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 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.

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.

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 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.

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.

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 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.

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.

In this worksheet, children build on their knowledge of the 3 times-table to explore the 6 times-table. Children work with the 6 times-table and use the multiplication facts they know to find unknown facts. Children explore the fact that the 6 times-table is double the 3 times-table. Extra reasoning activity attached. Answer sheets attached.

In worksheet, children practise rounding in order to estimate the answers to both additions and subtractions. They also review mental strategies for estimating answers. Children should be familiar with the word “approximate”, and “estimate” 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 and so on is appropriate. Extra reasoning sheet attached. Answer sheet attached.

Children find the areas of shapes that include half squares. Marking or noting which squares they have already counted supports children’s accuracy when finding the area of complex shapes. Using arrays relating to area can be explored, but children are not expected to recognise the formula. What can you do if the squares are not full squares?

In this worksheet, children apply the strategies they have learned so far to solve addition and subtraction problems with more than one step. Children choose the operations needed at each step and then perform the calculations using an appropriate mental or written method. Problems are presented in word form. The use of bar models can help children to illustrate problems of this kind. While the models will not perform the calculation, they will help children to decide what operations are needed and why. Ask, What is the key information in the question? What can you work out straight away? How does this help you to answer the question? How can you represent this problem using a bar model? Which bar will be longer? Why? Do you need to add or subtract the numbers at this stage? How do you know? With extra reasoning activity. Answer sheets included.

In this worksheet, children apply the strategies they have learned so far to solve addition and subtraction problems with more than one step. Children choose the operations needed at each step and then perform the calculations using an appropriate mental or written method. Problems are presented in word form. The use of bar models can help children to illustrate problems of this kind. While the models will not perform the calculation, they will help children to decide what operations are needed and why. Ask, What is the key information in the question? What can you work out straight away? How does this help you to answer the question? How can you represent this problem using a bar model? Which bar will be longer? Why? Do you need to add or subtract the numbers at this stage? How do you know?