Matematica per il 6° anno

In Year 6, children learn to systematically enumerate all possibilities of combinations of two variables and find pairs of numbers that satisfy an equation with two unknowns. Instead of guessing, pupils use structured approaches—such as ordered lists or tables—to ensure they identify every valid pairing.

A common error is writing pairs down at random rather than following a consistent pattern. Without a clear system, children frequently record duplicate pairs or overlook valid possibilities altogether, especially when tracking changes such as how the total number of combinations shifts after adding or removing an item.

In practice, tasks ask pupils to list all combinations or calculate the total number of different pairs that can be made. Tasks range from multiple-choice questions to word problems like working out how many pairs are left when one item breaks, finding the size of a group when the total number of pairs is already known, or exploring how many sets can be formed from three kinds of things.

In Year 6, children calculate the total boundary around rectangles using measurements in centimetres and metres. Building on earlier measurement of flat shapes, they work flexibly with rectangle dimensions: adding all four sides, using given measurements to find unknown side lengths, and exploring how different shapes compare in perimeter.

A frequent mistake happens when children add only the two labelled sides—length and width—and forget to account for the opposite two sides, resulting in half the actual perimeter. Children also commonly confuse perimeter with area, multiplying length by width rather than adding the lengths of all four outer edges together.

Worksheet tasks present rectangles with labelled dimensions or placed on a grid. Children solve questions such as finding the missing side of a rectangle when the perimeter is provided, determining which figure has the greater perimeter, verifying if a given perimeter calculation is correct, or using a ruler to draw a rectangle with the given perimeter.

In Year 6, children work with full four-quadrant coordinate grids. They plot points and transform them across the axes by sliding them horizontally and vertically, rotating them 90° or 180° around the central origin (0, 0), and scaling distances from the origin.

A frequent stumbling block is mixing up the x and y coordinates during movement. When translating points, children often mistakenly apply horizontal shifts (left or right) to the vertical y-coordinate, or forget how negative values behave when moving left or down past an axis. When rotating, confusion between clockwise and anticlockwise turns often leads to plotting points in the wrong quadrant.

Worksheet tasks focus on transforming specific coordinate points on a grid. Children practise tasks such as:

• Translating a point either right and up or left and down by a specified number of units.
• Rotating a point 90° or 180° about the origin.
• Dilating a point from the origin by multiplying its distance from the centre.

In Year 6, children move from box-style missing number sentences to expressing missing numbers algebraically. They solve equations where an unknown quantity is represented by a letter, using a single inverse operation to find the missing value.

A common mistake occurs when children misinterpret the relationship between the letter and its coefficient. For example, in an equation like 4x = 24, pupils may mistakenly see 4x as an addition problem and subtract 4, rather than recognising that the unknown has been multiplied by 4 and dividing instead.

In practice, printable tasks from the Solve the equation templates present clear, single-step problems such as x + 8 = 19 or 6y = 42. Children use mental math or written arithmetic to calculate and write down the single value that makes the equation true.

In Year 6, children calculate with fractions that have different denominators. Building on previous experience with denominators that were direct multiples of one another, they use equivalent fractions to rewrite both parts of an addition or subtraction problem so that they share a common denominator before completing the calculation.

A common error occurs when children add or subtract straight across, combining the numerators and the denominators directly (such as writing 1/3 + 1/4 = 2/7). This usually happens when pupils treat fractions as two separate whole numbers rather than remembering that fractions of different sizes cannot be combined until they are converted into equal parts.

Worksheet tasks provide targeted practice across these operations. Children solve direct calculation questions using Add fractions with unlike denominators and Subtract fractions with unlike denominators, or tackle contextual problems in How much altogether? Unlike fractions to find combined totals.

In Year 6, children calculate and compare the volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), extending to units like cubic millimetres (mm³). They build on earlier practical work with 1 cm³ blocks, moving from physically packing shapes to using multiplication (length × width × height) to determine the space inside a 3D shape.

A common error is confusing volume with surface area or perimeter. Children often add the three given dimensions together instead of multiplying them. When working with combined shapes, another frequent slip is miscalculating shared or missing edges before finding the separate volumes, leading to double-counting parts of the shape.

Tasks in this area reflect this progression clearly. Children start by determining the volume from unit cubes shown on isometric grids. They then advance to finding the volume of a rectangular prism from given side lengths, before tackling more complex questions such as calculating the volume of a solid made of two prisms by splitting an L-shaped block into two distinct cuboids.

In Year 6, children convert measurements of length between standard metric units, moving from smaller units to larger ones and vice versa. They work across millimetres, centimetres, metres, and kilometres, using decimal notation up to three decimal places to record their answers accurately.

A typical error occurs when children mix up whether to multiply or divide. For example, when changing a smaller unit into a larger one—such as centimetres into metres—pupils often multiply by 100 instead of dividing, or they confuse the conversion factors and scale by 10 or 1,000 by mistake.

Worksheet tasks build confidence through three core formats: children convert to a smaller unit of length, convert to a larger unit of length, or write a length in one unit to express mixed measurements as a single decimal value.

In Year 6, children learn to calculate and interpret the mean as an average. To do this, they add a set of values together to find the total and then divide that sum by the number of data points. Beyond just finding the number, they learn to understand what this average tells them about the data set as a whole.

A frequent error occurs when children mix up the number of items they need to divide by. Instead of counting how many data values are in the set, they might divide by the highest value, the largest bar on a graph, or miss a zero value entirely. Children also sometimes carry out the addition correctly but forget the division step altogether.

Worksheets provide practice across different formats:

• Find the mean: straightforward arithmetic tasks where pupils calculate the average from given lists of values.
• Mean from a bar chart: reading frequencies and values accurately from a graph before calculating the mean.
• The mean in everyday life: word problems where pupils interpret averages in realistic situations, such as test scores, weekly temperatures, or goals scored.

In Year 6, children apply the formula for the area of a rectangle (multiplying length by width) using standard units such as square centimetres (cm²) and square metres (m²). They also work in reverse: using properties of rectangles and inverse operations, they divide the total area by a known side length to deduce the missing side.

A frequent mistake occurs when finding an unknown dimension: children often subtract the known side from the total area instead of dividing, confusing the multiplicative relationship of area with additive measures. Another common confusion is mixing up area and perimeter, mistakenly adding the outer lengths when asked to find the surface space inside.

Worksheet tasks draw from three concrete formats: straightforward calculations in Area of a rectangle, algebraic reasoning where the area and one dimension are provided in Missing side of a rectangle, and practical word problems in Area of a rectangle in everyday life involving real-world surfaces like garden patches or floors.

In Year 6, children learn to use simple formulas by substituting numbers in place of letters. They apply the four operations to evaluate expressions, finding a concrete numerical result once the values of the variables are provided.

A common mistake occurs when a number and letter sit side by side, such as 3n. Instead of multiplying 3 by n, children often treat the number as a place-value tens digit, reading 3n as 34 when n = 4. Another frequent stumbling block is forgetting to follow the correct order of operations when working through formulas with more than one step.

Worksheet tasks provide targeted practice across three main formats:

• Value of an expression with a letter, where pupils replace a single letter with a given number to find the total.
• Value of a formula for given numbers, where pupils calculate outputs using given input values.
• How many times as large? Without calculating, where children compare expressions by looking at the relationships between terms rather than computing each total.

At this stage, children learn to generate and describe number sequences by working out the relationship between terms. They identify the underlying rule and use it to extend the sequence forward, focusing on patterns that increase or decrease by adding the same step each time, as well as sequences formed by multiplying by a constant number.

A common mistake occurs when children check only the first two numbers in a list and jump to a conclusion. For example, seeing 2 followed by 4 might lead a child to assume the rule is simply "add 2", without checking whether the next number is 6 (an addition pattern) or 8 (a multiplication pattern). Another frequent error is mixing up addition and multiplication steps partway through extending the chain.

Practice tasks present sequences with missing values for pupils to complete. Typical activities include:

• Pattern: add the same step, where children repeatedly add a fixed amount to write the next terms;
• Pattern: multiply by the same number, where each term is scaled by a set multiplier;
• Spot the rule and continue the pattern, where children must examine a given string of numbers, work out the operation being used, and fill in the missing numbers.

At this stage, children read and interpret line graphs that show change over time, specifically tracking distance across a journey. Using the horizontal axis for time and the vertical axis for distance, they read specific coordinates, calculate total distances travelled, and solve comparison and difference problems based on the visual data.

A common error occurs when interpreting flat, horizontal sections of the line. Children often assume that a flat line means the journey has ended or that movement has reversed, rather than realising that time is continuing while distance remains unchanged—meaning the traveller is stopped. Misreading unmarked grid intervals on time or distance axes is another frequent source of calculation mistakes.

Tasks provide a plotted journey line and ask children to extract key information:

• Trip graph: how far in total? Children read the maximum distance reached on the vertical axis to find the overall length of the journey.
• Trip graph: how long was the stop? Children identify the horizontal section of the line and calculate the difference between its start and end times.
• Trip graph: speed in the first part Children identify the distance covered during the first leg and divide it by the time taken to determine the speed.

In Year 6, pupils solve problems that require numbers to be rounded to specified degrees of accuracy. Building on work from earlier years where they rounded to the nearest whole number, children at this stage focus on rounding decimal values accurately to the nearest tenth or hundredth.

A common error is looking at the wrong place-value column to make the rounding decision. When rounding to the nearest tenth, for instance, children often look at the tenths digit itself rather than checking the hundredths digit directly to its right. Children also struggle when rounding causes a value to roll over into the next place value, such as rounding 4.98 to the nearest tenth, where the tenths digit rounds up to create 5.0.

Tasks provide focused practice using two template formats: Round to the nearest tenth and Round to the nearest hundredth. In these exercises, pupils work with numbers containing two or three decimal places, identify the relevant deciding digit, and rewrite the number to the requested degree of accuracy.

In Year 6, children learn to identify common multiples of numbers and pinpoint the least common multiple (LCM). They work systematically by comparing the times-table multiples of two or more given numbers to determine the lowest number that appears in both lists.

A frequent stumbling block is confusing multiples with factors, leading children to search for smaller divisors rather than larger products. Another common error is simply multiplying the two numbers together; while this always produces a common multiple, it often misses the least common multiple (such as giving 24 instead of 12 for the numbers 4 and 6).

In class, this skill appears in direct calculation tasks such as Find the least common multiple, where children practice with number pairs. They also apply the skill to real-world word problems in When together again?, calculating when repeating cycles—such as two buses on different timetables or two flashing signals—will happen at the same time.

In Year 6, children learn to multiply numbers with up to two decimal places by a whole number, such as calculating 3.45 × 6 or 8.2 × 4. They use standard written methods for multiplication, drawing on their understanding of place value to know how tenths and hundredths scale when multiplied.

A common error occurs when placing the decimal point in the final answer. Children frequently carry out the multiplication accurately as if working with whole numbers, but then misplace or omit the decimal point at the end, resulting in an answer that is ten or a hundred times too large (for example, writing 1380 instead of 13.8).

Worksheets for this skill feature two typical styles of tasks:

• Multiply decimals provides direct written calculations to solve, reinforcing fluency and accurate decimal placement.
• Multiply a length by a number of pieces sets the calculation within real-world measurement problems, such as finding the total length of six pieces of ribbon measuring 1.45 metres each.

In Year 6, children multiply and divide both whole numbers and decimals by 10, 100 and 1000. They identify the value of each digit in numbers with up to three decimal places (tenths, hundredths and thousandths) and calculate answers that also extend up to three decimal places.

A common error is trying to apply the shortcut of simply adding or removing zeros at the end of a number. This rule breaks down with decimals, leading children to write calculations like 4.5 × 10 = 4.50 instead of 45. Children need to understand that multiplying and dividing by powers of 10 shifts the digits to different place value columns, rather than just changing the zeros.

Practice tasks are drawn from templates for Multiply by 10, 100 or 1000 and Divide by 10, 100 or 1000. Children solve direct calculation problems that require moving digits one, two or three places to the left or right, using zero as a place holder where appropriate.

In Year 6, children build on finding factor pairs to identify common factors shared by two whole numbers and determine the highest one. They systematically check the factors of both values to find the largest single number that divides evenly into each without a remainder.

A common mistake is stopping at the first shared factor found—frequently 2 when working with even numbers—rather than testing remaining factor pairs to find the largest possible match. Children also commonly confuse factors with multiples, giving a larger common product rather than a divisor.

Practice tasks generally take two forms:

• Find the greatest common factor asks children to list factor pairs and identify the highest common factor for given number pairs.
• Share into identical packs applies the skill to practical word problems, asking children to find the greatest number of equal sets that can be packed from different quantities of items with none left over.

In Year 6, children work with positive and negative whole numbers positioned along a horizontal number line, counting forwards and backwards through zero. They learn that every positive integer has a corresponding negative opposite that sits the exact same distance from zero in the other direction (such as 5 and -5). Recognising numbers as directed distances from zero helps prepare pupils to plot positions across all four quadrants of a coordinate grid.

A common mistake occurs when children mirror positive counting habits on the negative side of the line. Because 5 is larger than 2, children often assume -5 should be positioned closer to zero than -2, essentially writing negative numbers backwards from left to right. They may also count tick marks starting from the far-left edge of the line rather than measuring steps outwards from zero.

Worksheets support this skill through direct visual practice. Typical tasks include:

• Read an integer on a number line: looking at a given point or arrow on a scaled line and naming the correct positive or negative whole number.
• Find the opposite number: identifying the value that balances a given integer symmetrically on the other side of zero.

At this stage, children compare the relative sizes of two quantities and find missing values using integer multiplication and division facts. They learn to spot the relationship between known amounts—such as identifying that one quantity has been doubled, tripled, or halved—and apply that same multiplier or divisor to determine the unknown amount.

A common hurdle is confusing multiplicative change with addition. For instance, if a recipe changes from 2 eggs to 6 eggs, a child might notice the difference of 4 and add 4 to the flour amount, rather than multiplying by 3. Children also occasionally apply the operation in the wrong direction, multiplying when they need to divide to scale down.

Worksheet tasks focus on these skills through two main formats:

• Complete the proportion, where children find the missing value in paired numeric statements or simple tables.
• Scale up from one group to another, presenting real-life contexts like recipes or grouped objects where children multiply to find how many items are needed for a larger set.

In Year 6, children calculate percentages of quantities and measurements, such as finding 15% of 360. They solve these by linking percentages to key fractional equivalents like 1/2 (50%), 1/4 (25%), and 1/10 (10%). To find values like 15%, children typically find 10% of the number by dividing by 10, halve that result to get 5%, and add the two parts together.

A common mistake occurs when children assume that every percentage calculation involves dividing by the percentage value itself. Because finding 10% means dividing by 10, a child might incorrectly divide by 20 to find 20%, or divide by 5 to find 5%, instead of using fractional equivalence or scaling from 10%.

Worksheet tasks give practice through two direct formats:

• Find the percent of a number, where children compute and write down the exact value for a given percentage and amount.
• Percent of a number — choose the answer, where children calculate the value and select the correct total from a set of multiple-choice options.

Children learn to use the core geometric facts that the interior angles of any triangle add up to 180° and the interior angles of any quadrilateral add up to 360°. Using addition and subtraction, pupils total the known angle measurements and subtract that sum from either 180° or 360° to calculate the single remaining angle.

A frequent mistake occurs when children mix up the two whole totals, incorrectly attempting to subtract the angles of a four-sided shape from 180° instead of 360°. Arithmetic slips are also common when adding three two-digit numbers together before subtracting from 360°, especially when regrouping across zeros.

Practice tasks focus directly on calculating missing values from labelled shape diagrams. Worksheets present either The third angle of a triangle, providing two known degree measurements to find the final corner, or The fourth angle of a quadrilateral, providing three known angles to find the fourth.

In Year 6, children learn to identify key parts of a circle and apply the rule that the diameter is always twice the length of the radius. At this stage, they move between these two measurements by doubling a given radius to find the diameter, or halving a given diameter to find the radius.

A common error occurs when children mix up the two terms and reverse the operation—doubling the diameter or halving the radius. Others confuse the visual representation, forgetting that the radius reaches only from the centre to the edge, whereas the diameter passes all the way across through the centre.

Worksheet tasks provide direct practice through two main formats: Diameter from the radius and Radius from the diameter. In each task, children look at a circle with a single measurement provided or read a given length, then multiply or divide by 2 to write down the missing dimension.

In Year 6, children extend their understanding of place value to work with numbers up to 10,000,000. They learn to read and write these multi-digit values accurately, state the exact value of any single digit (such as identifying that the 4 in 3,450,200 represents four hundred thousand), and order sets of large numbers.

A typical error happens when children compare numbers that share similar leading digits or include zeros as placeholders, such as 5,060,000 and 5,600,000. Instead of methodically checking the place value column by column from the left, children often glance at the whole number and misjudge which digit holds the larger place.

Practising this skill involves activities like Compare multi-digit numbers, where children place comparison symbols between large whole numbers. They also work on How many times as large? Place value, which asks them to determine how many times larger a digit becomes as it shifts across place value columns.

In Year 6, children carry out mental calculations with large numbers by spotting helpful number relationships rather than relying on column methods. They use known facts and the properties of operations—such as rearranging addends to find easy number bonds (commutativity) or breaking a calculation down using factor pairs and the distributive law—to solve problems efficiently in their heads.

A common mistake occurs when children work rigidly from left to right through a long calculation. For instance, when adding a list of numbers, they often add each value in sequence rather than reordering them to pair up numbers that make clean hundreds or thousands. In multiplication, children might split a factor into smaller parts to multiply mentally, but forget to multiply both parts before recombining them.

Tasks like Add the smart way and Multiply the smart way give children targeted practice with these strategies. Rather than setting out formal written algorithms, pupils look at multi-digit additions and multiplications, identify shortcuts like compatible pairs or factor combinations, and compute the answer mentally.

In Year 6, children build on earlier place value work to round whole numbers to a required degree of accuracy. At this stage, pupils use their understanding of digits and place value columns to round numbers to specific targets, working confidently with values into the thousands and tens of thousands.

A common mistake occurs when children look at the wrong digit to decide whether to round up or down. When rounding to the nearest ten thousand, for instance, a child might look at the ten thousands digit itself or jump to the hundreds column instead of looking immediately to the right at the thousands digit. Confusion also arises when rounding up triggers a change across multiple columns, such as rounding 39,700 up to the nearest thousand.

Worksheet tasks present whole numbers and ask children to round them to a designated target place. Typical activities include exercises where pupils Round to the nearest thousand and Round to the nearest ten thousand, reinforcing which multiple of 1,000 or 10,000 a given number sits closest to.

Children learn to translate word problems into simple algebraic equations by using a letter to represent an unknown value. In Year 6, they express these missing number problems algebraically and use inverse operations to calculate the solution.

A frequent stumbling block is translating the sequence of events into the correct mathematical order. When working out the missing value, children often perform calculations in the order the words appear rather than undoing the operations step by step in reverse.

Worksheet tasks take the form of short written puzzles. In Which number was it?, children read a clue describing operations applied to a mystery number and write an equation to identify it. In How many were there at the start?, they represent a changing quantity of items to determine the initial amount.

In Year 6, children compare and classify geometric shapes based on their properties and sizes. For four-sided shapes, this means looking closely at features such as equal side lengths, pairs of parallel sides, and right angles, rather than just relying on what a shape looks like at a glance.

A common difficulty arises when classifying overlapping shape families. Children frequently think of shapes as mutually exclusive categories and struggle to realise that a shape can belong to more than one group—for example, not seeing that a square also meets all the rules to be classified as a rectangle or a parallelogram.

Worksheet tasks reinforce this understanding by showing a shape and asking "What is this quadrilateral called?" based on marked sides and angles. Other questions challenge shape definitions directly with prompts like "Is a square also a rectangle?", prompting children to test the specific properties of each shape.

In Year 6, children divide numbers up to four digits by a two-digit whole number using the formal written method of long division. They work systematically down the page to find the quotient and learn to express leftover amounts as whole-number remainders, as fractions, or by rounding, depending on what a question requires.

A common stumbling block is estimating how many times a two-digit divisor fits into each part of the larger number. Children frequently misjudge these multiples or misalign their columns when subtracting and bringing down the next digit, which leads to calculation errors midway through the algorithm.

Worksheets using the long division by a two-digit number task template present multi-digit written problems set out in the traditional layout. Children work through each step of dividing, multiplying, and subtracting—for example, dividing a four-digit number such as 3,542 by 14—recording their intermediate steps clearly to arrive at the final answer.

In Year 6, children use their knowledge of the order of operations to solve calculations involving all four operations: addition, subtraction, multiplication, and division. They learn that any part of a calculation enclosed inside brackets must be worked out before completing the rest of the expression.

A common mistake is working through the calculation strictly from left to right and ignoring the brackets. For example, in an expression such as 10 - (2 + 3), a child might calculate 10 - 2 first to get 8, and then add 3 to reach 11, rather than working out the bracketed sum first (2 + 3 = 5) to find the correct answer of 5.

Tasks for this skill ask children to evaluate an expression with brackets. They are presented with a written arithmetic statement containing mixed operations and brackets, writing out each step in the correct order to determine the final value.

In Year 6, children build on earlier rounding skills to estimate answers to calculations and determine an appropriate degree of accuracy. For addition, they learn to round numbers to a suitable place value—such as the nearest thousand or ten thousand—before adding, giving them a reliable benchmark to check their work.

A common error occurs when children calculate the exact answer first and then round that result, defeating the purpose of an estimate. Another frequent mistake is choosing inappropriate degrees of accuracy, such as rounding numbers too aggressively to be useful or rounding different numbers in the same calculation to mismatched place values.

Practice sheets based on the Estimate a sum template present children with addition problems involving multi-digit numbers. Children round each addend to an appropriate value, find the approximate total, and use that estimate to verify whether a calculated answer makes sense.

Children tackle practical contexts where they must decide which operations and methods to use and why. At this stage, they work with increasingly large positive numbers, identifying the intermediate result needed before completing the final step using addition and subtraction.

A frequent error occurs when pupils stop after completing only the first calculation. Because word problems often present information sequentially, children easily mistake the intermediate answer for the final solution, or they latch onto individual keywords rather than working out how the different quantities combine across both steps.

Worksheet tasks use the two-step word problem (combine) template. A typical question describes a real-life situation—such as calculating items collected across different groups or dates—requiring children to carry out an initial addition or subtraction, store that total, and combine it in a second step to find the overall answer.

In Year 6, pupils compare and order fractions where denominators are not multiples of each other, extending their understanding to include fractions greater than 1. To make accurate comparisons, children learn to convert fractions into equivalent forms using a shared common denominator.

A common error occurs when pupils treat fractions as pairs of separate whole numbers. For example, a child might assume that 3/8 must be larger than 2/3 because both 3 and 8 are larger than 2, ignoring the relationship between the parts and the whole. Confusion can also arise with values greater than 1 if children do not convert mixed numbers and improper fractions into the same format before comparing.

Worksheets using the Compare fractions with unlike denominators template present pairs of fractions side by side. Children are asked to determine which is larger by writing out equivalent fractions with matching denominators and inserting comparison symbols between them.

Children learn to connect ratio and scaling to maps and scale drawings. Using a known scale factor, they multiply to scale a map measurement up to its real-world length or divide to scale an actual distance down to map size.

A frequent error occurs when pupils apply the wrong operation, such as multiplying when converting a real distance back onto the page, producing a map length that is impossibly large. Children also commonly struggle when shifting between units of measurement, losing track of how centimetres relate to metres or kilometres during the calculation.

Worksheet tasks based on Distance on a map and in reality provide a clear scale, such as 1 cm representing a set number of metres. Children are given either the map measurement or the real-world distance and calculate the missing value using multiplication or division.

In Year 6, children use common factors to simplify fractions into their simplest form. Building on earlier visual work with equivalent fractions, they identify shared factors between the numerator and denominator and divide both values to reduce the fraction.

A typical error is stopping too early when simplifying in multiple steps. For instance, a child might divide both numbers in 12/16 by 2 to get 6/8, but fail to notice that 6 and 8 still share a common factor. Another common mistake is dividing the top and bottom numbers by different values rather than using the same shared factor for both.

Worksheet tasks based on the Simplify the fraction template present a single fraction and ask children to rewrite it in its lowest terms by dividing out all common factors.

In Year 6, children learn to multiply simple pairs of proper fractions, such as calculating 1/4 × 1/2 = 1/8. They multiply the numerators together and the denominators together, then ensure the final answer is written in its simplest form.

A frequent mistake is confusing multiplication with addition and trying to find a common denominator before multiplying. Children also commonly carry out the multiplication correctly across the numerators and denominators but forget the final step of simplifying the resulting fraction.

Worksheet tasks from the Multiply fractions template present direct calculation problems pairing two proper fractions. Children work through each equation to calculate the product and simplify the fraction wherever needed.

In Year 6, children learn to divide proper fractions by whole numbers, such as calculating 1/3 ÷ 2 = 1/6, and explore how whole numbers divide by unit fractions. They learn that splitting a fraction into equal parts results in smaller fraction pieces, doubling the denominator when dividing by two.

A frequent mistake happens when children confuse the operation and multiply the numerator instead of the denominator, writing 1/3 ÷ 2 = 2/3. Because division with whole numbers usually produces a smaller answer, children can also become confused when dividing a whole number by a fraction results in a larger number.

Practice tasks such as How many unit fractions fit? help resolve this by asking children to find how many unit fractions (like 1/3 or 1/4) fit inside a given whole number. This builds a clear mental picture of division as grouping before moving on to purely numerical calculations.

In Year 6, children calculate unit and non-unit fractions of quantities where the answer is a whole number. Building on basic division, they use their knowledge of fractions and multiples to split quantities into equal parts and solve problems involving unequal sharing and grouping.

A common mistake occurs when working with non-unit fractions: children frequently remember to divide by the denominator to find one part, but forget to multiply that answer by the numerator. Another typical error is confusing the two steps entirely by dividing by the top number and multiplying by the bottom.

Tasks using the Find a fraction of a number template present direct arithmetic problems, such as calculating 3/8 of 40 or 2/3 of 18. Children divide the whole number by the denominator to find a unit fraction, then multiply that result by the numerator to reach the final whole-number amount.

In Year 6, children learn that a fraction represents the division of whole numbers. They connect the division symbol directly to the fraction bar, recognising that dividing one whole number by another can be written as a simple fraction, such as understanding 3 divided by 8 as 3/8.

A common mistake is reversing the positions of the numerator and denominator. Because children are used to dividing larger numbers by smaller ones, they often mistakenly write a calculation like 3 divided by 8 as 8/3 rather than keeping the first number on top as 3/8.

Practice tasks using the Write a division as a fraction template present children with a division sentence between whole numbers and ask them to write the equivalent fraction.

In Year 6, children learn to use common multiples to express fractions in the same denomination. While earlier work focused on pairs where one denominator was a direct multiple of the other, pupils now find common multiples for different denominators, rewriting equivalent fractions so that both share the same bottom number.

A typical mistake occurs when children find a suitable common denominator but forget to multiply the numerator by the same factor. This alters the value of the fraction rather than creating an equivalent one. Pupils also frequently multiply denominators together to find a shared multiple, missing smaller common multiples that keep numbers manageable.

Worksheets for this skill center on tasks where pupils find the least common denominator. A typical exercise presents two or more fractions with unequal denominators and asks children to identify the lowest common multiple, then rewrite each fraction into its equivalent form using that common base.

In Year 6, children learn to convert simple fractions into terminating decimals by understanding that a fraction represents division. In addition to recalling familiar equivalents such as 1/2, 1/4, 3/4, tenths, and fifths, pupils calculate decimal equivalents for fractions such as 3/8 by dividing the numerator by the denominator (calculating 3 ÷ 8 to get 0.375), as well as working with denominators that are multiples of 10 or 25.

A frequent error occurs when pupils write the numerator and denominator directly on either side of a decimal point, incorrectly converting 3/8 into 3.8 or 1/5 into 1.5. Another common difficulty is reversing the division, where children mistakenly divide the denominator by the numerator (calculating 8 ÷ 3 instead of 3 ÷ 8) because they are more accustomed to dividing a larger number by a smaller one.

Practice tasks using the Write a fraction as a decimal template present children with a single fraction—such as 3/8, 4/5, or fractions with denominators of 10 or 25—and ask them to calculate and write down the exact decimal value.

In Year 6, children calculate unknown parts of angles by applying key geometric rules. They know that angles on a straight line add up to 180° (a half turn) and angles around a point add up to 360° (a full turn). Using these totals and the fact that vertically opposite angles are equal, they add together given measurements and subtract from 180° or 360° to find the missing value.

A common error is confusing which total to use, such as subtracting from 180° for angles meeting around a central point, or using 360° for a straight line. When an angle is split into three or more parts, children also make arithmetic slips by subtracting only one known angle from the total while forgetting to account for the others.

In practice, tasks using the Find the missing part of an angle template present diagrams of angles meeting at a point or along a straight line. A child is given one or more measured angles in degrees—such as a straight line divided into 65° and an unknown angle—and writes down the calculation needed to work out the missing degree value.

In Year 6, children learn to use formal written division methods to solve calculations where numbers do not divide evenly, producing answers with up to two decimal places. Instead of recording a leftover remainder, they continue dividing into tenths and hundredths by placing a decimal point and adding zeros.

A common error occurs when children simply copy the remainder directly into the decimal places—for instance, recording a remainder of 3 as .3 rather than carrying the 3 into the tenths column to continue the division. Pupils also frequently forget to align the decimal point on the answer line directly above the decimal point in the number being divided.

Practice tasks using the Divide decimals template provide structured written division calculations, prompting pupils to divide numbers step by step and record answers accurately to two decimal places.

In Year 6, children calculate intervals across zero by finding the total distance between positive and negative integers. Rather than simply working with positive values, they use a number line to see how far a negative value sits below zero and how far a positive value sits above it, combining those steps to find the full span between them.

A frequent error occurs when children ignore the negative sign and simply subtract the two numbers as if both were positive. For example, when finding the distance between -4 and 3, a child might calculate 4 − 3 = 1, forgetting that moving from -4 up to 0 already takes 4 steps before adding another 3 steps to reach positive 3.

Tasks using the Distance between integers template present pairs of positive and negative numbers—often marked along a number line or set within real-world contexts such as temperature changes—and ask pupils to determine the full interval between the two values.

In Year 6, children use positive and negative whole numbers in everyday situations and calculate intervals that step across zero. Rather than just counting forwards and backwards, they learn to determine the total difference between a positive number and a negative number.

A common mistake occurs when children calculate the distance between a negative and a positive number by simply subtracting the smaller digit from the larger one. For example, a child might calculate the gap between -3 and 4 as 1 instead of 7. They overlook zero as a boundary and forget to combine the distance from the negative number to zero with the distance from zero to the positive number.

Worksheet tasks practice this skill through scenarios such as tracking negative points in a game. Children calculate a player's running total after gaining or losing points, or work out how many points a player with a negative score needs to earn to reach a winning positive score.

In Year 6, children build on their knowledge of multiplication tables and factors to tell prime and composite numbers apart. They are expected to recall the prime numbers up to 19 from memory and determine whether any whole number up to 100 is prime or composite by checking if it has factors other than 1 and itself.

A common mistake is confusing odd numbers with prime numbers. Children frequently mislabel odd numbers such as 9, 15, 21, or 27 as prime simply because they are not even, overlooking factors like 3 or 9. Many also incorrectly treat 1 as a prime number, or forget that 2 is an even number that is also prime.

Tasks using the Prime or composite? template present children with individual numbers up to 100 and ask them to classify each one. Children work through systematic checks—such as testing for divisibility by 2, 3, or 5—to confirm whether a number has only two factors or more.

In Year 6, children convert measurements given in mixed units into a single measurement, using decimal notation up to three decimal places. They apply their knowledge of metric conversions—such as 1,000 metres in a kilometre or 100 centimetres in a metre—to express the smaller unit as a decimal fraction of the larger unit.

A common error occurs when children ignore place value and write digits directly after the decimal point without placeholders. For instance, a pupil might write 3 metres and 5 centimetres as 3.5 m instead of 3.05 m, confusing hundredths with tenths.

In practice, tasks using the Write a length as a decimal template present children with a compound measurement, such as kilometres and metres, and ask them to rewrite it accurately as a single decimal measurement in kilometres.

In Year 6, children apply their knowledge of multiples and factors to reduce ratios into their lowest terms. Much like simplifying fractions, they divide each part of the ratio by a common factor. For example, given a ratio such as 12 : 18, pupils identify that both numbers share common factors and divide both sides by 6 to reach the simplest whole-number ratio of 2 : 3.

A frequent error occurs when pupils stop simplifying too early. When dividing by smaller factors in stages—such as halving 24 : 36 to get 12 : 18—children often assume they have finished, overlooking that the remaining numbers still share factors. Another common mistake is attempting to subtract a number from both sides rather than dividing, or dividing only one side of the ratio.

Practice worksheets focus on tasks where pupils are asked to Write the ratio in simplest form. Children are presented with direct, two-part ratios such as 15 : 20 or 14 : 21, requiring them to find the highest common factor and record the final simplified pair.

In Year 6, children build on their measurement skills by converting larger units of mass into smaller ones, specifically changing kilograms into grams. They multiply values by 1,000 using decimal notation up to three decimal places, such as converting 2.45 kg into 2,450 g or 0.125 kg into 125 g.

A common mistake occurs when children confuse metric conversions and multiply by 100 instead of 1,000, mixing up mass with length. Children also frequently misplace zeroes when working with decimals that have fewer than three decimal places; for example, they might mistakenly calculate 0.4 kg as 40 g instead of shifting the digits three places to reach 400 g.

Worksheet tasks prompt children to convert to a smaller unit of weight. Children encounter measurements written in kilograms with up to three decimal places and write down the equivalent amount in grams.

In Year 6, children build fluency with formal long multiplication by multiplying numbers up to four digits by a two-digit whole number (such as 2,418 × 35). They set the problem out in columns, calculating two partial products—first multiplying by the ones digit, then by the tens digit—and adding those values together to reach the final answer.

A frequent error occurs in the second row of calculation, where children often forget to insert a zero placeholder in the ones column before multiplying by the tens digit. Another common pitfall is mismanaging carried numbers, such as adding a carried digit before multiplying or confusing the regrouped numbers from the ones step with those from the tens step.

Worksheets using the Multiply multi-digit numbers (columns) template present these problems ready-aligned in standard vertical layouts with designated working space. Children work through each step on the grid, recording regrouped digits clearly beneath the lines before finding the sum of both rows.

At this stage, children read information from bar charts and use the values to solve comparison, sum, and difference problems. They read the scale across discrete categories to determine exact amounts, comparing heights or lengths of bars to work out which category has the highest or lowest value and calculating the precise difference between them.

A common error happens when children misread intervals on the scale, particularly when the axis increases in steps of 2, 5, 10, or 20 rather than single units. When the top of a bar falls halfway between marked gridlines, pupils often miscalculate the value by counting every line as one, which leads to incorrect totals and differences.

Tasks based on the Compare bars in a bar chart template present children with a graph displaying categorical data, such as club attendance or school survey results. Children answer questions requiring them to compare two or more bars, determine how many more items one bar represents than another, or combine values across categories.

In Year 6, children learn to calculate the area of parallelograms. They identify the base and the perpendicular height of the shape and multiply these two measurements together to find the total area in square units, such as square centimetres or square metres.

A common mistake is multiplying the base by the slanted side length rather than the perpendicular height. Because the slanted edge is visible on the outside of the shape, children often treat it like the height of a rectangle, forgetting that the height must meet the base at a right angle.

Tasks using the Area of a parallelogram template present diagrams of parallelograms with labelled side lengths and heights. Children must select the correct perpendicular measurements—ignoring any extra diagonal lengths provided—and complete the multiplication to calculate the area.

In Year 6, children learn to calculate the area of different types of triangles. Building on their understanding of rectangles and parallelograms, they identify the base and the vertical height, multiply these two dimensions together, and divide by two to find the total area.

A common error occurs when children use the length of a slanted side instead of the true perpendicular height, particularly in isosceles, equilateral, or obtuse triangles. Another frequent slip is simply multiplying the base and height together but forgetting the final step of halving the result.

Worksheet activities based on the Area of a triangle template present drawings of triangles with labelled measurements. Children must select the correct base and perpendicular height—ignoring any extra side lengths provided—and calculate the area in square units.

In Year 6, children work with numbers given to three decimal places. They build on earlier work with tenths and thousandths to recognise the exact place value of every digit after the decimal point, understanding how tenths, hundredths, and thousandths relate to one another.

A frequent stumbling block is confusing the tenths and hundredths positions. Children often mirror whole-number place value patterns, mistakenly assuming the decimal places begin with a "units" or "hundreds" column, which leads them to misidentify which digit sits in the hundredths place.

In practice, activities ask pupils to find the digit in the hundredths place from a given decimal number. Children look at numbers with up to three decimal places, locate the second digit to the right of the decimal point, and state its value.

In Year 6, children expand their understanding of coordinates beyond the first quadrant to work with the full coordinate grid. They identify and describe positions across all four quadrants, reading pairs of positive and negative numbers along both the horizontal x-axis and the vertical y-axis.

A frequent error at this stage is reversing the order of the numbers by reading the vertical value before the horizontal one. Children also often misread points with negative numbers, confusing which direction to count from zero or dropping negative signs entirely when recording a position such as (-3, -5).

Worksheet tasks present a full four-quadrant grid with a point marked at a specific intersection. Children trace the position down or up to the horizontal axis to find the first value, across to the vertical axis to find the second value, and write down the coordinates accurately as a pair within brackets.

In Year 6, children learn to recognise, describe, and build simple 3-D shapes by working with their nets. They develop the spatial reasoning needed to visualise how flat 2-D patterns of connected faces fold together into closed three-dimensional solids.

A common mistake is simply counting six square faces and assuming the pattern must form a cube. Children frequently overlook where faces will end up once folded, missing that certain arrangements cause two squares to overlap and leave another side completely open.

Practice tasks based on the Is it a net of a cube? template present children with various configurations of six joined squares. Children mentally fold the edges to determine which arrangements successfully create a complete cube and which ones fail.