Addition and Subtraction Keywords

Addition and subtraction word problems are commonly taught in Year 2 (Key Stage 1 in the UK) or second grade (in the USA).

The strategy to solve word problems is to firstly, write out the numbers involved and secondly, to decide which operation to use by reading the keywords in the question.

To solve addition and subtraction word problems, we try to read the question and look for keywords. The keyword list below will help to identify whether we have an addition or subtraction word problem.

Some common addition keywords are:

• Add
• Plus
• More
• Total
• Increase
• Together / Altogether
• Combined
• Sum
• Grow

If we see these words, we likely have an addition word problem.

Some common subtraction keywords are:

• Subtract
• Minus
• Take away
• Less / Fewer than
• Difference
• Decrease
• How many are left / remain?
• Change – in money questions
• Words ending in ‘er’, such as shorter, longer, faster.

Here is our first example of a word problem.

William has 20 counters and is given 7 more.

How many does he have in total?

We can see that we have the two addition keywords which are: ‘more‘ and ‘total‘.

When teaching word problems, it is useful to first write out the numbers that are in the text of the question.

We have 20 and 7.

The words ‘more‘ and ‘total‘ tell us that this is an addition word problem. We start with 20 counters and add 7 more.

Once we know that we have an addition word problem, then we can add the numbers.

20 + 7 = 27

William has 27 counters in total.

Here is another word problem example.

Phoebe has 12 cm of ribbon and Jack has 23 cm.

How much do they have altogether?

Our strategy is to first write out the numbers involved in the question.

We write down 12 and then 23. We can write the numbers above each other and line up the digits in each number.

There is only one keyword in this question which is altogether.

This in an addition keyword which tells us that we want to combine the two amounts to make a total.

We want to add the numbers 12 and 23.

It is common for children to write down the units involved in the question at this stage. However, it is easiest to just write down the numbers themselves and then to put the units in at the end of the question as part of checking the working out.

Adding the units column, 2 + 3 = 5.

Adding the digits in the tens column, 1 + 2 = 3.

Therefore 12 + 23 = 35 and so, we have 35 cm of ribbon in total.

We are measuring the length of ribbon in cm and so, we write ‘cm’ at the end of our answer.

Here is another word problem example.

I buy 2 sweets that cost 43 pence each.

How much do they cost in total?

Each sweet costs 43 pence and there are two of them.

We write down 43 twice in this question.

The keyword ‘total‘ tells us that this is an addition word problem.

We will add the two 43 amounts by writing their digits directly above each other without writing ‘pence’ at the end.

Adding the units, 3 + 3 = 6.

Adding the tens, 4 + 4 = 8.

The two sweets cost 86 pence in total.

We can write the pence or ‘p’ on the final answer now that the calculation has been done.

In this worded question, we have only one number in the text itself. There is only one ’43’ written.

It can help to draw a diagram when teaching word problems to children to help picture the situation.

Here is another word problem involving money.

Matthew has 35 pence.

He spends 13 pence.

How much does he have left?

We write down the numbers involved, which are 35 and 13.

In this word problem, the keyword is left.

Finding how much is left is a keyword for a subtraction word problem.

This means that we subtract the smaller number from the larger number.

To subtract 13 from 35, we write the larger number above the smaller number and line up the digits.

Subtracting the units column, 5 – 3 = 2.

Subtracting the tens column, 3 – 1 = 2.

35 – 13 = 22

This was a problem involving finding change with money.

Spending money and then receiving change is also very likely to indicate that a word problem is a subtraction one.

In this next worded problem, Adam has 59 grams of chocolate.

He eats 49 grams.

How much does he have left?

The first step of the word problem strategy is to write out both of the numbers involved in the question.

We have 59 and 49.

The second step is to identify keywords. The word left is a subtraction keyword.

We want to see how much is left after 49 grams have been subtracted.

We write the subtraction with the larger number above the smaller number.

Subtracting the units column digits, 9 – 9 = 0.

Subtracting the tens column digits, 5 – 4 = 1.

59 – 49 = 10.

There are 10 grams of chocolate remaining.

Here is another word problem example.

I have a candle that is 38 cm long.

After I light it, 11 cm melts away.

How long is the candle now?

This word problem is trickier in that there are not any direct keywords in the question.

However the phrase ‘melts away tells us that we are removing, or subtracting.

Again, when teaching word problems, drawing a diagram is a useful technique.

If no diagram or picture is given, it helps to draw the situation at the start and also the situation at the end.

Subtracting the digits in the units column, 8 – 1 = 7.

Subtracting the digits in the tens column, 3 – 1 = 2.

38 – 11 = 27

27 cm of the candle remains.

In this example, the candle reduced in size because we were removing length as it melted.

The candle has become shorter. Shorter is a word which ends in ‘er’, which can also indicate that we have a subtraction word problem.

‘er’ words often look for a difference between two values and finding a difference is a subtraction.

Again, it can help to draw the situation with a diagram to help understand what type of word problem we have.

Block diagrams are also known as block graphs. Block diagrams are one of the first methods for presenting data that a child will see in school. Block diagrams are often introduced before teaching bar charts in key stage 1 (or first grade).

A block graph is drawn on square grid paper. In a block graph the different categories are listed along the bottom of the graph below each square on the grid. The number of blocks in each category tell us how many of each category there are.

A block graph looks similar to a bar chart but it is different in a couple of ways. A block graph does not have spaces in between each category like a bar chart does. Each shaded block on a block graph is always worth one, whereas on a bar chart this is not the case. On a bar chart, each block value depends on the scale of the chart. On a bar chart the blocks are not separate and instead form one solid bar.

Sometimes, a block graph may contain images of items rather than a shaded in square, almost like a pictogram. However, in this lesson, as is the case usually, each block will be shaded in.

Here is our first example of using a block diagram.

In this example we will draw a block graph to show the number of each colour counter.

We start by writing the names of the colours below each square on the bottom of the block diagram.

Each counter is worth one block.

We can take away each counter as we count it so that we do not count it twice.

As we pick up and count each counter, another block is shaded in.

Each block is worth one counter. When teaching block graphs, it can be helpful to use different colours for each category.

In this example we are using the same colour blocks as counters.

To read a block diagram, read the number which is in line with the top of each set of blocks.

It may be helpful to use a ruler. You can line the ruler up with the top of the block and read across it to see the number.

In this example, we have a table showing the favourite colours of children in a class.

We will use this table to draw a block graph.

The number of children that prefer each colour is written next to the colour in the table.

The number next to each colour is the number of blocks that need drawing.

In this example, we are given a block graph and will use it to complete the table.

This block graph shows the number of pets owned by children in a class.

The mouse column contains 2 blocks. The top of the block is in line with a 2.

This means that there are 2 mice owned by children in this class. We write a 2 in the table next to ‘mice’.

There are 4 blocks in the cat column of the block diagram. The top of this set of blocks is in line with 4.

This means that there are 4 cats owned by children in this class.

There are 3 rabbits and 3 fish.

There are 5 dogs owned in this class. This is the tallest set of blocks.

There is only 1 hamster owned in this class. This is the shortest set of blocks.

When teaching children to read block diagrams, you can start by counting the number of blocks in each column but it is worth encouraging them to simply read off the number that the top of each set of blocks is in line with.

This skill follows through into bar charts and other reading other graphs later in school life. It is also much quicker.

Identifying the longest and shortest set of blocks is also worth doing.

You will often be asked to interpret information from block diagrams.

Here is an example of a question interpreting a block graph.

Which is the most popular pet?

The most popular pet is the pet that is owned by more children than any other pet.

It will be the pet that has the most blocks in its column.

The dog has 5 blocks and so, it is the most popular pet. The dog column is the tallest because it has the most blocks.

Here is another question interpreting data from this block graph.

What is the least popular pet?

The hamster is the least popular pet because it has the fewest blocks. The hamster has the shortest set of blocks.

Only 1 person has a hamster.

In this question we are asked what is the difference between the number of dogs and the number of hamsters.

How many more dogs are there than hamsters?

We can count how many blocks are in each and find the difference.

There are 5 dogs.

There is 1 hamster.

We can count upwards on the block graph to see how many more we need to get to 5 from 1.

There are 4 more dogs than hamsters.

5 is 4 more than 1.

To find the difference in maths, we can use subtraction. Subtracting the smaller number from the bigger number tells us the difference between the numbers.

5 – 1 = 4 and so, there are 4 more dogs than hamsters.

The hands on a clock always rotate in the same direction as they move around the clock. This direction is called clockwise, or CW for short.

A clockwise turn is a turn in the same direction as the movement of the hands on a clock.

If the front of an object is facing upwards (or forwards), then a clockwise turn starts by rotating to the right.

The opposite direction to clockwise is called anti-clockwise (in English) or counterclockwise (in American English).

An anti-clockwise turn is a turn in the opposite direction to the movement of the hands on a clock.

If the front of an object is facing upwards (or forwards), then an anti-clockwise (or counterclockwise) turn starts by rotating to the left.

Quarter, Half, Three-Quarter and Full Turns in Clockwise and Anti-Clockwise Directions

Clockwise and anticlockwise turns are often taught in schools after students have mastered quarter, half, three-quarter and full turns.

Below is an animation of a car turning in the clockwise direction.

Each of the lines shown in the background divide the circle into quarters.

The car is making a clockwise turn and so, the front of the car rotates in the same direction a the hands on a clock. The front of the car begins by rotating to the right.

As the front of the car faces right, it has made a quarter turn clockwise.

As the front of the car faces downwards, it is in the opposite direction to the direction it started in. It has made half a turn clockwise.

As the car continues to rotate clockwise, it is facing left. It has made a three-quarter turn clockwise. The car is in line with the third of the quarter turn lines that it comes to.

Once the car is facing back to where it started, we say it has made a full turn clockwise. We can see that the car has rotated through the whole circle area.

We will now compare quarter turns in both the clockwise and counterclockwise directions.

Here is a quarter turn clockwise.

The car finishes facing to the right because it started facing forwards.

Here is a quarter turn anti-clockwise. The car originally is facing forwards and so, the counterclockwise rotation begins by turning to the left.

The car finishes facing left.

We can see that a quarter turn clockwise leaves the car facing in the opposite direction to a quarter turn anticlockwise.

We will now look at a half turn clockwise.

Here is a half turn anticlockwise.

We can see that both a half turn in either the counterclockwise or the clockwise direction result in the car facing in the opposite direction to which it started.

The final position of the car is the same in both half turns, however the direction taken to get there was different.

Below is an animation showing the car performing a half turn in both the clockwise and anticlockwise directions.

Here is a three-quarter turn clockwise.

The car rotates through three-quarters of a turn. We can see that three of the four quarters of the circle are shaded in.

The car is now facing left.

A three-quarter turn clockwise results in the car facing in the same final position as a one quarter turn counterclockwise.

Below is a three-quarter turn anticlockwise.

We can see that a three-quarter turn anticlockwise results in the same final position as a one quarter turn clockwise.

Below is a full turn clockwise.

The car moves in the same direction as a clock until it has reached its starting point.

The car was facing forwards to begin with and so, the car is facing forwards after a full turn.

Here is a car making a full turn anti-clockwise.

We can see that a full turn counterclockwise results in the car facing in its original position.

A full turn clockwise results in the same final position as a full turn anti-clockwise. The direction traveled to get to this position was in the opposite direction.