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

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

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

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

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

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

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

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

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

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

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

<p>Building on from the previous worksheet, children add two 4-digit<br /> numbers with one exchange in any column.<br /> The numbers can be made using place value counters in a place value chart, alongside the formal written method.<br /> When discussing where to start an addition, it<br /> is important to use language such as begin from the “smallest<br /> value column” rather than the “ones column” to avoid any<br /> misconceptions when decimals are introduced later in the year.</p> <p>After each column is added, ask,<br /> “Do you have enough ones/ tens/hundreds to make an exchange?"<br /> 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.</p> <p>Extra reasoning activity sheet.</p>

<p>The numbers can be made using place value counters in a place value chart, alongside the formal written method.<br /> 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.</p> <p>After each column is added, ask,<br /> “Do you have enough ones/ tens/hundreds to make an exchange?”</p> <p>Extra reasoning sheet attached.</p>

<p>The numbers can be made using place value counters in a place value chart, alongside the formal written method.<br /> 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.</p> <p>After each column is added, ask,<br /> “Do you have enough ones/ tens/hundreds to make an exchange?”</p> <p>Extra reasoning activity sheet.</p>

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

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

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

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