The curriculum for Maths in Year 6

The Year 6 Math National Curriculum in the UK covers a range of topics designed to build upon the mathematical knowledge and skills developed in previous years. Here is a detailed breakdown of the main areas covered in Year 6:

**Number and Place Value:**

- Read, write, order, and compare numbers up to 10,000,000.
- Recognize the value of each digit in a number and multiply and divide numbers by 10, 100, and 1,000.
- Round numbers to the nearest 10, 100, 1,000, 10,000, and 100,000.

**Addition and Subtraction:**

- Add and subtract whole numbers with up to 6 digits using efficient methods.
- Use estimation and inverse operations to check answers.
- Solve addition and subtraction problems, including missing number problems.

**Multiplication and Division:**

- Multiply and divide numbers mentally, including decimals and large numbers.
- Use efficient written methods for multiplication and division.
- Solve multiplication and division problems, including scaling problems and finding factors and multiples.

**Fractions, Decimals, and Percentages:**

- Recognize and write decimal equivalents of fractions and vice versa.
- Compare and order fractions, including those with different denominators.
- Add and subtract fractions with different denominators and mixed numbers.
- Multiply proper fractions and mixed numbers by whole numbers.
- Find the percentage of a given amount.

**Ratio and Proportion:**

- Solve problems involving the relative sizes of two quantities using ratio and proportion.
- Solve problems involving percentage increase, decrease, or comparison.

**Algebra:**

- Use simple formulae.
- Generate and describe linear number sequences.
- Express missing number problems algebraically.
- Find pairs of numbers that satisfy an equation with two unknowns.

**Geometry:**

- Draw 2D shapes and make 3D shapes using modeling materials.
- Recognize and classify shapes based on their properties, including angles and lines of symmetry.
- Identify and describe the properties of triangles, quadrilaterals, pentagons, hexagons, and octagons.
- Calculate the area and perimeter of shapes.
- Identify and describe the properties of circles, including the radius, diameter, and circumference.

**Measurement:**

- Convert between different units of measure (e.g., kilometers to meters).
- Calculate the perimeter and area of rectangles and related composite shapes.
- Estimate, compare, and calculate different measures, including money in pounds and pence.
- Solve problems involving the calculation of time intervals.
- Use metric units of measurement (including centimeters, meters, and kilometers) and estimate and compare measurements.

**Statistics:**

- Interpret and construct pie charts and line graphs.
- Solve comparison, sum, and difference problems using information presented in bar charts, pictograms, tables, and other graphs.

Throughout Year 6, students are encouraged to develop their problem-solving skills, apply their mathematical knowledge to real-life situations, and explain their reasoning using mathematical language. They also learn to use a range of mathematical tools, such as calculators and measuring instruments, to support their understanding and problem-solving abilities.

#### Number Patterns-Online Practice Question

- Apply skills to complete geometric number sequences
- Demonstrate the ability to complete number sequences in ascending order🔒
- Engage in a comprehensive review of various types of number sequences🔒
- Solve word problems involving number sequences and their patterns🔒
- Utilize mathematical rules to accurately complete number sequences🔒
- Explore and understand the rules of divisibility in number theory🔒
- Apply the divisibility rules to solve word problems in real-life scenarios🔒
- Investigate and compute the highest common factor of given numbers🔒
- Analyze and calculate the lowest common multiple of given numbers🔒
- Identify and differentiate between prime and composite numbers🔒
- Learn and apply the process of prime factorization to express numbers as products of prime factors🔒

#### Place values-Online Practice Question

- Develop the ability to compare and order integers
- Practice comparing and ordering numbers with values up to millions🔒
- Master the skill of converting numbers between different place values🔒
- Learn to convert numbers between word form and digit form, specifically up to 10,000,000🔒
- Understand the arithmetic rules to identify whether a number is even or odd🔒
- Acquire a comprehensive understanding of place values at different levels🔒
- Arrange integers in ascending or descending order🔒
- Practice ordering numbers with values up to 10,000,000🔒
- Explore and comprehend the system of Roman numerals🔒
- Learn the concept and techniques of rounding numbers to the nearest whole or decimal place🔒
- Develop a deep understanding of the properties and characteristics of integers🔒

#### Addition & Subtraction-Online Practice Question

- Solve word problems that involve addition and subtraction of whole numbers
- Perform addition and subtraction operations with whole numbers up to millions🔒
- Select appropriate numbers to achieve a given sum or difference🔒
- Fill in the missing parts of addition and subtraction sentences🔒
- Solve word problems by making estimates for the sums and differences of whole numbers🔒
- Make approximate calculations to estimate the sums and differences of whole numbers🔒
- Determine the missing digits in addition and subtraction problems🔒
- Explore inequalities involving addition and subtraction operations🔒
- Study and apply the properties of addition in various contexts🔒

#### Multiplication-Online Practice Question

- Explore the box multiplication method for multiplying numbers🔒
- Select appropriate numbers to achieve a given product
- Make approximate calculations to estimate the products of numbers🔒
- Solve word problems by making estimates for the products of numbers🔒
- Explore inequalities involving multiplication operations🔒
- Learn and apply the lattice multiplication method for multiplying numbers🔒
- Identify and analyze patterns that emerge when multiplying numbers with increasing place values🔒
- Perform multiplication operations involving a two-digit number multiplied by a three-digit or four-digit number🔒
- Fill in the missing steps in the process of multiplying a two-digit number by a three-digit or four-digit number🔒
- Solve word problems that involve multiplying a two-digit number by a three-digit or four-digit number🔒
- Perform multiplication operations between two-digit numbers🔒
- Multiply numbers by a single-digit number🔒
- Solve word problems that involve multiplication by a single-digit number🔒
- Fill in the missing steps in the process of multiplying numbers by a two-digit number🔒
- Multiply numbers that end in zeroes🔒
- Solve word problems that involve multiplication of numbers ending in zeroes🔒
- Perform multiplication operations involving three or four numbers🔒
- Solve word problems that require multiplication of three or four numbers🔒
- Study and apply the properties of multiplication in various contexts🔒

#### Division-Online Practice Question

- Select appropriate numbers to achieve a given quotient
- Perform division operations by dividing numbers by one-digit divisors🔒
- Understand and interpret remainders in division problems with one-digit divisors🔒
- Solve word problems that involve division by one-digit divisors🔒
- Perform division operations by dividing numbers by two-digit divisors🔒
- Understand and interpret remainders in division problems with two-digit divisors🔒
- Solve word problems that involve division by two-digit divisors🔒
- Divide numbers that end in zeroes🔒
- Solve word problems that involve division of numbers ending in zeroes🔒
- Learn and memorize division facts up to 12🔒
- Solve word problems that require the application of division facts up to 12🔒
- Identify and analyze patterns that emerge when dividing numbers with increasing place values🔒
- Make approximate calculations to estimate the quotients of division problems🔒
- Solve word problems by making estimates for the quotients of division problems🔒

#### Mixed operations-Online Practice Question

- Perform addition, subtraction, multiplication, and division operations with decimal numbers
- Solve word problems that involve adding, subtracting, multiplying, and dividing decimal numbers🔒
- Perform addition, subtraction, multiplication, and division operations with whole numbers🔒
- Solve word problems that involve adding, subtracting, multiplying, and dividing whole numbers🔒
- Calculate the value of numerical expressions by performing the appropriate operations🔒
- Express mathematical relationships using symbols and numbers to form numerical expressions🔒

#### Fractions-Online Practice Question

- Apply arithmetic operations to fractions in the context of sequence
- Develop the ability to compare and order fractions and mixed numbers🔒
- Master the skill of converting between improper fractions and mixed numbers🔒
- Explore and identify equivalent fractions🔒
- Solve word problems involving finding fractions of a group🔒
- Calculate fractions of a given number🔒
- Apply fraction concepts to real-world scenarios involving finding fractions of a number🔒
- Solve word problems that involve finding fractions of a whole🔒
- Engage in a comprehensive review of fraction concepts🔒
- Analyze and work with geometric sequences that involve fractions🔒
- Represent and compare fractions using number lines🔒
- Understand and work with mixed numbers🔒
- Identify and analyze patterns in equivalent fractions🔒
- Arrange fractions in ascending or descending order🔒
- Round mixed numbers to the nearest whole or decimal place🔒
- Express fractions in their lowest terms🔒

#### Understanding decimals-Online Practice Question

- Make approximate calculations to estimate the products of decimal numbers
- Explore inequalities involving multiplication of decimal numbers🔒
- Multiply a decimal number by a power of ten to shift the decimal point🔒
- Perform multiplication operations between decimals and whole numbers🔒
- Solve word problems that involve multiplication of decimals and whole numbers🔒

#### Understanding fractions-Online Practice Question

- Perform addition and subtraction operations with fractions that have the same denominators
- Solve word problems involving addition and subtraction of fractions with like denominators🔒
- Utilize number lines to add and subtract fractions with the same denominators🔒
- Learn techniques for adding and subtracting fractions with different denominators🔒
- Apply addition and subtraction skills to solve word problems involving fractions with unlike denominators🔒
- Use number lines to add and subtract mixed numbers with the same denominators🔒
- Solve word problems that require adding and subtracting mixed numbers with like denominators🔒
- Apply number lines to add and subtract mixed numbers with different denominators🔒
- Solve word problems involving addition and subtraction of mixed numbers with unlike denominators🔒
- Perform addition operations with three or more fractions that share the same denominators🔒
- Solve word problems that involve adding three or more fractions with like denominators🔒
- Utilize number lines to add three or more fractions with different denominators🔒
- Solve word problems that require adding three or more fractions with unlike denominators🔒
- Add fractions with denominators of 10 and 100, up to a maximum of 4 fractions🔒
- Fill in the missing addition or subtraction sentences involving fractions🔒
- Break down fractions into different equivalent forms🔒
- Make approximate calculations for the sums and differences of mixed numbers🔒
- Explore inequalities involving addition and subtraction of fractions🔒

#### Problems based on fractions-Online Practice Question

- Perform division operations by dividing fractions by whole numbers
- Explore the concept of multiples in relation to fractions🔒
- Solve word problems that involve multiplication of fractions🔒
- Sort and categorize examples of multiplying fractions and whole numbers🔒
- Perform multiplication operations between fractions and whole numbers🔒
- Construct input/output tables to represent the multiplication of fractions by whole numbers🔒
- Use number lines to visualize and solve multiplication problems involving fractions and whole numbers🔒
- Select appropriate models to represent the multiplication of fractions by whole numbers🔒
- Perform multiplication operations between two fractions🔒
- Use models to demonstrate and solve multiplication problems involving two fractions🔒
- Sort and categorize examples of multiplying unit fractions and whole numbers🔒
- Utilize models to multiply unit fractions by whole numbers and understand the results🔒
- Represent and solve multiplication problems involving unit fractions and whole numbers using number lines🔒
- Understand and utilize the concept of reciprocals in fraction operations🔒

#### Ratio-Online Practice Question

- Find and determine the ratio between two or more quantities or values
- Recognize and identify ratios that are equivalent or have the same value🔒
- Organize and display ratios in a table format to establish patterns and relationships🔒
- Solve word problems that involve interpreting and working with scale drawings🔒
- Understand and calculate unit rates, which represent the ratio of a quantity to one unit of another quantity, and identify equivalent rates🔒
- Generate and write a ratio that is equivalent to a given ratio by scaling up or down the quantities involved🔒
- Solve word problems that require expressing relationships between quantities using ratios🔒

#### Decimals-Online Practice Question

- Develop the ability to compare and order decimal numbers
- Compare and determine relationships between decimals and fractions🔒
- Represent and compare decimals and fractions using number lines🔒
- Use number lines to compare and order decimal numbers🔒
- Convert decimal numbers between their standard and expanded forms🔒
- Utilize fractions to convert decimal numbers between standard and expanded forms🔒
- Express decimal numbers as equivalent fractions🔒
- Convert fractions into decimal numbers🔒
- Represent and locate decimal numbers on number lines🔒
- Identify and compare decimals that are equivalent to each other🔒
- Use models to represent and understand the relationship between decimals and fractions🔒
- Understand and interpret the place values of digits in decimal numbers🔒
- Arrange a mix of decimals, fractions, and mixed numbers in ascending or descending order🔒
- Arrange decimal numbers in ascending or descending order🔒
- Round decimal numbers to a specified place value🔒
- Interpret and comprehend decimal numbers expressed in words🔒
- Determine the decimal number represented by an illustration🔒

#### Problems based on decimals-Online Practice Question

- Perform addition and subtraction operations with decimal numbers
- Solve word problems involving addition and subtraction of decimal numbers🔒
- Select appropriate decimals to achieve a given sum or difference🔒
- Fill in the missing parts of addition or subtraction sentences involving decimals🔒
- Make approximate calculations for the sums and differences of decimal numbers🔒
- Explore inequalities involving addition and subtraction of decimal numbers🔒

#### Algebra-Online Practice Question

- Fill in a table of values to represent the relationship between two variables
- Use a given graph to determine the corresponding values and complete a table🔒
- Substitute given values into variable expressions and calculate the resulting output🔒
- Solve equations involving two variables to find the value of a specific variable🔒
- Plot points on a coordinate plane to graph the relationship between two variables🔒
- Determine the value of the variable in an equation involving whole numbers🔒
- Express the relationship between two variables using an equation🔒
- Translate word problems into variable equations to represent the given situation mathematically🔒
- Formulate expressions that involve variables to represent mathematical relationships🔒
- Convert word problems into variable expressions to represent the given scenario mathematically🔒

#### Coordinate planes-Online Practice Question

- Understand and interpret the coordinate plane as a map, where points represent locations on the map, and the coordinates indicate the position of objects or landmarks
- Plot given points on a coordinate plane by identifying their corresponding coordinates and locating them accurately on the x-axis and y-axis🔒
- Represent objects or figures on a coordinate plane by plotting their vertices or key points using coordinates🔒
- Place objects or figures on a coordinate plane that spans all four quadrants (Quadrant I, II, III, and IV) by identifying their coordinates and accurately positioning them in the respective quadrants🔒
- Understand the concept of quadrants on a coordinate plane and identify the four quadrants (Quadrant I, II, III, and IV) as distinct sections of the plane formed by the x-axis and y-axis🔒

#### Problems solving –Online Practice Question

- Determine and arrange items or elements in a specific order based on given criteria or conditions
- Solve problems by making educated guesses or assumptions, testing them, and adjusting them until a solution is found🔒
- Solve complex problems that require multiple steps or operations to reach a solution, involving various mathematical concepts and problem-solving strategies🔒
- Utilize Venn diagrams, which are graphical representations of sets, to analyze and solve problems related to overlapping or distinct sets of objects or elements🔒
- Solve word problems that contain additional or incomplete information, requiring critical thinking and problem-solving skills to determine the necessary data or constraints to find a solution🔒

#### Geometry-Online Practice Question

- Categorize quadrilaterals based on their properties and attributes, such as parallelograms, rectangles, rhombuses, trapeziums, squares, and other specific types
- Identify and classify triangles based on their side lengths and angle measurements, such as equilateral triangles, isosceles triangles, scalene triangles, and right triangles🔒
- Determine the measures of missing angles within triangles and quadrilaterals using knowledge of angle relationships and properties🔒
- Recognize parallelograms, which are quadrilaterals with opposite sides that are parallel and congruent🔒
- Identify rectangles, which are quadrilaterals with four right angles🔒
- Identify rhombuses, which are quadrilaterals with four sides of equal length🔒
- Identify trapeziums, which are quadrilaterals with at least one pair of parallel sides🔒
- Determine whether a given shape qualifies as a polygon, which is a closed two-dimensional figure with straight sides🔒
- Identify and count the number of sides in different polygons, including triangles, quadrilaterals, pentagons, hexagons, and other polygons🔒
- Identify quadrilaterals that have pairs of parallel sides, such as parallelograms and trapeziums🔒
- Distinguish between regular polygons, which have equal side lengths and equal angle measures, and irregular polygons, which have sides and angles of different lengths and measures🔒

#### Percentages –Online Practice Question

- Analyze and compare different percentages to determine their relative sizes
- Convert between different representations of numbers, including percents, fractions, and decimals🔒
- Calculate the value of a given percentage of a number🔒
- Solve word problems that involve determining the percentage of a given number🔒
- Analyze visual representations and determine the corresponding percentage🔒

#### Measurement-Online Practice Question

- Solve word problems involving the calculation of area and perimeter of various geometric shapes, such as rectangles, squares, triangles, and irregular shapes
- Determine the area and perimeter of shapes represented on grids or coordinate planes, including counting unit squares and measuring side lengths🔒
- Calculate the area of the region between two overlapping rectangles, considering the shared and non-shared areas🔒
- Find the total area of compound figures composed of multiple shapes, such as combinations of rectangles, triangles, and semicircles🔒
- Calculate the area of squares and rectangles by multiplying their length and width🔒
- Determine the area of triangles using the formula: Area = (1/2) * base * height🔒
- Calculate the perimeter of shapes with decimal side lengths, including squares, rectangles, triangles, and irregular shapes🔒
- Calculate the perimeter of shapes with whole number side lengths, including squares, rectangles, triangles, and irregular shapes🔒
- Apply the concepts of area and perimeter to real-world scenarios, such as determining the cost of materials needed based on their dimensions🔒
- Calculate the volume of cubes and rectangular prisms by multiplying the length, width, and height of the shape🔒
- Determine the volume of three-dimensional figures by counting the number of unit cubes required to fill them🔒

#### Money –Online Practice Question

- Solve word problems involving the addition and subtraction of money amounts, considering various currencies and denominations
- Perform addition and subtraction operations with money amounts, including different denominations and currency conversions if necessary🔒
- Solve word problems that involve dividing money amounts with decimals, such as splitting expenses or distributing funds among multiple individuals🔒
- Solve word problems that require multiplication of money amounts, such as calculating the total cost of multiple items or finding the total earnings from a given rate🔒
- Solve word problems that involve multiplying money amounts with decimals, such as calculating discounts, sales tax, or finding the total cost of items after applying a percentage off🔒
- Interpret and use price lists to determine the cost of items or services, considering different prices and quantities🔒
- Calculate and compare unit prices of items to determine the best value for money, considering different sizes, quantities, or packaging options🔒

#### Money –Online Practice Question

- Solve word problems involving the addition and subtraction of money amounts, considering various currencies and denominations
- Perform addition and subtraction operations with money amounts, including different denominations and currency conversions if necessary🔒
- Solve word problems that involve dividing money amounts with decimals, such as splitting expenses or distributing funds among multiple individuals🔒
- Solve word problems that require multiplication of money amounts, such as calculating the total cost of multiple items or finding the total earnings from a given rate🔒
- Solve word problems that involve multiplying money amounts with decimals, such as calculating discounts, sales tax, or finding the total cost of items after applying a percentage off🔒
- Interpret and use price lists to determine the cost of items or services, considering different prices and quantities🔒
- Calculate and compare unit prices of items to determine the best value for money, considering different sizes, quantities, or packaging options🔒

#### Understanding measurement-Online Practice Question

- Determine and select the appropriate unit of measurement from the Imperial system (e.g., inches, feet, yards, miles, ounces, pounds) based on the given context or situation.
- Determine and select the appropriate unit of measurement from the Metric system (e.g., millimeters, centimeters, meters, kilometers, milliliters, liters, grams, kilograms) based on the given context or situation.🔒
- Compare temperatures given in different units (e.g., Celsius, Fahrenheit) and determine which measurement is more reasonable or appropriate based on the given circumstances.🔒
- Compare and convert between different units of length in the Imperial system (e.g., inches, feet, yards, miles), and apply appropriate conversion factors.🔒
- Compare and convert between different units of volume in the Imperial system (e.g., fluid ounces, cups, pints, quarts, gallons), and apply appropriate conversion factors.🔒
- Compare and convert between different units of weight in the Imperial system (e.g., ounces, pounds, tons), and apply appropriate conversion factors.🔒
- Compare and convert between different units of length in the Metric system (e.g., millimeters, centimeters, meters, kilometers), and apply appropriate conversion factors.🔒
- Compare and convert between different units of mass in the Metric system (e.g., grams, kilograms), and apply appropriate conversion factors.🔒
- Compare and convert between different units of volume in the Metric system (e.g., milliliters, liters), and apply appropriate conversion factors.🔒
- Convert measurements between the Metric and Imperial systems, considering length, weight, volume, and other applicable units.🔒
- Solve problems or perform calculations involving mixed units of measurement in the Imperial system, such as combining different units of length, weight, or volume in a single calculation.🔒
- Solve problems or perform calculations involving mixed units of measurement in the Metric system, such as combining different units of length, mass, or volume in a single calculation.🔒
- Understand and apply the concept of precision in measurements, including the appropriate number of significant figures or decimal places based on the level of accuracy required.🔒

#### Time-Online Practice Question

- Perform addition and subtraction operations with mixed units of time, including hours, minutes, and seconds
- Convert time between the 12-hour clock system (AM/PM) and the 24-hour clock system (military time)🔒
- Convert time between different units, such as seconds, minutes, hours, days, weeks, months, and years🔒
- Calculate the duration or elapsed time between two given time points, accounting for hours, minutes, and seconds🔒
- Solve word problems that involve determining the start or end times based on given information, such as durations, elapsed time, or schedules🔒
- Interpret and use schedules or timetables that are based on the 24-hour clock system, considering different activities, events, or appointments🔒
- Interpret and use schedules or timelines that are based on the 12-hour clock system, considering different activities, events, or appointments🔒
- Identify and analyze patterns in time, such as recurring events, intervals, or sequences🔒
- Understand and apply concepts related to time zones based on the 12-hour clock system, considering the differences in time across different regions🔒
- Understand and apply concepts related to time zones based on the 24-hour clock system (military time), considering the differences in time across different regions🔒

#### Statistics –Online Practice Question

- Determine and compute the measures of central tendency (mean, median, mode) and dispersion (range) for a given data set to summarize and analyze the data
- Understand and apply the concept of combinations in probability, where the order of selection is not considered and the focus is on selecting a subset of objects or events from a larger set🔒
- Determine the probability of an event occurring by analyzing the ratio of favorable outcomes to the total number of possible outcomes, and apply probability concepts in different contexts🔒
- Differentiate between representative, random, and biased samples in statistical studies, and understand the impact of sample selection methods on the reliability and validity of data analysis🔒
- Analyze and interpret charts (such as bar graphs, line plots, or frequency charts) to extract and calculate the measures of central tendency (mean, median, mode) and dispersion (range) for a given data set🔒
- Use statistical data and probability concepts to make predictions or estimations about future events or outcomes based on patterns, trends, and probabilities observed in the data🔒
- Solve problems or exercises involving mean, median, mode, and range, where one or more values are missing from a given data set, and determine the missing value(s) to complete the analysis🔒
- Develop an understanding of the fundamental principles of probability, including the concepts of sample space, events, outcomes, and probability rules, and apply them in various probability scenarios and calculations🔒

#### Data handling –Online Practice Question

- Determine and select the most appropriate type of graph (e.g., bar graph, line graph, pie chart) to effectively represent and display different types of data and their characteristics
- Construct bar graphs to visually represent and compare categorical data, where the categories are represented on the x-axis and the corresponding frequencies or counts are represented by the height or length of the bars🔒
- Construct bar graphs to visually represent and compare continuous data, where the data values are grouped into intervals or ranges on the x-axis, and the corresponding frequencies or counts are represented by the height or length of the bars🔒
- Create line graphs to display and analyze the relationship between two variables, where the data points are connected by line segments, and the x-axis represents one variable while the y-axis represents the other variable🔒
- Create line plots (also known as dot plots) to display and analyze the distribution of a set of data, where data points are marked on a number line and their frequency or count is represented by the number of dots at each data point🔒
- Construct pictograms (also known as picture graphs) to represent and compare data using pictures or symbols, where each picture or symbol represents a certain quantity or value🔒
- Construct stem-and-leaf plots to organize and display numerical data, where the stems represent the leading digits and the leaves represent the trailing digits of each data point🔒
- Create frequency charts (also known as frequency tables) to summarize and display the frequencies or counts of different categories or values in a given data set🔒