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?”

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.

Children be able to add and subtract 10, 100 and 1,000 to and from a given number, using their place value knowledge rather than formal written methods. Ask, “What is the value of each digit in the number?” " How can you represent the number in a different way?" “Which digit or digits would change in value if you added a 10/100/1,000 counter?” “How do you write the number in words?” Watch for : Children may not yet have fully grasped placeholders, for example reading 309 as thirty-nine. 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.

Children identify multiples including finding all multiples of the number, and common multiples of set of numbers. They solve problems involving multiplication including using their knowledge of multiples.

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 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.

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.

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 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.

Building on from the previous worksheet, children add two 4-digit numbers with one exchange in any column. The numbers can be made using place value counters in a place value chart, alongside the formal written method. When discussing where to start an addition, it is important to use language such as begin from the “smallest value column” rather than the “ones column” to avoid any misconceptions when decimals are introduced later in the year. After each column is added, ask, “Do you have enough ones/ tens/hundreds to make an exchange?" This question will be an important one in this worksheet , as the children do not know which column will be the one where an exchange is needed. Extra reasoning activity sheet.

Children explore how to recognise if a number is a multiple of 3 by f inding its digit sum: if the sum of the digits of a number is a multiple of 3, then the number itself is also a multiple of 3. Challenge by asking : How do you find the digit sum of a number? How can you tell if a number is a multiple of 3? Are the multiples of 3 odd or even?

Use this worksheet to help children develop their understanding of adding and subtracting fractions with the same denominator, and denominators that are multiples of the same number. The worksheet is aimed at those working at age expected. This worksheet includes a challenge to help deepen children’s understanding and problem-solving skills. Answer sheet attached.

Use this worksheet to help children develop their understanding of adding and subtracting fractions with the same denominator, and denominators that are multiples of the same number. The worksheet is aimed at those working towards age expected. This worksheet includes a challenge to help deepen children’s understanding and problem-solving skills. Answer sheet attached.

Children use a place value chart and place value counters to answer the questions. They exchange the counters when needed. They then solve the calculations already written in the formal method.

Children compare fractions where the denominators are the same or where one denominator is a multiple of the other. They also compare fractions with the same numerator or by comparing it to one half. with answer sheets. Extra reasoning activity sheet

Children work out subtraction word problems and correct the mistake and explain the exchange and possible misconceptions.

In this higher ability worksheets, children subtract up to 4-digit numbers with more than one exchange, using the written method of column subtraction. With extra reasoning sheet with answer sheets They perform subtractions involving two separate exchanges (for example, from the thousands and from the tens) as well as those with two-part exchanges (for example, from the thousands down to the tens if there are no hundreds in the first number). Remember, when completing the written method, it is vital that children are careful with where they put the digits, especially those that have been exchanged. Two-part exchanges can be confusing for children if they are unsure what each digit represents or where to put it. Watch for not lining up the digits in the place value columns correctly. When exchanging a number, they may put the ones in the incorrect place. When exchanging over two columns, children may exchange directly from, for example, hundreds down to ones and miss out the exchange to tens. Some high-level questioning will challenge high achieving students. Does it matter which column you subtract first? How can you subtract two numbers if one of them has fewer digits than the other? If you cannot exchange from the tens/hundreds, what do you need to do? Which column can you exchange from?

In these worksheets, children subtract up to 4-digit numbers with more than one exchange, using the written method of column subtraction. They perform subtractions involving two separate exchanges (for example, from the thousands and from the tens) To support understanding, solve these subtractions alongside the concrete resources of base 10 and place value counters. With extra reasoning sheet. With answer sheets

Children use their knowledge of comparing fractions and order a set of three or more fractions. If equivalent fractions are needed, then one denominator will be a multiple of the other(s) so that conversions will not be complicated. C Bar models, fraction walls and number lines could be used to help children to see the relative sizes of the fractions, especially when conversions are needed. Children can consider the position of a fraction relative to 0, 1/2 or 1 whole. With extra reasoning sheet. You can support your child with set of questions: If a set of fractions all have the same denominator, how can you tell which is greatest? If a set of fractions all have the same numerator, how can you tell which is greatest? How can you use equivalent fractions to help? What are all the denominators/numerators multiples of? How can this help you find equivalent fractions? Which of the fractions are greater than 1/2? At first, children may need support to decide the best strategy when there are more than two fractions. Children may not look at both parts of the fractions when making their decisions about the order. You might use these support sentences: When fractions have the same denominator, one with the_____ numerator is the greatest fraction. When fractions have the same numerator, the one with the ______ denominator is the greatest fraction.