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Common multiples Core
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.
Square Numbers Foundation
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).
Square Numbers Higher
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.
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
Inverse operation to check answers Foundation
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
Square numbers Core
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).
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?
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?
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.
Round to check answers Core with extra reasoning sheet
In worksheet, children practise rounding in order to estimate
the answers to both additions and subtractions. They also review
mental strategies for estimating answers.
Children should be familiar with the word “approximate”, and “estimate” and
the degree of accuracy to which to round is a useful point for discussion. Generally, rounding to the nearest 100 for 3-digit numbers,
the nearest 1,000 for 4-digit numbers and so on is appropriate.
Extra reasoning sheet attached.
Answer sheet attached.
Multi-step addition and subtraction word problems Core extra reasoning sheet
In this worksheet, children apply the strategies they have learned so far to solve addition and subtraction problems with more than one step.
Children choose the operations needed at each step and then perform the calculations using an appropriate mental or written method.
Problems are presented in word form.
The use of bar models can help children to illustrate problems of this kind. While the models will not perform the calculation, they will help children to decide what operations are needed and why.
Ask,
What is the key information in the question?
What can you work out straight away? How does this help you to answer the question?
How can you represent this problem using a bar model?
Which bar will be longer? Why?
Do you need to add or subtract the numbers at this stage?
How do you know?
Multiply and divide by 6 with extra reasoning sheet. Core
In this worksheet, children build on their knowledge of the 3 times-table to explore the 6 times-table. Children work with the 6 times-table and use the multiplication facts they know to find unknown facts.
Children explore the fact that the 6 times-table is double the 3 times-table.
Extra reasoning activity attached.
Answer sheets attached.
Prime, Square and Cube Numbers Higher
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).
Multiples of 3
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.
Multi-step addition and subtraction word problems Higher with extra reasoning sheet
In this worksheet, children apply the strategies they have learned so far to solve addition and subtraction problems with more than one step.
Children choose the operations needed at each step and then perform the calculations using an appropriate mental or written method.
Problems are presented in word form.
The use of bar models can help children to illustrate problems of this kind. While the models will not perform the calculation, they will help children to decide what operations are needed and why.
Ask,
What is the key information in the question?
What can you work out straight away? How does this help you to answer the question?
How can you represent this problem using a bar model?
Which bar will be longer? Why?
Do you need to add or subtract the numbers at this stage?
How do you know?
With extra reasoning activity.
Answer sheets included.
Area of rectilinear shapes by counting squares Higher
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?
Area of rectilinear shapes Foundation
In this worksheet, children use the strategy of counting the number of squares inside a shape to find its area. They use marking or noting to help them count the squares without missing any.
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?
Equivalent Fractions Higher worksheet
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:
Higher worksheet - with answer sheet
Equivalent fractions - 3 differentiated worksheets
In these three worksheets, 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:
Foundation worksheet - with answer sheet
Core worksheet - with answer sheet
Higher worksheet - with answer sheet
Comparing and Ordering Fractions Core worksheet
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.