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Rounding Numbers within 1,000,000
Children round any number up to 1,000,000 to any power of 10 up to 100,000.
You may wish to practise counting in 100,000s first, and then
practise rounding to the nearest 100,000 before looking at mixed questions.
Ask,
“Which multiples of 100,000 does the number lie between?”
" How can you represent the rounding of this number on a number line?"
“Which division on the number line is the number closer to?”
" What is the number rounded to the nearest 100,000?"
Estimation and Inverse operation to check answers Higher reasoning
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
Efficient subtraction Higher
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.
Bundle
Adding two 4-digit numbers with extra reasoning sheets
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 sheets
Rounding to check the answers Core
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
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?
Multiples of 3 Foundation
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?
Mutiply and divide by 6 with extra reasoning sheet Higher
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.
Comparing and Ordering Fractions foundation worksheet
Building on their knowledge of equivalent fractions, in this worksheet children compare fractions where the denominators are multiples of the other.
Diagrams will help children to see which is the larger fraction and they should continue to use fraction walls and bar models until they are confident with the general rules.
Answer sheet included.
Comparing and Ordering Fractions Core worksheet
Use this worksheet to help children develop their understanding of comparing and ordering fractions with denominators that are multiples. If equivalent fractions are needed, then one denominator will be a multiple of the other or others.
This worksheet includes a challenge to help deepen children’s understanding and problem-solving skills.
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.
Core worksheet with answer sheet.
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.
Year 4 Tenths on a place value chart Higher ability
In this worksheet, children explore the tenths column in a place value chart, extending their previous learning to include numbers greater than 1.
They should know that 1 comes after 0.9, and when counting backwards that 0.9 comes after 1. Links can be made to the equivalence of 10 ones and 1 ten to support understanding.
Challenge your children with these questions:
What is the decimal point?
How many wholes/tenths are in this number?
Year 4 Tenths as decimals core reasoning worksheet
This is a reasoning worksheet for core students.
Children show their preference when it comes to showing the six tenths as a decimal.
They must then use all models to show four tenths.
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.
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?
Year 4 Tenths place value Foundation reasoning
In this foundation reasoning worksheet, children explore the smallest and the greatest decimal numbers. They can use the number cards and the place value chart to solve the question.
Children recognise and write decimal equivalents of any number of tenths.
It is important that they understand that 10 tenths are equivalent to 1 whole, and therefore 1 whole is equivalent to 10 tenths. Use this knowledge when counting both forwards and backwards in tenths. When counting forwards, you should be aware that 1 comes after 0.9, and when counting backwards that 0.9 comes after 1. Links can be made to the equivalence of 10 ones and 1 ten to support understanding.
You might like to use these supporting sentences to extend their learning:
There are _____tenths in 1 whole.
1 whole is equivalent to _____ tenths.
There is/are _________ whole/wholes and ____ tenths
The number is _____.
Year 5 Addition with more than four digits
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.
Bundle
Decimals reasoning
Includes:
Support mat
divide 1 digit number by 10
decimals as tenths - Foundation , core and higher
tenths on a place value chart - Foundation , core and higher
with extra 7 reasoning sheets
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?
Bundle
Order and Compare Fractions and extra reasoning sheets
In these well differentiated 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.
Compare fractions
Order fractions less than 1
Extra reasoning sheets attached
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.
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?
Bundle
Year 4 Subtraction
Children subtract whole numbers 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.
Subtraction with more than 4-digit numbers higher
In this higher ability worksheet, 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.
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.
Bundle
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.