Teaching Strategies, Tactics, and Methods

Base 10

Base 10 refers to the place value number system that uses decimal numbers and is commonly used worldwide. It is the basis of a place value number system called the decimal or denary system.

What is base-10?

Have you used numbers 0 – 9 to count? Then without even realizing it, you’ve used base-10!

Base 10 is a method of assigning a place value to numbers. It’s also known as the place value number system or decimal system, as the numerical value of a number relies on where the decimal point sits. In base 10, each digit in a place of a number can have an integer value ranging from 0 to 9. This system uses ten as its base number, which is why it is called the base-10 system. Base-10 blocks help children experiment with essential addition and subtraction within the realms of base-10.

Base 10 describes how much value each digit has in a whole number.

Each number = 10x the value to its right. For example:

345,862.127

Within this large number, each digit has a value of:

3 has a place value of 300,000 (three hundred thousand)

4 has a value of 40,000 (forty thousand)

5 has a value of 5,000 (five thousand)

8 has a value of 800 (eight hundred)

6 has a value of 60 (sixty)

2 has a value of 2 (two)

1 has a value of 1/10th (one-tenth)

2 has a value of 2/100th (two one-hundredths)

5 has a value of 5/1000th (five one-thousandths)

Why do we use base-10?

Numbers 0,1,2,3,4,5,6,7,8 and 9 are the digits before 10, a number with more than one digit to define it. Using extra digits at the end of a number represents how many times we have run out of that particular digit. It is known as the place value number system.

Numbers that are bigger than 1 and are on the left side of a decimal point will fit into the following place values:

• Ones (1).
• Tens (10).
• Hundreds (100).
• Thousands (1000).
• Ten thousand (10,000).
• Hundred thousand etc. (100,000).

If they are to the right of a decimal point, the place value appears differently:

• Tenths (10th).
• Hundredths (100th).
• Thousandths (1000th).
• Ten Thousandths (10,000th).
• Hundred thousandths etc. (100,000th).

The creation of base-10:

The use of Base-10 goes back to ancient civilizations. 10 was the best number to use as a base for counting, as humans have ten fingers. Counting using fingers has been a method of simplifying counting for thousands and thousands of years. In Ancient Egypt, a decimal system was prominent. Still, the Ancient Greeks and Romans took this knowledge and developed it into a base-5 system, which allowed mathematicians to count using only one hand.

Other countries previously used base-20 (using all fingers and toes to count). It is where base-10 developed and why it’s taught globally to help

Compound Sentence

A compound sentence is a phrase we use in English when connecting two clauses to create a complex sentence.

What is a compound sentence?

To answer ‘what is a compound sentence’, we can examine how to construct one. A compound sentence comprises two independent clauses (clauses that make sense on their own), and a coordinating conjunction will connect these clauses.

Most of the time, a compound sentence is used to join two related sentences together into a single idea. Using a compound sentence can help the writer to bring complex ideas together and make your writing smoother.

How do you make a compound sentence?

Now that we have established a compound sentence, we can look at how to make one when writing. Firstly, we need two independent clauses. For example:

• I baked cookies.
• I baked cupcakes.

These two clauses make perfect sense on their own. Although the ideas presented in them are also related to each other (they are both about baking). We can connect them using a coordinating conjunction to make a compound sentence. For example:

• I baked cookies, and I baked cupcakes.

You may have noticed that when you read these two examples, the second example (the compound sentence) flows more smoothly, as you don’t pause for the full stop! That’s how compound sentences can help writing at a faster pace.

Examples of Compound Sentences

As we have covered, we require a coordinating conjunction to connect two independent clauses and create a compound sentence. Let’s look at a few examples of compound sentences using different coordinating conjunctions.

• I’m going to the shop, for I have run out of milk.
• I like swimming, and I enjoy running.
• I have never been to France, nor have I been to Australia.
• She doesn’t like apples, but she loves bananas.
• Eat up your dinner, or you won’t have any pudding.
• He has a dog, yet he wants a cat too.
• It’s my friend’s birthday soon, so I’ll get them a present.

Conjunctions in compound sentences

Conjunctions are one of the essential parts of compound sentences. They’re needed to bring the independent clauses together and glue compound sentences. So, a solid understanding of conjunctions in compound sentences is definitely in order!

What are conjunctions?

Conjunctions are connecting words that bring together two or more clauses. They often show the relation between the two clauses of ideas, for example, showing one to be a result of the other or despising the other. They’re a fundamental building brick in any language. Without them, we would only talk in lots of short sentences, which would sound silly!

Examples of conjunctions in compound sentences

Next time you build a compound sentence, check out some of the conjunctions you could use to insert them.

And

Therefore

however

but

yet

although

Despite

For

either/or

neither/nor

in case

due to

by the time

in as much

until

since

because

supposing

provided that

When

furthermore

accordingly

meanwhile

subsequently

As you can see, the different conjunctions point to other links between the two clauses. The conjunction in a compound sentence is a simple and vital way to add meaning to your speech or writing.

Common Compound Sentence Mistakes

The most common mistake children (and adults!) make when writing compound sentences is accidentally creating a comma splice.

A comma splice is when two independent clauses are connected with a comma independently rather than coordinating conjunction.

Here’s an example of a comma splice:

• I went to the park today; it was loads of fun

The comma between the two clauses should be changed to a coordinating conjunction or a full stop to split them into two sentences.

• I went to the park today, and it was loads of fun.
• I went to the park today. It was loads of fun.

To avoid making comma splices, think about whether you could replace the comma with a complete stop and have the two sentences make sense. If so, something needs to change!

National Animal of the USA

The national bird of the USA is the bald eagle, and the national mammal of the USA is the American bison. So get ready to explore these critical animal symbols of the United States!

A Tale of Two Creatures: National Animals of the USA

What animal represents the US?

Did you know that the United States has two national animals to its name?

These are the bald eagle and the American bison. They were chosen as the national bird and the national mammal, respectively.

Here you can learn about these two creatures and why they were picked to represent the spirit of the nation. It’s excellent for exploring the history of the United States in social studies or finding out information about two all-American creatures.

What will children learn about the national animals of the USA?

Keep reading to find out answers to the following questions:

• When was the bald eagle chosen as the national bird of the USA?
• When did the American bison become a national animal?
• What do the national animals symbolize?
• What are fun facts about the bald eagle and the American bison?
• Where can I find teaching resources on the national animals of the USA?

The Bald Eagle – National Bird of the United States

When was the bald eagle chosen as the national bird of the USA?

The bald eagle was selected as the national bird of the USA back in 1782 when America’s independence was new, exciting, and on everyone’s minds.

It was placed on the Great Seal, used for government institutions, official documents, and the president’s flag, to name just a few places where you can see the bald eagle symbol in action. It’s one of the leading national symbols of the country, if not the main one.

Once hunted into near-extinction by farmers and fishermen, the bald eagle was under official government protection by the Bald and Golden Eagle Protection Act, which came into effect in 1940.

It prevented the extinction of the bald eagles, preserving them as our national emblem and as an essential part of wildlife in North America!

What does the bald eagle symbolize?

The bald eagle symbolizes strength and freedom, not just of the United States as a nation but of the American people.

Eagles, in general, feature as a national symbol of many countries. They are often chosen because they represent strength, courage, freedom, and immortality – to name just a few.

The bald eagle is especially significant because it is found only in North America. It makes it the perfect animal to represent the United States!

What are five fun facts about the bald eagle symbol?

1. Bald eagles were once endangered, but because of laws passed to conserve them and ban pesticides that harmed them, they’ve made a serious comeback.
2. Bald eagles can live up to 35 years in the wild and up to 50 in captivity.
3. Here’s a love story for the ages: bald eagles mate for life, with both the mother and the father taking care of the young chicks.
4. Bald eagles are only found on the continent of North America. They can be found up in Alaska and down in Mexico.
5. The wingspan of a bald eagle is between 5 ft 11 in and 7 ft 7 in. That’s longer than the height of the average American!

The American Bison – National Mammal of the USA

When did the American bison become a national animal?

The National Bison Legacy Act, which selected the bison as our national mammal, was passed on May 9, 2016.

It means that it’s a relatively new development. For example, the bald eagle has been the national bird since 1782, so the bison has a long way to go before it becomes the go-to answer for, “What is the national animal of the USA?”

What does the American bison symbolize?

As migratory beasts, bison are said to represent freedom. They travel widely across the United States, grazing as they go. In Yellowstone, bison can travel up to 1,000 miles, leaving and returning to fertile lands with excellent greens.

They also symbolize strength and might. Bison are terrifyingly strong creatures – you certainly don’t want to make one of these gentle giants angry.

Ultimately, they’re viewed as a symbol of the self-determination of the American people, which is why they’ve been chosen as the national mammal of the United States.

What are five fun facts about American bison?

1. In the 1800s, American settlers hunted the bison and massively depleted their numbers. As a result, the bison nearly went extinct!
2. Bison are commonly called “buffalo,” but they’re not buffalo! The only buffalo species live in Africa and Asia.
3. Bison can eat 30 pounds of prairie grass every day. As ruminants, their digestive systems are specially adapted to digesting it.
4. Bison is officially the largest mammal in North America, weighing up to 2,000 pounds (for bulls) or 1,000 pounds (for cows).
5. President Theodore Roosevelt once hunted bison, but he contributed to the movement to conserve and preserve this essential American species. What a turnaround!

More National Symbols of the USA

Anthem: “The Star-Spangled Banner”

Floral Emblem: Rose

Tree: Oaktree

Motto: “In God we trust.”

Flag: The American flag, also known as the Stars and Stripes, among other names.

Mind Map

A mind map is a visual diagram that organizes data or information around a single concept or topic. It is a great memorization tool and useful for revision.

A mind map is hierarchical, meaning information is organized based on importance. The main topic is usually in the center of the mind map, with links or branches to associated sub-topics and then further branches, or twigs, to ideas, themes, images, and more. A completed mind map will show the relationships and connections between these sets of information and how they form part of a whole concept.

Mind maps are helpful, as they can be drawn by hand and used as a more visual form of note-taking. For example, a type of spider diagram, a mind map, can be color coordinated and include images, drawings, and charts to help aid learning and memory. Mind maps are great for different types of learners and can be used across all subjects.

You can easily add information to your mind map without worrying about the order in which you add it. Add another branch or twig as necessary. You can organize information however you like and try out many different minds maps styles to find one that works best for you.

How to make a mind map

1. Write your topic or theme in the center of the page
2. Think of the sub-topics you want to add and start adding branches to these from the central topic
3. Add twigs to sub-topics as you think of more ideas and relevant information

Here are some things to remember

• Use short phrases or single words where possible. It will help you to recall information more easily
• Add colors, images, diagrams, and more to help you remember and revise certain information
• Get creative! Using a mind map can help you with note-taking, revision, and learning new concepts

What is the Life Cycle of a Frog?

Frogs can live in water and on land, making them amphibians. Before they become adult frogs, they go through a series of life stages, all of which happen underwater. The life cycle of a frog can appear complex for kids. However, we can break it down into four stages.

What are the four stages of the frog cycle?

Stage 1: Egg

Eggs are laid in a group in the water by the frog. These then hatch into tadpoles. A female frog can lay up to 4,000 eggs at any one time! These eggs float on the water in ponds, lakes, and rivers and look like a large mass of jelly. These eggs are known as frogspawn and will hatch into tadpoles.

Stage 2: Tadpole

When the eggs hatch, tadpoles emerge. These are the larvae of the frog. They don’t move very much for the first two weeks after emerging and will spend time absorbing the remaining yolk from their egg for nutrients.

The tadpole then spends time eating and growing. When tadpoles are young, they look much more like fish than frogs. They also have gills to allow them to breathe underwater. Tadpoles feed on algae and other plant life in the water to give them energy.

As the tadpole grows, hind limbs emerge like tiny frogs with tails. They also develop lungs to breathe out of the water while on land.

Stage 3: Young Frog

The juvenile frog grows front legs, and its tail gradually becomes shorter until it is no longer there. It is because there are nutrients within its tail that it absorbs as food. This young froglet is then ready to jump out of the water to experience life on land.

Stage 4: Adult Frog

As the frog develops into an adult, it will eat insects rather than vegetation. It can take up to four years before the frog becomes fully mature. Once it is, the frog can then lay eggs or fertilize them, and the life cycle of a frog can start all over again!

Our beautifully illustrated Frog Life Cycle Posters can adorn your classroom to remind your children of the importance of each stage.

What is frogspawn?

The eggs that frogs lay are called frog spawn. Frogspawn looks like a large clump of jelly. However, it is, in fact, a collection of thousands of frog eggs stuck together. Each egg has a tiny tadpole embryo surrounded by protective jelly that keeps the tadpole safe.

When the frogspawn is laid by the female frog, it will sit partially submerged in the pond water. The tadpoles inside each egg will slowly eat the jelly surrounding them and build their strength. Eventually, once all the jellies are eaten, the tadpoles will hatch.

A frog’s early life is complicated; only 10 of the 4,000 eggs will become adult frogs. It is because most of the frogspawn and tadpoles are often eaten by predators such as birds, fish, and newts.

How can I help take care of tadpoles?

Tadpoles have a high mortality rate, so many don’t grow into fully-fledged frogs. Threats to tadpoles include predators, such as birds, fish, mammals, and turtles, and a lack of oxygen in their water supply. Some scientists claim that tadpoles have a 4% chance of survival, meaning just four tadpoles in every 100 become adult frogs. Scary stuff, right?

Luckily, there are things we can do, as nature lovers, to give the humble tadpole a greater chance of survival. These activities are a great way to introduce young children to the wonders of nature. Why not try them out with your family this weekend?

Add rocks and oxygenating plants to your pond. Rocks provide tadpoles with much-needed shelter from predators, and oxygenating plants improve the quality of their water source. Arrowhead, eelgrass, fanwort, and water sprite are the best oxygenating plants.

Plant a tree near your water source. Ever seen a pond full of green water? That’s algae, which thrives in warm and sunny conditions. Unfortunately, the algae suck up all the oxygen, leaving none for other inhabitants, like tadpoles and frogs. To reduce the algae levels in your pond, plant a tree or shrub next to it to keep the water shaded and cool in the warmer months.

Feed them. Tadpoles feed on dead insects, vegetation, and algae in the wild. You can supplement their natural diet with some of these items: boiled spinach, fish food, boiled eggs, flies, and crickets.

Build an exit ramp. When the tadpoles’ limbs develop, they’ll need a way to get out of the water – a frog freeway, if you will. You can use plants, rocks, or bits of wood to create yours.

Something to bear in mind. Many animals rely on tadpoles to sustain them during the spring. It may seem cruel, but they’re a vital food source for birds, snakes, hedgehogs, newts, and other tadpoles! One main reason frogs lay so many eggs is that they know only a handful will survive. So, even though it’s not great news for the tadpoles, they play a significant role in their ecosystem, and we should be careful not to disrupt this natural balance too much.

To explore the wonderful world of frogs, why not go to a local pond and see whether you can see any frogspawn or tadpoles? It can be the perfect introduction to the life cycle of a frog, and you will get to see these amazing amphibians in their natural habitat!

Getting outdoors can be a great break from the classroom and make learning more meaningful. Seeing a frog in the wild, catching insects, and laying eggs is much more powerful than reading about them in books. Create a simple nature checklist to accompany your trip outside. Can your children spot frogspawn, a froglet, a lily pad, algae, insects, and other flora and fauna while on your mini field trip? Once you have hooked your budding naturalists, they will be eager to learn more about frogs!

Rectangle

A rectangle is a 2D shape that has four sides, four corners, and four right angles. Opposite sides of a rectangle shape are the same length, with one pair being longer than the other. If a rectangle’s sides were the same size, it would be known as a square.

What is a Rectangle?

A rectangle is a 2D shape that has four sides, four corners, and four right angles. Opposite sides of a rectangle shape are the same length, with one pair being longer than the other. If a rectangle’s sides were the same size, it would be known as a square.

The pairs of opposite sides are parallel to one another, which means that rectangles are also a type of parallelogram.

The word “rectangle” comes from the Latin word “rect,” which means “right,” and the Latin word “angulus,” which means “angle.” From those two words, we get “rectangle.” Each corner of a rectangle shape has a right angle of 90º.

A rectangle has two diagonals equal in length and intersects in the middle.

A rectangle is oblong. It has two pairs of parallel sides and four right angles.

A rectangle can also be known as an equiangular quadrilateral. It is because a rectangle is a quadrilateral shape (4-sided) with equal parallel sides, and all four corners have angles that are 90º. Because all the angles are 90º, a rectangle shape can also be called an equiangular quadrilateral.

Rectangle shapes are all around us. For instance, TVs, tablets, envelopes, pillows, towels, exercise books, mobile phones, and measuring rulers can all be rectangle shape.

Can you get children to think of rectangular things they might see daily?

Calculate the perimeter of a rectangle

Calculate the perimeter of a rectangle shape by adding the length and width before multiplying the sum of those two measurements by 2.

Calculate the area of a rectangle

You can calculate the area of a rectangle shape if you know its length and width. Then, multiply the length by the width to get the area.

Using the blue rectangle in the example above, this is the sum to work out the area:

3cm× 4 cm = 12 cm²

Remember to put a small 2 above the cm part to show the area of a shape.

Is a square a rectangle?

It is a question that will always come up or get asked. Is a square a rectangle? Luckily it’s got a pretty easy answer. Yes! A square is a rectangle, by definition. To figure this out, you must look at each shape’s definitions.

A square is a shape that has four equal-length sides and four 90-degree right angles. A rectangle is a shape with four straight sides and four right angles. That means that, by definition, a square can be classed as a rectangle. However, a rectangle cannot be classed as a square.

What is a Syllable?

Syllable

What is a syllable in English? A syllable is a unit of spoken language that forms an entire word or parts of words.

What is a syllable in English? – Examples:

Below are some examples of words with different numbers of syllables:

• ‘Tie’ has one syllable.
• ‘Rescue’ has two syllables – Res + cue
• ‘Alphabet’ has three syllables – Al + pha + bet
• ‘Activity’ has four syllables – Ac + tiv + i + ty
• ‘Electricity’ has five syllables – E + lec + tri + ci + ty

A word with only one syllable can be called monosyllabic. There are names for other syllable amounts in words, too: disyllabic for two, trisyllabic for three, and quadrisyllabic for four. Or, you can refer to them as polysyllabic if they have more than one!

An important thing to note is that the length of the word doesn’t affect the number of syllables it has. Instead, it’s all about the number of vowel sounds.

What are the six types of syllables?

Next up in our journey of learning ‘what is a syllable in English?’, we’ll learn about the different kinds of syllables. While there are two main types of syllables, closed and open, there can also be split into six other classes. Let’s learn a bit about what these are:

1) Closed Syllable

A closed syllable is a word unit with a single vowel that ends with a consonant. These have short sounds such as bat, plant, shop, and rabbit.

2) Open Syllable

An open syllable is a word unit that ends with a single vowel, such as go, me, you, and potato.

There are more types of syllables that you might come across in more advanced grammar, including:

• Magic ‘e’ or vowel-consonant -e;
• R-controlled syllables;
• Diphthong (vowel team);
• And consonant ‘le.’

3) Vowel-consonant-e Syllable (VCE)

These syllables end in a final silent ‘e’ (hence why they’ve nicknamed magic ‘e’ syllables) with a consonant just before the silent ‘e.’ The silent ‘e’ makes the vowel before the consonant have a long sound. Here are some examples:

• line
• cute
• mine
• pine
• mute
• home

This syllable is usually taught after children are familiar with short and long sounds and closed and open syllables. So here’s a teaching tip: to transition from closed syllables to VCE words, try adding a silent ‘E’ to CVC words. For example, ‘hat’ becomes ‘hate,’ and ‘tap’ becomes ‘tape.’

4) R-controlled Syllable (VR)

In r-controlled syllable words, there’s always a vowel followed by an ‘r.’ The ‘r’ gives the word a unique sound. Examples of VR words:

• her
• fur
• ear
• for
• purr

This kind of syllable is taught after open, closed, and VCE syllables.

5) Diphthong (vowel team) Syllable

A diphthong syllable usually has two vowels next to each other which are pronounced together, which is why they’re dubbed ‘vowel teams’ – the vowels work together as a syllable. The vowel combinations are typical:

• ai
• ay
• ow
• oe
• ie
• ee
• oi
• ea
• oa

Here are examples of words with diphthong syllables:

• tail;
• play;
• grow;
• oboe;
• eight;
• meet;
• beat;

For example, many words have the vowel combination ‘io’ in them, such as ‘lion’. With these vowel combinations, you split the syllable between ‘i’ and ‘o’ so that the word has two syllables. These syllables are still known as vowel teams.

6) Consonant ‘le’ Syllable

These syllables have no vowel sound – the silent ‘e’ at the end of the syllable works as the only vowel. You only pronounce the consonant and the ‘l’. Examples of words with the ‘le’ syllable:

• maple
• purple
• turtle
• ripple
• circle
• cycle
• tableTop of Form

What are Regular Verbs? Meaning and Examples

A regular verb is a verb that follows a predictable pattern when switching between tenses. In English, you can usually form the past tense of a regular verb simply by adding the suffix “-ed” or “-d” to the end of the verb. It applies to both the simple past tense and the past participle.

Regular verbs are an essential part of the language; luckily, they’re relatively easy to learn. So, now we’ve seen a standard verb definition, let’s break it down and find out the exact meaning of regular verbs and how they operate. We can also look at some frequent verb examples so you can see them in action.

We all use regular verbs daily, but we probably don’t notice them. Two in that sentence – “use” and “notice”- are examples of regular verbs. They can be transformed into the past tense simply by adding “-ed” or “-d” to the end of the verb:

• “I use a pencil to do my homework” becomes “I used a pencil to do my homework.”
• “I notice the trees on my way home” becomes, “I noticed the trees on my way home.”

So, a regular verb always takes this very predictable form when moving it from the present into the simple past tense.

Some more regular verbs examples include:

• walk – walked
• laugh – laughed
• jump – jumped
• talk – talked
• look – looked
• agree – agreed
• listen – listened
• dance – danced
• wonder – wondered
• wish – wished

As you can see, each of these verbs can very quickly be turned into its past-tense equivalent. It is why regular verbs are the first ones children learn – they make it as easy as possible for children to talk and write about what has happened in the past.

There are lots of regular verbs in English! Each behaves the same way as the regular verb examples we’ve given here. For example, if you want to talk about something that’s already happened, you add “-ed” or “-d” to the end.

Past participle regular verbs meaning and examples

A participle is a non-finite verb that can also be used as an adjective. For example:

• He looked at his burned finger.
• He has burned his finger.

The first sentence uses the word ” burned ” as an adjective. In the second, it is used as the past participle.

The past participle of a verb is always used with the verb “to have” (“He has burned his finger”). It is most often used to form the past perfect tense to describe an action that has already been completed.

Here are some more examples of past participle regular verbs:

• I have completed my homework.
• We had talked about it.
• They played in the garden.
• I have cooked my dinner.
• She has watched television.
• He had shouted to his friend.

The great thing about regular verbs is that they don’t change their form between the simple past tense and the past participle. You still form them simply by adding “-ed” or “-d” to the end of the regular verb.

What’s the difference between regular and irregular verbs?

It’s an irregular verb if it can’t be put into the past tense easily, if the verb doesn’t fit with the ending “-ed” or “-d,” or if the verb needs to change its form to make sense in the past. These are more tricky to learn because irregular verbs don’t follow the regular pattern you’d expect when you put them into the past tense. Some examples of irregular verbs include:

• eat – ate
• write – wrote
• go – went
• run – ran
• see – saw

English is full of irregular verbs, which must be learned on a case-by-case basis. Unfortunately, children are usually not taught irregular verbs until they have grasped how regular verbs work and feel confident using them.

What is a factor in Maths?

A factor in maths is one of 2 or more numbers that divide into a number without a remainder, making it a whole number. In other words, a factor is a number that divides another number evenly. There are no numbers left over after the division process.

For instance, 5 x 2 = 10, so 5 and 2 are factors of 10.

Any number can have a large number of factors. Many numbers have an even number of factors, but square numbers have an odd number.

For instance, 25 is a square number because it is the square of 5. Therefore, its factors are 1, 5, and 25.

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

Factoring is the opposite of expanding. You can find out more about factoring and expanding by reading on. There are also some teacher-made resources listed to support your teaching about factors. Top of Form

How to calculate factors in Maths

One of the easiest ways children calculate factors is to use a factor tree. It is a simple root-and-branch approach to determine which numbers can be multiplied to reach a particular number.

The main aim of using this method is to find prime factors, which are numbers that cannot be factored down anymore. Prime factors must be prime numbers because they are only divisible by themselves and by 1.

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 result of factorizing the number 24 is 2 x 2 x 2 x 3, with 2 and 3 both being prime numbers.

Every whole number that isn’t 1 can be expressed as the sum of its prime factors.

Factor pairs

What are factor pairs?

Factor pairs are a combination of two numbers that act as factors of a multiple, giving a known product or number when multiplied together.

Let’s look at the number 20. An example of factor pairs of 20 would be the multiplication sum of 10 x 2.

10 x 2 = 20

10 and 2 are the factor pair, and 20 is the product of this factor pair.

For the multiple of 20, the factors of 10 and 2 together aren’t the only factor pair that exist. For example, 5 and 4; are a factor pair of the multiple of 20, as 1 and 20.

Learning multiplication tables well can help children to understand factor pairs and identify them quickly. Why not ask your children to match all the possible factor pairs for a number to demonstrate the concept?

Different types of factor

Prime Factor

Many numbers have an even number of factors, while a prime number has only two factors; the prime number itself and the number 1. It means it only has one-factor pair.

It means a prime factor is a factor that is also a prime number.

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

Common Factor

When working out the factors of two or more numbers, you will often find that their factors overlap. We call these overlapping numbers common factors.

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

Highest Common Factor (HCF)

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

For example, the highest common factor of 24 and 6 is 6. It is because 6 goes into 6 once, and 6 goes into 24 four times.

What are the factors of 100?

The factors of 100 are all the numbers that make 100 when two are multiplied. Similarly, factor pairs of 100 are the whole positive or negative numbers that equal 100.

Factor pairs cannot include a fraction or a decimal number.

To find factors of 100, we must first take the numbers 1 and 100 and begin discovering the other pairs of numbers, which, when multiplied together, make 100.

Factors of 100:

• 1
• 2
• 4
• 5
• 10
• 20
• 25
• 50
• 100

What are the factor pairs of 100? To find both the positive and negative factor pairs of 100, take a pair and multiply the two numbers together to get 100. Here are some examples:

Positive Factor Pairs of 100

1 × 100 = 100 ⇒ (1, 100)

2 × 50 = 100 ⇒ (2, 50)

4 × 25 = 100 ⇒ (4, 25

5 × 20 = 100 ⇒ (5, 20)

10 × 10 = 100 ⇒ (10, 10

Negative Factor Pairs of 100

-1 × -100 = 100 ⇒ (-1, -100)

2 × -50 = 100 ⇒ (-2, -50)

-4 × -25 = 100 ⇒ (-4, -25)

-5 × -20 = 100 ⇒ (-5, -20

-10 × -10 = 100 ⇒ (-10, -10)

Factors of 100 by Prime Factorisation

Prime factorization refers to expressing a composite number as the product of the prime factors. There are three key steps to prime factorization:

To get the prime factorization of 100, we must divide it by its smallest prime factor, 2: 100 ÷ 2 = 50.

Next, divide 50 by its most minor prime factor.

Repeat this process until the product is 1.

The Division Method

In the same way that the factors of 100 can be found by multiplying numbers together, it can also be found through the division method. To carry out this division method, divide 100 by numbers, starting from 1, and see whether they leave you with a whole number or leave a remainder as well.

For example:

100 ➗ 1 = 100 (The factor is 1, and the remainder is 0)

100 ➗ 2 = 50 (The factor is 2, and the remainder is 0)

100 ➗ 4 = 25 (The factor is 4, and the remainder is 0)

100 ➗ 5 = 20 (The factor is 5, and the remainder is 0)

100 ➗ 10 = 10 (The factor is 10, and the remainder is 0)

100 ➗ 20 = 5 (The factor is 20, and the remainder is 0)

100 ➗ 25 = 4 (The factor is 25, and the remainder is 0)

100 ➗ 50 = 2 (The factor is 50, and the remainder is 0)

100 ➗ 100 = 1 (The factor is 100, and the remainder is 0)

However, if you were to divide 100 by 3, you would get a remainder of 0.333. So it means that 3 is not a factor of 100.

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 expressions together.

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

2x is 2 lots of x.

4 is 2 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 bracket.

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 2 by the number outside the bracket. In this case, that’s the number 2. So:

2(x+2) = 2 × x + 2× 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 factors are multiplied.

So, multiples result from a multiplication sum, whereas factors are the numbers that create the sum. Therefore, they are opposite concepts to each other.

What is the Mode in Maths?

The mode in maths is the value that occurs most often in a data set.

So in the last 2, 2, 3, 3, 3, 4, 5, 6, 6, the modal number is 3 as it appears most often.

The mode in maths is one of the key ways to detect the average within a set of data. By finding the standard, we can understand the most common value. Moreover, it might tell us something significant about the data set and can be very useful. Although analyzing data can be complicated, learning about the simple concepts of mode, median, mean, and range are helpful.

You can remember what the mode means thanks to the first two letters, “M” and “O.” Remember that the mode is the number that appears Most Often.

The mode in maths is not to be confused with other averages, such as the median, mean, and range. These are similar concepts to managing data sets, but each concept does something different with a group of numbers.

More Than One Modal Number

While, in an ideal world, there would be one modal number for each data set, this is not always the case. Often, a collection of data will have more than one mode.

Let’s look at an example to illustrate this.

Example 1: Find the modal number(s) in this set of data…

3, 3, 8, 3, 10, 21, 9, 4, 7, 4, 12, 4

If you look closely at the data above, you can see that the number 3 and the number 4 appearing three times. However, the rest of the scores only appear once. Therefore, there must be two modal numbers for this set of data.

The modal numbers are 3 and 4.

When a data set has two modes, it is called ‘bimodal.’

Example 2: Find the modal number(s) in this set of data…

88, 70, 70, 21, 88, 70, 70, 88, 90, 90, 90, 88, 35, 10, 90

By analyzing this data set, you can see three numbers appear 4 times. These numbers are 88, 70, and 90. It means that there are 3 modes for this set of data.

The modal numbers are 88, 70, and 90.

It is called multimodal when a data set has more than two modes.

Modal Classes

In some instances, you will find that each value in a data set occurs the same number of times. Finding the mode won’t be very helpful when working with data like this. Instead, you can group the data into ‘modal classes, and you can then identify the mode of each of the individual classes. It will give you an understanding of the data set as a whole.

For example, find the mode of this set of data:

1, 4, 2, 7, 8, 9, 10, 17, 19, 20, 32, 34, 37, 40, 43

Now, you have to separate your data into appropriate groups. Again, it’s essential to ensure all your groups are of equal sizes so you can accurately compare them.

The groups for this set of data are as follows:

1 – 4: 3 values (1, 4, and 2)

7 – 10: 4 values (7, 8, 9, and 10)

17 – 20: 3 values (17, 19, and 20)

31 – 34: 2 values (32 and 34)

36 – 39: 1 values (37)

40 – 43: 2 values (40 and 43)

One class contains more values than the others: 7-10 has 4 values. It means that the modal class is 7-10.

This method of dividing data into different groups and figuring out the modal class is advantageous when dealing with a data set containing anomalies (outliers/irregularities) that could skew the results.

Still unsure about finding the modal class? Let’s try another example!

Find the mode in this set of data:

20, 22, 25, 26, 27, 28, 29, 33, 46, 50, 57, 58, 59, 61, 63, 72, 74, 75

The first step is to analyze the data closely and find appropriate groups for your numbers. Remember to make sure all of your groups are the same size!

For this set of data, the groups would be as follows:

20 – 24

25 – 29

30 – 34

46 – 50

55 – 59

60 – 64

71 – 75

Now that you have your groups, you can figure out how many values each has.

20 – 24: 2 values (20 and 22)

25 – 29: 5 values (25, 26, 27, 28, and 29)

30 – 34: 1 value (33)

46 – 50: 2 values (46 and 50)

55 – 59: 3 values (57, 58, and 59)

60 – 64: 2 values (61 and 63)

71 – 75: 3 values (72, 74, and 75)

It is clear that the group ’25 – 29’ has more values than any other group. Therefore, the modal class for this data set is 25 – 29.

Advantages and Disadvantages of the Mode

Finding the modal value in a data set can be a good way of understanding the data better. However, as a measurement method, the mode has several downsides. Let’s have a look at some of the key advantages and disadvantages of finding the mode:

Benefits of finding the mode:

• The mode is super simple and easy to understand.
• The mode is not affected by extremely large or small values in a set of data.
• The mode is easy to find in a group of data.
• The mode can be located on a graph.

Disadvantages of finding the mode:

• There must be repeated values in a data set to find the mode.
• It is hard to find the mode when the data set contains a small number of values.
• A set of data can have 1 mode, more than 1 mode, or no mode at all

What is the Mode in Maths? – Why is it Important?

In schools, this topic is essential when closely linked to the National Curriculum. For example, in Year 5, children must describe and interpret different data sets in context (ACMSP120). In Year 6, they must analyze secondary data presented in digital media and elsewhere (ACMSP148).

Understanding the mode in maths is also essential for children’s observation and analysis skills. After recording data, the mode requires children to observe, analyze, and present their findings. In the long run, this can inspire children to look at more numerical information in everyday life, such as statistics in the news. In addition, it is good preparation for other topics and subjects, like science lessons.

Learning about the mode in maths gives children a fantastic opportunity to do independent research tasks. Children can use the Internet, newspapers, or observe events from everyday life to find data sets to practice finding the mode. For example, what was the modal average of all the students that took a test? From a scientific experiment, what was the most common temperature recorded?

Geography Of Asia

Asia is the largest continent on Earth. It makes up one-third of the world! Because of how big it is, Asia’s geography is highly diverse.

The Geography of Asia’s Continent

Asia is located in the eastern part of the Eurasian supercontinent. It’s the largest continent on Earth and makes up 60% of the world’s population! To the west of Asia’s part of Eurasia is Europe. Asia is bordered by three oceans – the Pacific, Arctic, and Indian. The continent of Asia is so vast that it contains both Earth’s highest and lowest points – Mount Everest and the Challenger Deep trench, respectively. There are 48 countries in the Asian continent. So you can imagine how diverse the geography, people, floral, and fauna are.

The geography of Asia’s continent has five major physical regions:
• Mountains
• Plateaus
• Plains
• Steppes
• Deserts
• Freshwater Environments
• Saltwater Environments

The Himalayas are a mountain system that separates the Indian subcontinent from the rest of Asia. The mountain system extends for an impressive 2,500 kilometers! Apart from being part of India, the Himalayas are also in Nepal, Bhutan, India, Pakistan, Afghanistan, and China. The highest mountain summit in the world, Mount Everest, is located here. The whopping 8,850-meter-tall summit passes through the Nepal-China border. The tectonic plate that the subcontinent of India is on is moving. It leads the Himalayas to grow around 5 centimeters every year!

The Tibetan Plateau is “the rooftop of the world” and is considered the most extensive and highest area. It’s about half the size of the United States of America and 5,000 meters above sea level. So for the same reason, the Himalayas are growing, and the Tibetan Plateau is rising too.Top of Form

The Climate, Flora, and Fauna of Asia

As the continent of Asia is so huge, each area has its unique climate, flora, and fauna. For example, China has more species of flowers than North and South America combined! China is known as the “Mother of Gardens” as the country is believed to be the originator of most species of plants. It includes roses, peonies, oranges, cucumber, peaches, and ginger. Wow!

Climate factors across Asia mean that the population is unevenly distributed. There are significant concentrations of people in Western Asia, eastern China, and India. Incredibly, Asia features the majority of climates known on Earth. Here are some of the environments of Asia, with an example country featured:

• Rainforest (The Philippines)
  • Grasslands (India)
  • Desert (Saudi Arabia)
  • Subarctic (Russia)
  • Temperate (Japan)

That being said, most Asia experiences what is known as a ‘continental climate.’ It means that the difference in Summer and Winter temperatures is significant. Southern Asia experiences the continent’s hottest weather, for example, Indonesia. On the other hand, Siberia once recorded a spine-tingling −67.8°C!

Speaking of Siberia, Lake Baikal is known as the “Galápagos of Russia.” Can you guess why? Because of how old the lake is, flora and fauna have been able to evolve for millions of years. It is an important study of evolution with an incredible 1,340 species of animals and 570 species of plants. Hundreds of these species are found nowhere else on Earth.

There are six tiger subspecies in Asia alone, including the hardy Siberian Tiger and the majestic Bengal Tiger. Sadly, only about 3,900 tigers remain in the wild in Asia. Of course, the Asian Elephant is distinguished from its African cousin by its small, fan-shaped ears. There are also 16 types of subspecies of bears, including Giant Pandas! These cuddly-looking giants are native to South Central China. Much like tigers, Giant Pandas are very vulnerable. There are only 2,060 in the wild.

Five fun facts about the Geography of Asia’s Continent!

1. China borders 14 different countries but only has one timezone. Russia also borders 14 countries but has 11 time zones!
2. The Arabian Desert, which spans an unbelievable 900,000 square miles, is only the fourth-largest desert in the world. But don’t worry; the Arabian Desert is still Asia’s most significant.
3. Have you heard about Taal Lake in The Philippines? Inside it, you’ll find an island; on the island, you’ll find another lake, and on that lake, you’ll find another tiny island!
4. Indonesia is made up of more than 17,000 islands.
5. The largest city in Asia, Tokyo (Japan), has a larger population than Canada!