Teaching Writing Numbers

When starting to learn how to write each number, start by forming the correct shape of each number by drawing over the top of tracing worksheets. Eventually begin to remove the tracings and try to form the number without using anything to trace over.

It is important to focus on keeping the stroke order and direction of the number consistent. If the number is drawn in the wrong direction, it is important to correct it quickly, to prevent the wrong muscle memory from developing. Return to using the tracing worksheets if this occurs.

Trace each number using dotted tracing sheets provided, making sure that the lines of each number are drawn in the correct order. Watch the animations provided to see the order to write each number.

It is important to have a correct pencil grip. If your child can draw letters of the alphabet, then they should also be able to draw numbers. Tracing activities are also provided below to help practise the correct stroke order for each number without needing to hold a pencil.

Writing the Number 0

To write the number 0, start with your pencil at the top, in the middle. Bring it down to the left and draw a circle back to the top in an anticlockwise direction. The circle should be taller than it is wide.

Here is the animation showing how to trace the number zero.

Use the following tracing activity on your computer to practise the number zero.

Interactive Activity: Tracing Zero(For PC)

Writing the Number 1

The number 1 is drawn with 3 different straight lines. Start by drawing the first small line up to the right and immediately draw the second longer line coming vertically downwards without taking your pencil off the page. Then take your pencil off the page and draw the third line from left to right along the base of the number.

Here is the animation showing how to trace the number one.

Use the following tracing activity on your computer to practise the number one.

Interactive Activity: Tracing One(For PC)

Writing the Number 2

The number 2 is drawn without taking the pencil off the page. Start by drawing a clockwise curve and then draw diagonally downwards to the left to draw a hook shape. Finally, move the pencil horizontally to the right to draw the base.

Here is the animation showing how to trace the number two.

Use the following tracing activity on your computer to practise the number two.

Interactive Activity: Tracing Two(For PC)

Writing the Number 3

To write the number 3, draw a clockwise loop but do not return fully to the beginning. Without taking the pencil off the page, come back horizontally to the right but this time, the clockwise loop will be drawn below the first clockwise loop. Again, do not complete this second loop.

Here is the animation showing how to trace the number three.

Use the following tracing activity on your computer to practise the number three.

Interactive Activity: Tracing Three (For PC)

Writing the Number 4

To write the number 4, start by drawing a line diagonally down to the left and then without taking the pencil off the page, draw a horizontal line from left to right. Take the pencil off the page and put it back where you started drawing. Draw a line vertically downwards, crossing through the horizontal line.

Here is the animation showing how to trace the number 4.

Use the following tracing activity on your computer to practise the number four.

Interactive Activity: Tracing Four(For PC)

Writing the Number 5

To write the number 5, start at the top left and draw a small line vertically downwards. Draw a loop clockwise until the pencil almost completes a full loop. Take the pencil off the page and place it at the top, at the starting point. Draw a horizontal line from left to right to draw the top of the 5.

Here is the animation showing how to trace the number 5.

Use the following tracing activity on your computer to practise the number five.

Interactive Activity: Tracing Five(For PC)

Writing the Number 6

To write the number 6, start at the top right and draw an anticlockwise loop by moving the pencil down to the left. Continue the loop all the way around but it should finish mid-way down the first part of the loop. Do not take your pencil off the page when drawing the number 6.

Here is the animation showing how to trace the number 6.

Use the following tracing activity on your computer to practise the number six.

Interactive Activity: Tracing Six (For PC)

Writing the Number 7

To write the number 7, start in the top left and draw a horizontal line from left to right. This is the top of the seven. Without taking your pencil off the page, draw a line diagonally down to the left, finishing below the point that you started at.

Here is the animation showing how to trace the number 7.

Use the following tracing activity on your computer to practise the number seven.

Interactive Activity: Tracing Seven (For PC)

Writing the Number 8

To draw the number 8, start at the top middle and draw an ‘s’ shape. This is drawn by drawing a ‘c’ shape and then a backwards ‘c’ shape below it. Then complete the lower loop of the ‘s’ shape and finally, complete the upper loop of the ‘s’ shape. The number 8 is drawn without taking the pencil off the page.

We can draw an ‘s’ shape and then the hand motion is an ‘s’ shape in reverse. Once you have drawn an ‘s’ shape, you complete the bottom loop to get back to the middle and then complete the top loop to make the 8.

Here is the animation showing how to trace the number 8.

Use the following tracing activity on your computer to practise the number eight.

Interactive Activity: Tracing Eight(For PC)

Writing the Number 9

To write the number 9, start at the top right and draw a counterclockwise loop, completing a full loop. Then without taking the pencil off the page, draw a vertical line straight downwards.

Here is the animation showing how to trace the number 9.

Use the following tracing activity on your computer to practise the number nine.

Interactive Activity: Tracing Nine(For PC)

Writing the Number 10

The number 10 is simply made up of the digits 1 and 0.

Every number is written using the digits from 0 to 9 above. Drawing larger numbers beyond 10 is a good way to practise these learning these digits.

Here is the animation showing how to trace the number 10.

Use the following tracing activity on your computer to practise the number ten.

Interactive Activity: Tracing One(For PC)

Interactive Activity: Tracing Zero(For PC)

How to Convert Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, follow these steps:

1. Keep the denominator of the improper fraction the same as the denominator of the mixed number.
2. Multiply the whole number part and the denominator part of the mixed number together.
3. Add the numerator of the mixed number to this result to get the numerator of the improper fraction.

A mixed number is a number made up of a whole number and a fraction side by side.

An improper fraction is one fraction that has a larger number as its numerator on top than its denominator on the bottom. By contrast, a proper fraction is a fraction that has a numerator that is less than its denominator.

We can easily convert between a mixed number and an improper fraction.

Here is an example of converting a mixed number to an improper fraction. We have 2   ² / ₃  .

The first step is to keep the denominator of the mixed number the same as the denominator of the improper fraction.

The denominator of the mixed number is 3 and so, the denominator on the bottom of the improper fraction is also 3.

The second step is to multiply the whole number and denominator of the mixed number together.

The whole number part is 2 and the denominator is 3. 2 × 3 = 6.

The third step is to add the numerator of the mixed number to this result.

The numerator of the mixed number is 2. 6 + 2 = 8 and so, 8 is the numerator on the top of the improper fraction answer.

The mixed number of 2   ² / ₃  written as an improper fraction is   ⁸ / ₃  .

Here is another example of how to convert a mixed number to an improper fraction. We have 3   ⁵ / ₇.

The denominator on the bottom of an improper fraction is the same as the denominator of the mixed number. Here, the denominator is 7.

We multiply the whole number with the denominator and then add the numerator to find the numerator of the improper fraction.

3 × 7 = 21 and then 21 + 5 = 26.

The mixed number of 3   ⁵ / ₇   can be written as an improper fraction as   ²⁶ / ₇.

26 is larger than 7 and so, this is called an improper fraction.

How are Mixed Numbers and Improper Fractions Related?

Mixed numbers and improper fractions are different ways of writing the same amount. An improper fraction is written as one fraction only and it has a larger numerator on top than its denominator on the bottom. A mixed number is written as a whole number alongside a fraction.

We can see in the diagram below that the mixed number of 2   ² / ₃   is the same size as the improper fraction   ⁸ / ₃  .

The whole number part of a mixed fraction tells us how many complete numbers we have.

Here we have 2 complete blocks shown in the diagram.

The fraction of a mixed fraction tells us how many fractional parts we have.

Here we have two thirds of a block as well.

In a mixed number, the total amount shown is the whole number plus the fractional number.

2   ² / ₃   means that we have 2 wholes and two thirds of a whole added together.

Instead of counting whole numbers and fractions, we can simply count the amount shown as one fraction. We will count the number of thirds we have in total. We count how many separate pieces there are in the diagram below.

In each complete block there are 3 thirds. There are 8 thirds shown in total.

Mixed numbers can always be written as improper fractions.

The relationship between mixed numbers and improper fractions is that the denominator of both is always the same. The whole number and the denominator are multiplied and then added to the numerator of the mixed number to find the numerator of the improper fraction.

The reason that the rule for converting mixed numbers to improper fractions works is that each whole number contains the the same number of fractional pieces as the denominator.

For example, each whole number in 2   ² / ₃   contains 3 thirds.

Therefore there are 6 thirds in the 2 whole numbers.

To find the total number of fractional pieces in each whole number, simply multiply the whole number by the denominator of the fraction.

Mixed Numbers and Improper Fractions on a Number Line

To write improper fractions on a number line, keep the denominator the same and increase the numerator by 1 at each new increment. To write mixed numbers on a number line, increase the numerator by 1 at each new increment but reset it to zero at each new whole number.

When teaching mixed numbers and improper fractions, it can be helpful to show both types of number either side of a number line. This allows us to compare the two types of number much more easily.

We can convert between mixed numbers and improper fractions by listig them on a number line.

Here is a comparison of mixed numbers and improper fractions on a number line. In this example, we are going up in halves.

We start at 0 and the denominators are 2. We count up in halves. Each increment shown is worth one half.

We can see that 1 is the same as   ² / ₂   and 2 is the same as   ⁴ / ₂  .

This is because 4 ÷ 2 = 2. 4 halves are the same as 2 wholes.

We count up in thirds on the number line. We can see that at each whole number, the numerator of the mixed number is reset to 0 and we do not write it.

For example, 1 is the same as   ³ / ₃   and 2 is the same as   ⁶ / ₃  .

Here is an example of comparing mixed numbers and improper fractions on a number line by counting up in quarters.

We can see how to convert between mixed numbers and improper fractions using a number line.

1 is the same as   ⁴ / ₄   and 2 is the same as   ⁸ / ₄  .

This is because 8 ÷ 4 = 2. There are 8 quarters in 2 whole numbers.

When teaching how to convert between an improper fraction and a mixed number, diagrams and number lines are helpful tools. Number lines are used to show the comparitive sizes of improper fractions and mixed numbers.

Why Convert a Mixed Number to an Improper Fraction

It is useful to write a number as a mixed number because the whole number part allows us to better understand the size of the number. It is useful to convert mixed numbers to improper fractions when doing calculations. Improper fractions can be easier to work with in calculations than mixed numbers since they follow the normal fraction rules.

Here is the mixed number 1   ³ / ₄  .

It is useful to have a number written as a mixed number because the whole number part tells us approximately how large it is.

Since the whole number part is 1, we know that this fraction is larger than 1 but less than 2 simply by looking at it.

We can write this mixed fraction as an improper fraction.

1 × 4 = 4 and 4 + 3 = 7.

1   ³ / ₄   is the same as   ⁷ / ₄  .

We can see that the improper fraction of   ⁷ / ₄   does not immediately tell us how large the number is compared to the whole numbers. Without doing any further calculations we cannot see if   ⁷ / ₄   is larger than 1, 2, 3 or any other number.

However the fraction   ⁷ / ₄   can be easier to work with when doing arithmetic with fractions.

When adding, subtracting, multiplying or dividing fractions we usually convert mixed numbers to improper fractions. They behave just like proper fractions, which are fractions that have a numerator less than the denominator.

How to Convert an Improper Fraction to a Mixed Number

To convert an improper fraction to a mixed number, follow these steps:

1. Divide the numerator on the top by the denominator on the bottom.
2. Write the whole number part of the answer.
3. Write the remainder as the numerator of the mixed number.
4. Write the denominator of the improper fraction as the denominator of the mixed number.

An improper fraction is a fraction that has a larger numerator than its denominator. It is the opposite of a proper fraction, which has a smaller numerator than its denominator.

A mixed number is a number that is made up of 2 parts: a whole number and a proper fraction. In a mixed number the whole number is written just before the fraction. A mixed number is also known as a mixed fraction.

For example, here is the improper fraction of   ⁷ / ₃  . In this question we will write it as a mixed number.

The first step is to divide the numerator on the top of the fraction by the denominator on the bottom of the fraction.

7 ÷ 3 = 2 remainder 1. We know this because 3 × 2 = 6 and then 6 is one less than 7.

Since 3 goes into 7 twice, we write a 2 as the whole number part of the answer.

The denominator of the mixed number is the same as the denominator of the improper fraction.

Here, the denominator will be 3.

The next step is to write the remainder of the division as the numerator on the top of the fraction in the mixed number.

7 ÷ 3 = 2 remainder 1. We write the 1 as the numerator in our answer.

The improper fraction   ⁷ / ₃  is written as a mixed number as 2   ¹ / ₃  .

Why Does the Rule for Converting Improper Fractions to Mixed Numbers Work?

The rule for converting improper fraction to mixed numbers works because the number of times that the denominator goes into the numerator tells us the number of whole numbers that can be made.

Here is   ⁷ / ₃  shown as a fraction. We have rectangles divided into thirds and we have seven of these thirds shaded in.

We can see that we have 2 whole rectangles shaded in and 1 remaining third.

Because we have 2 wholes, we can write a 2.

We have one third remaining, so we write   ¹ / ₃  next to the 2.

⁷ / ₃  written as a mixed number is 2   ¹ / ₃. We simply write the fraction immediately after the whole number in a mixed number.

Examples of Converting Improper Fractions to Mixed Numbers

To write an improper fraction as a mixed number, divide the numerator by the denominator. Write the whole number part down and write any remainders as the numerator of the fraction. The denominator is the same as the denominator of the improper fraction.

For example, here is   ⁵ / ₂  .

We divide the numerator by the denominator. 5 ÷ 2 = 2 remainder 1.

We write the whole number part of the answer as 2.

The remainder of 1 goes as the numerator of the fraction. The fraction is out of 2 as the denominator is the same as the improper fraction denominator.

The improper fraction of   ⁵ / ₂  is written as a mixed fraction as   2   ¹ / ₂  .

This means that 5 ÷ 2 = 2   ¹ / ₂  .

Here is another example of converting an improper fraction to a mixed fraction.

14 ÷ 3 = 4 remainder 2. This is because 4 multiplied by 3 equals 12. 12 is 2 less than 14.

We write the 4 as the whole number part of our answer and the remainder of 2 as the numerator of the fraction.

  ¹⁴ / ₃  is written as 4   ² / ₃  .

Here is a special case of converting an improper fraction to a mixed number.

We have   ³⁰ / ₃  .

30 ÷ 3 = 10. Three divides exactly into 30. There is no remainder.

If the denominator divides exactly into the numerator, the fraction can be written as a whole number.

We simply write the answer of 3.

Since there is no remainder, we do not need to put a fraction. Writing 3   ⁰ / ₃  would look strange, so we simply write 3.