Teaching Strategies, Tactics, and Methods

What is the Earth’s Crust?

The Earth’s Crust is the Outer Layer of the planet’s core. Lying above the mantle, the Crust forms part of the lithosphere and consists of tectonic plates that give a platform to all land on Earth.

Formed around 4.6 billion years ago. Earth’s crust solidified just after the planet itself did. Initially, it was heavily impacted by asteroid strikes and was very thin.

It makes up around 1% of the Earth’s volume.

What is the Earth’s Crust made out of?

There are two types of crust: Oceanic, which lies under the land of Earth, and Continental, which lies underneath the sea.

The Continental crust is the thicker of the two, at 30 to 50km thick, whereas the Oceanic is only around 5 to 10km thick.

Both crusts comprise 90% igneous rock and contain sedimentary and metamorphic rock. However, the Continental crust has less dense rocks than its counterpart.

Top 6 Facts about the Earth’s Crust

1. The oldest minerals found on Earth, zircons, are thought to have dated from approximately 4.3 billion years ago.
2. Beneath the crust, temperatures can reach up to 1,000 degrees Celsius.
3. Part of the Oceanic crust consists of lava that had erupted from a volcano.
4. The overall temperature is around 22 degrees Celsius.
5. The Continental crust is mountainous and can rise to 70km high.
6. Earthquakes are caused by hotter mantle parts rising through gaps in the Earth’s crust.

The Seven Wonders of the World are a group of places around the globe that are considered to be of great importance. These are The Colosseum in Italy, Petra in Jordan, Chichén Itzá in Mexico, Christ the Redeemer in Brazil, Machu Picchu in Peru, the Taj Mahal in India, and The Great Wall of China.

What are the Seven Wonders of the World?

The original seven wonders, also referred to as the Seven Wonders of the Ancient World, were:

• The Great Pyramid of Giza, Egypt;
• The Hanging Gardens of Babylon;
• The Statue of Zeus at Olympia;
• The Temple of Artemis at Ephesus;
• The Mausoleum at Halicarnassus;
• The Colossus of Rhodes;
• The Lighthouse of Alexandria.

The Seven Wonders of the Ancient World were remarkable, humanly-constructed landmarks from ancient, classical civilizations. This original list dates from the second century BC.

How many of the original Seven Wonders still exist?

The Great Pyramid of Giza is the only ancient wonder that still exists today. The other six have either disappeared or are in ruin.

Why are there only Seven Wonders?

Even though there are many hugely impressive ancient sights, there have only been seven ancient wonders of the world. The ancient Greeks believed seven represented perfection, a particularly significant number for them.

What are the new Seven Wonders?

In 2000, a campaign was started to decide on seven new world wonders. Over 100 million people voted to whittle over 200 places down to just seven. Then, in 2017, the new modern list of the Seven Wonders of the World, featuring landmarks still existing today, was finalized.

Let’s take a look at the current list of the Seven Wonders of the World:

1. The Great Wall of China

The Great Wall of China is the longest in the world! Several dynasties (ruling families) built the Chinese national symbol over hundreds of years (nearly 1,800), starting in about 220 BC. The wall was built to defend areas from invasions and had watchtowers built on the highest places. The famous landmark comprises many overlapping walls that measure a combined length of up to 20,000 kilometers. Millions of people visit the Wonder every year.

2. Taj Mahal, India

This magnificent landmark took 16 years and 20,000 workers to build! It was commissioned to be built in 1632 by Emperor Shah Jahan with the purpose of housing the tomb of his wife, Mumtaz. Architecturally, the building represents symmetry and balance, and the color of the exterior marble walls changes depending on the time of day. In the morning sun, the white marble looks a shade of pink. During the evening, it seems the color of milk and looks golden at night when lit by the moon. Because the Taj Mahal commemorates Shah Jahan’s love for Mumtaz, couples like to have their photographs taken with the building in the background.

3. Petra, Jordan

Petra is an ancient city carved into the rock. It is thought that it was built over 2,000 years ago by a group of people who lived in the Wadi Musa valley, called the Nabateans. However, not much is known about the Nabateans. The city fell to the Roman Empire in AD 106, and an earthquake in AD 363 damaged the town, which resulted in it eventually falling into disuse. The city ruins were rediscovered in 1812 by a Swiss explorer called Johann Burckhardt.

4. The Colosseum, Italy

The Colosseum, known as the Flavian Amphitheatre, was built between AD 70 and 80. It was used for fights, animal hunts, and public executions for four centuries. The floor could also be flooded to stage sea battles! Following the fall of the Roman Empire, the architectural masterpiece was used as a housing complex. Then, in 1349, a great earthquake destroyed parts of the structure. Despite the damage done over the years, it remains a top-rated tourist attraction today.

5. Christ the Redeemer, Brazil

Christ the Redeemer is a statue at the summit of Corcovado Mountain overlooking Rio de Janeiro in Brazil. The figure shows Jesus Christ with his arms spread out over the city. The statue is 30 meters tall, and the arm span of the statue is 28 meters!

The structure is the newest wonder, having been completed in 1931. At the time of its construction, Brazil was predominantly Catholic, and images of the Christ statue were spread throughout.

6. Chichén Itzá, Mexico

The Maya people built Chichén Itzá over 1,500 years ago. The city was an important political and economic center for The Maya people. You’ll find the Temple of Kukulkán (named after the serpent deity), sometimes called El Castillo. It has 91 steps on each of its four sides. An extra step was added at the top of the temple to total 365 steps – one for each day of the year. The top of the temple features a carving of Kukulkán.

7. Machu Picchu, Peru

Machu Picchu is the ruins of a city from the Incan empire that was built in the 15th century. The ruins are in the Andes Mountains, over 2,000 meters above sea level. Its walls and other architectural elements are cut into natural rock.

It’s not sure why the city was first built, although some sources suggest it was used as a royal retreat for the emperor, Pachacuti Inca Yupanqui. It is thought to have been used between the 15th and 16th centuries but was gradually abandoned over time. Today, it is a viral tourist site, so much so that the Peruvian government has begun limiting the number of people able to visit each year to preserve it.

What are the ancient Seven Wonders of the World?

Let’s delve a little deeper into the history of the ancient wonders:

1. The Great Pyramid of Giza, Egypt

The Great Pyramid of Giza was built around 2600 BC by the Egyptians and took 20 years to complete! It’s the largest of the three Giza pyramids and was constructed as a tomb for the Egyptian pharaoh Khufu. The pyramid’s perfect symmetry and unparalleled height (146.5 meters) made it an awe-inspiring sight that ancient tourists visited. Fun fact: it was the tallest human-made structure on earth for almost 4,000 years!

       2. The Hanging Gardens of Babylon

King Nebuchadnezzar II built the Hanging Gardens of Babylon as a gift for his wife, who missed the mountains and flowers of her homeland. They are believed to have been constructed around 600 BC in the ancient city of Babylon.

Babylon was a desert-like place, so creating a sanctuary of lush green trees, shrubs, and vines is quite an extraordinary achievement! But unfortunately, the gardens were destroyed by an earthquake in the first century AD.

However, it is possible that these mysterious gardens were purely mythical and never actually existed, as no archaeological evidence has ever been discovered.

3. The Statue of Zeus at Olympia

The Statue of Zeus stood at an enormous 12 meters high! It was built sometime around 432 BC by a Greek sculptor named Phidias to honor the chief of the Greek gods. It was located within the Temple of Zeus in Olympia, also the site of the first Olympic Games. The statue showed Zeus seated on a glorious throne, with ivory skin and golden robes. It was designed to inspire awe in worshippers and is considered pagan, which would explain why the statue was removed after the rise of Christianity.

4. The Temple of Artemis at Ephesus

The Temple of Artemis was built in the Greek colony of Ephesus, which is now part of Turkey. It was built in 550 BC to honor Artemis, the goddess of hunting. The magnificent building took over 120 years and only one night to destroy! In 356 BC, it was tragically set ablaze by a man named Herostratus, who did it simply in hopes of becoming known for destroying such a beautiful creation.

5. The Mausoleum at Halicarnassus

The Mausoleum at Halicarnassus was built between 353 and 350 BC near Bodrum in Turkey as a tomb for the Persian satrap (governor) Mausolus. Its construction was ordered by his wife, Artemisia II, who was so distraught at his death that she felt he deserved an extravagant tomb worthy of a king.

The impressive 41-meter-high structure combined Greek, Lycian and Egyptian architecture. No expense was spared; the mausoleum was filled with beautiful marble statues, temples, sculptures, and friezes.

The Mausoleum was the second longest surviving ancient wonder, after the Great Pyramid of Giza. However, earthquakes eventually destroyed it between the 12th and 15th centuries AD.

6. The Colossus of Rhodes

At 33 meters, the Colossus was the tallest statue in the ancient world – approximately the height of the modern Statue of Liberty. It was built by a Greek sculptor named Chares of Lindos sometime between 292 and 280 BC.

The statue was built to honor Helios, the Greek sun god, in celebration of the successful defense of the island after a year-long siege. Legend says that the people of Rhodes melted down abandoned bronze and iron weapons to help with its creation.

Unfortunately, the magnificent structure was destroyed by an earthquake in 226 BC and remained in pieces on the ground for hundreds of years.

7. The Lighthouse of Alexandria

The Lighthouse at Alexandria, estimated to have been between 115 and 145 meters tall, would guide ships through Alexandria’s harbor’s shallow, rocky waters. It was constructed in 280 BC on the Island of Pharos in Egypt.

It used a mirror to reflect the sun’s rays during the day and a fire at night. The light was supposedly visible over 30 miles away!

Unfortunately, much like most ancient wonders, the lighthouse was damaged by several earthquakes before completely collapsing during the 15th century.

What is an octagon?

An octagon is a 2D shape with eight sides, eight angles, and eight vertices.

Octagons can be regular or irregular. This depends on their shape and how they’ve been drawn.

Regular and Irregular Octagons

Regular octagons

When all sides and angles are equal, an octagon is regular.

Regular octagons also have the following:

• interior angles of 135°
• exterior angles of 45°

When you add up all the corners of an octagon, it equals 1080°. So when it comes to figuring out the total area of an octagon, we need to use the formula:

In this equation, a stands for the length of one of its sides.

Irregular octagons

Irregular octagons do not all have equal sides and angles.

The above example is also a concave octagon with an inward angle. Octagons without inward angles are called convex octagons.

What’s shaped like octagons in real life?

There are lots of things in daily life that are shaped like octagons. All you’ve got to do is look for them! The next time you’re out and about, why don’t you see how many things you can spot that are octagons? They don’t just have to be regular octagons, either. As long as they’ve got eight sides, they’re octagon shaped. Here’s a list of things we’ve found; see if you can think of yourself!

• Umbrellas – Deeding on the size of your umbrella, it’s usually octagon shaped. This allows lots of support while keeping the support beams out of your way. If umbrellas were square, the supports would need to be further down the handle to be as strong.
• Signs – In the UK, most stop signs are octagon shaped. There are hardly any other signs that take this shape. This makes stop signs more identifiable for drivers. Having to stop is essential when driving, so these signs need to be recognizable.
• Tiles – Now, we’re not saying every tile in the world is octagon shaped, but some are. This is because octagons slot together well. They’re also an excellent shape and can stand out.

Octagon Angles

For an octagon to be classed as an octagon, it has to have a certain amount of angles that add up to a more significant number. If it’s a regular octagon, these angles will add up to 1080. When that’s divided by 8 (the number of sides), that’s 135 degrees per angle.

If you want to make an irregular octagon, ensure all the angles add up to 1080 degrees. However, all the sides of the shape can be different lengths. Octagon angles can vary depending on whether you want a regular or irregular octagon.

What are regular shapes?

A regular shape is a shape with equal angles and sides – its sides are all the same length, and its angles are all the same number of degrees.

What are irregular shapes?

On the other hand, an irregular shape has sides of different lengths and angles of various sizes. Irregular shapes are shapes where the sides and interior angles are different. As a result, they can be more challenging for children to identify, as they don’t look like the conventional shape they are used to seeing when they are initially introduced to shapes.

Distinguishing between regular and irregular shapes

When distinguishing between regular and irregular shapes, it’s essential to look at their sides and angles. Are the sides and angles the same or different?

For example, children will learn about equilateral triangles and isosceles triangles. An equilateral triangle, by definition, has all sides of an equal length and equal angles, which makes it a regular shape. However, if you look at the image below, the sides of an isosceles triangle aren’t all the same length, and its angles are also different. This means that an isosceles triangle is an irregular shape.

Is the term ‘shape’ the same as a ‘polygon’?

In short, the two terms don’t mean the same thing. But when children learn about shapes at school, they may also hear them referred to as regular and irregular polygons. A polygon is a 2D shape with straight sides, and the standard and irregular shapes, which children will learn about, are all 2D shapes with straight sides. That’s why, in this instance, the terms can be used interchangeably.

What are some examples of regular and irregular shapes?

The best way to learn about shapes is to look at examples! Pupils will be expected to know whether a shape is regular or irregular, so let’s look at some of the properties of these polygons.

Examples of Regular Shapes

The table below includes examples of regular polygons for helping children learn the names. When learning about different shapes in Maths, children must see a visual representation to help them remember the properties.

For example, an equilateral triangle has three sides and three equal angles, which can be seen in the picture. Here’s something handy: it’s called ‘equilateral,’ which can be associated with ‘equal.’ That’s easy to remember and associate the name with its properties!

A helpful way of teaching about shapes is to have children match the visual representations with the properties and names of the figures. We’ve included some valuable resources at the bottom of the page, but looking at the table below can also be a helpful way of familiarising children with different regular shapes.

Examples of Irregular Shapes

You can see some examples of irregular shapes in the table below. It’s possible to keep adding to the list by including irregular heptagons, irregular octagons, etc.

What’s important to remember for irregular polygons is that although they might have one or two equal sides or angles, they’re still irregular. Only shapes with all their sides of equal length and all equal angles are regular.

How to Distinguish between Regular and Irregular Shapes

Before categorizing shapes into regular and irregular, children should be familiar with important shape names and their properties. But when they need to decide whether a polygon is regular or irregular, here’s a quick guide to what to look for:

1. If given just the name, try to visualize it. The terms can often give you some hints, too. For example, a right-angled triangle has a right angle, which means it cannot be a regular shape (an equilateral triangle’s angles are all 60°). So, it’s an irregular one.
2. Once you’ve visualized it or if you’ve been given an image, have a close look at the sides and angles. Of course, if you remember the properties of the shape (for example, a rectangle has equal angles, but not all sides are equal), then you have your answer. But looking at the sides and angles can help if you’re unsure.
3. First, answer the question in your mind: are all sides equal? Even if the polygon has two equal sides, if the others are of a different length, it’s an irregular form, and you’ve got your answer! But if all the sides seem to be equal, then have a look at the angles.
4. Do the angles appear to be equal? If they are and you’ve checked that the sides are equal, it’s a regular shape. If the angles are different, then it’s an irregular polygon.

What is maths division? Explained

Math division is breaking a number into equal parts and determining how many equal parts can be made. For example, dividing 15 by three means splitting 15 into three equal groups of 5.

The division is represented by the symbol ‘÷’ or sometimes ‘/’.

When dividing numbers, the number being divided is called the dividend.

The number which shows how many groups the dividend will be divided into is called a divisor.

And finally, the number that you end up with is called the quotient. See the example below:

10 ÷ 5 = 2

10 is the dividend;

5 is the divisor.

2 is the quotient

Kids will start learning about division as early as Year 1. This is because division is one of the four fundamental maths operations, so it plays a vital role in maths education. The other operations are addition, subtraction, and multiplication.

Throughout the years, children will practice using mental and written methods to complete this operation. They’ll also practice dividing whole numbers, fractions, and decimals and learn to achieve a division with a remainder.

They may also understand how division is essential and valuable in real life. For example, if they are playing a game and need equal numbers of people in groups to form teams.

Let’s have a look at some examples of dividing different types of numbers, including dividing:

• whole numbers;
• fractions by whole numbers;
• decimals.

Then, we’ll go into the different short and long-division methods, which children will need to know by the end of KS2.

Maths: Division of whole numbers

Whole numbers are any positive numbers that don’t have a decimal or fractional part. 1, 2, 15, 500, and 1546 are all whole numbers as they meet these criteria.

As children learn multiplication tables, they’ll practice dividing whole numbers. This is because all numbers part of the times tables is whole numbers!

They will also learn that division is the inverse operation to multiplication –in maths, division and multiplication do the opposite jobs to each other.

For example, if we divide 56 by 7, we get 8, which are all whole numbers.

56 ÷ 7 = 8

Children can learn to test their division skills by checking their answers with multiplication. Using the example above:

7 × 8 = 56

This is why children must know their timetables by heart. It helps them to learn and understand the relationships between different numbers. This comes in handy both in their future maths lessons and everyday life (for example, they may need to understand division to share things between groups of people).

Maths: Division of fractions by whole numbers

Children will learn to divide fractions by whole numbers in Year 5. That’s also one of the curricula aims for that school year, so it’s essential to master completing these calculations.

Let’s take the example below and look at what steps kids need to follow to find the answer.

First, let’s revise: fractions have a numerator (the top number) and denominator (the bottom number). In the fraction above, 2 is the numerator, and 3 is the denominator.

Now, what you need to remember when dividing a fraction by a whole number is that you must multiply the fraction’s denominator by the whole number. Look at the example below.

In this case, you can remember that division is the opposite of multiplication, so multiply the denominator by the whole number.

In the example below, you can complete one more step – simplifying the fraction to its simplest form.

Maths: Division of decimals

In Year 5, children will also learn how to divide decimal numbers.

The most important rule for dividing decimals is to make the divisor a whole number. This can be done by multiplying the divisor by 10, although each time you multiply the divisor, you must also multiply the dividend.

Don’t worry; we’ll show you how this is done in practice with the example below.

How to divide whole numbers by decimals:

3 divided by .04

(dividend) divided by (divisor)

1. Multiply the divisor by 10:

.04 × 10 = .4

2. This still isn’t a whole number, so we’ll do it once more:

.4 × 10 = 4

3. Now we want to do the same thing to the dividend:

3 × 10 = 30

4. Because we multiplied the divisor by ten twice, we’ll do the same to the dividend:

30 × 10 = 300

5. Now three divided by .04 has turned into:

300 divided by 4

How to divide decimals by decimals:

We want to do the same thing we did above, making sure that a divisor is a whole number:

5.2 divided by .8

.8 × ten is 8

5.2 × ten is 52

52 divided by 8

52 divided by eight is the same as 5.2/.8 and is easier to work out.

What if the dividend isn’t a whole number?

Let’s say you’re given this problem:

3.35 divided by .3

.3 × 10 = 3

3.35 × 10 = 46.5

A divisor is now a whole number, and the dividend isn’t. In this case, we remove the .5 from the dividend and then add it to the answer at the end:

33.5 divided by 3

turns into

33 divided by 3

the answer to this is 11

Now we take that .5 and add it to the answer:

33.5 divided by 3 = 11.5

What is a horizontal line? Definition

A horizontal line is a line that travels from left to right across the page. This is because horizontal lines are parallel to the horizon. This fact can help children to remember the meaning of horizontal lines.

What is a vertical line?

A vertical line goes up to down. So if you draw a horizontal line and a vertical line that intersect, they are perpendicular to each other.

Examples of horizontal lines

You can see horizontal lines all around you.

If you look out at sea from the shore, you will see the horizon where the sea meets the sky. Likewise, you lie horizontally when you lie flat on your bed or the sofa.

You can also find horizontal line segments in lots of different polygons. For example, several quadrilaterals have two horizontal lines. These include squares and rectangles.

A quadrilateral is a shape that’s four-sided and two-dimensional. Examples of quadrilaterals include squares, rectangles, and kites. ‘Quad’ means four, and ‘lateral’ means sides.

A quadrilateral can be regular or irregular, meaning the sides of a quadrilateral do not have to be the same length or angles. A shape must be 2D, closed, and have four straight sides to be a quadrilateral.

Quadrilaterals have four sides, four vertices, and four interior angles that add up to 360°.

Examples of Quadrilateral Shapes

• parallelogram
• rectangle
• square
• rhombus
• trapezium
• kite

Types of quadrilateral and their properties

• A rectangle is a quadrilateral with four right angles, like a square. However, a rectangle has two opposite sides that are longer than the other two opposite sides.
• A square has equal sides. Each corner is a right angle. A square is technically also a rectangle. The square is the only regular type of quadrilateral.
• A trapezium or trapezoid has a pair of parallel sides that are opposite to one another.
• A kite is easy: it looks like a kite! It has two pairs of sides that are next to one another. If the diagonal lines between opposite corners are drawn on, they meet at a right angle.

Can children spot different quadrilaterals in the world around them? Try looking out for road signs, books, and games for examples of varying quadrilateral shapes.

What are command words?

Command words are used in sentences to instruct or order an action to take place.

They are sometimes called imperative verbs and do not always need a subject.

Often a command will begin with an imperative verb or a time connective. Sometimes, a command word like “Stop!” may exist independently.

Imperative verbs

Command words are made up of what we call ‘imperative verbs’. These are also known as ‘bossy verbs,’ as they order someone to do something.

For example, “Eat your dinner” is a command sentence and uses the imperative verb eat.

When an imperative verb is used in a sentence, we refer to that sentence as an imperative. Imperative sentences are one of the four sentence types: imperative (command), declarative (statement), interrogative (question), and exclamative (exclamation).

What is the form of an imperative sentence?

In English, the typical form of an imperative sentence uses the base verb (command word) with no subject.

Here, ‘base’ refers to the root of a verb which is the version of a verb that doesn’t contain any endings (suffixes), such as -s, -ing, and -ed. Base forms are the same as the infinitive (e.g., to walk, to paint, to think), but without the ‘to’.

An example of a command word (base verb) in a sentence is “Move over!”

Imperative sentences can also take a positive or negative form, referring to present or future time.

Where are command words used?

Commands are used in many different places and situations. The context can affect how they are used and what form they take (such as varying degrees of politeness, urgency, or formality).

Some examples of contexts where command words may be used include:

• Instructions
• Recipes
• Conversations
• Rules
• Laws
• Sports

When we use command words, we may use shorter sentences to get to the point quicker. This can create a sense of urgency by ordering someone to complete the action quickly.

For example, in a game of football, it is the referee’s job to ensure players do not waste time. A referee may order players to “Hurry up!” or “Step away from the ball!”

In a recipe, command words are often combined with time connectives such as first, secondly, after, and last, e.g., “Next add the eggs to the mixture,” which has the time connective next and the command word add.

Command words in positive and negative imperatives

Below are some examples of command words in positive and negative imperatives, within different contexts:

Example context	Positive	Negative
Sport	Kick the ball!	Don’t touch the ball with your hand!
Recipe	Pour the milk into the measuring jug.	Don’t cut the carrots too small.
Supermarket	Put that chocolate back.	Don’t forget to bring your shopping bags.
Friends	Wait outside for me!	Please don’t be late!
Rules	Remember to check your book out.	Please don’t talk loudly.
Laws	Drive safely.	Don’t litter!

Command words and politeness strategies

Sometimes, it may not be appropriate to use short, snappy commands in a particular context as it can come across as impolite. Hence, the nickname ‘bossy’ verbs!

We can make commands sound more polite and less imposing on the listener in several ways. These include:

• Adding please at the beginning or end of what we say, such as “Please take the bins out.”
• Using intonation (spoken) or a question mark (written) to make a command sound more like a request; “Put it over there?”
• Use ‘I’d like you to’ + command or ‘I’d be grateful if you’d’ + command:

“I’d like you to stand in a line.”

“I’d be grateful if you’d carry a bag for me.”

A parallelogram is a quadrilateral that has two pairs of parallel sides. The opposing sides must be of equal length and measure. A parallelogram has four vertices and four edges.

Understanding parallelograms:

Parallelograms are used for students to calculate and estimate angles. Children must also ensure that all angles in a parallelogram add up to the correct amount. The right amount is 360°. For example:

In parallelogram ‘a’, four angles need to be measured/estimated. Furthermore, each opposite angle must equal the same number, so the answer is:

A parallelogram is a 2D shape with two matching pairs of opposite sides that are parallel and equal in length. The angles inside two sides must add up to 180°, which means that the angles inside the entire shape must add up to 360°.

What are the five properties of a parallelogram?

There are five main properties of a parallelogram. So why not introduce your class to the properties of parallelograms and then test their knowledge with a quiz to ensure they understand everything?

• The opposite sides are parallel.
• Opposite sides agree – they are the same in length and angle.
• Opposite angles are in agreement – they are the same.
• Angles must add up to 360 degrees (180 degrees with consecutive angles that are supplementary).
• When one angle is correct, all other angles are right!

What are the four types of a parallelogram?

There are four types of parallelograms, including three particular types. The four types are parallelograms, squares, rectangles, and rhombuses.

It may sound silly to say that squares, rectangles, and rhombuses are types of parallelograms. So bear with me – consider the properties of each of those shapes. They are all 2D quadrilaterals, with pairs of opposite sides that are the same and opposite angles that match each other.

Calculating the area of parallelograms

A parallelogram is essentially just a rectangle that has been pushed over slightly. This means that you can use the same calculation to find the area of a parallelogram as you would calculate the area of a rectangle.

It is pretty simple, so be sure that children know how to show their work.

In the diagram above, you can see that the height of the parallelogram is 10cm, and the base is 12cm.

Using the base and height of the parallelogram, you’re able to calculate the area of a parallelogram:

base × height = area

Using the above question as an example, can you work out the area of the parallelogram? Here is the answer with the working is shown:

10cm× 12cm = 120cm²

This is the correct area of the parallelogram. Make sure to put the little squared symbol above the measurement to show that it is the area of the shape.

Calculating the height or base of a parallelogram

Using the area and base numbers of the parallelogram, you’re able to calculate the base. You must do the opposite sum to the one that calculates the area.

area÷ height = base

Using the above question as an example, let’s calculate the base of the parallelogram:

300cm² ÷ 20cm = 15cm

This is the correct height of the parallelogram.

Calculating the perimeter of a parallelogram

To calculate the perimeter of a parallelogram, you need to know the length of the sides (s) and the base (b).

The length of the sides is not the same as the height. You can see this by using your knowledge of triangles. The side of the parallelogram is longer than the height. If you created a right-angled scalene triangle utilizing the height of the parallelogram and the side as two of its edges, the side would be the longest edge of the parallelogram.

The formula for calculating the perimeter of a parallelogram is: 2(b+s)

A mathematical or maths sum results from adding two or more numbers. It is the total of the numbers added together. For example, the sum of 3 and 7 is 10.

They are taught to kids in their Maths lessons and can appear as numerical sums or be structured as word problems.

Examples of Maths sums

Numerical sum:

7 + 3 = 10

20 + 15 = 35

120 + 57 = 177

5 + 17 + 60 = 82

Another example of a maths sum uses pictures and symbols instead of numbers. Each can represent a specific number; in this case, each fruit has the same value as 1. Sums with views are significant to use at the EYFS level to get young children interested in learning Maths. Young children can count each image to find the total.

In these examples, there are six pears and nine strawberries. This is worked out as we know each piece of fruit has a value of 1, so we can count how many there are and add them together. The numerical sums are 3+3 = 6 and 5+4= 9.

Word problem sum:

Math sums structured as word problems are suitable for kids solving real-life mathematical situations. For example, they can use money as an example that asks to find the total amount.

1- Bill has £50 and Ben has £42. What is the sum of money they have if they combine their money?

Answer = £92

2- Jerry has 15 marbles, Tom has eight, and Sally has 17. What is the sum of all their marbles?

Answer = 40 marbles