Year 2
(Entry into Year 3)
25 Hour Revision Course
Mathematics
Section 1 – Column Sums
2 hours
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Place Value: Using Columns for Numbers
Putting numbers in columns makes it easy for us to make lots of different numbers using the
same digits. The position or place of each digit – which column it is in – tells us its value.In the example
below, you can see that above the numbers, we have written Th, H, T, and U. These stand for
Thousands, Hundreds, Tens, and Units.
From this, you can see that we have 1 Ten and 4 Units. This is read as 14 (Fourteen).
In this example, we have 3 Hundreds, 7 Tens, and 8 Units. This is read as 378 (Three Hundred and
Seventy Eight)
In this example, we have 4 Thousands, 2 Hundreds, 5 Tens, and 6 Units. This is read as 4256 (Four
Thousand, Two Hundred and Fifty Six)
~2~
Addition
Whenever possible, you should try to add numbers in your head. To do this, you usually need to break
up, or partition, a number into its different parts (into tens and units, for example) before adding on
each part separately.
For example, when adding 28 to 46, it is simpler to break up 28 into 20 and 8 before doing any adding.
A number line can be used to help you.
+ 20
+8
46
66
74
To begin with, you might find drawing a number line helpful, but as you grow in confidence you should
be able to add two numbers that are both less than 100 in your head.
Have a go at answering the questions below in your head (you can draw a number line if it helps).
~3~
Addition using the Column Method
As well as adding up in our heads, we can also use the Column Method. This is particularly useful if
the numbers are too big to add in your head. The Column Method involves lining both sums above
each other with the Tens and Units in the right place. An addition sum using the Column Method
looks like this:
(H stands for Hundreds, T stands for Tens, and U stands for Units)
In this sum we have 314 (3 Hundreds, 1 Ten and 4 Units) plus 452 (4 Hundred, 5 Tens and 2 Units).
With Column sums, we always start on the right-hand side.
4 plus 2 is 6. This is put underneath, between the answer lines.
Next we look at the Tens Column, adding 10 and 50 together to make 60. The zero is dropped, and
the 6 is placed in the Tens Column.
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Finally, we look at the Hundreds Column, adding 300 and 400 to get 700.
~5~
Often we have to carry from one Column to the next. When this happens, we need to leave a mark to
remember to add it later.
For example,
Here, 7 add 5 is 12. We fill in the numbers like this:
For the next Column, we add the two numbers at the top (3 and 8) and then add the new number
below the answer box.
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Finally, add the numbers in the Hundreds Column.
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Using the information shown above, work out the following:
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~9~
~10~
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Subtraction
There are two ways of thinking about subtraction: counting back or counting on. Counting back is just
another way of saying ‘take away’.
For example,
-6
8
9
10
11
12
13
14
Counting on involves finding the difference between the two numbers by counting on from the
smallest to the largest.
Using the same example,
8
6
7
8
9
10
11
12
13
14
The result of each of these approaches is obviously the same. Which method you use will often depend
on the numbers you are working with. When the number you are subtracting is small (65 – 3), it usually
makes more sense to count back. When the number you are subtracting is large (65 – 62), it usually
makes more sense to count on.
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Work out the answers to the following questions in your head. You will first need to decide whether it
makes more sense to count back or count on.
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Column Subtraction
Column Subtraction is very similar to Column Addition, although here we introduce a new trick –
taking from another Column. This is necessary when the top number in the Column is smaller than
the bottom number, like this;
As 2 is less than 7, we have to take from 1 from the 4 in the Tens Column. To do this, we cross out
the number in the next column along on the left, and write the number one less than it above it. We
then take the one and put it next to the top unit that was too small originally. It should look something
like this:
We then subtract as normal.
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Now try some subtractions of your own.
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Section 2 – Number Bonds
2 hours
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Number Bonds
Number Bonds are simple sums that need to be learnt by heart.
For each of the sums below, please try to work out what the value of the missing number.
The first question has been done for you.
Addition To Ten
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Addition To Twenty
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Subtraction from Ten
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Subtraction from Twenty
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Simple Number Bonds to One Hundred
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Section 3 – Deductive Maths
1.5 hours
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Deductive Maths
Sometimes in Maths, when we are given the answer to one sum, we can use the answer to
work out the answer to other questions.
For example
Use this logic to work out the answers to the following questions;
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~33~
Number Sequences
Look at the following sequences of numbers and try to work out the next 3 numbers in the
sequences. For each line, please explain why you have given the answers you have.
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Working out Original Numbers
Read the questions below, and try to work out the original numbers
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Section 4 – Vocabulary of Maths
0.5 hours
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Vocabulary of Numbers
Cardinal Numbers
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~41~
Using the vocabulary above, please write out the following figures in words:
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Ordinal Numbers
Ordinal numbers refer to the position of a number in a list. Below is a list of ordinal numbers.
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Section 5 – Rounding
1 hours
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Rounding
Sometimes it is not necessary to give an exact answer. If asked how many children there are in
a school, for example, we would probably say ‘about 400’ rather than ‘387’. Here, we have rounded the
number to the nearest Hundred.
When rounding to the nearest Ten or nearest Hundred, you must first work out which two Tens or
which two Hundreds the number is between before then deciding which it is closest to.
For example, 84 is between 80 and 90, but it is closest to 80 (it is four away from 80 and six away from
90) and so if we had to round it to the nearest Ten we would round it to 80.
If a number is exactly half-way between two Tens or Two Hundreds, then we always round up. For
example, 250 is fifty away from 200 and fifty away from 300, but it is rounded up to 300.
For the numbers below, work out what two Tens the number is between and then say which it is
rounded to.
For example;
~46~
~47~
For the numbers below, work out what two Hundreds the number is between and then say which it is
rounded to.
For example
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~49~
Round the following numbers to the nearest 10
~50~
Section 6 – Multiplication
4.5 hours
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Multiplication
Multiplication can be thought of as repeated addition.
For example, 3 x 4 can be thought of as ‘3 lots of 4:
For each of the sums below, show the repeated addition required and find the answer.
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Below is a list of Times Tables. These need to be learnt off by heart. Take time to learn each one. Try
repeating them out loud, or get a friend or member of your family to sit with you and go through them.
It takes time, but this will be very important soon, and you will need to know everything here.
Next to the tables below, copy each sum out twice more for practice.
Two-times Table (2x)
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Three-times Table (3x)
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Four-times Table (4x)
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Five-times Table (5x)
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Six-times Table (6x)
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Seven-times Table (7x)
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Eight-times Table (8x)
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Nine-times Table (9x)
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Ten-times Table (10x)
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Eleven-times Table (11x)
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Twelve-times Table (12x)
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In the multiplication grid below, please fill in all of the sums as best as you can. Some
answers have been filled in for you.
(A Tip: Start with the times tables you already know – by filling in 1x, 2x, 5x, and 10x, you will see that
a large amount of the grid is quickly filled)
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Fill in the following multiplication grids in the same way. You will notice that it is not quite
as easy with these!
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In the multiplication grid below, please circle all numbers that are a multiple of 4.
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In the multiplication grid below, please circle all numbers that are a multiple of 5.
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Mental Maths Quiz
Work out the following multiplication sums as quickly as you can. Try to do them in your
head, but if you must write something, find the answer however you wish.
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Section 7 – Division
2 hours
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Division
Just as Multiplication can be explained as repeated addition, Division can be explained as
repeated subtraction. One method of dividing is by subtracting the second number as many times as
necessary until we reach zero.
For example;
÷
For each of the sums below, show the repeated addition required and find the answer.
÷
÷
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÷4
÷
÷
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Bus Stop Division
Another method that we can use to divide is the Bus Stop method. It is called this because the number
that we’re looking to divide hides under a roof where the answer sits.
For the sum above, start by working out how many times two goes into 1. It doesn’t, so we then ask
how many times 2 goes into 16. It goes into 16, 8 times, and we write the answer like this;
Some division will not give a nice, easy answer. Sometimes we are left with remainders. We work this
out like this;
Start by working out how many times two goes into two. It goes once, so we write 1 above the two.
Next we work out how many twos there are in five. There are 2 twos in 5, so we write a 2 above the
five. However, we are left with one left over. This is written on the side like this;
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The answer is 12, remainder 1.
Sometimes, we will be left with a remainder in the middle of the sum – If this is the case, we move it
into the next column.
Here we begin by working out how many twos there are in five. There are 2, with 1 remainder. The 2
is placed above the 5, while the one goes next to the 4. We then work out how many twos there are in
fourteen. There are 7, with no remainder, making the answer 27.
(As you can see, it is very important to know your Times Tables – if you are struggling to remember
how many times a number goes into another number, please revise the tables in the Multiplication
section)
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Solve the divisions below using the Bus Stop Method
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Section 8 – Factors
1 hours
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Factors
Factors are numbers that can be multiplied exactly with another whole number to produce a
third number, n. We can work out which numbers are factors of another by dividing n with potential
factors. The factors are the numbers that, when divided, give a whole number (integer).
For example:
Find all of the Factors of 6
From this, we can see that the factors of 6 are 1, 2, 3, and 6
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Hence, or otherwise, please find all of the factors of the following numbers;
~84~
NB.
It may help you to think of Times Tables when trying to work out factors. Which
multiples go into each of the numbers above?
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Section 9 – Fractions
2 hours
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Fractions
A Fraction is a numerical value that is not a whole number. In practice, this means part or
piece of a whole number. Well known fractions include a half, (1/2), or a quarter (1/4).
Fractions are made up of two parts;
𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
The Denominator is the total number of parts that a whole number has been split into. The Numerator
is the number of smaller parts that have been kept.
In the example below, we have divided a circle into six sections,
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This means that the denominator for this shape will be 6. We then colour a number of the sections in.
In this shape, 4 of the 6 sections are coloured in. This means that for this shape, the fraction will be
4
6
For each of the shapes shown below, please write the fraction beside it;
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For each of the shapes shown below, please colour in the required fraction;
𝟒
𝟖
𝟑
𝟓
𝟐
𝟔
𝟒
𝟓
𝟏
𝟔
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Adding Simple Fractions (8+)
Simple fractions are fractions where the denominator is the same for both parts of the sum. If the
denominator is the same, we simply add the numerators together.
For example;
1 1
2
+ =
3 3
3
+
=
Now work through the following questions below;
1 1
+ =
4 4
2 1
+ =
5 5
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3 2
+ =
7 7
4 2
+ =
6 6
5
3
+
=
10 10
4
6
+
=
17 17
9
5
+
=
18 18
20 15
+
=
50 50
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13 12
+
=
65 65
5
4
+
=
192 192
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Subtracting Simple Fractions
As with for adding Simple fractions, if the denominator is the same, we simply subtract the numerators.
For example;
2 1
1
− =
3 3
3
Now work through the following questions below;
3
1
− =
4
4
4 1
− =
5 5
6 2
− =
7 7
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2
2
− =
6
6
5
3
−
=
10 10
13
8
−
=
17
17
9
5
−
=
18 18
20
15
−
=
50
50
32 12
−
=
65 65
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60
17
−
=
192 192
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Section 10 – Doubling and Halving
1.5 hours
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Doubling and Halving
Doubling a number means to multiply it by 2.
e.g.
What is double 4?
Double 4 is 8
Halving is the opposite to Doubling, as it involves dividing a number by 2.
e.g.
What is half of 12?
÷
Half of 12 is 6
Using the information above, please work out what DOUBLE of the following numbers
is.
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~98~
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Now we will look at halving numbers – try to work out the answers to the questions below;
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Section 11 – Time
3.5 hours
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Important Facts about Time and Date
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Telling the Time using an Analogue Clock
Analogue clocks look like this. They are circles, often divided into 12 sections with a number on each.
This is very helpful for us. As you may already know, an hour is made up of 60 minutes, and 60 divided
by 12 is 5. This means that each number on the clock means that 5 minutes has passed. However, the
12 numbers also refer to 12 hours.
We tell them apart by using two different hands on the clock – one long and one short. The long hand
helps us to tell the minutes in the hour, while the short hand refers to the hours.
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The big hand (red) is pointing to 12, which means zero minutes, and the short hand is pointing to 2.
We say that this is 2 o’clock.
What time is it in the following clocks?
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Half-Past
When the long, red, minute hand is at the bottom of the clock, pointing at the number 6, that
means that 30 minutes have passed in the hour. At this point, 30 of the 60 minutes have passed, so we
say that it is ‘Half Past’.
At this point, we then have to work out which hour we are ‘Half Past’. To do this, look at the clock
again, and see where the short hour hand is. It has gone past one hour, but has not reached the next
hour.
For example;
In this example, the short, green, hour hand is between 6 and 7. This means that the time is 6.30.
Please work out the time for each of the clocks below;
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~111~
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Quarter past, and Quarter to
When the minute hand (long hand) rests on 3, 15 minutes have passed in the hour. We call
this ‘Quarter past (…an hour)’.
To find out which hour it is ‘Quarter past’, we need to look at the shorter hand.
In this example, the short, green, hour hand has moved just past 6. This means that the time here is
‘Quarter past Six’.
Now work out the time for each of the following clocks;
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~114~
When the minute hand (long hand) rests on 9, 45 minutes have passed in the hour. We call this ‘Quarter
to (…an hour)’.
To find out which hour it is ‘Quarter to’, we need to look at the shorter hand again. Instead of looking
at which hour we have just passed, we look at which hour is to come.
In this example, the short, green, hour hand is about to reach 3. This means that the time here is
‘Quarter to Three’.
Now work out the time for each of the following clocks;
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~116~
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For times which are not ‘Half Past’, ‘Quarter Past’, or ‘Quarter To’, we need to take a little extra care
when trying to tell the time.
On the clock above, you will notice that there are sixty little notches, each of which signifies one
minute. If the minute hand is in the right half of the clock, we use ‘Past’ and count the number of
minutes that have elapsed. For times that use past, we need to look at the previous hour to complete
the time.
For example;
~118~
On this clock, 22 minutes have past since 11, so the time is ’22 past 11’ or ’11.22’.
~119~
If the minute hand is on the left side on the clock face, we have to use ‘To’. As with ‘Quarter to’, we
need to look at the next hour so, for example,
From the top of the clock, count left. There are 8 minutes until we reach the red minute hand, and the
next hour is 10, so the time is ‘Eight Minutes to 10’.
Please work out the time for the clocks below;
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~121~
~122~
Section 12 – Money
1 hour
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Money
There are currently 8 coins in circulation in Great Britain – these are shown below. They are
1p, 2p, 5p, 10p, 20p, 50p, £1, and £2.
For each of the groups below, work out how much money is in each group.
1)
2)
3)
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4)
5)
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Section 13 – General Test
1.5 hours
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General Revision Test
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




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