In this lesson we are learning to solve missing number problems.

A missing number problem is a number sentence in which one or more numbers need to be filled in to complete it.

We will be learning how to find missing numbers in addition sentences, which involve a plus sign ‘+’ and an equals sign ‘=’.

We will begin with an example of the most commonly seen missing number problem, in which the missing number is at the end of the number sentence, after the equals sign.

In this first type of missing number problem, the missing number is simply the answer to the addition and it looks like a regular sum.

Here is the first example:

Addition sentences all contain a plus sign ‘+’ and addition means that we combine the values of the numbers either side of the plus sign.

In this example, to find the number in the box we think:

‘what is the total of 3 add 1?’

3 + 1 = 4 and so we write the missing number 4 in the box.

If the missing number is at the end of the number sentence after the equals sign, we can simply work out the sum before the equals sign.

Here is another example like this.

Since the missing number is after the equals sign, we simply need to work out the value of the sum before the equals sign.

We can add 5 + 3 by counting on three from five.

5 + 3 = 8

We can use this example to help us work out missing number problems where the missing number is due to be added to another number.

Below we have the same example but this time we have the answer of 8 and we have a missing number to be added to the five.

The easiest way to solve this is to compare it to the previous question, in which we already knew that 5 + 3 = 8.

Knowing addition facts can help us solve these missing number problems most fluently. Addition facts are combinations of pairs of numbers that add up to a given number.

However we can also count on from 5 and see how many more numbers we need to add to 5 to reach 8.

After 5 there is 6, 7 and 8 which is 3 more numbers.

Here is another example of an addition sentence with a missing number before the equals sign.

We will first solve this missing number problem by counting on from 3 to see how many more numbers we need to add to reach 6.

Starting at 3 and counting on, the numbers are: 4, 5 and 6.

This is 3 more numbers and so we write the missing number as 3.

When teaching these missing number problems, this counting on method can help to support the addition, however the aim is to build the knowledge of number facts first to make this process easier.

Knowing the addition fact that 3 + 3 = 6 means that the missing number can be simply written in.

To help remember the addition facts such as this, you can practise working them out as you encounter them. To work out that the missing number is 3, we can simply subtract the other number from 6.

6 – 3 = 3

We can just subtract the other number that we are adding from the answer.

Here is another example of finding a missing number in this position.

To solve this problem we think:

‘what number do we add to 7 to make 9?’

If we know our addition facts then we know that:

7 + 2 = 9

Alternatively we can subtract the other given number away from the total.

9 – 7 = 2

and so, we write the missing number as 2.

In this example, the missing number is at the beginning of the number sentence.

The missing number will be the number that we add to 1 to make the total of 7.

We can start at 1 and count on until we reach 7.

Alternatively, we know the addition fact that 6 + 1 = 7 and hence the missing number in the box in 6.

The missing number is still part of the addition as it is directly next to the plus sign ‘+’.

So, to find the missing number we can subtract the other number next to the plus sign away from the total.

7 – 1 = 6

6 is the missing number that we write in the box.

Here is our last example of finding a missing number in an addition.

Again the missing number is at the start of the number sentence.

It is not so much, where the missing number is in the equation but what it is next to.

It is next to the addition sign ‘+’ and so we know that we are combining its value with the other number, 3.

We think ‘what do we add to 3 to make 7?’.

We can count on from 3 until we reach the total of 7.

We have: 3 and then 4, 5, 6, 7, which is four more numbers.

Alternatively, we know the addition fact that 4 + 3 = 7.

We write the missing number of 4 in the box.

Since our missing number is next to the plus sign, we can subtract the other number next to the plus sign away from the total.

7 – 3 = 4

When teaching finding missing numbers in addition problems, we first need to identify which kind of missing number it is.

Either the missing number is at the end of the number sentence, alone after the equals sign or it is next to the addition sign.

If the number is after the equals sign, then it will be the result of adding the other numbers in the addition sentence (provided that we have a simple addition). If the number is next to the addition sign and we are given the total then we have three main strategies:

• Count on from the other number to see how many more it is to reach the total.
• Use number facts to remember which numbers add to make the given total.
• Subtract the other number next to the addition sign away from the total.

A number sentence is used to write down a relationship between numbers. They are made up of numbers separated by mathematical symbols, such as ‘+’, ‘-‘ and ‘=’.

A subtraction number sentence will contain the subtraction sign ‘-‘ and and equals sign ‘=’.

In this lesson we will look specifically at subtraction number sentences and learn how to write them.

Below is our first subtraction number sentences example.

We start with three counters.

We will take away one counter as shown.

The word we use for taking away is subtraction. The way to say remove one counter is subtract one.

To write subtract in Maths we use the subtraction sign ‘-‘.

The subtraction sign is also sometimes called a minus sign and it means that we take away the number on its right from the number on its left.

We can write the start of our number sentence as ‘3 – 1’, which is quicker than saying ‘three subtract one’.

We are left with 2 counters remaining after the subtraction of one from three.

In words we could say ‘three subtract one is the same as two’.

The mathematical way to say ‘the same as’ is to say ‘equals’.

The equals sign is ‘=’ and it means that the value on the left is the same as the value on the right.

We have our subtraction number sentence written above as 3 – 1 = 2.

If we remove one counter from three original counters we have two remaining and this number sentence tells us that if we started with three counters and then removed one, it is the same as if we simply started with two counters.

Here is another example of a subtraction number sentence.

Here we start with 5 counters.

The subtraction sign ‘-‘ comes next and tells us that we will be taking away some counters.

The number of counters that we will be subtracting is the number after the subtraction sign.

There is a ‘2’ after the subtraction sign and so, we will be taking away 2 counters from the original 5.

We are left with three counters and so, after the equals sign ‘=’ we write a 3.

The equals sign tells us that the amount on the left of the ‘=’ sign is the same as the amount on the right of the ‘=’ sign.

Starting with 5 counters but then removing 2 counters results in exactly the same as if we just started with 3 counters.

Here is another subtraction sentence example.

Since our missing number is after the equals sign, we want to know which number is the same as 6 – 5.

This means ‘six subtract 5’ and this means start with six counters and take away 5 counters.

We can see that we are left with one counter and so, 1 is the same as 6 – 5.

We write 1 at the end of our subtraction sentence as the answer.

Here is our final subtraction number sentence example and we want to know what symbol to put in the empty box.

We can’t put another number directly next to another number. We need to separate the numbers in our number sentence with mathematical symbols such as ‘+’, ‘-‘ and ‘=’ signs.

Here we have 4 counters and are removing 2 counters.

On the right we have 2 counters.

We start the subtraction number sentence with ‘4 – 2’ and so we can work this out.

4 subtract 2 leaves us with 2 counters remaining.

Therefore 4 – 2 is the same as the ‘2’ we have on the right.

To show that 4 – 2 and 2 are the same value, we can put an equals sign in between them.

We have 4 – 2 = 2.

We read this subtraction sentence as ‘four subtract two equals two’.

A number sentence is just a combination of numbers and mathematical symbols.

Some common mathematical symbols used in number sentences are:

• The plus sign (or addition sign): ‘+’
• The minus sign (or subtraction sign): ‘-‘
• The equals sign: ‘=’
• The less-than sign: ‘<'
• The greater-than sign: ‘>’

In this lesson we are only looking at addition number sentences, which will only contain the plus sign ‘+’ and the equals sign ‘=’.

Below is our first example of forming an addition number sentence.

We start with three counters on the left.

We also have two more counters.

We can collect all of the counters together and count them to see how many we have altogether in total.

Counting the counters, we have 5 in total. Three counters and two more makes a total of 5 counters.

We say that we have added three and two together.

Instead of writing down ‘three add two’ it is quicker to write ‘3 + 2’, where the ‘+’ sign is called a plus sign or an addition sign.

When teaching addition to children it is important to remember that the plus sign must separate the two numbers that we wish to combine together.

The next sign that we use is an equals sign, which is written as ‘=’.

Here the equals sign tells us that 3 and 2 combined together is the same as 5. Writing an equals sign means that the total value on the left of the equals sign is the same as the total value on the right of the equals sign.

It tells us that if we are given 3 counters and then 2 more counters, it is exactly the same as being given 5 counters straight away.

We use an equals sign to show that we have a correct number sentence.

We can see below that it is ok to write and equals sign between 3 + 2 and 5 but not in between 3 + 2 and 9.

We would actually use the ‘not equal to’ sign: ‘≠’ to show that 3 + 2 does not equal 9.

Below is another example of a correct addition number sentence.

We have 4 counters and then 3 more.

We will add the 4 counters to the three counters. Remember that this means that we want to see how many counters that we have in total and we write a plus sign ‘+’ in between the 4 and the 3.

If we count the total number of counters, we can see that there are 7.

To show that 4 add 3 is the same value as 7, we write an equals sign in between the 4 + 3 and the 7.

It is very common that the equals sign will appear directly before the ‘answer’ of a sum and whilst it can be helpful to think of the equals sign as meaning ‘the answer is’, it just means that whatever is on the left of this sign is the same value as whatever is on the right of the equals sign.

For example we could have written the addition number sentence the other way around:

Whilst it is not so common in school questions to have one number on the left of an equals sign and more than one number on the right, this is still a completely correct addition number sentence.

It just states that seven is the same value as four plus three more.

Furthermore, it is possible to have an addition on both sides of the equals sign, such as in the example below:

4 + 3 = 6 + 1 means that having 4 counters and then being given more 3 counters is exactly the same as having 6 counters and being given one more.

Either way, we have 7 counters. Both sides of the equals sign are equal to 7 and so an equals sign can be used to separate the left and right sides.

In the example below we have all of the numbers in our addition number sentence.

We have three numbers given to us, 2 , 2 and 4.

We are asked to completed the number sentence by filling in the blank.

It cannot be another number that goes in this box.

We know this since we do not put two numbers directly next to each other in a number sentence. We separate numbers with mathematical symbols.

We can see that we have 2 + 2. The plus sign tells us that we are combining the two numbers directly either side of the + sign together to make a total.

2 + 2 is 4 in total.

We have a 4 written in the number sentence at the end on the right. 2 + 2 is the same value as 4 and so we show this by writing an equals sign in between 2 + 2 and 4.

In this last example we are given three numbers: 5, 3 and 8.

We are asked to complete the number sentence by filling in the box in between the 5 and the 3.

Remember that we cannot put another number here directly next to other numbers. Therefore we are choosing a mathematical symbol to go here.

We can see that combining 5 counters with 3 counters is exactly the same as having 8 counters.

The word for the process of combining these counters to make a total is addition.

We add the 5 and the 3.

And so we put an addition sign or a plus sign in between the 5 and the 3 to show that we are combining them to make a total that is equal to 8.

This addition number sentence is read as ‘five add three equals eight’ and it means that combining 5 counters with 3 more counters is the same as simply having 8 counters from the start.

In this lesson, we will look at placing decimals on a number line. Specifically we will be counting in tenths on a number line.

In the animation below, we have a number line ranging from zero to one. To get from zero to one, there are ten equal steps, marked with a line.

We have divided a whole number into 10 parts. This means that we will be counting up in tenths, or 0.1s.

The first line on the scale corresponds to an increment of 0.1, which is the same as one tenth.

The second line is 0.2, which is two tenths.

The third line is 0.3, which is three tenths.

The fourth line is 0.4, which is four tenths.

The fifth line is 0.5, which is five tenths. This thicker line indicates that it is the halfway point between 0 and 1.

The sixth line is 0.6, which is six tenths.

The seventh line is 0.7, which is seven tenths.

The eighth line is 0.8, which is eight tenths.

The ninth line is 0.9, which is nine tenths.

The tenth line is 1, which is the same as ten tenths, or one whole.

We can see that to move from one line to the line to its right, we simply add 1 to the digit after the decimal point.

In the following animation, we will look at the decimal numbers between one and two on a number line. The following scale is the same as the previous, with ten equal increments.

Therefore, we will be counting in tenths, or 0.1s.

1 is the same as 1.0 but we simply write 1.

2 is the same as 2.0 but we simply write 2.

Starting from 1, we have 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 and 2.

We increase the digit after the decimal point by 1 at each new line.

It can be easy to visualise this in a similar way to counting past ten in whole numbers. If we ignore the decimal point, it is like counting 11, 12, 13, 14, 15 etc.

The thicker line, labelled as 1.5, indicates the halfway point between 1 and 2.

In the example below, we are asked to label the numbers on the scale that are indicated by the arrows. The scale ranges from two to three. We have the same number of increments, so we will be counting in tenths, or 0.1s.

To find the valued of the decimals marked on the number line with arrows, we can begin by counting up in 0.1s.

Starting from 2, we have 2.1, 2.2, 2.3 and 2.4. Our first answer is 2.4.

Continuing to count in 0.1s, we have 2.5, 2.6 and 2.7.

Our second answer is 2.7.

In the example below, we have another scale with ten increments. We will therefore be counting up in 0.1s (tenths) to find the values of the marks indicated by the arrows.

Starting from 14, we have 14.1 and 14.2, which is our first answer.

Continuing from 14.2, we have 14.3, 14.4, 14.5, 14.6, 14.7, 14.8 and 14.9, which is our second answer.

We could have also found 14.9 by counting back from 15.

In our final example below, we are not given the number on the left-hand-side of the scale. However, looking at the scale, there are still ten steps to get to the number on the right-hands-side, which is 20.

We are also given the values 19.3 and 19.4. We therefore know that the increments are tenths, so we will be counting in 0.1s.

If we count backwards from 19.3, we have 19.2, which is our first answer. We can continue to count backwards, and we have 19.1 and 19.

Next, we can count on from 19.4. we have 19.5, 19.6, 19.7 and 19.8.

To get 19.8, we could have also counted back from 20 (20, 19.9, 19.8).

How to Convert Centimetres to Millimetres

To convert centimetres to millimetres, multiply by 10. Every centimetre is worth 10 millimetres. For example, 5 cm = 50 mm because 5 × 10 = 50.

5 cm is the same as 50 mm.

5 cm = 50 mm

To multiply a whole number by 10, we can simply write a 0 on the end. 5 cm becomes 50 mm.

This trick to multiply by 10 will only work for whole numbers and will not work for decimal values.

Here is an example of converting centimetres to millimetres with a decimal number.

We are asked to convert 1.2 centimetres into millimetres. To convert cm to mm, we multiply the value by ten.

1.2 x 10 = 12

So, 1.2 cm is the same as 12 mm.

1.2 cm = 12 mm

We can see where 1.2 cm and 12 mm lie on the ruler in the clip below.

Notice that if we simply ‘added a zero’ to the end of the 1.2 decimal value, this would not have multiplied it by ten. We would have calculated an incorrect answer.

This is because 1.2 is the same value as 1.20.

A trick to help us multiply a number with only one decimal place can be to move the digit after the decimal point in front of the decimal point.

This has the same effect as simply removing the decimal point from our answer.

1.2 cm becomes 12 mm.

If you need further practice of multiplying a decimal number by 10 and wish to understand why this trick works, please watch our lesson on Multiplying by 10, where we explore this topic further.

In the following example, we have a decimal number. We are asked to convert 2.8 centimetres into millimetres. To convert cm to mm, we multiply by ten.

2.8 x 10 = 28

So, 2.8 cm is the same as 28 mm.

2.8 cm = 28 mm

We can see where 2.8 cm and 28 mm lie on the ruler in the clip below.

Again notice that ‘adding a zero’ will not work for multiplying a decimal number by 10.

Instead, you could use the trick for numbers that contain only one decimal place and remove the decimal point.

28 mm is shown on the ruler above as 28 individual millimetre marks away from the zero mark or simply 8 mm away from the 2 cm mark.

Centimetres to Millimetres on a Ruler

Each number written on a ruler is in centimetres. Millimetres are the smallest lines shown on a ruler in between each centimetre. There are ten millimetre lines between each centimetre.

Centimetres are written as ‘cm’ for short.

Millimetres are written as ‘mm’ for short.

Write a space between the number and the ‘mm’ or ‘cm’.

In the following example, we are asked to convert 8 cm into millimetres. We will convert cm to mm using a ruler.

To convert a length in centimetres into a length in millimetres, multiply the value in centimetres by ten.

To convert cm to mm, we multiply by ten.

8 x 10 = 80

So, 8 cm is the same as 80 mm.

8 cm = 80 mm

In the following example, we are asked to convert 11 cm into millimetres. To convert cm to mm, we multiply by ten.

11 x 10 = 110

So, 11 cm is the same as 110 mm.

11 cm = 110 mm

Teaching Converting cm to mm

When teaching converting centimetres to millimetres, it is helpful to use a large ruler to show the mm and cm increments. Using a large ruler or an interactive ruler online can be an easier way to show the comparison because mm on real rulers can be very small.

Below, we have a 15 cm ruler. We use it to measure a length in centimetres.

The distance between each number that is written on the ruler is one centimetre (1 cm).

The smaller divisions between each number are millimetres (mm).

The millimetre markings are the smallest lines on the ruler.

The distance between 0 and the first mark is one millimetre (1 mm).

The distance between 0 and the second line is two millimetres (2 mm).

The distance between 0 and the third line is three millimetres (3 mm).

This continues as we count along the millimetre lines of the ruler as can be seen in the image below.

Ten millimetres is at the same mark as the one centimetre mark.

So, we can see that 1 cm is the same length as 10 mm.

To convert from 1 cm to 10 mm, we multiply by ten.

There are 10 millimetres in one centimetre.

1 x 10 = 10

So, to convert centimetres to millimetres (to convert cm to mm), multiply the value in centimetres by ten.

Lattice multiplication is an alternative multiplication method to long multiplication or the grid method. Lattice multiplication is used to work out the multiplication of larger numbers.

We will introduce lattice multiplication by looking at a simple example to understand how to lay out the working out.

We will consider the example of ‘3 x 4’ using lattice multiplication and we begin by drawing a square. We then draw a diagonal line from the top right corner to the opposite corner in the bottom left.

3 x 4 = 12

We always write the units (or ones) of the answer to the bottom right of the diagonal line. So, we write ‘2’ in the orange shaded triangle.

We always write any tens of the answer in to the top left of the diagonal. So in this example, we write ‘1’ in the green shaded triangle shown.

If there are no tens in the answer, we write a zero to the left of the diagonal.

This is how we represent the number 12 in a lattice.

We can use this lattice structure to help us to multiply two 2-digit numbers.

Lattice Multiplication Example 1: 42 x 35

We begin by arranging the digits of 42 and 35 as shown in the image below, one number written on the top of the grid and the other number written on the right of the grid.

Each digit is lined up with its own box.

Next, we multiply each of the digits of 42 by each of the digits of 35. We write the answer to each multiplication in the corresponding square.

1) 4 x 3 = 12

2) 2 x 3 = 6

3) 4 x 5 = 20

4) 2 x 5 = 10

Notice that when we multiplied 2 x 3 to make 6, we still wrote a ‘0’ to the left of the diagonal line.

This is so that we know that we have worked out this multiplication already, whereas if we left a blank space, we might think that we have made a mistake or missed it out by mistake.

Once we have multiplied all of the digits and filled every box in the grid, we add the digits that are in each diagonal.

We add the numbers in each diagonal starting with the bottom right diagonal and moving left.

1) In the first diagonal, we have just zero. So, we write ‘0’ below.

2) In the next diagonal, we have zero, one and six.

0 + 1 + 6 = 7

So, we write ‘7’.

3) In the next diagonal, we have two, two and zero.

2 + 2 + 0 = 4

So, we write ‘4’.

4) In the final diagonal, we have one. So, we write ‘1’.

Once we have found the total of each diagonal, we now read the digits from left to right.

The digits that we have are: 1, 4, 7 and 0.

Therefore, 42 x 35 = 1470.

Lattice Multiplication Example 2: 56 x 35

We begin by arranging the digits of 56 and 35 as shown in the image below with one number written on the top of the lattice and the other number written on the right of the lattice.

We write each digit in line with the boxes.

Next, we multiply each of the digits of 56 by each of the digits of 35. We write the answer to each multiplication in the corresponding square.

Remember that we write the tens of each answer on the left of the diagonal in each box and the units of each answer on the right of the diagonal.

1) 5 x 3 = 15

2) 6 x 3 = 18

3) 5 x 5 = 25

4) 6 x 5 = 30

Now that all of the lattice squares have been completed, we add the diagonals, working from right to left.

1) In the first diagonal, we have just zero. So, we write ‘0’ below.

2) In the next diagonal, we have five, three and eight.

5 + 3 + 8 = 16

So, we write ‘6’ in this diagonal and carry the 1 over to the next diagonal.

3) In the next diagonal, we have two, five, one and the one that we carried.

2 + 5 + 1 + 1 = 9

So, we write ‘9’.

4) In the final diagonal, we have one. So, we write ‘1’.

We read the totals from left to right and the digits that we have are 1, 9, 6 and 0.

So, 56 x 35 = 1960

Lattice Multiplication Example 3: 86 x 67

We begin by arranging the digits of 86 and 67 as shown in the image below, with 86 written above the lattice and 67 written to the right of the lattice.

Next, we multiply each of the digits of 86 by each of the digits of 67. We write the answer to each multiplication in the corresponding square.

1) 8 x 6 = 48

2) 6 x 6 = 36

3) 8 x 7 = 56

4) 6 x 7 = 42

Now that we have multiplied all numbers in the lattice, we will add the numbers in the diagonals starting from the bottom right diagonal.

1) In the first diagonal, we have two. So, we write ‘2’ below.

2) In the next diagonal, we have six, four and six.

6 + 4 + 6 = 16

So, we write ‘6’ in this diagonal and carry the 1 over to the next diagonal.

3) In the next diagonal, we have five, eight, three and the one that we carried.

5 + 8 + 3 + 1 = 17

So, we write ‘7’ in this diagonal and carry the 1 over to the next diagonal.

4) In the final diagonal, we have four and the one that we carried.

4 + 1 = 5

So, we write ‘5’.

In the lattice multiplication method, we read the totals from left to right and the digits that we have are 5, 7, 6 and 2.

So, 86 x 67 = 5762

The lattice multiplication method is sometimes known as the Chinese method or Gelosia multiplication.

These methods are different names for the lattice multiplication method learnt above and you can print blank lattice method grids which are also available to download above for further practice of this topic.

A millimetre is a measurement of length, which is one tenth of a centimetre long. There are 1000 millimetres in one metre and ten millimetres in one centimetre.

Millimetres are often abbreviated to just ‘mm’ for short in the same way that centimetres are abbreviated to ‘cm’.

Each number that is written on a ruler is one centimetre in length.

Between each of the centimetre lines, there are many smaller lines that do not have numbers written on them.

Each of these smallest lines are millimetres and each line is one millimetre in length away from the line next to it.

Below is a ruler with one millimetre (or 1 mm) shown.

Remember that when measuring a length with a ruler, we start from the first line on the left of the ruler, which is the zero line.

The two red lines marked are one millimetre apart.

Since this is the first line we come to after 0, it is 1 mm.

We can continue to count these lines on our ruler.

Here is the second small line and so, this is 2 mm away from zero.

We can count further and this line below is 5 mm.

This line is slightly longer than the 1 mm, 2 mm, 3mm and 4 mm lines and slightly less than the 0 and 1 cm lines.

5 mm is half way in between 0 and 1 cm.

Therefore 5 mm is half of a centimetre.

The line is slightly longer so that it stands out and we can read half a centimetre more easily.

Once we count past 5 mm, we can count 6 mm, 7 mm, 8 mm, 9 mm and eventually get to 10 mm below.

Once we have counted 10 of the smallest lines, we have counted 10 mm.

We can see that we are on the 1 cm line, marked with a ‘1’.

10 mm is the same length as 1 cm.

Every centimetre on a ruler is worth 10 mm.

We will now look at an example of measuring an object in millimetres.

Our first example will be an object with a length that is less than 1 cm long.

Here we have a button and we will measure its width by lining up the leftmost part of the button with the zero line on the ruler as shown below.

We count the number of lines that we have until the lines on the ruler line up with the rightmost part of the button.

There are 8 lines and so, the button is 8 mm wide.

We could have counted 8 lines from zero, or we could have looked at the 5 mm line that is in the middle of 0 and 1 cm. From here we have another 3 millimetre lines.

5 mm + 3 mm = 8 mm

Alternatively, we could have seen that the button is almost at the 1 cm line.

The button lines up with a line that is 2 lines away from 1 cm.

1 cm is worth 10 mm and we could have subtracted 2 mm from 10 mm to get to 8 mm.

Below is an example of measuring the side length of a die.

Again we line the left side of the die up with the zero line on the ruler.

The die is 16 mm long.

We could have got this by counting 16 individual lines but this can be quite slow and it is easier to make a mistake in your counting.

The 1 cm mark is worth 10 mm.

We could have counted on 6 more millimetre lines from 10 mm to make 16 mm.

Alternatively, we know that the slightly longer line after the 1 cm mark is another 5 mm.

This is 15 mm, directly in between 1 cm and 2 cm.

The die length is one more line after the 15 mm mark and so it is 16 mm long.

Again we could have also realised that the right side of the die is 4 millimetre lines to the left of the 2 cm mark.

2 cm is worth 20 mm and if we count down 4 places from 20, we get to 16 mm.

We have included this final example to cover another mistake that children might encounter when measuring an image in a book.

The image is showing a 3D die and some children may measure the image all the way to the right hand side, not realising that this is the depth of the die.

It is important to explain that the length we are actually measuring is just the front edge and possibly show them a real die if they are making this mistake.

Centimetres are units of measurement that we commonly see on rulers and are written with the abbreviation ‘cm’.

Centimetres help to describe how long an object is.

Below is a 15 centimetre ruler. It has numbers from 0 to 15 and each number is a centimetre apart from the number next to it.

Centimetres are one of the common metric units of measurement and they are easy to compare to millimetres, metres and kilometres when we describe how long a distance is.

All of these words end in ‘metres’ so we know that we can compare them.

Some rulers have ‘inches’ on the other side and we cannot compare centimetres to inches as easily.

We typically write centimetres as ‘cm’ for short, with a space between the number and the ‘cm’.

The ruler itself is slightly longer than 15 cm, however the distance from the 0 line to the 15 line is 15 cm.

It is important to measure objects using the measurement lines on the ruler.

We always start from the ‘0’ line on the ruler and we line our objects up with this point.

A common mistake when learning to measure objects with a ruler is to not line up the object with the zero correctly.

When teaching measuring with a ruler it is important to stress that the measurement is taken from the zero mark and not the edge of the ruler.

Here is our first example of measuring centimetres using a ruler.

We will measure the length of this pencil sharpener.

Remember to line up the left edge of the pencil sharpener with the zero line.

The pencil sharpener’s right edge lines up with the 1. This means that the pencil sharper is 1 cm across in width.

Here is another example of measuring centimetres with a ruler.

We line up the left of the eraser with the zero line on the ruler.

The right hand side of the eraser lines up with the 4 on the ruler and so, the length of the eraser is 4 cm.

The final example of measuring centimetres using a ruler is given below.

We will measure the length of this pencil by lining its left tip up with the zero mark.

The right most tip of the pencil lines up with the 14 line and so, the pencil is 14 cm long.