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Year 4 Tenths on a place value chart core worksheet
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.
Subtraction with two exchanges Core with extra reasoning sheet
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?
Year 5 Compare Fractions less than 1 Higher with extra reasoning sheet
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
Subtraction with two exchanges Higher with extra reasoning sheet
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?
Subtraction with two exchanges foundation with extra reasoning sheet
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
Core worksheet Year 5 Order fractions with extra reasoning 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.
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.
Foundation worksheet Year 5 Order fractions with extra reasoning sheet
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?
Higher ability worksheet Year 5 Order fractions with extra reasoning sheet
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?
Subtraction with two exchanges higher with extra reasoning sheet
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
Year 5 Compare fractions Core with extra reasoning sheet
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
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Year 5 Subtraction
Children subtract whole numbers with more than four digits, including using formal written methods (columnar subtraction).
They are challenged by applying their knowledge in solving world problems.
They are supported by place value counters and place value chart.
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.
Year 5 Compare fraction less than 1 foundation with extra reasoning 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.
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Decimals Reasoning
These are year 4 reasoning activities.
Decimals - divide whole number by 10
Tenths as decimals - Foundation, Core and Higher
Tenths on a place value chart - Foundation, Core and Higher.
Buying a bundle saves you 31%.
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Addition
In these worksheets, 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.
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Comparing and Ordering Fractions
In these three worksheets, children build on their knowledge of ordering a set of three or more fractions.
If equivalent fractions are needed, then one denominator will be a multiple of the other or others.
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.
Bundle
Multiples of 3
These are three differentiated worksheets.
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.
In the higher ability worksheet ( with three faces), children explore how to recognise if a number is a multiple of 3 by finding 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?
In the foundation worksheet (one face), 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?
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Adding and Subtracting Mental strategies
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.
They use their knowledge of number bonds and place
value to add and subtract multiples of powers of 10.
If they know that 3 + 4 = 7, then 3 thousand + 4 thousand = 7 thousand
and 3,000 + 4,000 = 7,000.
Children need to be fluent in their knowledge of number
bonds to support the mental strategies.
How does knowing that 6 + 3 = 9 help you to work out 60,000 + 30,000?
“How can the numbers be partitioned to help add/subtract them?”
"Are any of the numbers multiples of powers of 10? "
“How does this help you to add/subtract them?”
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Adding and Subtracting 1s, 10s, 100s, and 1,000s
These are differentiated worksheets to support and challenge adding and subtracting 1s , 10s , 100s and 1,000 from any number.
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Powers of 10
In these worksheets, 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.