind, and not that the two short sides together must be longer than the longest side.

The tasks on this topic have the following titles:

• Triangle inequality: true or false – It is decided whether three given lengths form a triangle.
• The longest possible third side – For two given sides, the greatest permissible length for the third side is sought.
• Triangle inequality: how many lengths for the third side – It is counted how many lengths are possible for the third side.
• Third triangle side: choose the number – The task asks to determine the appropriate number for the third side.

In Year 5, the child practises written addition and subtraction of multi-digit whole numbers. In doing so, they write the numbers one under the other so that ones are under ones, tens under tens, and so on, and they calculate column by column. The curriculum does not specify a fixed number range for this skill. What matters is that the child can note down their calculation method and check the result.

Common mistakes usually have a clear cause:

• Subtracting across zeros: In tasks such as 4003 − 1278, the child simply subtracts 8 from 0 or leaves the 0 as it is. A unit for exchanging is missing: you have to borrow it from the next place that is not 0.
• Forgetting to carry: If the sum of a column is greater than 9, the tens digit is not carried over to the next column.
• Digits not lined up properly: If the numbers slip out of alignment, ones and tens get mixed up.

Typical tasks in this area are Written addition and Written subtraction, plus Written subtraction: exchanging across zeros, when exchanging across zeros is to be practised. Tasks such as Written addition: choose the result or true or false help to check results and recognise mistakes.

In Year 5, children round natural numbers to the nearest ten and to the nearest hundred. To do this, they look at the digit to the right of the place being rounded to. If it is 5 or more, they round up; otherwise, they round down. So 47 rounded to the nearest ten becomes 50, and 43 becomes 40.

A typical mistake: with three-digit numbers, the child looks at the wrong digit. When rounding 149 to the nearest hundred, the child considers the last digit 9 instead of the tens digit 4. This gives 200, but the correct answer is 100. Numbers where the digit is exactly 5 are also often rounded uncertainly.

The worksheets for this class include the following task types:

• Rounding to the nearest ten
• Rounding to the nearest hundred
• Rounding to tens: choose the result
• Rounding to hundreds: choose the result
• Rounding to tens: true or false

In this school year the child works with proportional relationships from everyday life, especially with amounts of money. For example: 100 g of cheese costs 5.40 Fr., 200 g costs 10.80 Fr. If a value is missing in a table or task, the child determines it using the ratio and completes the information. In doing so, the child first recognises that a relationship is proportional and then continues calculating.

A typical mistake is additive thinking: if the quantity doubles, the child simply adds a number instead of multiplying. For 100 g at 5.40 Fr. and 200 g at 10.80 Fr., the child may then write 300 g at 16.20 Fr. just because it adds 5.40 Fr. several times without considering the ratio. A second mistake arises when setting up the equation: the quantities are not in the correct places, so grams and francs get mixed up.

In class, the child encounters tasks like these, which appear in the material with solutions:

• Ratio equation: missing value

• Ratio equation: missing third term

• Ratio equation: choose the missing term

• Ratio equation: true or false

• Proportion in a word problem: convert to a different number of items

• Proportional assignment: complete the table

Your child can calculate the perimeter of a polygon by adding up all the side lengths. This also includes finding a missing side from the given perimeter and the other sides. Which numbers appear is shown by the example tasks on the worksheets; the curriculum points do not specify a fixed number range for this.

The curriculum also describes forming shapes with a given perimeter, for example triangles with 5, 6 or 7 matchsticks. There is no dedicated task template for this activity in this area.

Children often confuse perimeter and area. However, what is asked for is the path around the shape, not the area inside it. When finding a missing side, people often add instead of subtract: whoever adds up all the known sides must subtract this sum from the perimeter to get the last side. Often one side is also left out of the sum.

Suitable tasks from this area are:

• Perimeter of a polygon: Your child adds all sides and obtains the perimeter.
• Perimeter of a polygon: choose the result: The correct answer is selected from several solutions.
• Perimeter of a polygon: word problem (fence): The perimeter is interpreted as the length of a fence around a plot of land.
• Missing side from the perimeter and Missing side from the perimeter: choose the side: The side being sought is calculated or found among multiple-choice answers.
• Perimeter of a regular polygon: calculate the side: All sides are equal in length, so the perimeter is divided by the number of sides.

The curriculum states that children understand and use the terms diameter, radius and centre. The radius is the distance from the centre to the edge of the circle. The diameter runs from one edge across the centre to the opposite edge and is therefore twice as long as the radius. The curriculum point does not name a specific number range. Which numbers occur is shown by the example tasks.

A typical mistake is confusing radius and diameter. Often the radius is simply taken over as the diameter, or when converting, the value is not doubled or halved. The terms sound similar, and both lines start from the centre, which is why they are easily mixed up.

On the worksheets, the topic appears in these task types:

• Diameter from the radius: The radius is given, the diameter is to be found.
• Radius from the diameter: The diameter is given, the radius is to be found.
• Radius and diameter: true or false: Statements about radius and diameter are judged.
• Radius from diameter: choose the result: The correct answer is selected from several options.

The child can read and write whole numbers up to 1 million, and compare and order them. The curriculum also names counting forwards and backwards in suitable steps, for example from 320'000 in steps of 20'000, as well as the approximate position of a number such as 72'000 on a number line. The number range up to 1 million is formulated in the curriculum for the level and not only for Grade 5. The task types below show what this class specifically practises.

A typical mistake occurs with numbers that have zeros in the middle. When spoken, these zeros often get dropped, so for example 50'602 is written as 5602: the zero in the thousands place is overlooked, and all the following digits shift one place to the left. A second mistake concerns the value of a digit. In 72'000, the 7 is not worth 7, but 70'000. The place decides the value, not the digit alone.

On the worksheet, this skill appears in the following task types:

• Large numbers: compare – two or more large numbers are compared with each other.
• Place values: how many times as large – the child determines how many times as large the value of one place is compared with another.
• Place value decomposition: the missing addend – a number is broken down into place values, and a missing part is filled in, for example 72'000 + ? = 72'409.
• Number from place values (zeros in the middle) – the number is written from place values, and zeros in the middle must not be forgotten.
• Value of a digit: choose the answer – the child chooses the correct value of a marked digit from several answers.
• Place value: choose how many times as large – the child chooses how many times as large a place value is.

Your child learns to rework calculations so that they become easier. The Lehrplan 21 describes this goal across several school years. This includes adding and subtracting mentally with numbers such as 402 + 90, rewriting products by doubling and halving (8 · 26 = 4 · 52 = 2 · 104), and regrouping sums with brackets (136 + 58 + 42 = 136 + (58 + 42)). Results are also checked by simplifying, decomposing, or using inverse operations. In Year 5, the worksheets mainly show the types of tasks listed below.

A typical mistake when doubling and halving: the child changes only one of the two factors. For example, 8 · 26 becomes 16 · 26 instead of 16 · 13, because the product no longer stays balanced. Something similar happens with calculations involving numbers close to 100: for 99 · 7, people sometimes calculate 100 · 7 = 700 and forget to then subtract the 7 again.

The tasks have titles such as:

• Multiplying cleverly
• Adding cleverly
• Calculating cleverly: multiplying by a number close to 100
• Multiplying cleverly: true or false
• Adding cleverly with whole hundreds: choose the answer

The worksheets include solutions, so you can follow your child's calculation method together with them.

The child can give an approximate result before doing the exact calculation and use it to check whether an exact result could be correct. To do this, the numbers are rounded so that they can be added easily in one's head. The Grade 5 worksheets show this mainly for sums where rounding is done to hundreds.

It is typical for children to round only one of the two numbers, or to ignore place value when rounding, for example rounding 362 to 300 instead of 400. An estimate is also sometimes mistaken for the exact result. An estimate is a guide value and not an exact result.

The tasks are called, for example, Summe überschlagen: the child rounds the addends and writes down the estimated result. In Summe überschlagen: Überschlag auswählen, it chooses the suitable estimate from several options, and in Schätzen: wähle die Rundung auf Hunderter it decides which number to round to.

The curriculum describes estimating over several school years, including with decimal numbers as well as with products and quotients. For Grade 5, the tasks in this area only cover the sums with rounding to hundreds mentioned above.

Your child learns to compare two fractions where both the numerator and the denominator differ, for example 2/3 and 3/5. The curriculum names the denominators 2, 3, 4, 5, 6, 8 and 10 for this; 20, 50 and 100 are added for ordering fractions. These details describe the whole curriculum section across several years, not only Grade 5. Representations such as the circle or rectangle model and the number line are helpful here.

A typical mistake: the child concludes that the larger denominator means the larger fraction. In this way, 1/8 seems larger than 1/4, because 8 is larger than 4. Behind this is the idea of comparing numerator and denominator separately. However, a fraction tells how many parts of a whole you have. The more parts a whole has, the smaller each individual part is.

In Grade 5 there are worksheets with solutions for this, for example:

• Comparing fractions with different denominators: Two fractions with different numerators and denominators are compared with each other.
• Comparing fractions with one half: A fraction is compared with ½, for example to see whether it is larger or smaller.
• Comparing fractions with the same numerator: Here the insight helps that, when the numerators are equal, the fraction with the smaller denominator is the larger one.

Expanding a fraction means multiplying the numerator and the denominator by the same number. The fraction then looks different but has the same value, for example 1/2 equals 2/4. The Lehrplan 21 describes expanding fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50 and 100 using the rectangle model. The exercises in this class work with such fractions.

A typical mistake: the child multiplies only the denominator, for example 1/2 becomes 1/4, or it calculates the numerator and denominator differently, for example 1/2 becomes 2/3, because it increases both numbers by 1. The reason lies in seeing the fraction as two separate numbers instead of as one share. The rectangle model makes this clear: if a rectangle is divided into 2 halves and each half is halved again, this gives 4 equal parts. Of these, 2 are marked, so 2/4. The area is unchanged, only divided into smaller pieces.

The worksheets in this class contain the following task types for this, each with solutions:

• Expanding fractions: bring a fraction to a given larger denominator, for example 3/4 = 6/8.
• Expanding fractions: missing denominator: in an equation such as 3/4 = ?/8, find the missing denominator.
• Expanding fractions: what was it expanded by? read from two fractions which number was used to expand.
• Expanding fractions: true or false check whether a given expansion is correct, and name the error.
• Expanding fractions: choose the factor choose the correct expansion number from several numbers.

The child orders angles by their size and recognises whether an angle is acute, right or obtuse. The right angle serves as the point of comparison here: it corresponds to a corner, such as one found on a square or on a set square, and is marked with the familiar corner symbol. The term right angle and the symbol for the right angle are among the concepts the child should understand and use.

A typical mistake arises because children confuse the size of an angle with the length of its arms. A long line looks bigger, even though the angle does not become larger as a result. Likewise, the position of the drawing often does not help: an angle that lies at a slant is easily misclassified because one does not pay attention to the opening between the two lines.

One task on this topic is called Determine the type of angle. Here the child sees several angles in drawings and decides for each one whether it is acute, right or obtuse. The worksheets with solutions help to check the result. As an additional aid, one can compare the angle with a corner of the set square.

A divisor divides a number without leaving a remainder. The children learn to list all divisors of a natural number, for example for 16 the numbers 1, 2, 4, 8 and 16. This includes using the terms divisor and multiple confidently. The curriculum gives as an example that square numbers have an odd number of divisors. Divisibility rules, for example for 3, 4, 6, 8, 9, 25 and 50, are listed in the curriculum as an extension.

A typical mistake is to forget the 1 or the number itself. Anyone who writes only 2, 4 and 8 for 16 overlooks that every number is divisible by 1 and by itself. Divisors and multiples are also often confused: anyone who writes 12, 24, 36 for 12 has written multiples instead of divisors. A helpful approach (our own suggestion, not a curriculum goal) is to check the divisors in pairs, for example 1 with 16, 2 with 8, 4 with 4, instead of guessing.

The printed tasks in this area are:

• List all divisors of a number: write down all divisors of a given number.
• Divisors: how many are there?: determine the number of divisors of a number.
• Divisors of a number: choose the count: choose the correct number of divisors from given options.
• Divisors: smallest number with k divisors: find the smallest number that has exactly k divisors.
• Smallest number with k divisors: true or false: check whether a given statement about the smallest number is correct.

There is no separate task template for multiples in this area.

In 5th grade, your child mainly practises multiplying a single-digit number by a multiple of ten, for example 3 · 40 or 7 · 60. The curriculum describes a larger number range for this area (up to 4 place-value digits, for example 45 · 240). However, the tasks at this grade level show the introduction with single-digit numbers times multiples of ten.

A typical mistake is forgetting the zero at the end. For 3 · 40, the child calculates 3 · 4 = 12 and writes 12 instead of 120. The zero stands for the tens and is easily overlooked. One possible help is to first calculate the task without the zero (3 · 4 = 12) and then add the zero, because 40 consists of 4 tens.

The worksheets include three types of tasks with solutions:

• Multiplying by multiples of ten: The child calculates independently, for example 5 · 30.
• Multiplying by multiples of ten: true or false: The child checks given calculations such as 3 · 40 = 12 and decides whether they are correct.
• Multiplying by multiples of ten: choose the result: From several options, the child selects the correct result.

The child learns to write a length given in two units as a single decimal number: 2 m 35 cm becomes 2.35 m. The Lehrplan 21 requires writing measurements in compound units and converting between neighbouring units of measurement. The tasks in this class revolve around lengths. The curriculum point itself names no number range, so no range is given here either.

A typical mistake: the number of centimetres is placed after the decimal point as a whole number, without paying attention to the place values. 2 m 5 cm then becomes 2.5 m instead of 2.05 m. The reason: 5 cm are 5 hundredths of a metre, so the tenths place must be filled with a zero. It helps to picture the length as a number of centimetres before writing it in metres.

The worksheets in this area include the template Stating a length as a decimal number: the child receives lengths in two units and writes them as a decimal number in one unit. The solutions are included, so you can check the answers directly. As a personal idea, not a curriculum requirement: at home, one can measure objects with a tape measure and have the child write the length once as "metres and centimetres" and once as a decimal number in metres.

In the area of mass, the child converts between the neighbouring units kilogram (kg) and gram (g). The curriculum gives the example: 2000 g is 2 kg. The numbers used for calculating are not further restricted in the curriculum point. The curriculum points additionally name t and mg; however, the tasks in this area revolve around kilograms and grams.

A typical mistake arises when the child thinks of the conversion from the centimetre and calculates with 100. Then 3 kg wrongly becomes 300 g instead of 3000 g. It is helpful to remember that one kilogram has a thousand grams and that the gram is the smaller unit.

The tasks in this area include:

• Converting into a smaller unit of mass, for example kilograms into grams
• Converting into a larger unit of mass, for example grams into kilograms
• Mass in kilograms: choose the decimal number, where the matching decimal number for a weight in kg is selected
• Mass in kilograms: true or false, where statements in kg are checked for correctness
• Converting mass units: select the result, where the correct answer is chosen from several solutions
• Mass units: comparing and stating mass in one unit, which deepen understanding of the units

The Lehrplan 21 describes for the whole grade level that numbers up to 1 million are counted forwards and backwards in appropriate steps and ordered on the number line. In Grade 5, the tasks for this mainly show the ten-jump on the number line: the child sees where a number lies and jumps from there ten units forward or back.

A typical mistake is that, when making a ten-jump, the child only counts on by 1, i.e. moves stroke by stroke, instead of making a jump of ten. The position is also often read incorrectly, because not every stroke is labelled and the child has to determine the value of a stroke themselves.

In lessons and on worksheets, the following task types appear for this:

• Ten-jump on the number line: Starting from a marked number, the number that lies ten further left or right is determined.
• Ten-jump: choose the number: From several options, the correct number after a ten-jump is selected.
• Ten-jump: true or false: A given calculation or solution is judged as correct or incorrect.

The Lehrplan 21 names as a goal for mathematics that pupils multiply numbers with up to 4 digits, for example 45 · 240. This statement applies to the whole stage and not only to Year 5. What is concretely practised in this year is shown by the task templates: a multi-digit number is multiplied in writing by a single-digit number, for example 327 · 4.

A typical mistake: the child calculates from right to left, digit by digit, and forgets the carry or does not add it to the next digit. For 47 · 6, 6 · 7 = 42. You write down the 2 and carry the 4. Then 6 · 4 = 24, and with the carry it is 28. Often, however, the 4 is forgotten, and 24 comes out. The error arises because the multiplication facts and the carry have to be held in mind at the same time. Misaligned digits, because the figures are not neatly written under each other, also frequently lead to wrong results.

The task templates in this area cover different forms:

• Multiply in writing by a single-digit number: pure calculation tasks in columns.
• Written multiplication in a word problem: the multiplication is hidden in a short story and must first be recognised.
• Written multiplication: the missing factor: one factor is missing, for example ? · 6 = 258.
• Written multiplication: choose the missing factor: the matching factor is selected from several suggestions.
• Written multiplication: choose the result: the correct result is chosen from several solutions.

The child can use a statement that applies to several units to calculate the value for a single unit, for example the price per kilogram. The curriculum gives examples such as 300 g of cheese at 20 Fr./kg or a fuel consumption of 6 l per 100 km. These examples belong to the whole level. The worksheets' task types show exactly which numbers and tasks appear in Year 5.

Two errors are typical:

• The division is reversed. For 3 pieces for 6 Fr., the child calculates 3 : 6 instead of 6 : 3, because they do not consider what is being asked for.
• The unit is missing. The answer "2" without "Fr. per piece" remains unclear, and when comparing packages, people often look at the total price instead of the price per unit.

The worksheets contain four task types for this: Value for one as a real-life problem, where the question is how much one costs or weighs; Price per piece with the question of where something is cheaper; Value for one unit with selection of the correct result; and Value for one unit as a "true or false" task, where statements are checked. The solutions are included so that you can work through the calculations together.

The child can divide natural numbers by a single-digit number, for example 231 : 7. The curriculum describes this skill across several school years together. In Year 5, it is mainly practised with written division tasks. The child may calculate in their head or write down their own methods. If the number does not divide evenly, a remainder remains.

A typical mistake concerns the zero in the result. For 408 : 4, the result is 102. Many children write 12, because when bringing down the next digit they skip the 0, even though 0 : 4 = 0 occupies a place in the result. A second mistake arises when the remainder is not smaller than the divisor. Then the last partial calculation is not yet finished:

• The zero in the result is forgotten.
• The remainder is greater than or equal to the divisor.

Typical tasks in this area are:

• Dividing by a single-digit number in written form: Working through tasks such as 231 : 7 step by step.
• Zero in the result: Finding or selecting tasks where the result contains a zero.
• The missing dividend: The number being divided is missing and must be found.
• Choose the dividend: From several numbers, the suitable number to be divided is selected.
• Written division in word problems: The division is hidden in a text and must first be recognised.

The worksheets on this topic are printable and include solutions.

The child learns to find, in a data set (a series of values such as measurement results or survey results), the largest value (maximum) and the smallest value (minimum), and to analyse the data using these criteria. The curriculum point does not name a fixed number range, so you should not expect a specific range of numbers, but rather an understanding of the procedure.

A typical mistake is simply taking the first or last number in the list instead of comparing all the values. This happens because lists are rarely sorted and the eye fixes on the first number. With the range, the difference between maximum and minimum, another error arises: the child only states the largest value or calculates the difference in the wrong direction.

In the worksheets for this topic, the task appears as "Determining the range". A typical example is a short list, for instance temperatures on several days. The child first looks for the largest and the smallest value and then calculates the difference. The solutions on the worksheet help you follow the calculation steps.

Your child should be able to read and write decimal numbers and fractions. The curriculum point does not name a separate number range for this. However, the tasks in this area work with decimal numbers up to the thousandths place. Your child names each digit after the decimal point and recognises its place value: in 0.45, the 4 stands for four tenths and the 5 for five hundredths.

A common mistake occurs when the places after the decimal point are treated like a whole number. Then the zero as a placeholder is lost: 2.07 becomes 2.7, even though seven hundredths is only 0.07. A related mistake appears when comparing: 0.5 seems smaller than 0.45, because 45 is greater than 5. Both mistakes arise because the places are not thought of as tenths, hundredths and so on.

The worksheet tasks in this area look, for example, like this:

• Reading the hundredths digit: Your child determines the digit in the hundredths place of a decimal number.
• Place value of decimal numbers, value of a digit: Your child determines what value a single digit has in the number.
• Place value of decimal numbers, decomposition: Your child breaks a decimal number down into its place values.
• Place value of decimal numbers, choosing the thousandths digit: Your child selects the digit in the thousandths place.
• Decimal number, choosing the value of the digit: Your child selects, from given options, the correct value of a digit.

According to the Lehrplan 21, your child should be able to calculate with time measurements and convert quantities into neighbouring units of measurement. The curriculum item does not specify a number range. This section deals specifically with converting weeks into days: one week has 7 days, so 3 weeks equal 21 days.

A typical mistake is that the child treats the week like an ordinary number and adds 7 to the number of weeks, instead of multiplying by 7. 3 weeks then becomes 10 days instead of 21. This happens because the unit "week" is not understood as a group of 7 days.

The printable worksheets in this area contain three types of tasks:

• Weeks and days: how many days is that – converting a number of weeks into days.
• Weeks and days: choose the number of days – selecting the correct number of days for a given number of weeks.
• Weeks and days: true or false – checking statements such as "4 weeks are 28 days".

Months and years do not appear in the task templates listed here.

The curriculum point mainly requires the confident use of technical terms and symbols. It does not name a number range, because this is about concepts and not calculation. The set square (Geodreieck) is used for drawing and measuring. On the worksheets in this area, the ray (Strahl) also appears.

A line segment is often confused with a straight line. A line segment has two endpoints and ends there, while a straight line extends infinitely in both directions. A child who has not yet internalised this difference may answer statements about endpoints incorrectly. When counting segments on a straight line, only the directly adjacent sections are easily counted, while segments spanning several sections are overlooked.

The tasks in this area are printable worksheets with solutions, including:

• Line segment, ray or straight line? The child matches figures to the correct term.
• Endpoints of a figure: true or false The child checks statements about endpoints.
• Segments on a straight line: choose the number The child selects the correct number from given answers.
• Segments on a straight line: how many? The child counts the segments themselves.

Your child learns to reflect figures across an axis and to sketch the mirror image. This includes reflecting individual points and lines across an axis using a set square and ruler. The curriculum points do not specify a number range. They are formulated for a longer period. In Year 5, the tasks mainly show points with coordinates that are reflected across a straight line.

A typical mistake is that the mirror image lies on the same side of the axis as the original. Another mistake: the image lies on the other side, but at a different distance from the axis. Often the figure is shifted by feel, instead of placing each point the same distance away on the other side of the axis. It helps to count the distances to the axis or to measure them again with a set square.

Typical tasks in this area are:

• Reflect a point across a straight line: A point is reflected across a given straight line.
• Reflection across a vertical line: choose the coordinate: From several given options, the correct coordinate of the reflected point is selected.
• Axial symmetry: reflection across a vertical straight line: A figure is reflected across a vertical axis.
• Axial symmetry: true or false: It is decided whether a figure is axially symmetric.
• Axial symmetry: how many axes of symmetry: The number of axes of symmetry of a figure is determined.
• Axial symmetry: axis of a pair of points: For two points, the axis is sought across which they correspond to each other as mirror images.

The child can recognise and name the solids cube, cuboid, sphere, cylinder and pyramid when they occur in the environment or in pictures. The curriculum point does not specify a number range; it is about shape and name.

A possible stumbling block is that solids are named based only on a first impression. A cuboid, for example, is easily taken for a cube because both look angular. One possible cause is not paying attention to whether all sides are the same size. This is an observation from practice and not a requirement of the curriculum.

In the Mathematics area of Grade 5, there are three task types for worksheets with solutions:

• Which solid is this? Choose the name: The solid is matched to a name.
• Which solid is this?: The solid is named itself.
• Edges of a solid: true or false: Statements about the edges of a solid are checked.

The child decides, for a drawn figure made of six equal-sized squares, whether it can be folded into a cube. They check this in their imagination or by folding. The curriculum also describes drawing nets and representing prisms and pyramids. For this grade, the worksheets in this area mainly show checking cube nets.

A typical mistake: the child counts only the six squares and considers every connected shape to be a net. When folded, however, two squares then land on the same cube face while one face stays open. The figure looks right, but it does not fit together.

A task for this is called, for example, "Is this a cube net?". The worksheet shows several figures, and for each one the child decides whether it is a cube net. Giving a reason is helpful. As a suggestion for home: draw the figure on paper, cut it out and fold it. It quickly becomes clear whether all six faces form a cube.

The curriculum requires children to orient themselves to reference sizes such as 1 kB and to understand and use the prefixes Mega, Giga and Tera. In this class, the tasks mainly show what is concretely asked: converting gigabytes into megabytes, converting megabytes into gigabytes, and comparing amounts of data with each other. The curriculum does not specify a separate number range for this area; the numbers arise from the tasks themselves.

A typical mistake: the child does not remember that a gigabyte is larger than a megabyte. Because of this, the number is sometimes changed in the wrong direction after conversion. Anyone who wants to know how many GB a certain amount of MB corresponds to must remember that the number in the larger unit comes out smaller. It helps to think before calculating whether the result should become larger or smaller.

On the worksheet, the task looks something like this:

• Converting gigabytes into megabytes: The given value is in GB, and the value in MB is required.
• Megabytes into gigabytes: The correct result is chosen from several answers.
• Comparing amounts of data: Which amount is larger or smaller?
• Selecting the converted value: The suitable value is chosen from several offers.