Children explore the fact that the 6 times-table is double the 3 times-table. Children who are confident in their times-tables can also explore the link between the 12 and 6 times-tables. They use the fact that multiplication is commutative to derive values for the 6 times-tables.

This worksheet revisits learning from Year 3 around multiplying by 3 and the 3 times-table. Children explore the link between counting in 3s and the 3 times-table to understand multiples of 3 in a range of contexts. They use number tracks and hundred squares to represent multiples of 3. Ask: What is the next multiple of 3? What is the multiple of 3 before? How many 3s are there in?

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?

Recall multiplication and division facts for multiplication tables up to 12 × 12. Recognise and use factor pairs and commutativity in mental calculations. Watch for: Children may think that any number with 3 ones is a multiple of 3. An early mistake when counting in 3s will affect all subsequent multiples. Children may always begin counting from 3 to find a larger multiple of 3, when they could use the multiples they already know to find the new information.

Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3). Solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes. Children should recognise that when they multiply a number by itself once, the result is a square number, and so to find the cube of a given number, they can multiply its square by the number itself, for example 6 × 6 = 36, so 6 cubed = 36 × 6. Children use the notation for cubed (3) and should ensure that this is not confused with the notation for squared (2).

Children solve problems involving multiplication and division, including using their knowledge of factors and multiples and squares. Children explore the factors of square numbers and notice that they have an odd number of factors, because the number that multiplies by itself to make the square does not need a different factor to form a factor pair.

Children find common multiples of any pair of numbers. They do not need to be able to formally identify the lowest common multiple, but this idea can still be explored by considering the first common multiple of a pair of numbers. Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.

In this worksheet, children use counters and cubes to build square numbers, and also to decide whether or not a given number is square. They learn that square numbers are the result of multiplying a number by itself. Through their knowledge of times-tables and practice over time, they should be able to recognise the square numbers up to 12 × 12. In this worksheet, they are introduced to notation for squared (2).

In this worksheet, children use counters and cubes to build square numbers, and also to decide whether or not a given number is square. They learn that square numbers are the result of multiplying a number by itself. Through their knowledge of times-tables and practice over time, they should be able to recognise the square numbers up to 12 × 12. In this worksheet, they are introduced to notation for squared (2).

Estimate and use inverse operations to check answers to a calculation. Problem solving and reasoning questions for higher ability students with answers attached for easy check. Estimations can be used alongside inverse operations as an alternative checking strategy. Children use inverse operations to check the accuracy of their calculations, rather than simply redoing the same calculation and potentially repeating the same error. Estimations can be used alongside inverse operations as an alternative checking strategy

In this worksheet, children explore the inverse relationship between addition and subtraction. Addition and subtraction are inverse operations and addition is commutative and subtraction is not. Bar models and part-whole models are useful representations to help establish families of facts that can be found from one calculation. Children use inverse operations to check the accuracy of their calculations, rather than simply redoing the same calculation and potentially repeating the same error. Ask: What are the parts? What is the whole? Given one fact, what other facts can you write? What does “inverse” mean? What is the inverse of add/subtract

In this worksheet, children explore the inverse relationship between addition and subtraction. Addition and subtraction are inverse operations and addition is commutative and subtraction is not. Bar models and part-whole models are useful representations to help establish families of facts that can be found from one calculation. Children use inverse operations to check the accuracy of their calculations, rather than simply redoing the same calculation and potentially repeating the same error. Ask: What are the parts? What is the whole? Given one fact, what other facts can you write? What does “inverse” mean? What is the inverse of add/subtract

Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 Add and subtract numbers mentally with increasingly large numbers Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy. Children should be familiar with the word “approximate”, and the degree of accuracy to which to round is a useful point for discussion. Generally, rounding to the nearest 100 for 3-digit numbers, the nearest 1,000 for 4-digit numbers. Ask, “What place value column should we look at to round the number to the nearest 10/100/1,000/10,000/100,000 “How could you use your estimates to check your answers?” " Is the actual answer going to be greater or less than your estimate? Why?” One worksheet with answers attached.

In this worksheet, children practise rounding in order to estimate the answers to both additions and subtractions. They also review mental strategies for estimating answers Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 Add and subtract numbers mentally with increasingly large numbers Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

The purpose of this worksheet is to encourage children to make choices about which method is most appropriate for a given calculation. Children can often become reliant on formal written methods, so it is important to explicitly highlight where mental strategies or less formal jottings can be more efficient. Children explore the concept of constant difference, where adding or subtracting the same amount to/from both numbers in a subtraction means that the difference remains the same, for example 3,835 – 2,999 = 3,835 – 3,000 or 700 – 293 = 699 – 292. This can help make potentially tricky subtractions with multiple exchanges much simpler, sometimes even becoming calculations that can be performed mentally.

In this worksheet, children revisit the use of the column method for addition and learn to apply this method to numbers with more than four digits. Place value counters and place value charts are used for a support. These representations are particularly useful when performing calculations that require an exchange. Children may find it easier to work with squared paper and labelled columns as this will support them in placing the digits in the correct columns, especially with figures containing different numbers of digits. answer sheet attached.

The purpose of this worksheet is to encourage children to make choices about which method is most appropriate for a given calculation. Children can often become reliant on formal written methods, so it is important to explicitly highlight where mental strategies or less formal jottings can be more efficient. Children explore the concept of constant difference, where adding or subtracting the same amount to/from both numbers in a subtraction means that the difference remains the same, for example 3,835 – 2,999 = 3,835 – 3,000 or 700 – 293 = 699 – 292. This can help make potentially tricky subtractions with multiple exchanges much simpler, sometimes even becoming calculations that can be performed mentally. Number lines can be used to support understanding of this concept.

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.

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?” Extra reasoning sheet attached.