Teaching Strategies, Tactics, and Methods

Adverbial

An adverbial is a word or phrase that functions as a significant clause constituent that typically expresses/gives information about place (in my living room), time (in April), or manner (in a strange way).

What is an Adverbial?

An adverbial is a word or phrase that is used as an adverb to modify a verb or clause. Adverbs can be used as adverbials, but other words and phrases can be utilized this way, including preposition phrases and subordinate clauses. They can be used differently in a sentence to create different effects.

Adverbials are used to describe how, where, or when something happened. They are like adverbs,  typically made up of more than one word.

What are Fronted Adverbials?

Fronted adverbials are single words used at the beginning of sentences to give more information about the action in the main clause. They are “fronted” because they have been moved to the front of the sentence or in front of the verb. A comma must follow them.

Examples of Fronted Adverbials:

Fronted adverbials include the following words in bold:

• Occasionally, she would share her sweets.
• All of a sudden, he ran away.
• Unfortunately, there was nothing she could do about it.

What is an Adverbial Phrase?

Adverbial phrases help us understand things more clearly. An adverbial expression consists of two or more words that tell us more about a verb or an adjective. They appear as part of a sentence; if they are removed, it would no longer make sense. They tell us how, where, when, how long, and why something has happened.

Examples of Adverbial Phrases:

Adverbial phrases can use the following words in bold:

• He sat in silence.
• She drove the car as carefully as possible.
• He spoke to his best friend almost every day.

Different types of adverbials

There are a whole bunch of different types of adverbials that we use in the English language. They all have slightly different roles that help shape a sentence’s meaning. Here are some other kinds of adverbials that you may have heard of:

• Complements: a word, phrase, or clause that is necessary to complete the meaning of a sentence. If they are removed, the sentence will not make sense grammatically.
• Adjuncts: are part of a sentence’s core meaning, but the sentence still makes sense without them.
• Prepositions: some prepositions like ‘inside’ or ‘outside’ may be used as an adverbial to specify a location.
• Conjuncts: words that link two phrases or sentences together, for example, ‘however’ or ‘therefore.’
• Disjuncts: words that stand outside the syntactic structure of a text they are commenting on. They comment on the content or manner of what is being said or written. For example, phrases like ‘without a doubt’ and ‘hopefully.’

Adverbials vs adverbs

So what exactly is the difference between adverbs and adverbials? Although adverbs and adverbials are similar because they share the same modifying function, they do slightly different things. Adverbials perform functions in sentences, whereas adverbs focus on modifying verbs and actions within a sentence.

They are very similar and easy to get confused, and the difference between adverbs and adverbials isn’t always clear, so don’t worry if you feel a little lost. Here are two example sentences, one with an adverb and one with an adverbial:

Adverb: he stood and waited patiently

Adverbial: he stood and waited by the exit

Adverbial Phrase

An adverbial phrase is a Phrase built around an Adverb. In other words, it’s a phrase with multiple words that operates as an adverb, modifying a verb, adjective, or another adverb.

What is an Adverbial Phrase?

An adverbial phrase is a group of words that have an identical impact as an adverb. Adverbial terms can modify a verb, adjective, adverb, clause, or sentence.

Adverbial phrases make a sentence more interesting and exciting. They tell us how (manner), when (time), where (place), why (reason), and how long (this is another type of adverbial phrase of time). This extra information gives the reader more detail, so they can gain more insight and context about what’s happening in a text.

What are some examples of adverbial phrases?

An adverbial phrase must be a group of two or more words, one of which must be an adverb. Some examples of adverbial terms we might encounter often are:

• in a while
• after school
• it is every day
• very quickly
• in the classroom
• because they’re happy
• it went badly

This helpful infographic shows us how adverbial phrases can be used in sentences.

The adverbial phrase is highlighted in orange in the examples above. If they were removed from each sentence, the sentences would be straightforward and would not give us as much detail.

Without the adverbial phrase, we would not know the reason for not doing the bungee jump. So, if you’ve been wondering, ‘What is an adverbial phrase?’ you can now see that adverbial phrases help us to understand things by providing extra information.

How to use adverbial phrases in sentences

In silence	The class read the book in silence.
Behind the shed	Clare found her football behind the shed.
In the morning	We’ll take the dog for a walk in the morning.
In a minute	In a minute, I think I’ll have a slice of cake.
After the rain	There was a rainbow after the rain.
Most days	Most days, I have to get up at 7 am.
In the classroom	Everyone was well-behaved in the classroom.
Before school	Charley needed to find his homework before school.
In the distance	I could see a car coming in the distance.
Very slowly	The plant was growing very slowly.

What’s the difference between an adverbial phrase and an adverbial clause?

An adverbial phrase doesn’t have to contain a subject and a verb. However, it must include more than one word and function as an adverb, modifying a verb, an adjective, or another adverb.

On the other hand, Adverbial clauses have to contain a subject and a verb as well as an adverb. An example of this is:

‘He does his homework before he eats his dinner.’

In this sentence, ‘before he eats his dinner’ is an adverbial clause – it contains a subject (‘he’) and a verb (‘eats’) as well as telling us when (‘before’).

It’s worth noting that adverbial clauses are always dependent clauses, otherwise known as subordinate clauses. They can’t stand alone – in other words; they can’t make sense without the rest of the sentence. Adverbial clauses modify the main clause in a sentence (in this example, ‘He does his homework’). They give us more information about what’s happening in the main clause.

When is an adverbial phrase a fronted adverbial?

A fronted adverbial is an adverb, phrase, or adverbial clause used at the beginning of a sentence. Like common adverbial phrases, fronted adverbials give more detail and texture to a sentence, telling us when, where, how, or why something is done or has happened.

Some of the examples we’ve used above are fronted adverbials, such as:

• In a minute, I think I’ll have a slice of cake.
• Most days, I have to get up at 7 am.

The great thing about adverbial phrases and clauses is that we can often choose whether to use them at the beginning or the end of a sentence. For example, we can use our adverbial clause as a fronted adverbial:

• Before he eats his dinner, he does his homework.

This ability enables us to add variation to our writing, making it more interesting for the reader.

However, a fronted adverbial doesn’t have to be an adverbial phrase or clause. A single adverb can be a fronted adverbial all on its own. For example:

• Later, I’ll go to the cinema.
• Suddenly, the clouds disappeared.

How to punctuate adverbial phrases and clauses

The whole point of adverbial phrases and clauses is to make a sentence more sense. This won’t happen if you don’t use the correct punctuation. Luckily, it’s pretty easy to get it right!

The general rule is that if you’re using your adverbial phrase at the end of a sentence, it doesn’t need a comma. For example, there’s no need for a comma in the sentence ‘We’ll take the dog for a walk in the morning’.

However, if we use the adverbial phrase as a fronted adverbial, the sentence becomes, ‘In the morning, we’ll take the dog for a walk’. As we can see, this sentence has a comma because it needs one.

So, the general rule is that you need a comma after an adverbial phrase if you’re using it at the beginning of a sentence. Still, you don’t need a comma before an adverbial expression if you use it at the end of the sentence.

Polygon

A polygon is a flat two-dimensional shape with even sides that are fully closed. The sides must be straight, not curved. Polygons can have any number of sides.

Regular and irregular polygons

Polygons can be either regular or irregular. A regular polygon is one in which each side is the same length and at the same angle.

An irregular polygon has sides or angles of differing lengths and sizes. Although it must still have straight sides that are all joined up, or it would not be a polygon.

What is a polygon shape?

A polygon shape is a two-dimensional shape with straight sides that all join up. Here are some examples of polygon shapes:

Regular Triangle
• three equal sides
• three equal angles

Regular Quadrilateral (Square)
• four equal sides
• four equal angles

Regular Pentagon
• five equal sides
• five equal angles

Regular Hexagon
• six equal sides
• six equal angles

Regular Heptagon
• seven equal sides
• seven equal angles

Regular Octagon
• eight equal sides
• eight equal angles

What are some particular kinds of polygons?

Quadrilaterals are polygons with four sides, but quadrilaterals with the same sized sides and angles have a unique name – they are called squares. For example, a rectangle is a rectangle if a polygon has four right-angled corners, but two opposite sides are longer than the other pair of sides.

There are also three different kinds of triangles with unusual names:

• An equilateral triangle, which is regular as all of its sides and angles are the same size
• An isosceles triangle is an irregular-shaped triangle
• A right-angle triangle, named so because one of its angles is a right angle

Concave, convex, simple, and complex polygons

There are several other types of polygons and regular and irregular polygons. For example, a polygon can be regular, irregular, concave, or convex.

When answering the question “what is a polygon?” in KS2, students will be expected to be able to define a convex polygon and a concave polygon.

Here are simple definitions of convex polygons and concave polygons:

• A convex polygon is a shape with no angles pointing in, which means that none of its internal angles measures more than 180°.
• A concave polygon is a shape with some internal angles that are greater than 180°, and these angles will point inwards.

Calculating the size of the angles in a polygon in KS2:

When learning about polygons in KS2, children will learn to use the rule that all internal angles in a regular polygon are equal to help them calculate the size of interior angles in different common shapes. Luckily, they don’t have to measure each angle in a polygon. Instead, a helpful formula can help them work out the interior angles.

Use the following formula to work out the interior angles of a regular polygon:

(n-2)×180º ÷ n

n = the number of sides

So, for example, to work out the interior angles in a regular hexagon:

First, count the number of sides (6)

Secondly, subtract 2 from the number of sides as per the formula (6-2 = 4)

Next, multiply by 180º to learn the sum of all angles in shape (4 ×180º = 720º)

Finally, divide your answer by the number of sides to work out the size of each interior angle in a regular polygon(720º ÷ 6 = 120º).

Examples of polygon shapes

Polygon shapes are all around us. So many objects around us form a polygon, from triangles to decagons, from the natural world to artificial things. We’ve put together a list of the most common polygon shapes, from three-sided shapes to ten-sided shapes, and examples. We’ve also developed some simple rules to help you remember their names!

How to remember the names of polygon shapes

Triangle. Triangles have three sides, so to help us remember, we can think of a tricycle with three wheels. The “tri” at the beginning of the tricycle is the same as “tri” at the beginning of the triangle. Some examples of triangles in real life include a slice of pizza, traffic signs, and a billiards rack!

Quadrilateral. Quadrilaterals have four sides, so that we can think of quad bikes with four wheels. Some examples of quadrilaterals in the real world include a deck of cards, a chess board, and books.

Pentagon. Pentagons have five sides, and we hold a pen with five fingers. Examples of pentagons include the black sections on a football, a pencil, and okra.

Hexagon. Hexagons have six sides, so we can focus on the “x” in the word “hexagon” and the “x” at the end of the word “six”. Some real-life examples of hexagons include honeycombs and metal nuts.

Septagon. Septagons have seven sides, and “sept” sounds similar to “sev” so we can think of a septagon as a “seven-agon”.

Octagon. An octagon has eight sides, so that we can imagine an octopus with eight tentacles. An example of an octagon in the real world is an open umbrella.

Nonagon. Nonagons have nine sides, and nonagons sound very similar to “nine-again”! The US Steel Building in Pittsburgh, Pennsylvania, is a real-world example of a nonagon.

Decagon. Decagons have ten sides, and there are ten years in a decade. Some countries, such as Australia, Belize, and Hong Kong, have ten-sided coins.

 

To identify how to work out the area of a square and calculate the area of other common shapes, we first need to address the burning question, what is the area?

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

You can think of the area inside a given shape or space. It refers to how much space is taken up. The larger the shape, the larger the area and perimeter of the shape. Not to be confused with volume, area only refers to space taken up by a flat or 2D object.

As children work with different 2D shapes and work out the area of each, they will discover that different shapes require the use of different formulas and methods to find the area.

Finding the area of different shapes

Now we know what an area is, we can look at different methods to find areas of different shapes. To calculate the area of a shape, you require two measurements, length and width. How you calculate these two measurements and what you do with them to work out the area will vary, depending on the shape.

Children will learn how to calculate the area of different shapes in primary school. They will start by calculating the area of squares and rectangles using the grid method. Then, using this method, they have to count the squares inside a shape to work out the area in cm². Later, they will learn different formulae for working out the area of different shapes.

How to work out the area of a square

When it comes to knowing how to find the area, finding the area of a square is the best place to start. To find the area of a square, we multiply two sides together. As all sides are the same length, it doesn’t matter which two we pick! Let’s take a look at this example together:

1. We know that this square’s sides are 8 cm each.
2. To find the area, we need to multiply two of them together.
3. So, we work out that 8 × 8=64.
4. We answer that the area of this square is 64 cm².

Let’s look at how to calculate the area of another square. Soon, your class will have conquered the first step to area mastery.

1. This time, our square has sides of 11 cm each.
2. To find the area, we need to find the answer to 11 × 11.
3. To make this easier, we could work out 11 × 10 and add an extra 11.
4. 11 × 10=110, so 110 + 11=121.
5. Our final answer is that the area of our square is 121 cm².

How to calculate the area of a rectangle

Now that we know how to find the area of a square, it’s time to move on to the next level of challenge. Working out the area of a rectangle isn’t any more difficult than it is with a square, though we need to be sure that we’re multiplying the length by the width this time. Let’s try this example:

1. We’re finding the area of this rectangle, which is 4 m in length and 7 m in width.
2. So, to find out the area, we multiply both of them together.
3. We need to work out that 4 × 7=28.
4. Our final answer is that this rectangle has an area of 28 m².

As you can see, working out the area of a rectangle is as simple as a quick multiplication question. So let’s try one more:

1. We will find the area of a rectangle with a length of 9 cm and a width of 6 cm.
2. To find the area, we need to find the answer to 9×6.
3. We know that 9 × 6=54, so our final answer is that the area is 54 cm².

How to calculate the area of a parallelogram

A parallelogram is like a rectangle that has been pushed to one side. It is a quadrilateral, like a square and a rectangle, because it has four straight sides and four corners. To calculate the area of a parallelogram, you still use the same formula for a square or a rectangle: height × width.

In this example, the area of the parallelogram is 120 cm².

How to find the area of a triangle

Our third challenge is working out how to calculate the area of a triangle. It’s less daunting than it sounds, though, as there’s only one extra step involved. We need to work out half of the total of the base multiplied by the height. In a nutshell, it’s like working out the area of a rectangle, but we halve the multiplication problem before we solve it! Let’s try this example:

1. Here, we can see that the triangle’s base is 9 m, and the height is 10 m.
2. We need to work out 1/2 × (9 × 10) to get our answer.
3. As we know that 9 × 10=90, all we need to do is halve this value.
4. 90÷2=45. Our final answer is that the area of this triangle is 45 m².

Your class will soon have mastered three types of areas. Let’s give another example of how to work out the area of a triangle a go before we give them an activity to practice with:

1. This time, the base of our triangle is 12 cm, and the height is 8 cm.
2. We need to calculate 1/2 × (12 × 8) to find our answer.
3. 12 × 8=96, so we must work out half of 96.
4. 96÷2=48. Our final answer is that the area of this triangle is 48 cm².

How to calculate the area of a circle

There are a few things we need to know when calculating the area of a circle, and it’s always good to start with the basics. First, a circle is a 2D shape — like any other 2D shape, its area is the amount of space it covers. Bigger circle, bigger area.

Unlike polygons (such as squares, triangles, or parallelograms), we can’t multiply together the length of the sides to find the area. So instead, we use the distance from the edge of the circle to the center.

To find out how to work out the area of a circle, you need to know two words to do with circles:

• Radius: The radius is the distance from the center of a circle to anywhere on its edge.
• Diameter: The diameter is the distance from one side of the circle to the other, through the middle.

The diameter is twice the radius; the radius is half the diameter. Keep reading to find out how to work out the area of a circle using the diameter.

Let’s break that down into a few easy steps:

Step 1: The first step in finding the area of a circle is finding the radius.

Step 2: Once you have the radius, you must square it (multiply it by itself).

Step 3: Now, you must multiply that value by pi. This stage requires using a calculator, as pi is a significant number. However, it can be carried out without a calculator by multiplying your value by 3.14159. Although, this will give you a less accurate answer.

The result of this equation will give you the area of your circle.

The formula is: π × radius × radius or π × radius², simplified to π × r².

How to work out the area of a circle using the radius

• Area of a circle = π × radius × radius

Pi is a Greek letter, spelled pi, and pronounced like pie. Pi is a constant, which means it never changes. It is also irrational, which means it never ends and never repeats. The first 20 digits are:

• 3.14159265358979323846…

If you’re using π to find a circle’s area (or circumference), you can use the π button on your calculator or round it to 3.14.

Example 1 — Find the area of a circle using a radius of 5 cm. Give your answer correct to 1 decimal place.

Area = π × radius × radius

We know the radius, so put it into the formula above:

• Area = π × radius × radius
• Area = π × 5 × 5
• Area = 78.5 cm2 (to 1d.p.)

Make sure you give the correct units. Like any other area, the area of a circle is given in square units. That may be cm2, m2, mm2 or km2, among others.

Let’s go through another example.

Example 2 — Find the area of a circle using the radius of 17 cm. Give your answer correct to 1 decimal place.

Area = π × radius × radius

We know the radius, so put it into the formula above:

• Area = π × radius × radius
• Area = π × 17 × 17
• Area = 907.9 cm2 (to 1d.p.)

How to work out the area of a circle using the diameter

In maths, you will not always be given the radius of a circle. However, it is still possible to find the area. Here are the steps you must take to work out the area of a circle using the diameter:

Step 1: Find the radius

The radius is equal to half of the diameter. So, to find the radius, we must divide the diameter by 2:

radius = diameter ÷ 2

Step 2: Use the formula using the radius

Now that we know the radius, we can use the same formula for the area.

Area = π × radius × radius

We are multiplying r by itself in this equation, which means we are squaring it. So, the formula can be simplified into this:

• A= π ×r2

Finally, because this is an algebraic formula, we can remove the × sign:

• A= πr2

Let’s put this into practice with an example.

Example 1 — Find the area of a circle using a diameter of 14 m. Give your answer correct to 1 decimal place.

Be careful! We have been given the diameter in this question, but we need the radius to find the area.

The radius is half the diameter:

• radius = diameter ÷ 2
• radius = 14 ÷ 2
• radius = 7 m

We can now find the area as before:

• Area = π × radius × radius
• Area = π × 7 × 7
• Area = 153.9 m2

Here’s another example of how to find the area of a circle using the diameter:

Example 2 — Find the area of a circle using a diameter of 32 m. Give your answer correct to 1 decimal place.

The radius is half the diameter, so:

• radius = diameter ÷ 2
• radius = 32 ÷ 2
• radius = 16 m

Now, we can find the area using the original formula:

• Area = π × radius × radius
• Area = π × 16 × 16
• Area = 804.2 m2

How to work out the area of a circle using the circumference

In some cases, you will find that a circle’s radius and diameter are unknown. Fear not; you can still calculate the area of a circle using the circumference. The circumference is the total distance around the circle. The formula for finding the area of a circle using the circumference is:

C = 2πr

Key:

• C represents the circumference
• r represents the radius
• A represents the area

Step 1: Solve for ‘r’

We can take this formula for the circumference and use it to find the value of the radius. To do this, the formula will be:

r = C/2π

Step 2: Replace ‘r’ in the formula

Now, we can replace ‘r’ in the original formula for the circumference with this new expression:

A = π(C/2π)2

Step 3: Simplify the formula

This formula is quite confusing to look at, so let’s simplify it. The simplified version of this formula for the area of a circle is:

A = C2/4π

Now you have a fool-proof formula for calculating the area of a circle.

Let’s put all of this into practice with an example!

Example 1 — Find the area of a circle using the circumference of 30 m. Give your answer correct to 1 decimal place.

A = C2/4π

Now, we have to put the measurements of the circle into this formula.

A = 302/4π

A = 900/4π

Area = 71.6 m2

How to work out the area of a border

Sometimes, you will encounter a maths problem asking you to find the area of a border, which is a shape within another shape. In this instance, the process for working out the area is slightly different. Let’s work through it with an example:

Work out the area of a rectangular path with a height of 4 meters. The width of this rectangle is 20 meters, and the height is 15 meters.

There are two ways to go about finding the area:

1. You could work out the area of this path by splitting it into four rectangles and using the formula discussed above to work out each area. Then, you could add them together to find the total area of the path.

1. The other, arguably more efficient, way to work out the area of the path is to calculate the area of the whole shape and the area of the internal shape. Then, subtract the area of the inner shape from the area of the entire shape, and you will be left with the area of the path.

The second method would go as follows:

Step 1: Find the area of the whole shape. Height x width = 15 × 20 = 300 m²

Step 2: Use the path width to work out the area dimensions of the internal shape. If the width of the whole shape is 20 m, and the width of the path is 4 m, we must subtract 4 from 20 on each side.20 – (4 × 2) which becomes20 – 8= 12 metres

So, the width of the internal shape is 12 meters. The same method can be used to find the height of the inner shape.

The height of the whole shape is 15 meters, and the width of the path is 4 meters, so we must subtract 4 from 15 on each side.15 – (4 × 2)whichbecomes15 – 8= 7 metres

The height of the internal shape is 7 meters.

Step 3: Now that we have the dimensions of the internal shape, we can use them to work out the area using our rectangle formula.Height x width=7 × 12= 84 m²

Step 4: Finally, we have both of the measurements we need to work out the area of the path. So, the last step is to subtract the area of the internal shape from that of the whole shape:300 – 84= 216

So, the area of the path is 216 metres²

How to find the area of a shape: irregular shapes

Sometimes, you will come across complicated shapes without a straightforward formula for finding the area in maths. However, if you find yourself in this position, fear not, as there are some simple steps you can carry out to find the area.

Step 1: The first step in finding the area of a complicated shape is to break the figure down into more specific sections. These sections will be smaller shapes within the larger, more complicated one. Looking for right angles and parallel lines is best when finding these smaller shapes.

Step 2: Work out the area of your individual, smaller shapes. This step will look different depending on what forms you are working with. If you need help with this bit, you can look at our sections on how to find the area of a square, circle, etc.

Step 3: Now, you must add the areas of your shapes together, giving you the total area for your irregular shape.

What is a Heptagon?

A heptagon is a seven-sided polygon.

It is also known as a septagon.

Heptagon comes from two words: ‘hepta’, meaning seven, and ‘gon’, meaning sides. So, if you put this together, the word ‘heptagon’ directly translates to ‘7-sided shape’.

Heptagon Examples

Regular Heptagon

A heptagon is regular if all of its sides and angles are equal.

The sum of the angles of a regular Heptagon is 900°.

Irregular Heptagon

A heptagon is irregular if it has seven unequal sides and angles.

Irregular heptagons can all look very different.

Heptagons in real life

A variety of objects around us are heptagons.

These include signs, mirrors, and 50-pence pieces. Just look for any seven-sided shapes, and you’re bound to come across some Heptagons in your day-to-day life.

What is the numerator of a fraction?

The numerator is the number right above the line in a fraction. For instance, in the fraction 3/5, the numerator is 3.

The numerator of a fraction shows how many parts we have out of the whole, while the denominator below the line shows how many equal parts there are in total.

For example, the fraction ⅜ shows that something (let’s say a pizza) has been divided into eight parts or pieces, but only three are left. Perhaps someone has eaten the other five pieces of the pizza, so only three remain from the original eight pieces.

If the numerator is 1, the fraction is called a unit fraction.

What is a denominator?

The denominator is the number below the line in a fraction. It shows the total amount of parts that something has been divided into.

When do children learn about fractions in primary school?

In Year 2, children need to be able to identify a half, a quarter, and three quarters. These are basic fractions, which you can use simple visual aids to help explain. For example, the circle below shows half as half of a circle and as the fraction 1/2.

In Year 3, children are taught about fraction notation; they learn how to use a numerator, denominator, and fraction bar to write a fraction. In addition, they find out that the top number in a fraction is a numerator, and the bottom number is a denominator. Using diagrams can help children understand fraction notation with a visual representation.

For Years 3 and 4, children find out about equivalent fractions. For example, they learn that a half is the same as two quarters or four eighths. A great way to help children understand equivalent fractions is with a fraction wall that shows the concept in a brightly colored visual way.

From Year 4 to Year 6, children learn about the relationship between fractions and decimals. They also need to understand how to simplify fractions using division.

Fun facts about fractions

• The number on the top of a fraction (the numerator) does not have to be smaller than the number on the bottom (the denominator). However, if the numerator is greater than the denominator, it is an improper fraction. An improper fraction can be simplified to a mixed number.
• If the numerator is 0, the entire fraction becomes 0.
• When the numerator and denominator are the same, the fraction becomes 1 because the sum of the parts is the same as the sum of the total.
• A fraction with a numerator of 1 is called a unit fraction.
• Fractions and decimals are both ways of representing numbers smaller than 1.

A pentagon is a flat 2D shape with five sides and five vertices.

The word “pentagon” comes from the Greek word “pentagonos”, which means “five-angled”. A regular pentagon has five internal angles that form corners. The angles in all the corners or regular and irregular pentagons will always add up to 540º.

What are the parts of a pentagon?

These 5-sided shapes have five parts:

• Side: one of the five line segments that together create the pentagon.
• Vertex: the point where two sides meet is called a vertex.
• Diagonal: a line connecting two vertices that aren’t one of the five sides.
• Interior angle: an inside angle formed by two sides of the pentagon is known as an interior angle.
• Exterior angle: an angle on the outside of the pentagon formed by two adjacent sides is called an exterior angle.

How many vertices does a pentagon have?

Pentagons have five vertices (also known as corners). In addition, pentagons have five places at which the five sides meet to form an angle.

Revision:

• A vertex is a point where two or more lines meet.
• The plural of vertex is vertices.

Properties of pentagons

There are different types of pentagons, but they share some common characteristics. So let’s have a look at what they are.

Regular and irregular pentagons:

• are flat 2D shapes;
• have five straight sides;
• have five interior angles that add up to 540°.

Regular vs. irregular pentagons

Properties of regular pentagons:

• All angles are equal.
• All sides are of equal length.
• All interior angles are 108° each.
• All exterior angles are 72°each.

Properties of irregular pentagons:

• Not all angles are equal – they are different sizes.
• Not all sides are of equal length.

Convex and concave pentagons

In maths lessons on shapes, young learners might come across these types of shapes. So let’s have a look at what their properties are.

Convex pentagons:

• None of the interior angles are greater than 180°.
• All the corners point out of the shape.
• It can be regular or irregular.

Concave pentagons:

• One corner points into the shape (remember that caves go in).
• One interior angle is greater than 180°.
• Always an irregular pentagon.

Finding the perimeter and area of a pentagon

The perimeter of a pentagon

The perimeter of a polygon is the length of its outline. It is the length of each of its sides added together. Children can imagine the concept of a perimeter by thinking about walking outside a field.

To find the perimeter of a regular pentagon, you have to multiply the length of one of the sides by five.

To find the perimeter of an irregular pentagon, you have to add up the length of each side since not all five are the same length.

Area of a regular pentagon

The area of a polygon is the space inside the shape. For example, the area inside a field would be all the space inside the field’s perimeter. The area of a shape is measured in cm², m², etc.

It is a bit more tricky to find the area of a pentagon. To find the area of a quadrilateral (a polygon with four sides), you must multiply the base by the height. The formula is base × height.

Here are the steps for finding the area of a regular pentagon:

1. Divide the pentagon into five triangles by drawing five lines from the center of the pentagon.
2. Calculate the area of one of the triangles using this formula: ½ × base × height.
3. Multiply the area of one of the triangles by five to find the total area of the pentagon.

Real-life examples of pentagons

Pentagons are not very common shapes to see in your everyday life, but you may still spot them here and there. Here are some examples of where you can spot these 5-sided polygons in the wild:

• The American Department of Defence in Washington, D.C. is pentagon-shaped if you are looking at it from above – and its name is The Pentagon because of its shape.
• Footballs have sections that are pentagon-shaped, as well as some that are hexagons. Have a look next time you have a kickabout!
• Petunias are a type of flower with five sides to look like pentagons. Do you have any in your garden?
• Okra is a type of vegetable from Africa that is often used in the Caribbean, Creole, Cajun, and Indian cuisine. If you cut a cross-section from okra, it is pentagonal.
• An inverted pentagon (with the points joined by internal lines but with no outside lines) is a star. It is also sometimes known as a pentagram.
• Starfish have five long fingers, which would form a pentagon if you joined the tip of each finger with a line.

Why is The Pentagon a pentagon?

The American Department of Defence in Washington, D.C., is named like the 5-sided shape and has the form of a pentagon. But why did they decide on this shape when building this vital place?

The answer is simple: it is easier and faster to walk in it.

In 1941, at the beginning of World War II, the American President, Roosevelt, decided that a new building was needed during that difficult time. The American architect George Bergstrom chose to take advantage of the shape of the building to reduce the distance people would have to walk from one office to another within a place that everyone knew was going to be massive.

Going from one side to another was faster in a 5-sided shape building compared to a traditional rectangular shape, and a circular building would have been more challenging to build. So it is how the Pentagon, a massive concrete and steel building with a total floor area of almost 7 million square feet and 17.5 miles of corridors, ended up having this shape.

How can you make a 5-sided shape for your children?

One of the best ways to teach children about a geometric shape or to help them remember it is to help them create one themselves. Here are some easy steps you can follow to make a regular 5-sided shape together using just a strip of paper:

• Make a long strip of paper. If you’re aiming for the regular pentagon, you must ensure it is the same width. The color can have any color you like. Let children pick their favorite one to make it even more fun.
• Next, you have to make a knot with the paper, a pretzel-like knot.
• Tighten the knot, keeping the paper flat. Be careful not to break it.
• Fold back or trim off the excess paper.
• That’s it! Your 5-sided shape is ready to be admired! All sides should be equal in length, and all angles should be the same.

What is a connective in English?

Connectives are words or phrases that link sentences (or clauses) together. Connectives can be conjunctions, prepositions, or adverbs. Whichever form they take, we use connectives constantly in written and spoken English.

Connectives are the often overlooked ‘smaller’ functional words that help us link our writing. You might like to think of them as the glue of the literary world, allowing our words to flow and lead on from one to another without sounding awkward. Essentially, we wouldn’t be able to speak or write in complete sentences without connectives!

Connectives can go from ‘and’ or ‘next’ to ‘consequently’ or ‘meanwhile.’

Connectives in English commonly fall into three categories:

• conjunctions
• prepositions
• adverbs

We’ll talk about conjunctions later on, but for now, here’s everything you need to know about prepositions and adverbs:

• A preposition is a linking word in a sentence used to show where things are in time or space. For example, there are prepositions of place, time, direct, ion, and agency. Prepositions are generally placed before the noun or pronoun to which they are referring in a sentence. For example: in, at, on, under.
• An adverb is a word that describes how an action is carried out. Adverbs can change or add detail to a verb, adjective, another adverb, or even a whole clause. Adverbs are sometimes said to describe manner or time. But, to put it simply, they tell you how, when, where or why something is being done. For example: slowly, sadly, upwards, North, here.

We use these connectives for a range of different reasons. First, they add specific meaning to a sentence, so we use them for further clarity when writing.

What is a connective phrase?

Before moving on, it’s worth noting that connectives can sometimes be more than one word. Phrases like ‘as well as’ and ‘in addition to’ can connect different phrases or sentences the same way as single words.

As well as this, conjunctions are sometimes used at the start of a sentence rather than in the middle. For an example, look no further than the start of the previous sentence!

Other examples of connective phrases include:

• For instance
• Such as
• On the other hand

Connectives and clauses: how to use connectives in clauses

Connectives and punctuation join different main and subordinate clauses in a sentence. Using connectives between clauses creates something called a compound sentence. Compound sentences are only possible by using connectives to join two main clauses together in a sentence.

For example, you could say: ‘I like blue cars, and I like red cars.’

Using the connective ‘and’ joins together two main clauses that would make sense. For example, the following sentences show how connectives can be used to join two clauses in a sentence:

• I like bananas, and I like grapes.
• Zoe can be rude at times, but she is a nice girl.

The formula below is a simple way to remember how to create these sentences for yourself!

A prepositional phrase usually includes a preposition, a noun, or a pronoun and may consist of an adjective. However, it doesn’t have a verb.

What is a Prepositional Phrase?

A prepositional phrase includes the object that the preposition in a sentence is referring to and any other words that link it to the preposition.

For example: “He hid beneath the duvet.”

A prepositional phrase usually includes a preposition, a noun, or a pronoun and may include an adjective. However, it doesn’t have a verb.

Examples of Prepositional Words

About

Before

For

To

After

Behind

From

Under

At

By

Over

Up

In

During

Past

With

Argument Text

An argument text is where the writer is either ‘for’ or ‘against’ an issue or subject or presents the case for both sides.

What is an argument text?

An argument text is where the writer is either ‘for’ or ‘against’ an issue or subject or presents the case for both sides.

A typical example of an argument text a kid may write about in primary school is whether students should have to wear school uniforms.

Kids learn about argument texts in Key Stage 2, Year 3 to Year 6.

How to write an argument text:

• Introductions are often used to start
• Formal language is used
• Sophisticated connectives help with a proper tone
• Paragraphs used to break up ideas
• Writers’ opinions and views supported by facts
• The aim is to persuade the reader to consider and potentially agree with the writer

Kids will be asked to write their argument text in school, and they need to know the features of one first. Research is essential as kids must understand their topic and have facts. A good argument text is supported by solid research. Linking paragraphs and using strong opening and closing sentences will help their overall argument text and make it more persuasive.