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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?
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.
Year 5 Multiples
A multiple of a number is any number that is in its times-table.
A multiple is the result of multiplying a number by a positive integer. Children find sets of multiples of given numbers. Children understand and use rules of divisibility, which will be built upon in later learning.
Ask, “How do you find the multiples of a number?”
“What do you notice about the multiples of?”
“What is the same and what is different about them?”
“Can a number be a multiple of more than one number?”
Higher Ability Year 5 Place Value Numbers to 100,000
Children be able to add and subtract 10, 100 and
1,000 to and from a given number, using their place value
knowledge rather than formal written methods.
Ask, “What is the value of each digit in the number?”
" How can you represent the number in a different way?"
“Which digit or digits would change in value if you added a 10/100/1,000 counter?”
“How do you write the number in words?”
Watch for :
Children may not yet have fully grasped placeholders, for
example reading 309 as thirty-nine.
Children may rely on the column method of addition and
subtraction when this is not necessary.
Children may not use, or may misplace, the comma when
writing numbers greater than or equal to 1,000.
Place Value Numbers to 100,000 Higher Ability
In this worksheet, children explore numbers up to 100,000. They are introduced to the ten-thousands column in a place value chart and begin to understand the multiples of 10,000. This can be reinforced using a number line to 100,000.
Both place value counters and plain counters are used in place value charts, allowing for discussion about the values of the columns.
Place Value Numbers to 100,000 Foundation
In this worksheet, children explore numbers up to 100,000. They are introduced to the ten-thousands column in a place value chart and begin to understand the multiples of 10,000. This can be reinforced using a number line to 100,000.
Both place value counters and plain counters are used in place value charts, allowing for discussion about the values of the columns.
Watch for:
Children are likely to use “thousands” and “millions” in
everyday speech more often than “tens of thousands” or
“hundreds of thousands”, so they may miss out place value
columns in between.
Children may find numbers with several placeholders
difficult, for example 40,020
Children may need support in deciding when to use the
word “and” when saying numbers, for example 3,200 does
not use “and” but 3,020 does.
Compare and Order Numbers to 100,000
They can use a variety of representations to help them, such
as place value counters, place value charts and number lines,
but the main focus of the worksheet is to compare and order using
the place value of the digits within the numbers. Children first
compare pairs of numbers and then move on to ordering sets of
three or more numbers
Powers of 10 Higher
In this worksheet, children are challenged by exploring the relationship between numbers in the word problems.
They look at columns that are further apart, for example considering the number of thousands needed to make 20,000 and then multiples of 20,000. Children are challenged by word problems.
Ask,
If you move a digit one place to the left in a place value chart,
how many times greater is the value of the digit?
If you move a digit two places to the left in a place value
chart, how many times greater is the value of the digit?
Watch for:
Children may not realise that the overall effect of,
for example, × 10 followed by × 10 is × 100.
Partition Numbers to 1,000,000 Higher
Children are challenged to partition the numbers in more flexible ways.
Watch for : Children may be less familiar with non-standard partitioning and need the support of, for example, place value counters to see alternatives.
Ask:
“How else can you say/write “15 tens” or “15 thousands”?”