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 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

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.

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.

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 activity sheet.

Children use place value chart to solve calculations that involve up to two exchanges. They have support of pace value chart and numbers written down under each value column. They then solve word problem with support of calculations already written down for them. As an extension, they find the missing number in the bar model and use formal method to solve this calculation with the greater number written for them already.

Children solve subtraction calculation involving up to two exchanges. They correct the mistake and explain why the mistake was made. They solve two step word problem and find the missing number in the calculations , involving finding the possible greater number and explain how they solve this calculation. Extra reasoning activity attached

Compare and order fractions whose denominators are all multiples of the same number. Identify and write equivalent fractions of a given fraction. Children compare fractions and explain how they know if the fraction is smaller or greater. They are challenged by word problems and working out the greater fractions within the word problem. They correct mistakes made by another child. They use number line comparing the position of the fraction to 0 and 1 or one half. Extra reasoning sheet attached

Children subtract up to 4-digit numbers with more than one exchange, using the written method of column subtraction.They solve 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).

Children subtract up to 4-digit numbers, with one exchange. They complete the formal written method alongside any visual resources to support understanding. Before subtracting each column, ask, Do you have enough ones/tens/hundreds to subtract ____ ? If not, then an exchange is needed. The exchange could take place from the tens, hundreds or thousands, but there is only one exchange per calculation

These are subtraction worksheets targeted at Year 4. There are 3 well differentiated worksheets and 3 reasoning activities with answers included. The first worksheet includes place value counters and base ten to help with subtraction, and reminders to exchange. The second worksheet includes place value, base ten tables and some word problems with subtractions. The third worksheet includes word problems to solve subtractions with 4-digit numbers. The reasoning activities include missing digits or numbers.

Children compare fractions where the denominator or numerators are the same. The examples and bar models support them. They find the equivalent fractions by using bar models. Extra reasoning sheet attached.

There are three differentiated worksheets with answers plus three differentiated reasoning worksheets. They practice subtraction of two 4-digit numbers with one exchange in any column. Working towards: children supported by visual clues and word bank. Working above: children are challenged by word problems, missing numbers and reasoning problems.

In these worksheets, children subtract up to 4-digit numbers with more than one exchange, using the written method of column subtraction. Children perform subtractions involving two separate exchanges With extra reasoning sheet with answer sheets (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). To support understanding, solve these subtractions alongside the concrete resources of base 10 and place value counters. When completing the written method, it is vital that children are careful with where they put the digits, especially those that have been exchanged. Remember, two-part exchanges can be confusing for children if they are unsure what each digit represents or where to put it. You can support the children with some questioning alongside their work, for example, Do you need to make an exchange? 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 foundation worksheets, children order a set of two 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. Bar models, fraction walls and number lines are used to help children to see the relative sizes of the fractions, especially when conversions are needed. Children should look at the set of numerators especially when the denominators are the same. 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. Useful supporting sentences for parents. When fractions have the same denominator, the one with the_____ numerator is the greatest fraction. When fractions have the same numerator, the one with the ______ denominator is the greatest fraction. With extra reasoning sheet. Key questions for parents: 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?

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.

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.

In this worksheet, children subtract whole numbers with more than four digits, including using formal written methods (columnar subtraction). Place value chart and place value counters can be used for support. It is useful when performing calculations that require an exchange. Squared paper and labelled columns will support children in placing the digits in the correct columns. Children experience both questions and answers where zero appears in columns as a placeholder. For a support ask, “Which number goes at the top when using the column method?” “Does it matter if the numbers have different numbers of digits?” “How do you know which digits to “line up” in the calculation?” “How do you know if the calculation is a subtraction?”

Add and subtract numbers with up to four digits using the formal written methods of columnar addition and subtraction where appropriate Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why