Add and subtract numbers mentally with increasingly large numbers. In this worksheet, children recap and build on their learning from previous years to mentally calculate sums and differences using partitioning. Children explore strategies such as compensation and adjustment to mentally calculate the answer to questions such as 73,352 + 999 or 16,352 − 999. Children need to be fluent in their knowledge of number bonds to support the mental strategies. "Are any of the numbers multiples of powers of 10? " “How does this help you to add/subtract them?” "What number is 999 close to? “How does that help you to add/subtract 999 from another number?”

Add and subtract numbers mentally with increasingly large numbers. In this worksheet, children recap and build on their learning from previous years to mentally calculate sums and differences using partitioning. They use their knowledge of number bonds and place value to add and subtract multiples of powers of 10. If they know that 3 + 4 = 7, then 3 thousand + 4 thousand = 7 thousand and 3,000 + 4,000 = 7,000. Children need to be fluent in their knowledge of number bonds to support the mental strategies. How does knowing that 6 + 3 = 9 help you to work out 60,000 + 30,000? “How can the numbers be partitioned to help add/subtract them?” "Are any of the numbers multiples of powers of 10? " “How does this help you to add/subtract them?”

In this worksheet, children recap their learning and extend their understanding to dealing with 4-digit numbers and adding and subtracting multiples of 1,000. The focus is on mental rather than written strategies. It is important to explore the effect of either adding or subtracting a multiple of 1, 10, 100 or 1,000 by discussing which columns always, sometimes and never change. For example, when adding a multiple of 100, the ones and tens never change, the hundreds always change and the thousands sometimes change, depending on the need to make an exchange

Add and subtract numbers with up to four digits using the formal written methods of columnar addition and subtraction where appropriate Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

In this worksheet, children recap their learning and extend their understanding to dealing with 4-digit numbers and adding and subtracting multiples of 1,000. The focus is on mental rather than written strategies. It is important to explore the effect of either adding or subtracting a multiple of 1, 10, 100 or 1,000 by discussing which columns always, sometimes and never change. For example, when adding a multiple of 100, the ones and tens never change, the hundreds always change and the thousands sometimes change, depending on the need to make an exchange.

In this worksheet, children build on their knowledge of rounding to the nearest 10, 100 and 1,000. It is important that children hear and use the language of “rounding to the nearest” rather than “rounding up” and “rounding down”, as this can lead to errors. Number lines are a particularly useful tool to support this, as children can see which multiples of 10, 100 or 1,000 the given numbers are closer to. When there is a 5 in the relevant place value column, despite being exactly halfway between the two multiples, we round to the next one. Watch for : The language “round down”/”round up” and so round 62,180 to 61,000 (or 61,180) when asked to round to the nearest 1,000.

In this worksheet, children build on their knowledge of rounding to the nearest 10, 100 and 1,000. It is important that children hear and use the language of “rounding to the nearest” rather than “rounding up” and “rounding down”, as this can lead to errors. Number lines are a particularly useful tool to support this, as children can see which multiples of 10, 100 or 1,000 the given numbers are closer to. When there is a 5 in the relevant place value column, despite being exactly halfway between the two multiples, we round to the next one. Watch for : The language “round down”/”round up” and so round 62,180 to 61,000 (or 61,180) when asked to round to the nearest 1,000. Ask: “Which multiples of 10, 100, 1,000 does the number lie between?” " Which multiple on the number line is the number closer to?" " What is the number rounded to the nearest 10, 100, 1,000?"

In this worksheet, children challenge their knowledge of rounding to the nearest 10, 100 and 1,000 by solving word problems. It is important that children hear and use the language of “rounding to the nearest” rather than “rounding up” and “rounding down”, as this can lead to errors. Number lines are a particularly useful tool to support this, as children can see which multiples of 10, 100 or 1,000 the given numbers are closer to. When there is a 5 in the relevant place value column, despite being exactly halfway between the two multiples, we round to the next one. Watch for: The language “round down”/”round up” and so round 62,180 to 61,000 (or 61,180) when asked to round to the nearest 1,000. Ask: “Which multiples of 10, 100, 1,000 does the number lie between?” " Which multiple on the number line is the number closer to?" " What is the number rounded to the nearest 10, 100, 1,000?" “Which place value column should you look at to round the number to the nearest 10, 100, 1,000?” “What happens when a number is exactly halfway between two numbers on a number line?”

The number 5 is important when you are rounding numbers. To round any number you need to follow a rule. To round 17,842 to the nearest 100, you need to round the digit in the hundred column. Look at the digit to its right, in the tens column to see which multiple of 100 you need to round the number. The digit in the tens column is 4. This number is closer to 17,800 than 17,900, so you need to round it to 17,800. Rounding to two decimal places means rounding to the nearest hundredth. One decimal place means to the nearest tenth.

Children round any number up to 1,000,000 to any power of 10 up to 100,000. You may wish to practise counting in 100,000s first, and then practise rounding to the nearest 100,000 before looking at mixed questions. Ask, “Which multiples of 100,000 does the number lie between?” " How can you represent the rounding of this number on a number line?" “Which division on the number line is the number closer to?” " What is the number rounded to the nearest 100,000?"

Children build on their learning to round any number within 100,000 to the nearest 10, 100, 1,000 or 10,000. They should be confident with multiples of 10,000 and the process of rounding should also be familiar. Children need to realise that the midpoint of two multiples of 10,000 ends in 5,000, so they need to look at the digit in the thousands column to determine how to round the number. Be careful with the language of “round up” and “round down” in case children mistakenly change the wrong digits when rounding. The previous multiple of 10,000 is ____ The next multiple of 10,000 is ____ Ask, “Which multiples of 10,000 does the number lie between?” “Which place value column should you look at to round the number to the nearest 10, 100, 1,000, 10,000?” “What happens if a number lies exactly halfway between two multiples of 10,000?”

In this worksheet, children extend their knowledge to deal with larger numbers while consolidating their understanding of the place value columns that have been introduced this year. They partition numbers in the standard way (for example, into thousands, hundreds, tens and ones). Watch for: Children may make mistakes with the order of the digits when partitioning/recombining numbers with many digits. You can use these supporting sentences: The value of the first digit is _________. The value of the next digit is ___________. ________ is equal to _______ thousands, ________ tens and _____-ones.

Children are challenged to partition the numbers in more flexible ways. Watch for : Children may be less familiar with non-standard partitioning and need the support of, for example, place value counters to see alternatives. Ask: “How else can you say/write “15 tens” or “15 thousands”?”

Children first compare pairs of numbers and then move on to ordering sets of three or more numbers. Ask, " When comparing two numbers with the same number of digits, if their first digits are equal in value, what do you look at next?" " What is the difference between ascending and descending order?" “What is different about comparing numbers with the same number of digits and comparing numbers with different numbers of digits?”

In this worksheet, children deal with larger numbers while consolidating their understanding of the place value columns. They partition numbers in the standard way (for example, into thousands, hundreds, tens and ones) as well as in more flexible ways (for example, 16,875 = 14,875 + 2,000 and 15,875 = 12,475 + 3,400). Watch for: Children may make mistakes with the order of the digits when partitioning/recombining numbers with many digits.

In this worksheet, children explore numbers up to 100,000. They are introduced to the ten-thousands column in a place value chart and begin to understand the multiples of 10,000. This can be reinforced using a number line to 100,000. Both place value counters and plain counters are used in place value charts, allowing for discussion about the values of the columns.

In this worksheet, children are challenged by exploring the relationship between numbers in the word problems. They look at columns that are further apart, for example considering the number of thousands needed to make 20,000 and then multiples of 20,000. Children are challenged by word problems. Ask, If you move a digit one place to the left in a place value chart, how many times greater is the value of the digit? If you move a digit two places to the left in a place value chart, how many times greater is the value of the digit? Watch for: Children may not realise that the overall effect of, for example, × 10 followed by × 10 is × 100.

In this worksheet, children develop their understanding of place value by exploring the relationship between numbers in different columns. As well as adjacent columns, they look at columns that are further apart, for example considering the number of tens needed to make 2,000 and then multiples of 2,000. Children can use both place value charts and charts to support their understanding. Exchanging with place value counters as extra support is also helpful. Ask, “How can you tell if a number is a power of 10?” “Is this number a multiple of a power of 10?” “How can you tell?” Watch for: Children may not realise that the overall effect of, for example, × 10 followed by × 10 is × 100.

Children encountered numbers up to 10,000 in Year 4. In this worksheet, they revise this learning in preparation for looking at numbers to 100,000 and then 1,000,000. A variety of pictorial and concrete representations are used, including base 10, place value counters, place value charts and part-whole models. The ability to use place value charts needs to be secure. Ask, “What is the value of each digit in the number?” “Which digit or digits would change in value if you added 1 counter?” “How do you write the number in words?” Watch for: Children may not yet have fully grasped placeholders, for example reading 602 as sixty-two. Children may rely on the column method of addition and subtraction when this is not necessary. Children may not use, or may misplace, the comma when writing numbers greater than or equal to 1,000.

In this worksheet, children explore numbers up to 100,000. They are introduced to the ten-thousands column in a place value chart and begin to understand the multiples of 10,000. This can be reinforced using a number line to 100,000. Both place value counters and plain counters are used in place value charts, allowing for discussion about the values of the columns.