In this worksheet, children add 3- or 4-digit numbers with no exchanges, using concrete resources as well as the formal written method. The numbers being added together may have a different number of digits, so children need to take care to line up the digits correctly. Even though there will be no exchanging, the children should be encouraged to begin adding from the ones column. With extra reasoning activity sheet Add numbers with up to four digits using the formal written methods of columnar addition. Solve addition two-step problems in contexts, deciding which operations and methods to use and why.

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?”

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.

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 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

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?"

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

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 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

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.

Use this worksheet to help children develop their understanding of comparing and ordering fractions with denominators that are multiples. If equivalent fractions are needed, then one denominator will be a multiple of the other or others. This worksheet includes a challenge to help deepen children’s understanding and problem-solving skills. Bar models, fraction walls and number lines will still be useful to help children to see the relative sizes of the fractions, especially when conversions are needed. Children should look at the set of fractions as a whole before deciding their approach, as comparing numerators could still be a better strategy for some sets of fractions. Core worksheet with answer sheet.

In this worksheet, children explore the tenths column in a place value chart, extending their previous learning to include numbers greater than 1. It is essential that they understand that 10 tenths are equivalent to 1 whole, and 1 whole is equivalent to 10 tenths. Remind them that when counting forwards, 1 comes after 0.9, and when counting backwards that 0.9 comes after 1. Be aware that when the number of tenths reaches 10, they may call this “zero point ten” and write 0.10 rather than exchanging for 10 tenths for 1 whole.

This is a reasoning worksheet for core students. Children show their preference when it comes to showing the six tenths as a decimal. They must then use all models to show four tenths. As this is the first time that children may encounter decimal numbers and the decimal point, model making, drawing, writing decimal numbers and showing that the decimal point is used to separate whole numbers from decimals is extremely helpful. Children look at a variety of representations of tenths as decimals on the number line. This leads to representing the tenths in the bar models and finally in the place value charts. The place value chart shows how tenths fit with the rest of the number system and to understand the need for the decimal point. Watch for: Children may forget to include the decimal point. Children may confuse the words “tens” and “tenths”. You might ask them: "If a whole is split into 10 equal parts, then what is each part worth?

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. As a support in this step the place value counters, and place value charts will be extremely helpful. These representations are particularly useful when performing calculations that require an exchange. Ask, “Will you need to make an exchange?” “Which columns will be affected if you do need exchange?” " How do you know?" Watch for: Children may not line up the numbers in the columns correctly.

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.

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.

They can use a variety of representations to help them, such as place value counters, place value charts and number lines, but the main focus of the worksheet is to compare and order using the place value of the digits within the numbers. Children first compare pairs of numbers and then move on to ordering sets of three or more numbers

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.

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?”