This is reasoning activity targeted at Year 5. Before children attempt this worksheet, they should attempt to order fractions in the main worksheet displayed on the website. 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.

This is reasoning activity targeted at lower ability Year 4. The number line in this question is a visual resource to support the understanding of decimal numbers. Before children attempt this worksheet, they should encounter, practice writing and reading decimal numbers and the decimal point, model making, drawing and showing that the decimal point is used to separate whole numbers from decimals in the main worksheet displayed on the website. 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? "If a whole is split into 10 equal parts, then what are the three parts worth?

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 reasoning worksheet children are supported to describe the value of each digit in the decimal numbers. Children read and write the numbers using place value counters in a place value chart, as well as working out the value of each digit in the number. Children use place value counters to represent decimal number. Ask, “What is the value of the digit ____ in the number ____?” You can use this supporting sentence to help your child. ________tenths are equivalent to ______ whole. ________ hundredths are equivalent to ________ tenths. ________hundredths are equivalent to ______ whole. When reading or writing a number, children may say “one point fourteen" instead of “one point one four”. • When there are hundredths and tenths but no ones in a number, children may forget to include the zero placeholder in the ones column.

This worksheet uses a hundred piece of base 10 as 1 whole. It shows children that they can exchange, for example, 10 tenths for 1 whole, or 10 hundredths for 1 tenth. A hundred square where each part represents 1 hundredth, or 0.01, can also help children to see the relationship between a hundredth, a tenth and a whole. They use place value counters to represent decimal number. Ask, “How can you represent this number using a place value chart?” “What is the value of the digit ____ in the number ____?” You can use this supporting sentence to help your child. ________tenths are equivalent to ______ whole. ________ hundredths are equivalent to ________ tenths. ________hundredths are equivalent to ______ whole. When reading or writing a number, children may say “one point fourteen" instead of “one point one four”. • When there are hundredths and tenths but no ones in a number, children may forget to include the zero placeholder in the ones column.

These worksheets display numbers with up to 2 decimal places. Using a hundred piece of base 10 as 1 whole, a ten piece as a tenth and a one piece as a hundredth shows children that they can exchange, for example, 10 tenths for 1 whole, or 10 hundredths for 1 tenth. A hundred square where each part represents 1 hundredth, or 0.01, can also help children to see the relationship between a hundredth, a tenth and a whole. Children make decimal numbers using place value counters in a place value chart and read and write the numbers, as well as working out the value of each digit in the number. They also explore partitioning decimal numbers in a variety of ways. When reading or writing a number, children may say “one point twenty-four” instead of “one point two four”. When there are hundredths but no tenths in a number, children may forget to include the zero placeholder in the tenths column. You can use these questions to challenge your child. Can you partition the decimal number different ways? How many tens are there in 100? How many ones are there in 10/100? How many 0.1s are there in 1? How many 0.01s are there in 0.1?

his is a PDF file. These worksheets display numbers with up to 2 decimal places. Using a hundred piece of base 10 as 1 whole, a ten piece as a tenth and a one piece as a hundredth shows children that they can exchange, for example, 10 tenths for 1 whole, or 10 hundredths for 1 tenth. A hundred square where each part represents 1 hundredth, or 0.01, can also help children to see the relationship between a hundredth, a tenth and a whole. Children make decimal numbers using place value counters in a place value chart and read and write the numbers, as well as working out the value of each digit in the number. They also explore partitioning decimal numbers in a variety of ways. When reading or writing a number, children may say “one point twenty-four” instead of “one point two four”. When there are hundredths but no tenths in a number, children may forget to include the zero placeholder in the tenths column. You can use these questions to support your child. How can you represent this number using a place value chart? What is the same and what is different about a tenth and a hundredth? What is the value of the digit

Children look at a variety of representations of tenths as decimals, up to the value of 1 whole. This leads to adding the tenths column to a place value chart for children to see how tenths fit with the rest of the number system and to understand the need for the decimal point. Useful challenging questioning: How are decimals like fractions? using a model? How can you convert between tenths as fractions and tenths as decimals? How is 2/10 like 0.2? How is it different?

Model making, drawing and writing decimal numbers, showing that the decimal point is used to separate whole numbers from decimals. Children look at a variety of representations of tenths as decimals, up to the value of 1 whole. This leads to adding the tenths column to a place value chart for children to see how tenths fit with the rest of the number system and to understand the need for the decimal point. Children may forget to include the decimal point. If the number of tenths reaches 10, children may call this “zero point ten” and write 0.10 rather than exchanging for 1 one. Children may confuse the words “tens” and “tenths”. Questions to help with understaning the topic: If a whole is divided into 10 equal parts, what is the value of each part? How can you represent the decimal How are decimals like fractions? using a model? How can you convert between tenths as fractions and tenths as decimals? How is 1/10 like 0.1? How is it different?

With extra reasoning activity sheet. Children use their knowledge of comparing fractions and order a set of three 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. C Bar models, fraction walls and number lines could be used to help children to see the relative sizes of the fractions, especially when conversions are needed. Children can consider the position of a fraction relative to 0, 1/2 or 1 whole. You can challenge your child with set of questions: 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? How can you use equivalent fractions to help? What are all the denominators/numerators multiples of? How can this help you find equivalent fractions? Which of the fractions are greater than 1/2?

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?

Children use their knowledge of comparing fractions and order a set of three 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. C Bar models, fraction walls and number lines could be used to help children to see the relative sizes of the fractions, especially when conversions are needed. Children can consider the position of a fraction relative to 0, 1/2 or 1 whole. With extra reasoning sheet. You can support your child with set of questions: 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? How can you use equivalent fractions to help? What are all the denominators/numerators multiples of? How can this help you find equivalent fractions? Which of the fractions are greater than 1/2? 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. You might use these support sentences: When fractions have the same denominator, one with the_____ numerator is the greatest fraction. When fractions have the same numerator, the one with the ______ denominator is the greatest fraction.

In this higher ability worksheets, children subtract up to 4-digit numbers with more than one exchange, using the written method of column subtraction. With extra reasoning sheet with answer sheets They perform 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). Remember, when completing the written method, it is vital that children are careful with where they put the digits, especially those that have been exchanged. Two-part exchanges can be confusing for children if they are unsure what each digit represents or where to put it. Watch for not lining up the digits in the place value columns correctly. When exchanging a number, they may put the ones in the incorrect place. When exchanging over two columns, children may exchange directly from, for example, hundreds down to ones and miss out the exchange to tens. Some high-level questioning will challenge high achieving students. Does it matter which column you subtract first? 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 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 worksheets, children subtract up to 4-digit numbers with more than one exchange, using the written method of column subtraction. They perform subtractions involving two separate exchanges (for example, from the thousands and from the tens) To support understanding, solve these subtractions alongside the concrete resources of base 10 and place value counters. With extra reasoning sheet. With answer sheets

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 compare fractions where the denominators are the same or where one denominator is a multiple of the other. They also compare fractions with the same numerator or by comparing it to one half. with answer sheets. Extra reasoning activity sheet

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.

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

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).