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In this worksheet, children develop their understanding of equivalent fractions within 1, mainly through exploring bar models. Children begin by finding equivalent fractions by splitting up models into smaller parts in a range of different ways. The key learning point is that as long as each of the existing parts are split equally into the same number of smaller parts, then the fractions will be equivalent. A common misconception is that children believe they can only split up existing parts into two equal sections, which limits the number of equivalent fractions that they will find. Children begin to use fraction walls to help create equivalent fraction families. Includes: Core worksheet - with answer sheet

Use this worksheet to help children develop their understanding of an area by counting the squares. The worksheet is aimed at those working at age expected. In this worksheet, children use the strategy of counting the number of squares inside a shape to find its area. Ask, What can you do to make sure you do not count a square twice? How can you make sure you do not miss a square? Does your knowledge of times-tables help you to find the area? Can you use arrays to find the area of any shape? Includes answer sheet.

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?

The worksheet is aimed at those working towards age expected. 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 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.

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.

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?

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.

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).

The worksheet is aimed at those working towards age expected. 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 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).

The worksheet is aimed at those working towards age expected. 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 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

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.

The worksheet is aimed at those working towards age expected. 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.

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.

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