Roman Numerals to 20

Roman Numerals to 20

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Roman Numerals Chart 1 to 10

Before learning the numerals 11 to 20 first watch our lesson on Roman Numerals 1 to 10.

roman numerals 1 to 10 chart

Roman Numerals Chart 11 to 20

Roman Numerals 11 to 20 chart

  • The Roman numerals 11 to 20 are simply ten larger than the Roman numerals 1 to 10.
  • We start with the numeral ‘X’, which is worth 10.
  • We add the numerals for 1-10 after this X.

The Roman numerals 11 to 20 are simply the same as the Roman Numerals 1 to 10 but with an X numeral in front.

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17 written in Roman Numerals

  • XVII is made of the numerals X, V and two I‘s.
  • X is worth 10, V is worth 5 and I is worth 1.
  • XVII is the same as 10 + 5 + 1 + 1.
  • XVII is worth seventeen.
  • VII is 5 + 1 + 1, which equals 7.
  • If we know that VII is 7, then we can make 17 by simply writing an X numeral in front.

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Roman Numerals to 20 Interactive Question Generator

Roman Numerals to 20: Interactive Questions

Roman Numerals to 20 Worksheets and Answers

Writing Roman Numerals to 20

The Roman numerals to 20 are made up of the following three numerals.

roman numerals I V and X

  • I = 1
  • V = 5
  • X = 10
  • We can add up to three of the same numeral together in a row to make larger numbers.

    For example, two I numerals is two lots of one and makes a total of 2.

    2 is written as II in Roman numerals.

    2 in roman numerals

    We can write III as 3. This is because we have three I numerals. 1 + 1 + 1 = 3.

    3 in roman numerals

    We cannot write 4 as IIII because it uses four I numerals. The most we are allowed to use together is three.

    Instead we write 4 as IV, which is an I before a V, which means 1 before 5.

    4 in roman numerals

    We can count on from 5 to make larger numbers.

    VI means V plus I, which means 5 plus 1.

    VI is 6 in Roman numerals.

    6 in Roman Numerals

    Similarly 7 is written as VII because V + I + I means 5 + 1 + 1.

    8 is VIII because V + I + I + I means 5 + 1 + 1 + 1.

    Again we can’t write 9 as VIIII because it uses four of the same numeral at once. We are only allowed to write three of the same numeral at once.

    Instead, 9 is written as 1 before 10. We write IX because I is 1 and X is 10.

    Here are the Roman numerals to 10. Please visit our lesson on Roman numerals 1 to 10 for our video lesson. When teaching the Roman numerals to 20, we recommend first learning these numerals to 10.

    roman numerals chart of numerals 1 to 10

    11 is ten more than 1, 12 is ten more than 2, 13 is ten more than 3 and so on.

    The numbers 11 to 20 are simply 10 more than the numbers 1 to 10.

    To write the Roman numerals to 20, simply add the numerals for the numbers 1 to 10 to the numeral X.

    X is worth ten and when writing any numerals after this, it will add ten to those numerals.

    Here are the Roman numerals 11 to 20 formed by writing an X numeral in front of the numeral that is 10 less in value.

    Roman Numerals to 20 chart

    For example, 11 is ten more than 1.

    The numeral for 1 is I.

    Therefore to write 11, we write an X and then the numeral for 1.

    11 is written as XI in Roman numerals.

    11 in Roman Numerals

    XI means X + I, which is 10 + 1.

    10 + 1 = 11.

    Similarly, 15 is ten more than 5.

    Therefore to write 15, we write an X and then the numeral for 5.

    The numeral for 5 is V.

    15 is written as XV in Roman numerals.

    15 in Roman Numerals

    XV is X + V, which means 10 + 5.

    It is important to note that we always need to write the larger numerals first when adding Roman numerals.

    We have to write XV in that order because X is worth 10 and V is only worth 5.

    We cannot write V then X as it breaks this rule. We simply write an X and then the smaller value numerals.

    Here we have XVII.

    This means X + V + I + I, which means 10 + 5 + 1 + 1.

    XVII are the Roman numerals for 17.

    17 in Roman numerals

    VII is 7 and so, if we remember how to write 7, then we simply write an X in front to make 17.

    Remember that 4 is written as IV because we can’t use four I numerals.

    IV is one before five, which is four.

    XIV is simply IV with an X numeral before it.

    XIV is X + IV, which means 10 + 4.

    14 in Roman Numerals

    Remember that we only add Roman numerals when they are decreasing in size.

    I is less than V and so we do not add IV to make 6.

    Instead we subtract I from V to make 4. It is easiest to read IV as 1 before 5.

    6 is 1 after five, which is written as VI.

    Here is the final list of the Roman numerals for 11 to 20. We can see the numeral X highlighted in blue, with the numerals following shown in red.

    Roman Numerals to 20 list

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Now try our lesson on Rounding Off to the Nearest 10 on a Number Line where we learn how to round numbers to the nearest ten.

Roman Numerals 1 to 10

Roman Numerals 1 to 10

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Roman Numerals Chart 1 to 10

roman numerals chart 1 to 10

  • This is a list of the Roman numerals 1 to 10.
  • I is the Roman numeral for 1.
  • V is the Roman numeral for 5.
  • X is the roman numeral for 10.
  • We can use any of the numerals I, V or X up to three times in a row.
  • We can add a numeral by writing it to the right of another.
  • Two ‘I’ numerals is 2 and three ‘I’ numerals is 3.
  • We can subtract 1 from 5 or 10 by writing I to the left of V or X.
  • 4 is written as IV, which is one before five.
  • 9 is written as IX, which is one before ten.

I = 1, V = 5, X = 10.

We can add these numerals together up to 3 times in a row to write other numbers.

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Writing 2 in Roman Numerals

  • I is the roman numeral for 1.
  • We can add multiple I numerals together by writing them next to another.
  • We have two I numerals, which is 1 + 1.
  • II is worth 2 in Roman numerals.

Writing 4 in Roman Numerals

  • I is worth 1 and V is worth 5.
  • We can subtract from V by writing I before it.
  • We have an I before a V which means 1 before 5.
  • 1 before 5 is 4.
  • IV is worth 4.

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Roman Numerals 1 to 10 Interactive Question Generator

Roman Numerals 1 to 10: Interactive Questions

Roman Numerals 1 to 10 Worksheets and Answers

Roman Numerals 1 to 10 Explained

What are Roman Numerals

Roman numerals are a different system of writing numbers. Instead of using the digits of 1, 2, 3, 4, 5, 6, 7, 8, 9 or 0, Roman numerals use the capital letters of the alphabet: I, V, X, L, C, D and M.

To write larger numbers, numerals can be added by writing them next each other.

Roman numerals to 10 are written using the three numerals of I, V and X.

I is the first Roman numeral. I is the roman numeral for 1.

1 in roman numerals I

1 in Roman Numerals

We can add two ones together to make 2. We add numerals by writing them next to each other.

II is made from two I numerals. II means 1 + 1.

2 in roman numerals

II is worth 2.

2 is written as II in Roman numerals. writing 2 in roman numerals

We can add up to three of each numeral.

We can add three I numerals to make III.

III means 1 + 1 + 1.

3 is written as III in Roman numerals.

writing 3 in roman numerals.

We can only use three Roman numerals together at once.

We have already used three I numerals to make III.

To make larger numbers, we need to use the numeral of V.

V is the Roman numeral for 5.

writing 5 in roman numerals as V

So far we have:

I = 1

II = 2

III = 3

V = 5

5 in roman numerals

4 is written a little differently in Roman numerals.

We are not supposed to write more than 3 of the same numeral together. We can’t write IIII for 4 because this contains more than three I numerals.

Instead we use the fact that 4 is one less than 5.

We can write 4 as one less than five.

Roman Numerals 1 to 5

We write 4 as one before five. 1 is written as ‘I’ and 5 is written as ‘V’.

To write 1 before 5, we write I before V.

4 in roman numerals

4 is written as IV in Roman numerals.

4 written in roman numerals

Here is a chart showing the Roman numerals to 5.

Roman numerals to 5 chart

We have I for 1, II for 2, III for 3, IV for 4 and V for 5.

Roman Numerals chart for the numbers 1 to 5

To make the numbers larger than 5 using Roman numerals, we count on in ones from five.

5 is written using the numeral of V.

We can count on from five using the numeral of I. We can use up to three I numerals at once.

6 is one more than five. To write one more than five, we write an I after a V.

6 is Roman numerals is VI. VI is V + I, which is 5 + 1.

6 in roman numerals

7 is two more than five. To write two more than five, we write two I numerals after a V numeral.

7 in Roman numerals is VII. VII is V + I + I, which is 5 + 1 + 1.

8 is three more than five. To write three more than five, we write three I numerals after the V numeral.

8 in Roman numerals is VIII. VIII is V + I + I + I, which is 5 + 1 + 1 + 1.

Roman Numerals chart showing numbers to 10 in numerals

The Roman numeral for 10 is X.

10 in roman numerals is X

In the same way that we wrote 4 as IV, we write 9 as IX.

9 in roman numerals as IX

We cannot write VIIII for 9 because it would mean using four I numerals. We are only allowed to use three at most.

We write 9 in Roman numerals as IX, which is an I before an X. 1 before 10 is 9.

Both 4 and 9 are different to the other Roman numerals because they have an I before another numeral.

4 is one before 5 and so is written IV.

9 is one before 10 and so is written IX.

These are the only numbers in the list of Roman numerals to 10 that behave like this.

When teaching Roman numerals, 4 and 9 are most commonly written incorrectly.

Some students can think that IV is 1 + 5, rather than reading it as 1 before 5.

It is important to show the difference between 4 and 6.

4 is IV and 6 is VI. If a smaller numeral is written before a larger value numeral then we subtract the smaller numeral away from the larger numeral.

There is no Roman numeral for zero.

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Now try our lesson on Roman Numerals to 20 where we learn how to read and write Roman numerals up to 20.

Comparing Number Sentences using <, > and =

Comparing Number Sentences using <, > and =

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Comparing Number sentences example ks2

  • Here we need to fill in the missing symbol between 30 + 10 and 80.
  • We work out the addition sum on one side of the missing symbol.
  • 30 + 10 = 40.
  • We can see that 40 is to the left of 80 on the number line.
  • 40 is less than 80 and so we use the less than sign, ‘<'.
  • We say that 30 + 10 < 80.
  • The less than sign always points at the smaller number and opens up to the larger number.

Work out the sum on one side of the missing symbol box.

Insert a less-than or greater-than symbol which points at the smaller value side.

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Comparing subtraction sentence using less than and greater than signs example

  • We first work out the side which has the subtraction sum.
  • 20 – 2 = 18.
  • 18 is further to the right of 15 on the number line.
  • 18 is greater than 15 and so 15 is less than 18.
  • We use the less-than symbol, ‘<' to say that 15 is less than 18.
  • We write 15 < 18 and so 15 < 20 - 2.
  • The less-than sign always points to the smaller value and opens to the larger value.

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Comparing Number Sentences Missing Symbol Worksheets and Answers

How to Compare Number Sentences using Greater-Than and Less-Than Signs

We use less-than and greater-than signs to compare numbers.

‘<' is the less-than symbol.

‘>’ is the greater-than symbol.

less than greater than

Each sign is chosen in a number sentence so that the symbol points to the side that has the smallest value.

Each symbol then opens up to the side that has the greatest value.

We can use a number line to decide which side of a number sentence has the greatest value.

When teaching comparing number size, a number line is useful to help visualise the size of each value.

Here are the multiples of 10 from 0 to 100 shown on a number line.

multiples of ten from 0 to 100 shown on a number line

When comparing number sentences at KS1 and KS2 (up to fourth grade), most children will be expected to use greater-than or less-than symbols for numbers up to 100.

In this example we have a missing symbol between 30 + 10 and 80.

We first evaluate the addition sum on the left of the missing symbol problem.

30 + 10 = 40.

Comparing Number sentences to 100 example using a number line

40 is less than 80 because it is further left on the number line.

We can use the less-than symbol ‘<' to write this mathematically.

We can think of the symbol like an arrow, pointing to the smaller value. We can also think of it as an open mouth opening up to the larger value.

We can write 40 < 80.

40 is the smaller number and so, the less-than symbol points at 40.

Because 40 < 80, we can also write 30 + 10 < 80.

Here is our next example of comparing number sentence values.

We have a missing symbol between 90 + 4 and 60.

example of comparing number sentences using a greater than sign

We first work out the value of 90 + 4.

90 + 4 = 94, which is to the right of 60 on the number line.

This means that 94 is greater than 60.

We use the greater-than symbol, ‘>’ to write this comparison mathematically.

60 is smaller than 94 and so, the arrow will point at 64. The ‘mouth’ will open up to the larger value of 94.

We can write 94 > 60 to say that 94 is greater-than 60.

Because 94 > 60, we can also write 90 + 4 > 60.

In this next example of comparing a subtraction sentence we have a missing symbol between 15 and 20 – 2.

We first evaluate the subtraction of 20 – 2.

Comparing a subtraction sentence using less than sign example

20 – 2 = 18, which is to the right of 15 on the number line.

18 is greater-than 15 and so the symbol opens to the 18 and points to the 15.

We can write 15 < 18 and so, 15 < 20 - 2.

In this next example we have a missing symbol between 12 + 14 and 26.

We first evaluate the addition of 12 + 14.

using an equals sign in a missing symbol number sentence problem

12 + 14 = 26, which is the same as on the other side of the number sentence.

12 + 14 is the same value as 26 and so, we use an equals sign ‘=’ to show this.

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Now try our lesson on Rounding Off to the Nearest 10 on a Number Line where we learn how to round to the nearest 10.

Giving Change

Giving Change

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Giving Change from 50p example

  • This toy costs 45 pence but we only have a 50p coin.
  • We cannot pay 45 pence exactly and so we pay with the 50p coin.
  • 50p is 5 pence more than 45p.
  • We will be given this 5 pence back as a 5p coin.
  • The money we are given back is called change.
  • Since we started with 50p and now have 5p, our money has gone down by 45 pence.

Change is the money given back if you pay more than an item costs.

These happens when you do not have the exact amount of money.

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Giving Change example with pence coins

  • We have 10p + 10p + 10p + 5p, which makes 35 pence in total.
  • This banana costs 32 pence.
  • We have more than 32 pence but we cannot pay for the banana exactly.
  • 35 – 32 = 3.
  • 35p is 3 pence more than the cost of the banana.
  • We are given this 3 pence back as change.
  • There is no 3 pence coin and so, the change is given back as a 2p coin plus a 1p coin.

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Giving Change Worksheets and Answers

Giving Change with British Money

What is change?

Money comes in certain values which are written on coins or notes. Because of this it is unlikely that you will always be carrying the exact amount of money needed to pay for something.

If this is the case then we need to pay more than the cost of the item and then get the extra money back.

The money given back is called change. Change is the difference between the cost of the item and the money given to pay for it.

In the example below we have four coins: three 10p coins and one 20p coin.

In total this is 50 pence.

We want to buy a spinning top for 30 pence.

Giving Change when buying a toy with pence

We can pay for the spinning top with 30p from our 50 pence. We can pay using the three 10p coins.

In this example, we have 20p left. We were able to pay for it directly with the coins we had and so, we were not given change.

We started with 50 pence and spent 30 pence.

To see how much money we have remaining we subtract the cost of the item from the amount of money we started with.

50 – 30 = 20

We have 20 pence remaining after purchasing the toy.

Here is an example with four coins: three 10p coins and a 5p coin. We have 35p.

We want to buy a banana which costs 32 pence.

Giving Change in british money example

This time we cannot pay for the banana exactly. If we give three 10p coins, then we spend 30 pence and if we give the remaining 5p coin, we have paid 35 pence.

We give an amount greater than the cost of the banana and so we give 35 pence.

35 is 3 more than 32 and so, we have spent 3 pence too much.

To keep it fair, we are given this 3 pence back as change.

We are given a 1p and 2p coin, worth 3 pence.

In this example of giving change, we have 44 pence.

We want to buy a toy teddy bear which costs 43 pence.

Giving Change when buying a toy with english money

We cannot spend exactly 43 pence and so we hand over all of the money.

44 pence is 1 pence more than 43 pence and so, we have spent 1p more than the cost of the bear.

We are given this 1p coin back as change.

Here we have a 50p coin and want to buy a toy car which costs 45 pence.

We can only hand over the 50p coin and wait to receive change.

We can work out the change by thinking ‘How much more than 45 is 50?’.

Giving Change example of buying a toy car

50 is 5 more than 45 and so, we receive 5p back as change.

In this next example we have a 50p coin and a 20p coin. We want to buy an apple which costs 63 pence.

50p plus 20p is a total of 70 pence.

We will need to pay with both coins and wait to receive change.

Giving Change example of buying an apple

We can think ‘How much more than 63 is 70?’.

70 is 7 more than 63 and so, we receive 7 pence back as change.

7p can be made using a 5 pence coin and a 2 pence coin.

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Now try our lesson on Counting US Coins: Dimes, Nickels, Pennies & Quarters where we learn about the different US coins.

Multiplication as Repeated Addition

Multiplication as Repeated Addition

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a flamingo has 2 legs

what is multiplication as Repeated Addition example

  • Each flamingo has 2 legs.
  • The multiplication sign ‘×’ can mean ‘lots of’
  • We can write ‘1 lot of 2’ as ‘1 × 2’.
  • We can write 2 + 2 as ‘2 × 2’. This is 2 lots of 2.
  • We can write 2 + 2 + 2 as ‘3 × 2’. This is 3 lots of 2.
  • We can write 2 + 2 + 2 + 2 as ‘4 × 2’. This is 4 lots of 2.

The multiplication sign ‘×’ can mean ‘lots of’.

The number before the ‘×’ sign tells us how many times we are adding the number after the ‘×’ sign.

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a bicycle has 2 wheels

Multiplication as Repeated Addition

  • Each bicycle has 2 wheels.
  • Here are 4 bicycles.
  • To find the total number of wheels, we add them.
  • We have 2 + 2 + 2 + 2.
  • We have 4 lots of 2.
  • The multiplication sign ‘×’, means ‘lots of’.
  • 4 ‘lots of’ 2 can be written as 4 × 2.
  • We know that 4 × 2 = 8 from our times tables.

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Multiplication as Repeated Addition Worksheets and Answers

What is Multiplication as Repeated Addition?

Multiplication is a repeated addition of the same number. The multiplication sign is written as ‘×’.

The number before the multiplication sign tells us how many times we are adding the number that comes after the multiplication sign.

An example of multiplication is 5 × 3. This means 5 lots of 3 or 5 equal groups of 3. It means to add 3 five times.

5 × 3 means 3 + 3 + 3 + 3 + 3. Multiplication is the same as repeated addition.

What is multiplication as repeated addition

Here are some more examples of multiplication as repeated addition.

Each flamingo has 2 legs.

each flamino has 2 legs

Multiplication as Repeated Addition example of adding legs

  • 1 lot of 2 can be written as 1 × 2.
  • 2 lots of 2 can be written as 2 × 2. As repeated addition it means 2 + 2.
  • 3 lots of 2 can be written as 3 × 2. As repeated addition it means 2 + 2 + 2.
  • 4 lots of 2 can be written as 4 × 2. As repeated addition it means 2 + 2 + 2 + 2.
  • We can see that 2 + 2 + 2 + 2 requires us to add 4 lots of 2. This is relatively long to write out and not a quick way to work out the total.

    It is quicker to write 4 × 2. Also we know that 4 × 2 = 8 through memorising the times tables.

    Multiplication is useful because it is a faster way to do repeated addition and it is easier to write. Learning times tables is important because it allows us to calculate repeated additions immediately and it is necessary for understanding further concepts such as algebra.

    Here is an example of writing repeated addition as a multiplication.

    Each box of eggs contains 6 eggs.

    each box of eggs contains 6 eggs

    Here are 3 boxes of eggs.

    To find the total number of eggs in the three boxes, we do an addition.

    Multiplication as Repeated Addition 2.gif

    We have 6 + 6 + 6 in total. We have 3 sixes added together.

    We have 3 lots of 6.

    We can write this as 3 × 6.

    From our times tables, we should know that 3 × 6 = 18.

    There are 18 eggs in total.

    Here is another example of multiplication as repeated addition.

    Each bicycle has 2 wheels.

    a bicycle has 2 wheels

    Here are 4 bicycles.

    To find the total number of wheels on 4 bicycles, we will add the number of wheels on each bike to make a total.

    example of Multiplication as Repeated Addition to find the total bike wheels

    We have 2 + 2 + 2 + 2.

    We have 4 lots of 2.

    We can write this repeated addition as 4 × 2. There are 8 wheels in total on 4 bicycles.

    Here is another example of multiplication as repeated addition.

    Each horse has 4 legs.

    a horse has 4 legs

    We will find the number of legs on 5 horses.

    Multiplication as Repeated Addition to find the number of legs on 5 horses

    We have the repeated addition of 4 + 4 + 4 + 4 + 4.

    We have 5 lots of 4.

    We ca write this as 5 × 4.

    From our times tables, 5 × 4 = 20.

    There are 20 legs on 5 horses.

    Here is an example where there are 3 cubes in each set.

    We have 5 sets of cubes.

    Teaching multiplication as Repeated Addition to find the number of cubes

    In total we have 3 + 3 + 3 + 3 + 3.

    We have 5 equal groups of 3.

    We can write this as 5 × 3.

    From our times tables we know that 5 × 3 = 15.

    There are 15 cubes in total.

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Now try our lesson on Order of Multiplication where we learn rules about the order of multiplication.

Sorting 2D Shapes

Sorting 2D Shapes

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Sorting Shapes with a Carroll Diagram

Comparing and Sorting 2D Shapes using a carroll diagram

  • A Carroll Diagram is used to sort shapes by placing them into the boxes that are in line with their properties.
  • We will sort this isosceles triangle using the Carroll diagram.
  • The triangle has 3 corners.
  • Therefore it will belong in the column that says ‘4 corners or less’.
  • All of its sides are not the same size. The base is smaller than the other two sides.
  • Therefore it belongs in the row that says ‘sides of different lengths’.
  • We put the triangle in the box that is in line with these two properties.

A Carroll Diagram is a table of mathematical properties.

Each shape is placed into the box that is in line with its properties.

Sorting Shapes with a Venn Diagram

Comparing and Sorting 2D Shapes with a Venn diagram

  • This Venn diagram is used to sort shapes by placing them into the circles which represent their properties.
  • The left circle will contain shapes that contain a right angle.
  • The right circle will contain shapes that have sides that are the same length.
  • All of the angles on a square are right angles.
  • Since it contains a right angle it needs to be placed somewhere inside the left circle.
  • All of a square’s sides are the same length.
  • Because all of the sides are the same length, the square must also be placed inside the right circle.
  • We need to place the shape inside both circles.
  • The square needs to be placed in the overlapping area since it contains the properties of both circles.

On a Venn Diagram, each circle represents a different property.

The shapes are placed inside the circles which represent the properties that the shape has.

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example question of Sorting 2D Shapes on a venn diagram

  • The left circle on the Venn diagram is for shapes that contain a right angle.
  • The right circle on the Venn diagram is for shapes in which every side is the same length.
  • The square contains a right angle and has sides that are the same length.
  • It belongs in both circles and so, it is sorted into the overlapping area in the middle.
  • The rhombus (diamond) does not contain any right angles but does have sides that are the same length.
  • It belongs in the right circle but not in the left circle.
  • The pentagon does not contain a right angle but its sides are all the same length.
  • It belongs in the right circle but not the left circle.

  • This triangle contains a right angle, however its sides are not all the same length.
  • It is sorted into the left circle but not the right circle.
  • This trapezium does not contain a right angle.and its sides are not all the same size.
  • It does not belong in either circle and it is left outside.
  • This octagon does not contain a right angle but all of its sides are the same size.
  • It is placed in the right circle but not the left circle of the Venn diagram.

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Supporting Lessons

Sorting 2D Shapes Accompanying Activity Sheets

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Sorting 2D Shapes on a Carroll Diagram Worksheets and Answers

Sorting 2D Shapes on a Venn Diagram Worksheets and Answers

How to Sort 2D Shapes using a Venn or Carroll Diagram

Sorting Shapes by their Properties

Sorting shapes by their attributes is a skill that is learnt at late KS1/ early KS2 (first to third grade) after learning the names and properties of common shapes.

We can list the properties of shapes using a table. There are many shape properties and many shapes and we will look at some in this example.

We will first sort these shapes to decide whether they contain straight sides.

Comparing and Sorting 2D Shapes to see if they have straight sides

  • A circle does not have straight sides – it as curved sides.
  • A triangle has 3 straight sides.
  • A square has 4 straight sides.
  • A rectangle has 4 straight sides.
  • A pentagon has 5 straight sides.

We will now count the corners of these shapes to see if they have more than 3 corners.

Remember we need more than 3 corners to tick the shapes that have this property. When teaching sorting shapes, it is a common mistake to include shapes that have exactly 3 corners, which is not correct.

3 corners is not the same as more than 3 corners.

Comparing and Sorting 2D Shapes by the number of corners

  • A circle has 0 corners, which is not more than 3.
  • A triangle has 3 corners, which is not more than 3.
  • A square has 4 corners, which is more than 3.
  • A rectangle has 4 corners, which is more than 3.
  • A pentagon has 5 corners, which is more than 3.

We will now sort the shapes by whether they contain parallel sides.

what are parallel lines

Parallel sides are sides that face in exactly the same direction.

Comparing and Sorting 2D Shapes by whether they contain parallel sides

  • A circle only has 1 side and so, it does not contain parallel sides.
  • A triangle does not have parallel sides.
  • A square has 2 pairs of parallel sides. The top and bottom sides are parallel and the left and right sides are parallel.
  • A rectangle has 2 pairs of parallel sides. The top and bottom sides are parallel and the left and right sides are parallel.
  • A pentagon does not have parallel sides.

We will now sort the shapes by whether they contain a right angle.

A right angle is exactly 90 degrees. It looks like a ‘capital L’ shape.

Comparing and Sorting 2D Shapes by whether they have a right angle

  • A circle does not contain a right angle.
  • A triangle does not contain a right angle.
  • A square contains right angles. All of its angles are right angles.
  • A rectangle contains right angles. All of its angles are right angles..
  • A pentagon does not contain any right angles.

Shapes are most commonly sorted using both a Venn diagram or a Carroll diagram. A Carroll diagram is different from a Venn diagram in that in a Carroll diagram objects are put into a table, whereas on a Venn Diagram objects are put into circles. On a Venn diagram, each circle is a different property and each object can be in more than one circle. However, on a Carroll diagram, the object can only go in one particular grid, in line with two of its properties.

Sorting Shapes on a Carroll Diagram

A Carroll diagram is a table that can be used for sorting shapes by their attributes. The shapes will be placed inside the table in line with the properties in the rows and columns that describe it.

To sort shapes using a Carroll Diagram use these steps:

  • Read the properties at the top of each column and decide which column applies.
  • Read the properties on the left of each row and decide which row applies.
  • Place the shape inside the box that lines up with the chosen column and the chosen row.

Here is an example of sorting shapes with a Carroll diagram. We have an isosceles triangle. It has 3 corners and its two sloping sides are a different length to its base side.

The triangle can only go in one of the four boxes shown in the Carroll diagram.

We first read the column properties. We have the choice of ‘4 corners or less’ or ‘more than 4 corners’.

Sorting a triangle shape on a carroll diagram

The triangle has 3 corners which is ‘4 corners or less’. It needs to be sorted into the left column.

We now need to decide if it belongs in the top-left box or the bottom-left box.

We have a choice of ‘sides the same length’ or ‘sides of different lengths’.

Even though this triangle has 2 sides that are the same length, this is not enough to say that every side is the same length. The base side is smaller than the other two.

We must sort the triangle into the row for the property ‘sides of different lengths’.

We place the shape in the box that lines up with the properties that the shape has. It needs to go in the left column because it has ‘4 corners or less’ and it needs to go in the bottom row because it has ‘sides of different lengths’.

The isosceles triangle is sorted into the bottom-left box of the Carroll diagram.

We will now arrange the rest of the shapes in the Carroll diagram.

Sorting Shapes by corners and sides using a carroll diagram

  • The rhombus (diamond) contains 4 corners and has sides that are all of equal length.
  • The pentagon has 5 corners, which is ‘4 or more’ corners. It also has sides that are all equal in length.
  • The square contains 4 corners and has sides that are equal in length.
  • A rectangle contains right angles. All of its angles are right angles.
  • The final shape has 6 corners, which is ‘4 or more’ corners. Its sides are not equal in length.

Here is another example of sorting shapes on a Carroll diagram.

In the two columns, we are sorting the shapes to decide if the sides are curved or straight. sort Shapes using a carroll diagram

  • The circle has a curved side. It has less than 4 sides because it has 1 side.
  • The rhombus (diamond) has straight sides. It has exactly 4 sides.
  • The triangle has straight sides. It has less than 4 sides.
  • The ellipse (oval) has a curved side. It has less than 4 sides.
  • The trapezium has straight sides. It has exactly 4 sides.

Sorting Shapes on a Venn Diagram

A Venn diagram is an area which contains circular zones, which represent mathematical properties. To sort the shapes using a Venn diagram, we place the shapes inside the circles which represent the properties that the shape has.

To sort shapes using a Venn Diagram use these steps:

  • Place each shape inside the circles of which properties it has.
  • If the shape belongs in more than 1 circle, then it must be placed in the overlapping area of these circles.
  • If the shape does not belong in any circle, then it is placed on the outside.

Here is an example of sorting a shape using a Venn diagram.

We have two circles and we will decide where to place this square.

The left circle is for shapes that contain a right angle.

The right circle is for shapes in which all of the sides are the same length.

We have a choice of sorting the square into the following positions on the diagram:

  • Inside the left circle.
  • Inside the right circle.
  • In the overlap of both circles.
  • Outside of both circles.
  • Sorting a square example on a venn diagram

    All of the angles on a square are 90 degree right angles. Therefore it does contain a right angle.

    Because the shape contains a right angle, it must be placed somewhere inside the left circle.

    All of the sides of a square are the same size.

    Because all of its sides are the same size, it must be placed somewhere inside the right circle.

    The square contains both properties represented by both circles and so, it needs to be placed inside both circles.

    The square must be placed in the middle zone, where the two circles of the Venn diagram overlap.

    We will now sort the remaining shapes on the Venn diagram.

    Comparing and Sorting 2D Shapes on a venn diagram

    • The rhombus (diamond) does not contain a right angle. All of its sides are the same length. It belongs in the right circle only.
    • The pentagon does not contain a right angle. Its sides are all the same length. It too belongs in the right circle only.
    • The triangle contains a right angle. Its sides are not all the same length. It belongs in the left circle only.
    • The trapezium does not contain a right angle and all of its sides are not the same length. It belongs outside both circles.
    • The octagon does not contain a right angle but its sides are all the same length. It belongs in the right circle only.

    Here is another example of sorting shapes on a Venn diagram.

    This time the left circle is for shapes with more than 3 sides and the right circle is for shapes that contain a parallel set of sides.

    sorting shapes by their sides using a venn diagram

    • The circle does not have more than 3 sides and it does not have parallel sides. It belongs outside of both circles.
    • The square has more than 3 sides and it has parallel sides. It belongs in the overlapping area of both circles.
    • The kite has more than 3 sides but it does not have parallel sides. It belongs in the left circle only.
    • The pentagon has more than 3 sides but it does not have parallel sides. It belongs in the left circle only.
    • The triangle has 3 sides. This is not more than 3 sides. It does not have parallel sides. It belongs outside of both circes.
    • The irregular pentagon has more than 3 sides and it does not have parallel sides. It belongs in the left circle only.
    • The ellipse (oval) does not have more than 3 sides and it does not have parallel sides. It belongs outside of both circles on the Venn diagram.
    • The trapezium has more than 3 sides and it has a set of parallel sides. It belongs in the overlap of both circles.

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Now try our lesson on Names of 3D Shapes where we learn the names of various common 3D shapes.

Different Combinations of Coins to Make an Amount

Different Combinations of Coins to Make an Amount

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summary of different combinations of coins

  • Both combinations of coins below have the same total value of 33 pence.
  • The 20p coin is worth the same as four 5p coins.
  • The 10p coin is worth the same as two 5p coins.
  • The 2p coin is worth the same as two 1p coins.
  • The single 1p coins shown are the same value.

We can add a combination of coins to make another coin.

Start by adding the largest value coins.

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Different Coins Same Amount example of making 33 pence

  • Here we have six 5p coins and three 1p coins.
  • We will try to add the coins to make any of the coins listed at the top.
  • We can add four 5p coins to make 20p.
  • The remaining two 5p coins make 10p.
  • The three 1p coins make 3p but there is no 3p coin.
  • We can add two of the 1p coins to make 2p.
  • Both combinations of coins add to make 33 pence.

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Combinations of Coins Worksheets and Answers

How to Make an Amount using Different Combinations of Coins

To make a different combination of coins with the same value as another, group the coins into values that add to make other coins, starting with the largest value coins.

It helps to have a list of the other coins that can be chosen and to write down these values when you can make them.

Here is an example of finding an equivalent amount of money to the amount shown.

We have: two 10p coins, a 5p coin and two 1p coins.

Different combinations of coins that make the same amount of 27 pence

We start by adding the coins with the largest value. We will add the two 10p coins.

Two 10p coins are worth 20p. There is a 20 pence coin and so we will write this down.

The 5p coin cannot be added to two 1p coins to make a new coin. This is because there is no 6p or 7p coin.

We keep the 5p coin as a 5p coin.

The remaining two 1p coins can be added to make 2p. There is a 2p coin which can be used instead of two 1p coins.

The total of the money is 27 pence.

27 pence can be made from the first combination of money: two 10p coins, one 5p coin and two 1p coins.

27 pence can also be made from the new combination of coins: one 20p coin, one 5p coin and one 2p coin.

It is possible to make this amount of money in many other ways. For example we could simply have twenty-seven 1p coins.

In this lesson we will be looking to add coins together to make the amount with the least amount of coins.

In this example we have the following collection of coins:

Six 5p coins and three 1p coins.

Different combinations of coins to make amounts of money example of making 33 pence.

We start by adding up the largest value coins. We will start by adding the 5p coins.

We cannot make 50p because six 5p coins added together makes 30p.

We will try and make 20p. This is the same as four 5p coins added together.

We write down 20p now that we have counted four of the six 5p coins.

There are two 5p coins left, which can make 10p.

The three 1p coins make 3p in total but there is not a 3 pence coin. We can use two of the 1p coins to make a 2p coin and then leave the final third 1 pence coin as a 1p.

The total of this amount of money is 33 pence.

33 pence can also be made from a 20p, a 10p, a 2p and a 1p coin.

The 20p is the same value as the four 5p coins, the 10p is the same value as the other two 5p coins and the 2p plus the 1p are the same as three 1p coins.

In this example, we have the following coins:

Two 20p coins, one 10p coin, two 2p coins and a 1p coin.

We will start by adding the largest value coins.

We can add two 20p coins to make 40 pence. However there is no 40p coin.

40p is only 10p less than 50p and we have a 10p coin.

20p plus 20p plus 10p is the same as 50p.

We can write down 50p.

Making a combination of coins that add to make 55 pence

We can add the two 2p coins to make 4p and again, there is no 4p coin. We can add the 1p coin to this amount to make 5p.

The two 2p coins plus the 1p coin can be replaced with a 5p coin.

The total of the money is 55 pence.

Instead of using the original combination of coins, we can also make 55p from a single 50p coin and a single 5p coin.

In this example we have three 10p coins, two 5p coins and three 2p coins.

example of different Coins used to make the same amount of money of 46 pence

We start by adding the largest value coins to try to make another coin.

If we add the three 10p coins, we have 30 pence. There is no 30 pence coin.

Even if we add the two 5p coins to this amount, we would only have 40 pence. There is no 40 pence coin. Because we cannot make the 50p coin with this money, we will try to make the next value coin, 20p.

Instead, two 10p coins can be used to make 20p.

The remaining 10p plus the two 5p coins can be used to make another 20p coin.

The three 2p coins add to make 6 pence. There is no 6p coin.

Instead this value of 6p can be made from a 5p coin plus a 1p coin.

The amount of 46 pence can be made from two 20p coins, one 5p coin and one 1p coin.

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Now try our lesson on Counting US Coins: Dimes, Nickels, Pennies & Quarters where we learn the values of American coins.

Subtraction Facts to 20

Subtraction Facts to 20

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learning the number bonds to 20

  • To subtract from 20 it helps to know the number bonds to 20.
  • To learn the number bonds to 20, start with the number bonds to 10 and put a ‘1’ tens digit in front of one of the numbers in the pair.

Subtraction Facts to 20 example of 20 subtract 8 equals 12

  • 20 – 8 can be worked out using number bonds.
  • The number 2 adds to 8 to make 10.
  • 20 is ten larger than 10 and so, 12 adds to 8 to make 20.
  • 10 – 8 = 2 and so, 20 – 8 = 12.

When subtracting from 20, the answer is ten more than if we had subtracted from 10.

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Subtraction Facts to 20 example finding a missing number

  • Here we have 20 – something = 5.
  • The missing number is the number that we add to 5 to make 20.
  • 5 + 5 = 10 and so, 5 + 15 = 20.
  • Therefore 20 – 15 = 5.
  • The missing number is 15.
  • The missing number is 10 larger than the number bond to 10 that goes with 5.

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Subtraction Facts to 20 Worksheets and Answers

What are Subtraction Facts to 20?

Number facts to 20 are the pairs of numbers that add to make twenty and they are often written in the form of a sum.

Subtraction facts to 20 are subtraction sums in which we are subtracting from 20.

To subtract from 20 we should know the number bonds to 20. The number bonds to 20 are pairs of numbers that add to make 20.

number bonds to 20 list

To learn the number bonds to 20, start with the number bonds to 10 and add a ten to one of the numbers in each pair. We do this by adding a ‘1’ tens digit in front of one of the numbers.

learning the number bonds to 20 using the number bonds to 10

Here is our first example of subtracting from 20.

We have 20 – 8.

From the number bonds to 10 we know that 8 + 2 = 10.

Subtraction Facts to 20 example of 20 subtract 8

8 + 2 = 10 and so, 8 + 12 = 20.

Because 8 + 12 = 20, 20 – 8 = 12.

The missing number in this subtraction fact is 12.

To subtract a number from 20, we can see how many more we add to this number to make 20. To subtract a single digit number from 20, the answer will be 10 more than this number’s number bond to 10.

For example, we subtracted 8 from 20 and so we add 10 to the number that adds to 8 to make 10. We add 10 to 2 to get the answer of 12.

Here is another example of subtracting from 20. We have 20 – 6.

Subtraction Facts to 20 example of 20 subtract 6

Using the number bonds to 10, 6 + 4 = 10.

Therefore 6 + 14 = 20.

And so 20 – 6 = 14.

The missing number is 14, which is 10 more than 6’s number bond to ten.

In this example we will subtract a 2-digit number from 20. We have 20 – 12.

Subtraction Facts to 20 example of 20 subtract 12

We can see that 12 ends in a ‘2’.

2 + 8 = 10

And so, 12 + 8 = 20.

The answer to 20 – 12 is 8.

To subtract a 2-digit number from 20, the answer will be the number bond to ten of the number that is 10 less than the number being subtracted.

In this example we are subtracting 12 and so the answer is the number bond to ten that goes with 2.

8 is the answer.

In this example we are finding the missing number in the middle of a subtraction fact to 20.

20 – something = 5.

The missing number is the number that can be added to 5 to make 20.

Subtraction Facts to 20 example finding the missing number of 20 subtract something equals five.

5 + 5 = 10 and so,

5 + 15 = 20.

The missing number is 10 more than the number bond to ten of the answer.

Here is an example of 20 – something = 3.

Subtraction Facts to 20 example of 20 subtract something equals three.

We start by looking at the answer to the subtraction, which is 3.

3 + 7 = 10 and so,

3 + 17 = 20.

Therefore 20 – 17 = 3.

The missing number is 17, which is ten more than 3’s number bond to ten.

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Now try our lesson on Addition using the Compensation Strategy where we learn how to add numbers using the compensation strategy.

Combining Coins to Make an Amount

Combining Coins to Make an Amount

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example of combining coins to make a particular amoount of 36 pence

  • We will combine a set of coins to make a value of 36 pence.
  • We start with the largest value coins.
  • 50 pence is too large so we can cross it out.
  • We can take one 20 pence.
  • We cannot add another 20 pence because we would have more than 36 pence.
  • We cross out 20 pence.
  • We can add ten pence more to make 30 pence.
  • We cannot add another ten pence and so, we cross it out.
  • We can add 5 pence to make 35 pence.
  • Finally, 1 pence more makes 36 pence
  • We can make 36 pence from a 20p, 10p, 5 and 1p coin.

Start with the largest value coins.

Cross the coins off if we cannot add another without making a value larger than we need.

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Adding Coins to Make a Particular Amount Worksheets and Answers

How to Add or Combine Coins to Make a Particular Value

To add coins to make a particular value, start by looking at the largest value coins. If the coin’s value is larger than the value being made, cross off the coin. Continue to add coins, crossing them off if adding them to the total takes the total over the value needed.

Here is an example of making a particular value.

Find a combination of coins that add to make 52 pence.

We start with the largest value coin, 50 pence.

50p is less than 52p and so, we can take one 50p coin.

If we add another 50p coin, we have too much. We need 2 more pence to get to 52p.

Add Coins to make the value of 52 p

We can make 52p using a 50 pence coin plus a 2 pence coin.

In this example we will make 61 pence.

Adding coins to make 61 p

We can start with 50 pence, which is less than 61p.

If we add another 50p, we will have more than 61p and so, we cross it off.

If we add a 20 pence to the 50p coin, we have 70p, which is more than 61 pence. We do not take a 20 pence coin.

If we add a 10 pence coin to the 50p coin, we have 60p.

We need 1 more pence to make 61p.

61 pence can be made from a 50 pence coin, a 10 pence coin plus a 1 pence coin.

In this example, we will look at how to make a value of 27 pence using coins.

50 pence is the largest pence coin and it is too much. It is larger than 27 pence. We cross it off immediately.

We can take one 20 pence coin.

combining coins to make the value of 27 pence

If we add a 10 pence coin to the 20 pence coin, we have 30 pence. This is too much and so, we cross off the 10 pence coin.

We can take one 5 pence coin.

20 + 5 = 25. We have 25 pence so far.

We can take a 2 pence coin to make 27 pence.

In this example we will make 36 pence.

50 pence is already too large and so, we cross it off.

Finding a group of coins that add to make 36 pence

We can take a 20 pence.

Another 20 pence would make 40 pence and this is too large. We cross off the 20 pence coin now.

We can instead add a 10 pence to the 20 pence coin. This makes 30 pence.

Adding another 10 pence to 30 pence would make 40 pence and so, we do not add another 10p coin.

We can add a 5p coin to make 35 pence.

We can finally add a 1 pence coin to make 36 pence.

In this example we are finding a group of coins that add to make 44 pence.

Again, 50p is too large.

Combining coins to make a value of 44 pence

We can take a 20 pence coin.

This time we can add a second 20 pence coin to make 40 pence.

We cannot take a third 20p coin because 40 pence plus 20 pence equals 60 pence. We cross off the 20 pence coin.

We continue to go through the coins to see if we can add to the 40 pence we have so far.

Adding 10 pence takes us to 50p, which is too large.

Adding 5 pence takes us to 45p, which is too large.

We need 4 more pence to get from 40p to 44p.

We can add two 2 pence coins.

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Now try our lesson on British Money Maths: Introducing Pound Sterling Coins where we learn about pound sterling coins.

Writing Numbers to 100 in Words

Writing Numbers to 100 in Words

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Here are the numbers 1 to 20:

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Reading and writing numbers 20 to 100 list

  • There is a pattern to reading numbers that are larger than 20.
  • The tens digit tells us which multiple of ten we are working in.
  • The units digit is simply read after this multiple of ten.
  • We put a hyphen ‘-‘ between the multiple of ten and the number represented by the units digit.

If a number is greater than 20, first read the multiple of ten that we are working in and then read the units digit afterwards.

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Read Write Numbers to 100 Example questions

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Writing Numbers in Words: Interactive Questions

Writing Numbers to 10: Interactive Questions

Writing Numbers to 100: Interactive Questions

Writing Numbers to 100 in Words Worksheets and Answers

How to Read and Write Numbers to 100 in Words

Here are the numbers from one to twenty written in words.

reading the Numbers 1 to 20 guide

Before teaching reading numbers to 100 in words, it is first important to be familiar with the numbers to twenty.

We will continue by looking at the pattern in reading the numbers from 20 to 100.

To read numbers to 100 in words, first read the multiple of ten given by the tens digit and then read the units digit immediately afterwards. There should always be a hyphen ‘-‘ separating the multiple of ten and the number given by the units digit. The numbers ‘one’ to ‘nine’ repeat, written after each new multiple of ten.

Here is a list of the multiples of ten written in words:

  • 20 – Twenty
  • 30 – Thirty
  • 40 – Forty
  • 50 – Fifty
  • 60 – Sixty
  • 70 – Seventy
  • 80 – Eighty
  • 90 – Ninety

We will first learn how to read numbers in the twenties in words.

20 is the number twenty. All 2-digit whole numbers that start with a ‘2’ digit are in the twenties.

Reading the numbers in the twenties

21 starts with a ‘2’ and so it is in the twenties. Therefore we first write ‘twenty’.

21 ends in a ‘1’ in the units column and so we simply write a ‘one’ after the ‘twenty’.

21 is written in words as ‘twenty-one’. We put a hyphen between twenty and one.

22 is written as ‘twenty-two’.

23 is written as ‘twenty-three’

24 is written as ‘twenty-four’.

25 is written as ‘twenty-five’

26 is written as ‘twenty-six’.

27 is written as ‘twenty-seven’

28 is written as ‘twenty-eight’.

29 is written as ‘twenty-nine’

We can see that as long as we know the numbers from 1 to 9, we simply put a ‘twenty’ in front of them to write numbers in the twenties.

30 comes after 29.

30 is read as ‘thirty’ and is the first 2-digit number that starts with a 3.

Here we will read and write the numbers in the thirties. The numbers in the thirties are the 2-digit whole numbers that start with a 3.

Reading and writing numbers in the thirties in words

31 starts with a ‘3’ and so it is in the thirties. Therefore we first write ‘thirty’.

31 ends in a ‘1’ in the units column and so we simply write a ‘one’ after the ‘thirty’.

31 is written in words as ‘thirty-one’. We put a hyphen between thirty and one.

32 is written as ‘thirty-two’.

33 is written as ‘thirty-three’

34 is written as ‘thirty-four’.

35 is written as ‘thirty-five’

36 is written as ‘thirty-six’.

37 is written as ‘thirty-seven’

38 is written as ‘thirty-eight’.

39 is written as ‘thirty-nine’

Again, we simply repeat the numbers 1 to 9 but with the word ‘thirty’ in front of them. The thirty and the units number are separated by a hyphen.

40 comes after 39.

40 is read as ‘forty’. It is a common mistake to spell forty as fourty, with a ‘u’, like the number four. This is incorrect and forty is spelled without a ‘u’.

All 2-digit whole numbers that start with a ‘4’ are in the forties.

They start with the word ‘forty’, are followed by a hyphen and then the units number.

Reading and writing numbers in the forties in words

41 starts with a ‘4’ and so it is in the forties. Therefore we first write ‘forty’.

41 ends in a ‘1’ in the units column and so we simply write a ‘one’ after the ‘forty’.

41 is written in words as ‘forty-one’. We put a hyphen between forty and one.

42 is written as ‘forty-two’.

43 is written as ‘forty-three’

44 is written as ‘forty-four’.

45 is written as ‘forty-five’

46 is written as ‘forty-six’.

47 is written as ‘forty-seven’

48 is written as ‘forty-eight’.

49 is written as ‘forty-nine’

We can see that the rule learnt previously continues.

We simply write the multiple of ten indicated by the first digit and follow this with a hyphen and then the final digit.

After forty, the next multiples of ten are fifty (50), sixty (60), seventy (70), eighty (80) and ninety (90).

pattern and guide for reading the numbers 1 to 100

The numbers continue to end in ‘one’, ‘two’, ‘three’, ‘four’, ‘five’, ‘six’, ‘seven’, eight’ and ‘nine’.

The last number in this pattern is 99, which is written as ‘ninety-nine’.

After ninety-nine comes one hundred, 100.

100 is read as one hundred

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Now try our lesson on Ordering Numbers to 100 where we learn how to order the numbers to 100.

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