Teaching Strategies, Tactics, and Methods

The place where an organism life is known as a habitat. The word itself comes from a Latin word meaning ‘it dwells.’

For example, the Amazon River flows through the Amazon rainforest. The primary habitat of the giant otter sometimes called the ‘river wolf,’ is the river itself. Sometimes the giant otter rests on swampy land next to the river. Living in the swamp may be a frog. The swamp is another example of habitat – as it’s a place where that organism lives.

Habitats comprise physical factors, resources, and other organisms a species will need to interact with to survive.

• Soil, moisture, and temperature are some physical features of a habitat that will influence which organisms can live there.
• Resources are things like water and nutrients (through food sources).
• Other organisms may be potential mates of the same species, prey, or other species that help support them. For instance, both bees indeed need flowers, and flowers need bees within their habitat.

Children will learn about the importance of shelter, water, food, and space within a habitat. They’ll learn about how within an animal’s home, they’ll have everything they need to be able to find food and successfully raise young.

For example, a pride of lions will need the following:

• Space – lots of room to roam and hunt
• Water – they can get this from their food or a lake or stream
• Food – large prey animals like antelope, buffalo, zebra, and giraffe
• Shelter – to protect themselves from the hot sun and hide from prey and predators, lions need plants such as shrubs and trees

This makes savannah and grassland ideal habitats for lions. However, their range – the part of their world – is different from their habitat. Today, lions’ range is limited to parts of Sub-Saharan Africa and a small amount of western India.

What are Different Habitats

Habitats vary hugely. They can be vast and tiny, filled with many other species, or isolated, very hot or cold.

There are lots of different habitats that are home to a wide variety of different types of animals. These include:

• Grassland / Savannah
• Rainforests
• Arctic Habitat
• Deserts
• Mountains
• Oceans
• Coral Reefs

Natural Habitats

A natural habitat is an ecological or environmental area where a specific species lives. It’s the place in nature where that species of plant or animal calls home. To better understand this, think of a zoo. Zookeepers need to study where a specific animal lives to replicate the animal’s natural habitat.

Natural habitats are land and water areas that contain certain environmental conditions and types of plant and animal species. These habitats are naturally occurring – meaning that humans haven’t created them.

Natural habitats are affected by soil and bedrock, water conditions, and microclimate. Therefore, some habitat types are protected to safeguard ecological diversity and the habitats of different species.

Types of natural habitats include forests, wetlands, deserts, and Arctic tundra.

Habitat is simply the place where something lives. So, the ocean habitat is where marine animals and plants live.

It’s a prominent place, joining small seas covering over 70% of the Earth’s surface. As a result, the ocean habitat is the largest habitat on Earth.

The ocean is a marine habitat, which means it contains 35g of salt for every kilogram of water and is incredibly salty.

Even though many animals (that includes humans!) can’t drink seawater, and possibly because it spans the entire planet, the ocean habitat contains the most incredible diversity of life on Earth.

From the freezing polar caps (where ice float in the water) to the warm tropics (where coral reefs abound), you’ll find marine organisms that have adapted to their wet and salty environment.

They thrive in the ocean habitat.

What makes marine habitats different from each other when it’s the same ocean habitat?

Maybe you think that it will be uniform because the ocean habitat is only one habitat.

But actually, two simple things have a massive impact on the marine organisms that live in the ocean: temperature and pressure.

That means the organisms that thrive in the tropics will likely die in the polar regions and vice versa.

Those living in the ocean’s upper layers will not make it to the bottom layers of the deep zone.

Why is the ocean habitat critical?

Any discussion on ocean habitat for kids should include an answer to the question, “Why is the ocean habitat important?”. There are many reasons why it’s essential. For example, coastal and ocean habitats protect the creatures that live in them and humans. In addition, wetlands and mangroves act as adequate buffers against storms and reduce flooding that could be dangerous to coastal communities.

Ocean habitats are also important when it comes to mating. Without it, such animals as salmon won’t be able to lay and fertilize their eggs. Young fish will also not reach maturity without ocean habitats.

Ocean temperature: How does the temperature of ocean water vary?

Just like on land, there are temperature variations in the open ocean, not only vertically (from the upper layers to the bottom) and horizontally (from the equator to the poles).

Unlike land, water temperature changes a lot more slowly. That means places close to the ocean often have milder seasons than landlocked ones.

From the top, the ocean starts warm (because of the sun) and gets colder the deeper you go.

Ocean pressure: How does pressure change with ocean depth?

Pressure increases the deeper you go.

At sea level, the air surrounding you will press against your body at roughly 14.6959 pounds per square inch (mean value of 101,325 pascals). But because the liquid inside you pushes outward using the same force, you don’t feel it.

But if you were to dive deeper, the water would start pressing against you in ever-increasing force.

For every 10.06 meters (33ft), the pressure increases.

If you go deep enough, your body won’t be able to cope with the pressure. So to survive, a human will need a more flexible body and even more flexible organs.

This means that marine animals who live in the ocean are built differently. Whales, for example, have bendy ribs and lungs that safely collapse.

Those organisms that live in the ocean’s depths have some fascinating abilities.

Monthly planning involves using a monthly planner template to organize your month. For teachers, it can include what topics you’ll cover when you assess students, what homework or projects you’ll set, and more. In addition, teachers will have done their long-term planning for the year, so using a monthly planner template for monthly planning allows for more specificity and detail.

Monthly planning for children

Children can benefit from monthly planning too. Filling out a monthly planner template and sticking it up somewhere at home means children will be more organized. They’ll know what to pack for each day and be able to prepare for projects or assessments weeks in advance.

Monthly planning will improve organization and time-management skills. Plus, it’s excellent for children with anxiety related to school. Monthly planning will help them visualize their month ahead, so nothing comes as a surprise. The same goes for SEN children who may benefit from extra preparation time. Monthly planner templates like the example below are ideal for students who feel they may benefit from more structure to their school month.

Monthly planning for parents

A filled-out monthly planner template will give parents a clearer picture of how children spend their time in school. In addition, monthly planning means parents can get more involved in their child’s education and support children with their work.

When parents know what children are learning in school, it makes talking about it at home more accessible. Asking children what they found interesting about a specific topic becomes simple, as does reading ahead with children for upcoming subjects. Going through the plan with children will reinforce the idea that organization skills are valuable and will nurture this critical area of a child’s development.

Why is monthly planning important for teachers?

Monthly planning helps to reinforce a regular teaching schedule and keeps in line with the longer-term yearly plan. It helps you stay organized and plan lessons weeks, meaning less stress and more time to provide extra support where necessary. Monthly planning also protects against any difficulties that may arise throughout the year, meaning teachers will be more prepared for whatever happens.

Using a monthly planner template will even benefit pupils. Children will feel more comfortable once settled into a routine and have more time to adjust to changing topics or circumstances.

More advantages of monthly planning for teachers:

• You can share digital copies with others
• You’ll be able to look back at the end of each month and assess your performance
• There’s more opportunity to look at how short-term goals can contribute to long-term goals
• Preparing in advance means less stress so that you can perform better as a teacher

Vygotsky’s Sociocultural Theory believes children learn from their culture, mentors, and their influences and then adapt it to their current situations. It also says children have a “zone of proximal development,” which starts with what they know and extends to what they can learn with guidance.

An overview of Sociocultural Theory?

The sociocultural theory was created by Russian psychologist Leo Vygotsky in the early 1900s. His theory was in response to the leading idea of the time: Behaviorism.

It stresses that social interaction and the role of those around us is the most significant element of our psychological development. According to sociocultural theory, human learning is mainly drawn from how we interact with others and the influence of figures we believe are more skilled and trusted examples.

It differs from other theories at the time, which focused on how individual behaviors could be explained as part of each instance. Instead, Vygotsky theorized that our psychological development is guided by people senior to us in mentor-type roles, such as teachers, doctors, parents, and other authority figures. This includes the society and social groups we are raised in, values and beliefs from our family, mentors, and the cultures we grow up in.

Vygotsky’s ideas did not receive much attention until years after his death. His views were not widely known in Russia until after the end of Stalin in the 1960s, coming to the United States and abroad some twenty years later.

Why is Sociocultural Theory critical?

Sociocultural theory is essential as it was a massive shift away from beliefs that all humans developed based on biological instinct, seeing us as more akin to animals. His work was led by his understanding that children learn from interactions, process them, and then exhibit similar behaviors in their contexts.

On a basic level, this viewpoint leads to the modern view of a child’s development and how important it is for teachers to understand their children’s environments. Not only from a developmental perspective but also from how the classroom and learning environment can make students more comfortable and aid their development. Equally, it highlights how behavior is often a symptom of a child’s background and upbringing.

What are the critical aspects of Sociocultural Theory?

There are notable areas of Sociocultural Theory that have grown in influence over time.

Vygotsky theorized that we develop psychological tools like writing, language skills, and strategies for learning. Which of these take on the most important in our lives is defined by the culture we grow up in, meaning we learn to develop the tools that have shown value in our upbringing and reflect our cultural values and needs. Simplified, we know what tools are most prominent or valuable in our development and use them accordingly.

The scope of a child’s development was crucial to Vygotsky’s work. He believed learning in children should be mostly related to where they were in their development, which led to him arguing that in what is called a zone of proximal development. The zone of proximal development (ZPD) essentially refers to what a person cannot understand or do alone but can achieve with guidance; the difference between what can be completed independently and what they can achieve with guidance or collaboration. Scaffolding is now a common phrase in classrooms and extended from here.

Another crucial part of Sociocultural Theory is private speech. This relates to how children speak to themselves to guide their actions. This was seen as critical, as it proved that children were acting beyond instinct and how it developed with age. Private speech starts aloud but extends into internal conversations, much more akin to how adults process their decisions. Vygotsky believed that you could see how children use their influences and the information they are given as part of this process, developing new skills and evolving language from others, guiding how they think and act.

How can I use Sociocultural Theory in the classroom?

Teachers will use Sociocultural Theory consistently without realizing it. For the most part, it comes with assessing what a child can do and then considering what they will be able to do with instruction and guidance to stretch their capabilities.

Teachers can use Sociocultural Theory by:

• Scaffolding: Scaffolding in teaching is when a teacher strategically puts support into a lesson. Providing support for children to practice and consolidate a particular skill, perhaps by giving a writing frame, word bank, or structured task sheet.
• Using their peers: Grouping students together to discuss ideas can bridge children’s gaps in their learning. Equally, children can work together and collaborate to solve problems.
• Differentiation: By knowing what your students are capable of, you can challenge them in a way that helps their progress. The challenge that reflects their zone of proximal development will allow children to expand their knowledge, unlike tasks that are too difficult and give the child no scope to learn.
• Adult guidance: The teacher or teaching assistants in the room can work with a child or group of children, allowing them to encourage correct perceptions and tackle misconceptions. It is essential that this is used as a tool and that adults are then used elsewhere to enable children to develop and exhibit independent learning.

A teaching assistant (also known as a classroom assistant, pupil support assistant, teacher’s aide, or TA) assists teachers by providing teaching and learning support in whatever way possible.

So what exactly is a teaching assistant? Some TAs provide more general assistance, while others specialize in certain areas of education, such as literacy, numeracy, music, specific learning needs, disability support, English as a second language, or behavior. There are also specialist teacher aides in language and culture for Aboriginal and Torres Strait Islander students in Australia.

Classroom assistants can be found in schools from early years to secondary. The number of TAs in one school can vary widely depending on the necessity and amount of funding provided.

What duties are involved?

A classroom assistant’s duties are likely to vary considerably, although they do exactly what you think a TA might do – assist the primary teacher and students. Their exact duties depend on the teaching assistant they are and what is required of them by the teachers and students they support.

What is a TA’s day-to-day?

A typical teaching assistant’s day may involve tasks like:

• Preparing classrooms for lessons
• Helping teachers plan lessons
• Listening to students read or reading to students
• Tidying up the classroom before and after lessons
• Helping students who require additional support
• Supporting teachers with managing class behavior
• Looking after upset or injured students
• Making resources for teachers and students
• Providing support out of hours, such as during exams or on school excursions
• Helping with extracurricular activities like breakfast and after-school clubs
• Carrying out administrative tasks
• Supervising students if the teacher is temporarily unavailable or supporting another group within the class

How else does a TA help the teacher?

TAs have the invaluable task of ensuring that each student gets the same level of support. For example, suppose a teacher has to spend additional time with a particular group of less able students. In that case, the TA will keep the remaining students occupied and on-task to continue their learning.

Essentially, a TA is there to be where the teacher isn’t. So, for example, if a teacher feels that a particular student may benefit from more one-on-one guided reading sessions, then it’s likely that the TA will take this on.

How do I become a classroom assistant?

There is no current need for professional qualifications to become a classroom assistant. Entry-level positions require basic literacy and numeracy skills (GCSE or equivalent level) and some experience in working with children. For most schools, the TA’s expertise in working with children does not necessarily have to have been in an educational setting.

However, having an entry-level qualification in educational support is often helpful, as people with such qualifications have a professional advantage. These qualifications generally come in certificates or diplomas, which are available to study at local colleges or through apprenticeships. For more specialized TA positions, specific capabilities may be required.

How can teaching assistants progress?

Once you have been a classroom assistant for some time, you may wish to progress further in your career. If that is the case, there are multiple options available to you.

For instance, some experienced teacher’s aides will go on to train as primary, secondary, or special education teachers. For people who have their hearts set on becoming teachers from the get-go, working as a classroom assistant is one great way to start a teaching career and pick up valuable experience working with children.

Other teaching assistants may wish to become more specialized in their profession by taking on additional training, such as:

• First aid certificate
• Training based on specialist skills, such as integration aiding, supporting gifted and talented pupils, providing support in certain school subjects, or helping students with English as a second language
• Understanding the role of play in child learning
• Understanding how to monitor and track student progress
• Training on observation and evaluation
• Learning how to engage disaffected students
• Providing an inclusive environment for all students
• Developing skills in learning intervention
• Make sure you listen to the feedback

Types of Government in Ancient Greece

Throughout the centuries, Ancient Greece witnessed various governments and systems of rule. This happened because the people of Ancient Greece were never settled on the answer to the fundamental question, “who should rule and how?”

Unable to settle on an answer to the question, governments in the Greek world took on diverse forms. Across different Greek city-states and centuries, power was expressed in other forms of rule. Even in the same city, such as Athens, the type of government could change quickly.

Fortunately, historians can learn a lot about the different governments of Ancient Greece because it was common for Greek scribes to write down the history of their city. For example, it is possible to piece together a complete account of the city of Athens from over 150 surviving political speeches and 20 000 inscriptions.

Greek Democracy Facts

The modern word, democracy, is taken from the Greek language. It means ‘demos,’ which refers to the entire citizen population. This form of government was not widespread throughout every Greek city-state, but it was incredibly influential in places such as Athens, Argos, Syracuse, and Rhodes. Athens is, however, the state that we know the most about.

The assembly of Athens (a gathering of all citizens who were allowed to vote) would gather on Pynx hill. This was a unique meeting place for Athens. The assembly was held at least once a month and could accommodate 6000 citizens. Any male citizen over 18 was allowed to speak during this assembly and vote on important matters for the city.

The ‘citizens’ of Athens made up about 10/20% of the city’s total population, and of these people, it is thought that only around 3000/6000 actively participated in politics. During this time, critics of Democracy, such as Thucydides and Aristophanes, pointed out that an excellent public speaker or popular leader could easily sway the demos.

Greek Monarchy Facts

In the Greek world, monarchies were rare and were challenging to separate from the rule of a tyrant. The most famous monarchies were Macedonia, Epeiros, and Sparta. In Macedonia and Epeiros, the monarch’s power was absolute, save for a ‘puppet’ assembly, with few legal rights.

Sparta is most famous for its system of two kings! Although not absolute monarchs, they held great power during the war. During peacetime, the kings were kept in check by an assembly of city elders known as the ephors.

This assembly of city elders held certain powers during peacetime; they could even put a king on trial or exile them!

Greek Oligarchy Facts

A Greek Oligarchy is a system of government in which a select group of people, sometimes tiny in number, ruled over a city or land.

Oligarchies were likely the most common form of city-state government in Ancient Greece and often occurred to restore order and peace after democracy had failed in a city. Unfortunately, not much is known about this rule despite being a common occurrence.

We know that an oligarchy of 400 citizens ruled in Athens during the 4th century BCE, a reaction to the breakdown of democracy in the city. Also, in 404 BCE, an oligarchy of ‘The Thirty Tyrants’ in Athens was a ruthless regime!

Greek Tyrant Facts

Tyrants were the most feared of Ancient Greek rulers. They ruled without assistance or management and often took their power by killing their predecessor.

Although, Greek tyrants were not seen as evil rulers (as the word signifies today). Tyrant meant that the rule looked after their interests instead of the people.

Syracuse, in Sicily, was ruled by a tyrant for several generations in the 4th and 3rd centuries BCE.

In Athens, they felt that tyranny was the exact opposite of democracy because democracy had allowed the citizens of Athens to feel a certain level of superiority.

As aspiring actors, your little learners must become familiar with their roles. Here’s the thing, sometimes, it feels like too many techniques. Right? How do you know what works and what doesn’t?

From hot seating to thought tapping, we’ll look at methods that can help deepen understanding of the character.

So, what is hot seating?

Hot seating is an exercise for developing a role in drama lessons, rehearsals, and other creative arts. However, this approach isn’t set in stone for art-based environments. You can adapt this technique for situations like World Book Day or knowledge tests on historical figures.

In traditional approaches, the pupil in the hot seat will sit in front of their pieces (typically arranged in a semi-circle). However, characters can sit in pairs or groups. For example, a team could consist of Jack and Jill. At the same time, a group could adopt the three little pigs.

The teacher will then take on a facilitator role and guide the questioning.

Sometimes, specific roles will require research. You can set this as a warm-up task before the exercise itself. It’s equally important that the rest of the group research their questions.

What is hot seating in drama?

Now, we probably understand the basics of hot seating. But what is hot seating in drama?

In creative lessons, we can use hot seating as a group activity. Even though the character under questioning will recount specific events, this activity gives the whole class a chance to engage. In particular, students can explore motivation or multiple perspectives. As well as experiences relating to a specific theme, topic, event, or idea.

It’s essential that you, as the teacher, prepare the person or people who will be in the hot seat. Most importantly, you should help them determine who they are, where the interview will take place, and why they are in the hot middle.

In many ways, this can quickly be done. Whether you use textual evidence, personal experience, or other forms of research for preparation, you can help children morph into the mindset of their chosen character.

Once comfortable with their role, your next step is to brief the students outside the hot seat role. Because what is hot seating without an audience? Depending on their purpose, they might need support for their question preparation. For instance, they might become journalists at a press release or characters from the same play.

The audience’s questions should be substantial. After all, their purpose is to encourage a response relevant to the dramatic situation.

How to help develop a character

When we ask ourselves, “what is hot seating?” we often focus on the exercise. However, for optimum character development, it’s essential to reflect on the experience afterward.

How you reflect on the situation is entirely up to you. However, you can use the questions below for inspiration.

• How did stepping into the character’s shoes feel?

• Did you gain any new insight into the character’s motivations while sitting in the hot seat?

• Or did you gain any new insight about yourself from the character?

• What key issues do you think are facing the character and their actions?

• For your character, what is hot seating helpful with?

You could also ask the students about the finer details of their character. Like home life, family relationships, fears, hobbies, childhood, and even hopes. As they provide answers, you can note down specific mannerisms which they can practice later in the performance, such as:

• Tapping feet.
• Twisting hands.
• Speaking slowly and deliberately.
• The tone of voice.
• Eye contact levels.
• Head scratching.
• Stutters.

What is hot seating beneficial for in teaching?

Now, we can see the benefits of this technique in drama. Let’s look at other areas where hot seating can help. In particular, what is hot seating in class?

Planning a Story

It’s said that we all have one story or novel inside us just waiting to be written. However, the writing process isn’t always easy for most people, especially children who are always learning new vocabulary and sentence structures.

Why is planning a story important?

• It provides a focussed list of things you want to write about.
• It will help the narrative of the story flow easily.
• It will stop you from getting stuck.
• You can see your ideas written down and work out if your story makes sense.
• You can keep track of your characters.
• You can work out if your ending is possible before you write loads of content.

Step 1 of planning a story: Condense your plot into just one sentence

You can ask your class to start by writing a one-sentence summary of their story.

It doesn’t matter much at this point about how many characters you’ll write about or what their names will be. You could use a general term like ‘a professional dog walker’ in your sentence.

The important part is that you understand your goal and can keep it in mind as you go through the writing process.

For example;

‘A dog walker learns one of the dogs has gone missing, so embarks on a quest to find them, meeting many different people and animals along the way.’

Step 2 of planning a story: Describe the story

Now you can expand on step one by filling in the details. A great way to structure this is to split the story into three, which becomes the plot. The three sections are known as the following;

1. Beginning
2. Middle and,
3. End

The beginning must be super exciting and keep people engaged in the story and want to discover what happens. This is where you’ll introduce your main characters and set the scene and time of the story.

The middle of the story is used to develop the themes and reveal more about your characters. It’s usually where lots of exciting things happen in the plot too.

Some popular themes in children’s books include;

• Courage
• Friendship
• Belonging
• Family
• Growing up
• Anger

Step 3 of planning a story: Characters

It would help if you considered who will be in your story and ensured they are exciting and valuable to the plot. For example, there’s no point in going into detail about your character’s next-door neighbor if they only say hello to your main character once and don’t come back into the story.

Properties of Acids

All acids contain hydrogen ions (H+). These determine how strong or weak an acid is. For example, strong acids release all hydrogen ions when added to water, transforming the water into an acidic solution. On the other hand, weak acids only let go of some of their hydrogen ions, making for a less concentrated solution.

So, the higher the concentration of hydrogen ions in water or aqueous solutions, the stronger the acid. Strong acids typically have pH levels between 1 and 3, while weak acids register in the 4-6 range on the pH scale.

pH = power of hydrogen. The pH scale, which runs from 0 to 14, measures how many hydrogen ions are present in a water-based solution. The pH scale goes like this:

0-6: acid

7: neutral

8-14: base

Acids and Bases – What’s the Difference?

 

Characteristic	Acid	Base
Behavior in aqueous solutions	Acidic substances release hydrogen ions (H+) in aqueous solutions.	Bases release hydroxide ions (OH-) when added to water.
Smell	Acids can have a powerful, acrid odor.	Typically base substances are odorless, with ammonia being the main exception.
Taste	Sour.	Bitter – a bit like eating soap.
Feel	Acids should be treated carefully – they can cause skin irritation and burning.	Bases can feel slippery because they react with the fatty acids in your skin. Some commands are also harmful, so take care when handling them.
Litmus test result	Acids will turn the litmus paper from blue to red.	No change on its own. Able to neutralize results of a positive acid test and return litmus paper to blue.
Can they conduct electricity?	Yes, in aqueous solutions	Yes, in aqueous solutions
pH level	< 7	> 7

Common Acids

Acids aren’t just confined to the science lab; they’re a large part of everyday life. From food to cleaning products and fizzy drinks to digestion, acids have a hidden role in many aspects of our daily lives. Here are five of the most common everyday acids:

1. Acetic acid – or HC2H3O2, to its friends – gives vinegar its sharp flavor. Malt vinegar is between 5-20% acetic acid.
2. Carbonic acid is an aqueous solution of carbon dioxide to water, known as carbonated or fizzy water.
3. Citric acid is a natural acid in all citrus fruits, e.g., lemons and limes.
4. Hydrochloric acid is a solution of hydrogen chloride in gastric acid, which helps us break down and digest food. Also known as HCl, hydrochloric acid is a strong, corrosive acid.
5. Sulphuric acid is a highly corrosive substance in car batteries and cleaning products.

Facts about Acids

• Under the Bronsted-Lowry definition, an acid is any substance capable of donating a proton or hydrogen ion.
• A Lewis acid is a compound that forms a covalent bond by absorbing electron pairs.
• An Arrhenius acid is a substance that increases the number of hydrogen ions in a water solution.
• To be considered an acid by any definition, a substance must have a pH level of below 7.
• The word acid comes from the Latin words “acidus” and “acere,” meaning sour.
• The chemical opposite of an acid is a base. Base substances contain negatively charged hydroxide ions (OH-) and can neutralize acids. Bases that are not water-soluble are known as alkalis.

A fraction is a number that is used to represent a whole number that has been divided into equal parts. For example, if we divide a cake into eight equal parts and take one piece, this would mean that 1/8 of the cake is gone and 7/8 is left.

What is a Factor in Maths?

A factor in maths is one of two or more numbers that divides a given number without a remainder.

In other words, a factor is a number that divides another number evenly.

For example, 5 X 2 = 10, so 5 and 2 are factors of 10.

Any given number can have many factors.

Factors are found not just in numerical sums but also in algebraic equations.

Factoring is the opposite of expanding.

How to Calculate Factors

One of the easiest ways to calculate factors is to use a factor tree.

This simple root-and-branch approach determines which can be multiplied to reach a particular number.

The main aim of this method is to find prime factors: numbers that cannot be factored down anymore.

A factor tree for the number 24, for example, would look like this:

24

4 X 6

2 X 2 X 2 X 3

Therefore, the factor of 24 is 2 X 2 X 2 X 3.

Every number that is not one can be expressed as the sum of its prime factors.

Factor Pairs

What are factor pairs?

Factor pairs are about whichever possible combination of two numbers that act as factors of a multiple, which will give a known product when multiplied together.

A factor pair is two numbers that multiply together to yield a common multiple.

Example:

Ten × 2 = 20, with 10 and 2 acting as factor pairs, with a product of 20 and factors of 10 and 2.

For the multiple of 20, 10 and 2 aren’t the only factor pairs.

5 and 4 are factor pairs of the multiple of 20, as are the numbers 1 and 24.

Different Types of Factor

Prime Factor

What is a prime factor in maths? Most numbers have an even number of factors, while a prime number has only two factors – the prime number itself and the number 1- and, therefore, only a one-factor pair.

This means a prime factor is simply a factor that is a prime number.

In other words, it is a number greater than one but one which cannot be divided precisely except by itself or by 1.

This fantastic video will quickly explain how to calculate the prime factor in a sum.

Common Factor

When working out the factors of two or more numbers, you will often find that their elements overlap.

We call these overlapping numbers ‘common factors’.

For example, using the model of 18 and 24, common factors which will multiply into both include 1, 2, 3, and 6.

Highest Common Factor

As you may have guessed, the highest common factor in a sum is the highest number of the common elements you have identified.

What is a factor in Algebra?

In algebraic equations, factors are expressed differently from the sums we have seen before.

Here, factoring, or factorizing, is done by finding an expression by multiplying simpler terms together.

For example, if you are asked to factor 2x+4:

2x is 2 lots of x.

4 is two lots of 2.

So, to factorize the sum, we combine the two:

2x+4=2(x+2).

The opposite of factoring is expanding.

Expanding a bracket means multiplying each term by the expression outside the frame.

You’ll see it is much like factoring, just the other way around. Knowing how to expand will help you to remember how to factor.

We can expand the answer we got above by following this process.

For example, with the expression 2(x+2), we multiply both x and two by the number outside the bracket. In this case, that’s the number 2. So:

2(x+2) = 2 X x + 2 X 2 = 2x+4

Both expanding and factorizing make use of the skills of simplifying algebra.

What is the Difference Between a Factor and a Multiple?

Although factors and multiples are directly linked, they are two different things.

Where factors refer to the numbers that can be multiplied to reach a number, a multiple is a result after the elements are multiplied.

So, multiples result from multiplication, whereas factors are the numbers that create the sum.