Teaching Strategies, Tactics, and Methods

Sensory language refers to the use of words to create a connection to any of the five senses. In literature, sensory writing gives the reader a vivid image or description of something. The use of sensory language is a potent tool and will help children to create more detailed imagery in their writing.

Our senses help us perceive the world around us; this is why writers use sensory language. It helps us to connect to an image, description, action, or scene.

Examples of Sensory Writing

When we talk about sensory language, we’re mainly talking about adjectives. Adjectives describe words that give more detail to a noun. Here are some examples of sensory language for each of the five senses:

Still not sure? Here are some further examples: the sensory language is integrated into complete sentences; this can give you an excellent idea of using these words in your writing!

• She could see the picturesque, deserted beach in the distance. The water sparkled in the sunlight, and the sand shimmered with bright shells and shiny pebbles.
• He could hear the loud, annoying buzz of the blue bottle fly. Frustratingly, it was louder than the soft, tinkling music spilling out of the radio. So he switched the channel to roaring, clanging rock music to dry and drown out the sound of the fly.
• After they had mown the lawn, their garden smelled fresh and earthy. It was delightful, mingling with the floral, aromatic scent of the rose bushes – much nicer than the odorous, overpowering smell of fake flowers pumped out at work.
• The tarmac felt hot in the sun and rough underneath his palms. He couldn’t wait to get in between his soft, silky bedsheets at the end of the day.
• The curry was spicy, but it also had a lovely sweet tang. It might have been too hot, but the cool, minty yogurt balanced it.

The Benefits of Sensory Writing

As we’ve already established, sensory language is used in writing to create vivid imagery in the reader’s mind. Introducing your students to sensory language in literacy and English lessons will help them understand how to use it and to what effect.

Setting

Sensory writing is highly effective in helping describe places and settings. Not only is it essential that the reader has a clear idea of what somewhere looks like, but you can also tell the sounds and smells of a place. Appealing to the reader’s senses will effectively create a clear image in their mind. In addition, it can help them feel like they have been transported to the location you’re writing about. Finally, it can aid their enjoyment

Character

Character descriptions often benefit from the use of sensory language. Sensory language won’t just give us an idea of what a character looks, smells, or sounds like, but it’ll also help establish their role. For example, in some literature, sensory language can help indicate whether a character is bad or good.

An excellent example of this is the idea of physiognomy! It is the idea that a character’s external appearance indicates their characteristics and internal reality. You see this often in fairy tales, where a princess’s beauty reflects her kindness, and a witch’s ugliness reflects her wickedness. It was also trendy in the gothic movement, often featuring attractive young heroes and heroines battling against disfigured villains.

There are lots of ways you could use this to your advantage in sensory writing. Sometimes, writers subvert readers’ expectations regarding a character’s outward appearance. They harness preconceptions about physiognomy to make someone appear better or worse than they initially are and gradually reveal their character. A handsome prince might not be as dashing as he initially appears, and a disfigured character might be the kindest in the story. Physiognomy is quite an outdated belief system, so have fun playing around with expectations.

Sensory writing can also describe a character’s actions and feelings. For example, is the character sitting comfortably somewhere? What can they feel where they’re sitting? The function of sensory language is to provide a graphic presentation or image that appeals to the senses.

These are just a few examples of how sensory language can improve children’s descriptive writing. You could start by introducing them to adjectives and adverbs before showing them how they can describe things in more detail in their writing.

Where Can Sensory Writing Be Used?

Sensory language is featured in all types of creative writing. It includes poetry, plays, scripts, fiction, songs, speeches, and more. Please encourage students to use sensory language during creative writing sessions to build their vocabulary and the world they’re creating with their words.

Sensory language can even be used in factual writing, such as diary entries. For example, sensory language in a diary entry will help you accurately capture your feelings and experiences. You will then be able to look back through your diary and revisit how you felt at that moment.

Activities to Help Children Writing From the Senses

Sensory Lucky Dip

Compile a series of word cards, with each card containing a different thing that you can sense. For example, you could have hot coffee, vanilla beans, petrol, or fresh laundry for the smell cards. Divide the cards up by sense and put them face down in individual piles or separate bags. Each child can take one card for each purpose. They’ll hopefully have an excellent or strange mix of different senses! Before they get writing, please encourage them to stop and think about where and how these senses could come together. Then, they can write a short descriptive paragraph incorporating all the reasons they’ve drawn at random.

Real-World Writing from the Senses

Take inspiration from your surroundings! Without thinking too hard, get children to write down the first thing they can see, hear, feel, smell, and taste; this should be quick fire. They can then write down a paragraph using everything they’ve jotted down that they can sense. It should provide an excellent snapshot of where they were at that particular time.

Writing from Sensory Memory

As a class, brainstorm things that different sensory feelings make you think about. Maybe the smell of mints makes one child think of their grandpa. Perhaps the sight of the ocean makes another child remember an excellent holiday they went on with their family. Maybe the taste of sticky toffee pudding makes a third child think of their school dinners. You could even bring in a series of items to trigger some of these memories, such as a jar of coffee, a picture of the countryside, or a piece of silk. Get physical and tactile with these items, as they can help trigger specific memories! Once children have shared some of their memories, challenge them to write a paragraph evoking that particular memory as closely as possible, using the sensory language they’ve brainstormed.

Physical Writing from the Senses

Similarly, bring in a series of objects with solid sensory value. For example, it might be a solid-smelling perfume, a material with a distinctive touch, such as velvet, or a bit of chocolate or biscuit for a special treat! Once children have engaged with each item, challenge them to write a short paragraph describing in detail each item from a sensory standpoint, using as much rich sensory language as they can.

In geometry, a shape can be defined as a form characterized by its number of sides, the size of its angles, and dimensions. Children will learn to recognize 2D and 3D shapes and study their properties.

List of Geometric Shapes and their Properties

Let’s look at some examples of shapes for kids in math, which children will learn about. Depending on the properties, they’ll identify the shapes in math as:

• a 2D or a 3D shape;
• a regular or irregular shape.

Examples of 2D Shapes in Math

Here are some 2-dimensional shapes for kids. These shapes are taught in schools, and their properties are also included in the table below.

Examples of 3D Shapes in Math

• Sphere – no edges, no vertices, perfectly round

• Cube – 12 edges, 8 vertices, 6 square faces

• Cuboid – 12 edges (not all the same length), 8 vertices, 6 rectangular faces

• Triangular prism – 9 edges, 6 vertices, 5 faces (2 triangular and 3 rectangular)

• Cylinder – 2 curved edges, no vertices, 2 flat and circular faces

• Cone – 1 edge, 1 curved surface, 1 flat face (a circle)

Examples of Regular and Irregular Shapes

Shapes in math can also be categorized depending on whether they’re regular or irregular.

Regular shapes have angles that are all the same size and sides that are all the same length. Examples of common shapes include:

• equilateral triangles;
• squares;
• regular pentagons;
• regular hexagons;
• regular octagons;
• regular octagons.

On the other hand, the angles and sides of irregular shapes aren’t all the same. Some examples are:

• isosceles triangles;
• right-angled triangles;
• scalene triangles;
• irregular quadrilateral;
• irregular pentagons;
• irregular hexagons;
• and more.

Shapes in Math – Frequently Asked Questions

What are the basic shapes my child will learn about?

In math lessons, children will learn the properties of a wide selection of shapes. But here are 16 shapes for kids that are stumbled upon most often:

• isosceles triangle
• equilateral triangle
• scalene triangle
• right-angled triangle
• square
• rectangle
• pentagon
• hexagon
• heptagon
• quadrilateral
• circle
• cuboid
• cube
• pyramid
• cone
• cylinder

Is a triangle a regular or an irregular shape?

A triangle can be regular or irregular, depending on its properties. For example, an equilateral triangle is standard, while isosceles and scalene triangles are irregular.

Why is learning about shapes in math essential?

Learning about shapes in math lessons helps develop children’s problem-solving skills and improves their ability to organize visual information.

Also, they’ll practice their logical thinking and learn how to apply what they know about specific shapes to conclude.

Right-angled triangles are triangles containing a single 90° angle.

It is called a right angle. The right angle is usually in one of the bottom corners, but it doesn’t have to be.

They come in isosceles and scalene variations.

Right-angled isosceles triangles

These have one right angle and two other equal angles of 45°.

They have two equal sides and one long side. The hypotenuse of a triangle is always its longest side.

Scalene right-angled triangle

These have one right angle but two other unequal angles.

It has no equal sides.

Like all triangles, the three angles on these triangles always add up to 180°.

Finding the area of a right-angled triangle

The area of a right-angled triangle uses the same formula as the area of any triangle. It helps to think of a triangle as half of a quadrilateral (a 2D shape with four sides). A right-angled triangle is the same as half of a square or a rectangle because of the right angle.

The formula for finding the area of a right-angled triangle is 1/2 × base × height.

The bottom line of the triangle is the base, and the line at the side is the height. So if you were finding the area of a rectangle, you would multiply the base by the height. However, because a triangle is half the size of a rectangle, you have to multiply the product of the base and the height by 1/2 to get to half of the answer.

For example, imagine the orange right-angled triangle in the picture above.

If the base was 10 cm and the height was 6 cm, we would multiply those together to get 60 cm².

Then, we would multiply that by 1/2 to get 30 cm². That would be the area of the right-angled triangle.

Don’t forget: when you write the area of a shape, you must put a small “2” above the measurement. For example, cm² or m².

Maps are diagrammatic representations of the world, showing physical features like roads, rivers, mountains, and more. People who create maps are cartographers, and they help us navigate the world.

Map skills help us read maps and ascertain information from their symbols and scales. They’re essential for directions, recognizing the different features of a landscape, and more.

What are some different types of maps?

There are different types of maps that serve other purposes. For example:

• Road maps display roads and transport links to help drivers get from one place to another.

• Topographic maps show the shape of the Earth’s surface using contour lines, color gradients and shaded relief. They’re used for hunters, hikers, geologists, and surveyors.

• Geologic maps show the rocks and sediment below the surface of a geographic area and are used to plan construction projects.

• Weather maps show the forecasted temperatures, precipitation, and so on. They frequently appear in newspapers and on television and can help people plan.

• Maps in a geographical atlas show how land is used and things like population density and political boundaries between states and nations.

Map skills require familiarity with the following:

• Scale
• Compass directions
• Grid references
• Map’s essential
• Title

Scale

Scales help users calculate the distance, height, size, and dimensions of features on a map. Scales are often written as a ratio between the size of phenomena in real life and their relative representation on a map. For example, on a 1:100,000 map, one cm on the map represents 100,000 cm (or 1 km) in real life.

The most common maps in the UK are Ordnance Survey maps. These come in several scales:

• Travel maps have a scale of 1:125,000 and are used by drivers traveling long distances.
• Landranger maps are 1:50,000 and are helpful to drivers going shorter distances.
• Explorer maps are 1:25,000 and are generally used by walkers.
• Landplan maps are 1:10,000. They show individual streets clearly and might be used by town planners.

Types of scales

As well as ratio scales, there are also line scales and word scales.

Line Scale

Word scales

Word scales are shown like this:

Let’s say we measure the distance on a map between two cities, and the measurement is 4 cm. We then multiply that measurement by 3 to calculate the accurate distance between the two places. So 12 km would be the distance if you walked between the two cities.

Compass directions

Compasses have been used for over 2000 years, and understanding compass directions is an essential map skill.

The compass has four main points: north, east, south, and west. These are called compass points. It’s helpful to use phrases to remember the order, for example: Never Eat Silly Worms or Naughty Elephants Squirt Water.

For a more accurate reading, we can add another four points to the compass between the four we have already outlined; this gives us north-east, south-east, south-west, and north-west. The compass in the image below is oriented towards the northeast.

Grid references

Ordnance Survey maps are covered in a series of blue grid lines. These numbered squares help users identify a specific point on a map with a four or six-figure grid reference.

The vertical lines are called eastings, as they increase in value the further you travel east.

The horizontal lines are called northings, as their value increases the further north you move.

Four-figure grid references

Using the two digits of the easting and the two digits of the northing creates a four-figure grid reference.

It is the reference for the bottom left corner of a map square, making it easier to search for features.

Remember: Always start with the eastings first (use the phrase ‘along the corridor and up the stairs to get the correct order).

Six-figure grid references

We can make references even more precise by adding an extra number to the easting and northing; this helps pinpoint a more accurate location for the feature you’re looking for.

Imagine each square is a 10×10 grid. If the feature is halfway along the easting or northing, the extra number will be 5.

This extra number helps to pinpoint a feature to a place within 100 m on the map.

Essential/Legend

How do we define legend in geographical terms? A map essential or legend helps us understand the information on the map. It describes what different symbols represent to identify things like roads, buildings, and landscape features. To define legend in geography further, we can look at an example. Below is an example of a map essential for roads.

Title

The title for a map will give you an insight into what information it stores. In addition, it can include information on location, demographics, and other areas of interest that’ll make the map easier to read.

Putting your Map Reading Skills into Practice

Now that you’re familiar with some essential map reading skills let’s look into how effectively to read and use a map. If you’re going out on an adventure, here are some steps that you can take to maximize your map reading skills:

Step 1: Choosing the correct map

Before you start on your journey, you must select the correct map. There are tons of different styles of maps, including paper ones and digital ones. Of course, there are pros and cons to each type of map, but some will be more suited to your specific journey than others.

Let’s dive into the two main categories of maps: paper and digital.

• Paper Maps

One of the main benefits of paper maps is that, unlike their digital counterparts, they will never run out of battery. Therefore, if you are setting off on a long journey, it may be better to select a paper map, as you won’t have to worry about it dying when it eventually runs out of charge. Instead, you’ll be able to walk confidently along your journey, trusting that your paper map will always be there.

Even though they are more reliable, paper maps are sometimes less convenient than digital ones. An excellent option would be to carry both maps with you on your journey. Then, you can navigate along your journey using a digital map, keeping your paper map on hand as a backup.

Another massive benefit of using a paper map is that they tend to provide better spatial awareness. Thanks to technology, many people have lost their spatial awareness; this can negatively affect driving, parking, walking, orienteering, and more. Using a paper map when trying to navigate your journey, then, is an excellent way to increase your spatial awareness.

When you rely too heavily on a digital map, your eyes are glued to a screen instead of focusing on your surroundings; this disconnects you from the world around you and makes you unable to navigate your journey successfully. When using paper maps, on the other hand, you get to see things on a broader scale, with excellent detail about your surroundings, which is much better for navigation.

• Digital Maps

Technology has revolutionized how we navigate the world around us. But, compared to traditional paper maps, they have many advantages regarding orienteering.

Here are some quick-fire benefits of using digital maps:

• They are versatile and customizable, meaning that you can change the topography (the arrangement of the natural and artificial physical features of an area) and the location of objects on your map.
• They are often more accurate than paper maps.
• They offer automatic routing and allow you to control any deviations you wish to take from the decided course.
• They will not wear away over time as paper maps will.

In addition to the advantages above, there are lots of cool things that digital maps allow you to do:

• They allow you to plan out and program your walking, running clearly, and cycling routes.
• They provide handy information about your journey, such as how long it will take, how far you will travel, how high you climb, and more.
• They sometimes suggest different routes to you, allowing you to see routes others have suggested (if you are using an app).
• Some digital mapping apps allow you to share your route with others; this is a helpful safety feature, as you can let loved ones know exactly where you’re going when you get lost or off course.

Step 2: Orientate your map

Before you embark on your journey, you must get your map orientated; this is pretty simple; remember that the top of the map is north, and you should hold the map in a way that allows you to read all the writing on it.

If you are struggling with orienting your map, a good tip is to hold the map close to the ground, as this can make your route much easier to visualize and follow. You can also fold the map to see the area where you are. Then, turn the map, so it lines up correctly with the ground.

It’s essential to remember to keep turning your map as you move; this ensures that you are always traveling in the right direction.

You can also orientate your map using a compass. To do this, line up the north lines on the map with the north tip of the compass needle. Then, change your hold on the compass when you change direction to ensure your map stays orientated to the north.

Step 3: Thumb the map!

This step may sound a bit weird, but it’s super essential. Thumbing the map is where you slide your thumb along the route on your map; this is an excellent way to help you stay on track and monitor your journey.

If you travel with other people, such as a group of friends or classmates, there will typically be quite a few distractions around you as you try to navigate your journey. In this instance, thumbing the map helps you stay on track with your route.

Step 4: Think ahead and anticipate the next step in your journey

When you are out on an adventure, it is essential to look at the big picture of your route; this means thinking a few steps ahead and anticipating what the next steps of your journey will look like.

Having to check in with your map constantly can be annoying or inconvenient, especially if you carry lots of things with you or run along your route; this is why memorizing your map is such an excellent idea. You may not be able to remember your map fully, but you can always memorize the essential landmarks and different stages you will come across in your journey.

Memorizing some of your journeys will also help you increase the speed of your orienteering. While this isn’t overly essential if you travel for fun, speed is crucial to orienteering if you participate in a competition or race.

You can also use trail signs if they are available to keep you right, in addition to regularly checking back in with your map.

Step 5: Ensure to use of handrails

When you are out orienteering, you will find linear features, known commonly as handrails, that can keep you along your journey. These handrails include rivers, streams, walls, fences, and more. They are called handrails because you can cling to them, and they will keep you on track with your route.

As you travel along your journey, it is essential to keep an eye on these handrails, as they will give you a good indication of where you are. For instance, you can spot a big bend in a river or fence on your map and line it up with your surroundings.

Step 6: Notice both artificial and natural features

When navigating along your route, it is essential to pay attention to both synthetic and natural elements around you; this will give you a more solid understanding of your whereabouts and is a more reliable navigation method.

You may encounter issues if you only use artificial features to get your bearings. For instance, artificial structures, such as fences, walls, and hedges, may have changed since your map was made. For this reason, natural features can often be more reliable, as things like cliffs and streams don’t change too quickly.

Trail signs are some of the best artificial features to keep you on track with your journey. These will tell you exactly where you are, which you can cross-reference with your map to ensure you are on the right path.

Another reason it is essential to pay attention to trail signs is that they will signal unsafe or restricted areas. Depending on where you are, signs will likely tell you when a specific place is dangerous to travel in or part of someone’s private property. There may also be helpful signs in areas where you are allowed to walk that tell you what is and isn’t allowed there. For instance, there may be no dogs allowed signs, which are essential to look at if you’re traveling with your pet.

If you follow these few simple steps, you’ll be able to put your map-reading skills into practice and successfully navigate your route!

A stamen is the male reproductive organ of a flower.

The stamen comprises two parts: the anther held up by a filament.

The anther produces pollen grains that are used during pollination. First, the pollen is released when the flower opens its anther. Then, the flower relies on animals, insects, and the wind to carry the pollen to the stigma of another flower.

The pistil is the female part of a flower. A flower with both male and female parts is called a perfect one.

A flower with only male or female parts is an imperfect flower.

Translation is a term used in geometry to describe the movement of shapes from one position to another.

The translation of shapes is one of 4 transformations that can be made to forms, which are:

1. Translation
2. Rotation
3. Reflection
4. Dilation

The translation of a shape will move it up, down, left or right, but the dimensions and appearance of the shape will stay the same. To correctly translate a shape, each point must move at an equal distance.

It’s essential to note that this is not translation if a shape is made larger, smaller, or rotated.

Pupils will first be introduced to the topic by learning about 2D shape translations. So let’s have a look at how that’s done.

Introducing children to the translation of shapes

In KS2, they will be taught how 2D shapes can be moved around a page without altering the shape using squared paper. They’ll practice completing 2D shape translations of:

• triangles;
• squares;
• pentagons;
• rectangles;
• hexagons;
• and more.

To describe the translation of shapes, you have to say how many squares the shape has moved to the left or right and how many it has moved up or down.

A guide to 2D translations of shapes

Let’s have a look at how you can translate a 2D shape.

For example, let’s say the class is tasked with translating the right-angled triangle shown below to the required number of squares.

1. First, look at what direction the shape needs to be translated to. In the example above, that’s to the right.
2. Next, check how many squares. It’s been given that you must translate it 3 to the right in our example.
3. Now, it’s time to translate it. As the shape is given on a coordinates grid, use the squares – count three squares to the right.
4. Finally, ensure you check your answer to ensure accuracy. Look at the final drawing – is the shape translated in the correct direction with the right amount of squares?

Talking your class through each step of the translation of shapes, as in the example above, is an excellent way to ensure they understand how the process works.

What is a fraction?

A fraction is a number used to represent a part or several parts of something. For example, your class may be familiar with foods such as ½ a sandwich, ¼ of a pizza, or a whole cake (yum yum).

It’s essential to remember that there are two primary components of a fraction. The top number is called the numerator. It is used to show how many parts of something there are. The bottom number is called the denominator. This part shows how many features something has to be divided into. Going back to the kitchen to find an example, ½ of a cake would mean one piece of a whole cake has been split in two.

How to Simplify Fractions

Knowing how to simplify fractions need not be a challenge! First, you can simplify fractions by using a common factor that both parts of the fraction (the numerator and denominator) can divide into.

How to simplify fractions using a common factor

When it comes to fractions, you ideally want to have the simplest form of that fraction. A fraction can be simplified if the numerator and the denominator are divisible by the same number (known as a common factor). It makes it easier to solve calculations where you have to add, subtract, divide or multiply fractions together.

Let’s see how this works by taking a look at an example: Simplify 2/8

Let’s work through the process together to simplify 2/8. We can see that both numbers that make this fraction are even, meaning that two would be a common factor. When simplifying fractions, we must ensure that whatever we do to the top, we also do to the bottom. With this in mind, we can divide both fraction parts by 2.

2÷ 2 = 1

8÷ 2 = 4

And there you have your new simplified numerator and denominator, ready to embrace the simple life as 1/4.

How to simplify fractions using a Highest Common Factor

As with most maths methods, there’s more than one. You can also simplify your fractions by finding the highest common factor. To try our previous example of 2/8 this way, you start by placing both the numerator and denominator over the numerator to see if we can create whole numbers:

1. As you can see, 2/2 gives us 1, and 8/2 gives us 4.
2. Now that we’ve divided these down as far they can go, we can put the fraction back together.
3. As a result, our final answer is that 1/4 is the simplest form of this fraction.

Sometimes, we can’t simplify the numerator down to 1, as not all numerators and denominators can divide perfectly. In this case, we must find the highest number that both can divide into. It is known as the Highest Common Factor (HCF). Let’s try an example of this together:

1. We’re going to see if we can simplify the fraction 12/16.
2. As a start, we know that this fraction can be simplified by dividing it down by 2, seeing as both the numerator and denominator are even numbers.
3. By doing this, we come to 6/8. But we still have two even numbers, so this isn’t the simplest form. So let’s divide it by two again.
4. Finally, we’ve come to 3/4. 3 and 4 don’t have any common factors, so 3/4 is our final answer.

That was a long-winded way to find our fraction. We could have used the highest common factor to save ourselves a step. So let’s try again, but with HCFs in mind.

1. We’re going to see if we can simplify the fraction 12/16 (déjà vu, anyone?)
2. We will identify the common factors of both numbers within our fraction. For example, 12 and 16 are multiples of 2 and 4. 4 is the most common factor.
3. Divide the numerator and the denominator by 4 to get your simplified fraction.3/4 is our final answer.

How to Simplify Improper Fractions

Improper fractions, also known as top-heavy fractions, are fractions in which the numerator (the number above the line) is more significant than the denominator (the number beneath the line).

For example, 12/10, 15/3, and 4/2 are all examples of improper fractions.

We generally follow the same steps as common fractions when simplifying improper fractions. An all-essential rule (so important we’re saying it twice) is that whatever you do to the top, you must do to the bottom!

1. Identify a common factor (a number that multiplies with another to make your given number) of both the numerator and denominator.
2. Divide the numerator and the denominator by that same factor.
3. You have a simplified fraction. Congratulations. But wait, could your fraction be simplified further?

Ideally, you would use the highest common factor (HCF) to simplify your fraction. But when working with more significant numbers or if you lack confidence with certain times tables, that won’t always be possible. So instead, you can repeat the above steps until your fraction either contains two prime numbers or the numerator and denominator no longer share a factor higher than 1.

How to simplify improper fractions examples:

• Let’s take 14/7 as our first example.

14 and 7 are both in the 7 times tables, so 7 is a factor of both. We divide both numbers by 7 to get our new simplified fraction: 2/1. It cannot be simplified further.

• Now let’s try 16/8.

We may quickly spot that as both numbers are even, 2 would be a possible factor to divide both numbers by. Let’s try that. That gives us 8/4. Yes, it’s more straightforward, but it isn’t in its simplest form. That’s because we didn’t use the highest common factor to divide by. We must simplify it once (if dividing by 4) or even twice more (if dividing by 2) to find this fraction in its simplest form.

Let’s go back to the start and see if we can find the HCF to save us some time. Both numbers can be found in the 2, 4, and 8 times tables. The highest number there is 8 so let’s go with that. Dividing the numerator and denominator by 8 gives us 2/1, a fraction in its simplest form, in just 1 step.

• For our last example, the answer isn’t going to be 2/1! We have 35/12.

They aren’t even numbers, so they can’t be divided by 2. Moreover, they don’t share any common factors other than 1; how unhelpful! In this case, 35/12 is already in its simplest form.

How to Simplify Algebraic Fractions

Teaching simple fractions and how to simplify them can be challenging on their own. When algebra is thrown into the mix, it’s natural for your class to feel nervous. However, simplifying algebraic fractions isn’t too challenging once it’s broken down, we promise.

Let’s work through an example to see how it’s done:

²ˣ⁄₄ₓ

It may look very complex, but simplifying algebraic fractions shouldn’t be too terrifying if you know how to simplify fractions. To simplify this fraction, we must find a number that can divide into 2 and 4. Thankfully the numerator of this fraction is 2, which makes our job much easier. It leads to:

²ˣ⁄₄ₓ ÷ 2 = ˣ⁄₂ₓ

That already looks much better, but we can simplify it even further. Much like we usually look for a number, we can divide the numerator and denominator by; we can do the same with x. When we divide our example by x into both sides, we get:

ˣ⁄₂ₓ ÷ x = ½

It may take some getting used to, but it does make sense! However, more complicated fractions can’t be solved in so few steps. This one looks even more daunting, but we’ll show you just how you manage it:

²⁽ˣ⁺¹⁾⁄₄₍ₓ₊₁₎

You may be scratching your head, wondering where you start. You’ll get this without bothering if you know the basics of simplifying algebraic fractions. Your immediate thought may be to divide both sides by 2 as we’ve done before. Instead, however, we can divide both sides by x+1, which gives us the following:

²⁽ˣ⁺¹⁾⁄₄₍ₓ₊₁₎÷ x+1 = ²⁄₄

See, we knew you had it in you! Now, all there is to do is simplify this fraction even further by dividing the numerator and denominator by 2 to get:

²⁄₄ ÷ 2 = ½

You may find yourself simplifying algebraic fractions that have numerous expressions and brackets on them, such as:

² ⁽ˣ⁺¹⁾ ⁽ˣ⁺²⁾⁄₄ ₍ₓ₊₁₎ ₍ₓ₊₂₎

However, as long as these expressions are the same on the top and the bottom, the process is the same as in our earlier example.

Tricky words are words that early readers will struggle with. It might be because they have unusual spellings, contain new sounds and graphemes, or don’t follow ordinary phonemic rules. However, we often use many tricky words, so teaching kids how to spell and pronounce them is essential.

What are commonly misspelled words in English?

While you are planning spelling tests and revision support, there are some words that a lot of us need. For example, did you know that ‘misspell’ is one of the most commonly misspelled words in the English language? Check out this list of tricky words to spell that are often filled with errors. You could use this to test spelling through quizzes, tests, or even a Spelling Bee!

• acceptable
• a lot
• argument
• calendar
• column
• conscious
• definitely
• discipline
• embarrass
• exceed
• fiery
• height
• humorous
• jewelry
• library
• license
• maintenance
• miniature
• misspell
• occasionally
• possession
• receipt
• questionnaire
• referred
• rhyme
• separate

What is the most complex word ever?

If you want to challenge your little ones with tricky words to spell, why not try these tongue-twisting harsh terms?

• Sesquipedalian: This one even means ‘given using long words!
• Onomatopoeia: This word represents a particular sound and is often used for literary effect.
• Supercalifragilisticexpialidocious: Most of us remember the classic Mary Poppins character and her famous tongue-twisting song. The Oxford Dictionary defines this as a ‘nonsense word typically used by children.

More how to teach tricky words in phonics techniques:

• Encourage children to sound out the parts of the word they know and give children support with sounds they don’t know. For example, pupils can use the same tricky word, ‘ want,’ to pronounce the ‘w’ sound before they demonstrate how to pronounce the a sound.
• Teach children more letter-sound correspondences. For example, the letter ‘a’ is pronounced differently in ‘ran’ and ‘was.’ If children recognize both letter-send posts, it is easier to read new words.
• Compile a list of tricky words and write them out in different forms. For example, you can use colorful pens, write them in sand or play dough. Practice and repetition are essential when teaching tricky words in phonics, so pick activities children can repeat and remember.

What is the difference between high-frequency and tricky words to spell?

High-frequency words – A sight or high-frequency word is a commonly used word that children should be able to memorize by sight. Retaining this information is essential for children to recognize within three seconds without decoding. These words include: no, the, of, words, number, part, made, and find.

 

Tricky words – Tricky or phonically irregular words differ from sight words as children need longer to decode. They are words that cannot simply be sounded out in their head. Tricky words should be learned through various methods and not just by sight, as it may lead to difficulty understanding other tricky words that do not follow the same pattern.

What are Tricky Words in Phonics?

There are plenty of examples of tricky words out there. Any word with different sounds to individual phonics and phonics blends could be tricky.

For Phase 2, words like ‘I,’ ‘no,’ and ‘into’ are tricky because they can’t be correctly pronounced using phonics. In phase 3, terms like ‘he,’ ‘she,’ and ‘me’ use a long vowel sound for the e, despite not including double letters in the word.

Phase 4 includes ones like ‘some’ –pronounced the same as ‘sum’ – and ‘one,’ which sounds like ‘won.’ For Phase 5, words like ‘Mr’ and ‘Mrs’ are tricky because they’re contractions of the longer words ‘mister’ and ‘missus.’

What are the skills used in phonics?

There are five different phases used in phonics to help develop and improve reading and writing skills:

• Letter sounds – There are 42 letters to be learned in the English language.
• Letter formation – Using sensory methods to understand the way words are formed.
• Blending – Blending word sounds to read and write words.
• Sounds in words – Using auditory learning to understand sounds in words.
• Tricky Words – These are irregular spellings.

If you’re wondering just what is a Carroll Diagram, then you’re in the right place. So put, a Carroll Diagram (sometimes known as Lewis Carroll’s square or a bilateral diagram) is a way of sorting objects, numbers, and shapes by their traits. It looks like a table and allows people to sort data with more than two criteria into boxes visually using yes/no situations. For example, numbers or objects are categorized as ‘x’ (having an attribute x) or ‘not x’ (not having an attribute ‘x’). Sometimes, people describe these two categories as either ‘true’ or ‘false.’

Sometimes, Carroll diagrams have two attributes, like the one above. Doing this can help children to spot patterns, mainly where things like frequency are concerned. If you’d like to explore how this might work, you could get your class or child to make a Carroll diagram showing the prime numbers. You could try variables like prime and not prime vs. even and not even for the different attributes. You might want to limit your Carroll diagram to the first 49 or 50 numbers to keep things simple.

Although it’s most common for Carroll diagrams to be used in primary school, they are sometimes favored outside of education because of how accessible they make specific data. Researchers, for example, might use Carroll diagrams to make sense of what we already know about a particular subject or phenomenon.

Who is the Carroll Diagram Named After?

The Carroll diagram is named after Lewis Carroll, the author of Alice in Wonderland. He was a mathematician who specialized in symbolic logic. Lewis Carrollproduced several works about mathematics when he was working at Oxford University, and he also invented the Carroll Diagram. So, the diagram is also known as ‘Lewis Carroll’s square.’

What’s the Difference Between a Venn and Carroll Diagram?

Just like Carroll diagrams, Venn diagrams encourage students to sort data methodically and allow them to explore the relationship between data sets. Each circle represents an individual set of data. However, unlike Carroll diagrams, Venn diagrams overlap circles to create an intersection where data that belongs to both data sets can be placed. Any data that cannot be on the Venn diagram is placed outside the circles.

An equilateral triangle is a type of triangle. It is a regular polygon with unique properties: all three sides are equal in length, and all three angles in the corners are 60º.

Examples in real life can include traffic signs and tortilla chips.

You can remember the things that define an equilateral triangle because the name sounds like it has “equal” in it.

What are the three properties of an equilateral triangle?

Here are the three properties of an equilateral triangle:

• It is a regular polygon with three sides.
• All three sides are equal in length.
• All three angles are congruent and similar to 60º.

Remembering the properties of an equilateral triangle is very simple. There are three properties, which can help retain the properties since there is one for each corner or side of the triangle.

Finding the perimeter and area of equilateral triangles

Perimeter

Finding the perimeter of an equilateral triangle is easy. All sides are the same length, so all you must do is multiply the length of one side by three.

Area

To find the area of an equilateral triangle, you use the same formula as you would for any other triangle.

A triangle is half the size of a quadrilateral, so you have to halve the measurements you would use to find the quadrilateral area.

That formula is: ½ × base × height

What are the four types of triangles?

The four types of triangles are:

• equilateral;
• scalene;
• isosceles;
• right-angled.