Making learning fun for children is the secret to effective learning since it is simpler for youngsters to remember things when they see them in action. Additionally, it enables kids to recognize other perspectives and respond accurately to questions about them.

They will also be able to relate mathematical ideas to their surroundings, classroom, and home.

Witnessing an acute angle in real-life

Less than 90° angles are referred to as acute angles. From obtuse angles to right angles, all of these triangles and angles have some real-life uses too. Following are a few instances of acute angles in real life:

1. Letter V makes an acute angle

Amazing uses of the alphabet in mathematics! Is it not? The inner side of the “V” forms an acute angle that is less than 90 degrees when the lines are joined, as can be seen. Because they are used so frequently in both speech and writing, the alphabet aid in children’s memorization of the incidence of acute angles.

2. When the clock strikes 1 or 2 o’clock, it forms an acute angle

Every instant, the clock’s hands show the passing of time. The minute and hour hands frequently rest in different positions, creating varied angles as a consequence, in an effort to show the time to us. However, at particular times or situations, such as when the clock strikes 1 or 2 o’clock and parallelly 10 or 11 o’clock, it forms an acute angle.

3. The pizza slice forms an acute angle

Who doesn’t enjoy pizza? Well, especially among kids, it’s the most popular street food. We adhere to the customary rules of eating pizza in order to make it easier for us to do so. With the use of a cutter, we often cut the entire circular pizza into triangles of identical size, typically cutting them into more than four slices to give the impression of extra portions. Therefore, such slices show an acute angle that kids may readily understand.

4. Few roads signs which show directions from acute angles

One common road sign that shows directions from an acute angle is the “Yield” sign. This sign is typically triangular in shape, with the point of the triangle facing downward. This means that the angle formed by the two sides of the sign is acute.

Another example of a road sign that shows directions from an acute angle is the “Stop” sign. This sign is also typically triangular in shape, with the point of the triangle facing upward. This means that the angle formed by the two sides of the sign is again acute.

5. Few exercise postures form acute angles

Acute angles are common in many different types of exercise and can be used to help improve balance, flexibility, and strength. There are many different exercise postures that involve acute angles. Some examples include:

The downward dog poses in yoga. In this pose, the body forms an inverted “V” shape, with the hands and feet on the ground and the hips and buttocks pointed upward. This creates an acute angle between the arms and legs.

The plank position in pilates. In this position, the body is supported on the forearms and toes, with the body forming a straight line. This creates an acute angle between the arms and the legs.

6. A pair of open scissors

The most crucial item in a student’s life is a pair of scissors, which they use for projects, homework, activities in class, and just for play. Acute angles may be seen when scissors are opened in a way that results in an angle that is less than 90 degrees, which is a skill that can be taught to students during the craft session. Additionally, maintaining the right angle is necessary so that the scissors may be extended in a way that ensures proper cutting.

7. Alligator’s open mouth

The mouth of an alligator frequently serves the purpose of grabbing prey and thoroughly devouring it. It makes use of the proper angle to perform the function of opening the mouth. If we observe it carefully, there is almost no chance for any creature to open its mouth at an angle greater than that. As a result, when an alligator opens its jaws, it does so at an acute angle.

8. The beak of birds all form acute angles

It should come as no surprise that since birds are such adorable little creatures, they would likewise adhere to the fact that indicates that animals may only extend their mouths less than 90 degrees. The fact that the peaks of the birds can only open at extremely tiny angles, symbolizes an acute angle, which is easily observed on terraces or in birdhouses.

9. The road makes an acute angle

The angle formed by a road as it curves. When a road curves, the inside of the curve forms an acute angle with the straight section of the road leading into the curve

10. Branches of a tree

It is obvious that long trees contain a lot of lengthy branches, which assist link the tree’s whole body. In order to properly grasp a tree, branches are often closely attached. On the tree’s uppermost portion, it is possible to see that the branches linking the leaves and emerging from the trunk form an angle that is often smaller in size.

Acute Angles: Inculcating the concept by employing everyday use items

When they discover something doesn’t interest them, kids have a hard time staying focused. It’s important to keep the class engaging for them. Ah, geometry, lines, and angles. At first, it seems like such a difficult subject, but with the correct approach, everything can be made interesting.

Here are some exercises that the instructor may use to encourage student participation while also teaching about acute angles.

1. Calculate angles in images

Finding angles on a cute image of an animal, plant, or anything else is much more enjoyable. Print the required image, distribute protractors, and start determining angles.

This angle activity may be completed alone, or you can print it out on a sheet of paper the size of a tabloid and distribute copies to small groups. The page might be passed around so that each student could discover one angle at a time, or each student could be given a specific angle to find. Challenge your pupils to measure the angles on different categories ranging from easy to hard levels.

2. Hands-on measuring

 Provide students with protractors and have them measure the angles of everyday objects, such as the angle formed by a book resting on a table, or the angle formed by the arms of a chair. This activity can help students understand how to use a protractor and how to measure angles in real-world situations.

3. Create a display of angles.

Learning about angles and the many sorts and terminologies may be challenging. It is essential to have a classroom display to aid pupils in remembering the various words and angles. It’s more of a teacher-centered work than student-centered work. It will require getting the posters made. 

4. Angles in the environment

 Take students on a walk around the school or community and have them look for examples of acute angles in the environment. For example, they could look for the angle formed by the roof of a house, the angle formed by a road as it curves, or the angle formed by the blades of a pair of scissors. This activity can help students understand how acute angles are used in everyday life.

Apart from some everyday use items, some angles manipulatives, and classroom activities can also help with the inculcation of the concept. 

Conclusion 

In conclusion, acute angles are an important part of geometry and can be found in many different settings in real life. They are common in everyday objects and structures, such as the hands on a clock, the roof of a house, and road signs. Acute angles are also used in many different exercise postures to help improve balance, flexibility, and strength. Overall, acute angles play a significant role in many different aspects of our lives.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 10 Examples Of Acute Angle In Our Daily Lives appeared first on Number Dyslexia.

Geometry is a subject that many students find difficult, yet others may find it enjoyable to study. Nevertheless, it is taught to kids from a young age for various reasons, the most crucial of which is that it is used in everyday life. Students need to have a solid understanding of this idea.

Learning geometry becomes imperative for students as it has many practical applications. Angles, a crucial component of geometry, are present everywhere around us. Many of the patterns we encounter in our everyday lives have them as a component of their basic structure. They can be found at home, in school, or in the neighborhood. Despite their relative rarity in everyday life, reflex angles are an important concept in geometry and have many practical applications.

A glimpse into the world of reflex angle

Reflex angles are always larger than straight angles, which are half circles (180°), and smaller than full circles (360°), which are wide angles. Reflex angles always have an acute, obtuse, or right angle on the opposite side of them which can easily be observed.

Reflex angles are all around us, and we may readily perceive them. Here are a few instances of reflex angles that we see regularly.

1. Hands of a clock

 The clock’s hands make an angle of 270 degrees in a clockwise orientation, which is greater than 180 degrees and less than 360 degrees. Therefore, the angle created between the clock hands at 9 o’clock is a reflex angle.

2. Pizza

Pizza, an Italian cuisine, has quickly become more well-known. To eat a pizza, we follow the accepted procedures for eating it. We sometimes use a cutter to slice the entire circular pizza into identical-sized triangles, usually cutting them into more than four slices to create the illusion of extra servings. When we remove one slice of pizza, all the other pieces come together to form a reflex angle.

3. Pieces of cake

We celebrate our birthdays by cutting a cake, a long-standing tradition in western culture and particularly popular with kids. The cake is divided into multiple portions and served the same way as pizza. Like when we take a piece of cake out, the entire thing forms a reflex angle.

4. The Chinese Fan makes a reflex angle.

Most of the time, kids like playing with toys and gear that make them feel adrenaline-pumped. Most toys are produced in China, giving them distinction and a sense of origination from China. When the highly well-known Chinese fan is opened, it generates a reflex angle more significant than 180 degrees and provides wind power and a cooling effect in hot weather.

5. A Pac-Man measures a reflex angle

The popular PC game Pac-Man from the 1980s is now accessible on mobile devices. It is a video game in which Pac-Man, a ball-shaped character, consumes every dot in a maze. The Pac-Man’s mouth expands at a tremendously wide angle, more than 180 degrees, to consume every dot.

6. The exterior angle of the letter V

The foundation of any language, which is also helpful in geometry, is the alphabet. As can be seen, the outside of the “V” creates a reflex angle that is precisely opposite the acute angle, which is less than 90 degrees, where the lines are united. Children can better remember the prevalence of acute angles thanks to the alphabet since they are used frequently in speech and writing. 

Angles can be fun! More ways to teach about angles

Finding a unique approach to teaching kids to recognize simple angles and to calculate and recognize other angles configurations? Here are some entertaining yet important angle games for kids and some of the favorite teaching tools you can use to help pupils comprehend reflex angles. 

1. Examining Letter Angles

This is an easy technique to introduce angles to children that has practical applications. They should use a ruler to make the first letter of their names. 

After that, use the ruler to draw arbitrary lines inside their letter and color as they choose. The next step is to locate as many angles as possible and measure each one! This angling activity is simple, enjoyable, and produces stunning results.

 2. Door and masking tape

Begin by sticking a piece of masking tape to the door at a height that is easily accessible to the students.

Have the students use a protractor to measure the angle formed by the masking tape and the edge of the door. Once the students have measured the angle, have them record the measurement in their notebooks. Repeat the process with a few different pieces of masking tape, measuring different angles formed by the tape and the edge of the door.

3. Drawing angles

 Have students draw a series of angles using a protractor and a straight edge. For example, they could draw a reflex angle, a right angle, and a straight angle and exchange their sheets with their peers to check, measure, and compare the sizes of the angles. This activity can help students understand the difference between the various types of angles and how to draw them accurately.

Conclusion

Children may find it challenging and perplexing to detect angles, but an ideal technique may significantly influence them. Children might find learning entertaining and engaging with the correct tools and humor, for example, using methods of gamification like online games and activities to teach about angles can act in children’s favor. 

Additionally, discovering angles in the real world will encourage students to study mathematics as a core subject. For pupils to discover the various angles of the world, teachers only need to pick the proper perspective.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 6 Common Examples Of Reflex Angle In Our Daily Lives appeared first on Number Dyslexia.

But, these two- geometry and trigonometry- are not alike. Instead, they have quite a few differences between them. In the following, we will explore geometry and trigonometry and how they differ. So, let’s first know these two in simple terms.

What is geometry?

Geometry is all about various shapes. Looking around, you will find that different things are different shapes. For example, your book and your pencil are not of the same shape. Your book is either square or rectangular. But your pencil is cylindrical. When you draw a dot on a page, it is a ‘point,’ and you use some straight lines when you draw a house. So, geometry considers all these shapes and studies them.

What is trigonometry?

Trigonometry is all about triangles. If you do not know what a triangle is, let us give an example to you. A slice of pizza is triangular. You must have seen the traffic cones on the road, haven’t you? That structure is triangular. So, trigonometry measures the angles and sides of a triangle, especially a right-angle triangle. Here is an example to help you understand what a right angle is. When the clock strikes three, the hands make a right angle.

The above information is the basic knowledge about the two terms geometry and trigonometry. Now, let’s move on to exploring the differences.

Major Differences

Though both concepts deal with shapes, there are quite a few differences between geometry and trigonometry. Check them out in the following points.

1. Area of study

Geometry is concerned with shapes, lines, planes, and points. It focuses on exploring the relationship among various shapes. You can measure all possible shapes by using geometry and its theories.

Trigonometry, on the other hand, deals with triangles only. Even in situations where there are only two lines and one angle (for a triangle, you need three lines and three angles), trigonometry takes the help of imaginary lines to draw a triangle and solves the problem.

2. Study of properties

Geometry studies the properties of all types of geometrical figures. Be it a simple structure like a line or a complex structure like a hexagon- geometry covers everything. Properties of triangles of different types, like right-angle, equilateral, acute, obtuse, etc., are all included within the geometry’s scope.

But, trigonometry does not concern any geometrical shapes other than a triangle. To be more specific, trigonometry studies the properties of a right-angle triangle. If you are thinking of learning what a circle is, you have to find it in geometry. But, if you are thinking of calculating how high the lamp post on the road corner is, you have to learn trigonometry.

3. Branch of mathematics

Geometry is the direct branch of mathematics covering geometric calculations, theories, and formulas. So, without knowing mathematics properly, you will not be able to ace geometry.

Trigonometry is also a part of mathematics. But, trigonometry is derived from geometry only. As we told you in the previous point, all triangles are geometric shapes, just like everything else. But, trigonometry concerns the triangle only. So, if there were no triangles in geometry, trigonometry would not be able to explore them. Thus, we can call trigonometry a subset of geometry. Similarly, geometry is the superset of trigonometry.

4. Study of angles

Suppose you spill some water on the floor. Now you have a splatter of water. If you wonder how much area the water has covered, you have to do some complex math with geometric calculations. You have to measure the length and width of each water stain and then calculate the total. In this measurement process, you take the help of angles and sides. Thus, geometry is about studying the properties of angles and calculating their sums.

Trigonometry focuses more on the measurement of angles. Let’s take the example of the lamp post again. To measure its height using trigonometry, you need to find the angle, its shadow is making with the road. Thus, when it comes to angles, trigonometry deals with the measurements only.

5. Categories

Geometry has three broad categories. These are plane geometry, spherical geometry, and solid geometry. We told you earlier that any shape is under geometric concern. Now, there are a lot of various shapes. So, it becomes difficult to gauge them all if you do not classify them.

• Any shape similar to a circle or sphere is under spherical geometry.
• Shapes existing on a flat surface (like a piece of paper) are included in the plane geometry.
• The three-dimensional shapes (like the boxes you get from Amazon, the ball you play with, etc.) are under solid geometry.

Trigonometry is broadly categorized into four categories. These are core, analytic, spherical, and plane.

• In core trigonometry, you study only right-angle triangles by using two things- sine and cosine. Mathematicians mostly use this category.
• You use plane trigonometry when you find the height and distances of angles of a plane triangle. If you become a mechanical engineer, a physicist, an architect, or a chemist, you will use trigonometry extensively.
• Spherical trigonometry measures triangles on a sphere. For example, the earth is a sphere. This trigonometry is of great use to astronomers, mapmakers, navigators, etc.
• Analytic trigonometry is just another part of core trigonometry. Both scientists and engineers use this.

6. Terminologies used

Trigonometry uses some specific terms. These are unique, and you do not find them in any other part of mathematics. There are six such terms or ratios used here. These are sin, cosine, tan, cot, sec, and cosec.

Geometry has some specific terminologies also, but those are not as unique as trigonometry. Some common geometric terms are straight angle, right angle, line, point, ray, etc. However, you will find these words in other areas also. Thus, concerning the terms used, geometry and trigonometry differ.

7. History

Both geometry and trigonometry have their origin in Greece. But both were not introduced by a single person. Euclid was a great Greek mathematician. We call him the ‘Father of Geometry.’ As for trigonometry, we have another Greek mathematician named Hipparchus. These scholars first used geometry and trigonometry years ago. In 3000 BC, we find geometric records. Trigonometry is comparatively more recent, starting from 190 BC.

8. Grade in school when you learn geometry and trigonometry

In elementary and middle school, you learn almost all aspects of mathematics in small parts. But, when you reach high school, your grades determine which math course you will take. It takes till ninth grade to read and learn core geometry. In this grade, the teachers teach about parallel lines, the Pythagorean theorem, etc.

In junior year, your course contents might already have trigonometry included. After passing ninth and tenth grade with geometry in high school, you get Algebra II. Here you learn about basic and advanced identities and theories of trigonometry.

9. Uses in real life

Geometry and trigonometry have extensive uses in our daily lives. From constructing a house to drawing a piece of art, geometric and trigonometric knowledge play essential roles. Geometry is used in developing video games, designing robots, building structures like monuments, and sports like soccer, badminton, cricket, baseball, etc. For example, the shape and area of a cricket bat determine how hard and far it can hit a ball to add scores on the board.

Trigonometry is also used in our daily lives, but not in all the sectors where geometry finds its use. You must have seen how NASA launches rockets and spaceships into space. They determine the location of launching these by using trigonometry. When you play Mario, you actually see the outcome of a trigonometric calculation on screen. If we ask you the height of the tallest mountain in the world, we know you will have your answer ready and say it is Mount Everest. Experts measured it by trigonometry only. Thus, trigonometry is used in various real-life situations.

Other differences between geometry and trigonometry include: Pythagoras’ theorem is essential in trigonometry, and most trigonometric measurements are based on this theorem. However, geometry includes using various other theorems and formulas besides the Pythagorean theorem.

Summing up

Here is a tabular presentation of the differences we mentioned above:

Wrapping up

To sum up, everything we have mentioned above concludes that trigonometry is the wing of mathematics where triangles, specifically right-angle triangles, are studied. In contrast, geometry is about exploring the properties of all geometric shapes.

In mathematics, both are important. When you put mathematics into real-life situations, you will see that you need to implement both at various levels. Despite their differences, geometry and trigonometry are integrally associated.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post Geometry Vs Trigonometry: ELI5 The Difference appeared first on Number Dyslexia.

It is a fundamental part of math that students must be good at. Students can better grasp the concepts and principles by engaging in geometry activities. Many types of geometry activities can be used in the classroom, including worksheets, puzzles, and projects. 

However, Geometry is a challenging but rewarding subject that high school students should take advantage of. Now imagine teaching it to your students using unique and innovative games. as it is all about forms and how we perceive them.

It is also significant in our daily activities like culinary arts, video games, and products such as medical devices and even vehicles. These are places where we don’t even notice geometry is being used. So, let’s look at some unique activities with an element of fun so that you can deploy them in your next geometry class, which is proven to be equally helpful for students with dyscalculia. 

Geometry activities for high schoolers

Geometry is a subject that both students and teachers look forward to. Shapes, lines, degrees, angles, and more concern geometry and its versatility which is essentially a part of our everyday. Therefore, several enjoyable activities help students understand ideas and allow them to practice fully. But, have you ever noticed the various resources available around us to engage in more fun frolics (example: books). So, let’s dive deep and have a look at these fun activities that can make geometry learning engaging and interesting for you.

1. The 3D shape activity

A fun way of getting started and breaking the ice is by giving students toothpicks, play dough, slime, or marshmallows and encouraging them to create 3D objects such as prisms, circles, and cubes. It’s a helpful approach for children to learn about the qualities of 3D forms in the actual world! A child’s brain is a sponge that soaks up information and learns best through play. Perhaps, playing with 3D shapes using everyday materials that are easily available at home or in the classroom may help children drastically.

You can share a list of shapes on the board and set a timer. Children can make 3D shapes out of toothpicks and playdough while ticking off the shapes from the list. This will help your child learn about angles, volume, surface area, and more. 

2. What shape is your land?

This activity is about finding the area of different lands. This can be turned into a fun classroom activity by asking the students to measure their classroom area. Teachers can provide students with measuring tapes and all necessary items for demarkations and calculations.

For this activity, students can be allocated into 4 teams. The teacher can give different situations to each team. Some of them can be:

Team 1: Find out the area of the entire classroom, and then subtract the area which is the teacher’s area, which constitutes of the teacher’s desk, cupboard, and the area near the blackboard.

Team 2: Calculate the total area of the class, and then subtract the total covered area. The covered area here constitutes an area with benches, cupboard, and a teachers’ table.

Team 3: Calculate the total area of the class, and compare the distance between each row.

Team 4: Calculate the total area of the class, and of how much area a bench takes up. Now calculate how many benches can fit into the empty space of the classroom.

To make this activity more fun and challenging, a rule like “whichever team first finishes wins” can be introduced. This activity helps students understand concepts such as area and perimeter and allows them to practice using these concepts in a real-world setting. This activity also benefits students by allowing them to use their geometry knowledge to solve a problem.

3.  Set up a geometry scavenger hunt.

The geometry scavenger hunt can be fun and engaging to learn geometry. To set up the hunt, start by hiding objects around the room or house that have geometric shapes. Then, give each 5 clues in the form of a riddle. The players need to solve the riddle in order to find the hidden object. As they search for the objects, they will need to identify the shape, name its properties, and explain how it is used in the real world. Once everyone has found all of the shapes on their list, you can discuss the different ways that geometry is used in everyday life.

This activity is not only a great way to learn about geometry, but it is also a fun way to get everyone moving and interacting with each other. The activity is helpful in making them learn more about shapes and figures, recognizing and identifying them while learning more about their properties. With shapes like hexagons and quadrilaterals, that is otherwise confusing, such activities act as a catalyst to lesson learning and resolve confusion at-a-go.

4. Shape-identifying BINGO

Shape-identifying BINGO is a game that can be played in a classroom to help students learn about geometry. Each student is given a card/ BINGO template with different shapes in the game. The object of the game is to identify the shapes using clues and hints given by the teacher. Once determined, student(s) can mark them off their list. The first player to mark off all of the shapes on their card is the winner.

Shape-identifying BINGO can help students learn about various geometry concepts such as identifying shapes, naming shapes, and understanding spatial relationships. The game can also help students develop fine motor and problem-solving skills.

5. Junior Architects

Each one of us has the perfect picture of our dream home in our minds. This thought can be turned into a creative activity for high schoolers. Teachers can ask students to calculate the area of their house as homework, and the next day when they arrive to the class with the measurements, they can modify the exterior and interiors as per their liking.

For example, if the garden is a total of 100 sq. ft, the student if needed, can add a pool right in between, which can be around 70sq.ft. The same can be done with bedrooms. The student can modify the balcony of their room and add that area to their room area to expand it and make it bigger. This will not only teach students volumes about the area and other concepts related to geometry but also push their creative buttons the most. 

6. Let’s talk about Symmetry

Symmetry being a crucial concept of geometry can be inculcated through a fun activity. It is a well-known fact that symmetry can be found in nature, and in all man-made things, which also includes the 7 wonders of the world. Students in this activity can be asked to pick any one of the 7 wonders of the world, and then browse its dimensions on the internet and jot them down on a piece of paper.

Students can also be asked to get printouts of the monument that they chose. Later, these dimensions can be used to mark on the printout, and this will teach the students how the monuments are made in symmetry.

To make this activity even more interesting, students can be asked to perform this activity with natural things like flowers. Students can measure dimensions and notice the symmetry in these objects. 

This activity will encourage students to know more about the concept and will inculcate them to learn and grasp more about symmetry.

7. The Shape Quilt

The shape quilt can be a fun activity to teach high schoolers about complex shapes, rhombuses, and trapezoids. Through this activity, teachers can also ask students to demark various angles. Basically, on a piece of paper, various dots need to be formed to enable the students to join the dots and make shapes and angles. 

Once dots are added, the paper would look something like this:

The students will now connect the dots and mark shapes and angles, and in return get points for the same. The points can be allocated as per:

Rhombus: 1 Point

Trapezium: 2 Points

Parallelogram: 2 Points

Right Angle: 1 point

Obtuse Angle: 2 Points

And so on…

These points and the shapes and angles can be changed by the educator as per their preference. In the end, whoever scores more, wins the game. This game would be best played by 2 people on one sheet. The twist of the activity is that one student can draw one line at a time. As the dots come to an end, there would now be no scope for more shapes or angles, and this is where the game will come to an end.

To make the game even more exciting, teachers can introduce rules like if the other student makes a shape using any previously drawn shape by the opponent, they get double the points. For example, if the student draws any shape made out of the right angle, they will get the sum of the points for the right angle and the shape they made.

Geometry activities: Helping theory turn practical

There is a very strong reason why teachers and parents support the deployment of activities to make sure that the learning does not remain in theory. For example, you can’t just put a baby in the water and trust them to swim. They must see and touch the water and practice, explore, and feel it. Then students gradually learn the more difficult components of swimming, such as floating, moving limbs, retaining your breath underwater, and so on.

This is very similar to geometry. Students who have never had a solid knowledge of the fundamentals of geometry will struggle. Geometry’s barrage of knowledge can easily drown them. Regardless of what level of geometry is taught, a lesson that involves fundamental geometry is not only necessary but also critical. Give your students enough time and space.

When they indulge in these smart yet with a tinge of fun games, they come face to face with many practical applications and an understanding of geometry. Math, in particular, is not just limited to their textbooks, it goes much beyond that, and teachers can help them explore that side of it!

Conclusion

Geometry influences us in even the most fundamental aspects of our lives. It helps us comprehend certain concepts and enhances our life quality in whatever shape it takes. Your geometry lesson has something for every student: hands-on practice, real-world applications, and possibilities for entertaining classroom activities. Games are an engaging approach to engage students in learning and make the experience unforgettable.

Use these exercises to reinforce essential ideas and keep students interested in their studies. If you wish to make it fun on some days, don’t shy away from using these quotes too. They’ll be geometry experts in no time!

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 7 Fun Geometry Activities For High School Students appeared first on Number Dyslexia.

Math is broadly divided into various branches with different usages and applications of each one. Algebra, Geometry, and Arithmetic are 3 branches of math with each focusing on different aspects of calculations. By understanding the difference between these 3, individuals can benefit from a detailed analysis of mathematics. 

Students can better organize their ideas and build a solid foundation after being clear with the fundamentals of math. As these branches of math have real-world applications, students and teachers should know the correct usage to understand them briefly. It is prominent to know what makes them different and how they are interrelated. 

Algebra vs geometry vs arithmetic: Basic difference

While all three branches of math are used in schooling and the real world, there is a difference in each branch. Let’s understand the meaning and application to know the difference between them.

1. Algebra

An algebraic expression is a basic combination of constants and variables related by the signs of the basic procedures of addition, subtraction, multiplication, and division. Variables like x, y, and z are used to solve a word problem. Being capable of comprehending algebra as a topic is more essential than just being able to solve equations. The concepts of algebra are utilized in various branches of math. Algebra helps in the discovery of the missing values in algebraic expressions and equations. 

2. Geometry

A subfield of mathematics called geometry examines objects’ dimensions, placements, angles, and sizes. Geometry involves using different shapes concerning height, area, distance, or other mathematical expressions. It is a math branch specializing in a particular set of objects. While geometry generally deals with shapes, it is commonly used in various science and technology-oriented fields. 

3. Arithmetic

The word “arithmetic” is derived from the Greek word “arithmos,” denoting the study of counting numbers and the attributes of the standard mathematical operations. Mathematical operations involving numbers are the foundation of arithmetic. It serves as the starting point for mastering multiple regions of mathematics. Being the oldest branch of math, Arithmetic includes the following aspects.

• Addition (+)
• Subtraction (-) 
• Multiplication (x) 
• Division ()

Arithmetic also includes the mathematical concepts of square roots, exponentiation, and percentage. Students can also learn the difficult subjects of logarithmic and trigonometric functions. 

Challenges students might face

Math is not a tough subject but students are likely to face difficulties as math deals with numbers, shapes, sizes, units of measurement, and extensive usage of formulas. Check the most common challenges faced by students in the 3 branches of math. 

Difficulties a student might face while studying Algebra

1. Lack of Understanding of Variables and Constants

One challenge students face in Algebra is the difference between variables and constants. The lack of understanding of the basic concept hampers their overall knowledge of the subject matter, suggests research. Students who cannot differentiate between the two face difficulty solving algebraic word problems as sometimes, variables are designated as constants. For example, x, y, and z might be designated as variables but a, b, and c as constants; this creates confusion and misunderstanding in the concept. 

2. Simplification of Fractions

Algebra involves solving and simplifying fractions to get the answer. However, most students do not follow the correct steps due to a lack of understanding of the order of steps to reach the desired answer. Hence, students face difficulty simplifying algebraic fractions even after the correct formula but incorrect steps.

3. Poor Grasp on Arithmetic

Solving Algebra questions and equations requires substantial knowledge of basic math. Students who are poor at arithmetic and number theory suffer while solving complex word problems. This can lead to unreasonable errors while solving equations. 

Difficulties a student might face while studying Geometry

1. Lack of Understanding with Formulas

Geometry involves various formulas and the correct steps to derive the answer. Most students do not understand the reason behind a certain formula and try to memorize it. Students who cannot comprehend why a formula is made are likely to make mistakes while solving questions. As formulas have a mathematical approach, it is important to understand their applicability.

2. Poor Visual Ability

As students deal with different shapes and sizes, they need to have good visual abilities. When students read problems on a circle or a triangle, they find it challenging to imagine the exact shape in their minds. If students do not know how an object looks or analyzes the correct structure, they are likely to make mistakes.

3. Poor Vocabulary

Wondering how vocabulary happens to be one of the challenges faced in geometry? Students have to solve multiple problems to understand the core concepts of geometry. However, most students struggle with the correct vocabulary for an object or a tool. For example, they might have seen a tool but would be unaware of the term bisector. Hence, unawareness of the right vocabulary leads to misconceptions about the correct application of a tool or an object. 

Difficulties a student might face while studying Arithmetic

1. Struggle with Addition and Subtraction

While most students gradually learn the fundamentals of Arithmetic, it can be challenging for some children to understand them. Students with Dyscalculia might also face a problem with basic addition or Subtraction due to their math learning disability. With such students, the challenge can be extremely bothersome as they find it difficult to calculate numbers, count through fingers, or be quick at math.

2. Lack of Understanding of Time and Directions

Arithmetic also involves a basic understanding of time and directions. Students face the challenge of exactly determining the time by observing the clock. It can be confusing to differentiate between the small and big hands of the clock. Similarly, students might not be able to tell which is right and which one is left in the matter of direction. These difficulties arise due to a lack of factual knowledge and grasp of arithmetic concepts.

3. Struggle with Application of Arithmetic 

Arithmetic can be challenging and bothersome to students who lack application skills. Some students are not able to identify which operation will be used in which particular situation and end up counting everything. For example, some students simply forget the applicability of arithmetic operations while grocery shopping. They might start counting the total bill or time taken to reach the store through fingers, leading to mistakes.

Where do we use algebra, geometry & arithmetic: Basic application

Math is used in everyday living right from calculating the timings for daily activities to analyzing the shopping budget, distance to travel, and making financial investments. Hence, here is the opportunity to learn about the basic applications of Algebra, Arithmetic, and Geometry.

1. Algebra

• Algebra is used in sports activities as players mentally calculate the distance, speed, and force required to hit the goal.
• Cooking often involves algebraic calculations to understand the weight of ingredients, the baking temperature, and the time required to complete the meal preparation.
• Scheduling the day also requires good knowledge of Algebra as you are likely to calculate the time to wake up, have breakfast, reach school/office, and the hours required for each.

2. Geometry

• Astronomers use geometry to follow stars and calculate satellite and planet distances.
• Mathematics and art are related in several ways since both involve understanding figures, patterns, and shapes. 
• Geometry is highly used in constructing buildings, monuments, and parks as they comprise distance, multiple angles, shapes, and lines to make them perfect.

3. Arithmetic 

• Arithmetic is used in everyday life for basic calculations in grocery shopping, bills, and saving money, where addition, subtraction, and percentages are used.
• Basic sequence arrangement in theaters, stadiums, or auditoriums is also made through Arithmetic.
• Individuals also use Arithmetic concepts to calculate the amount of work completed in a week, the distance required to reach a destination, and count the minutes required to complete particular footsteps while jogging.

Are these interrelated?

While they complete different branches of math, Algebra, Geometry, and Arithmetic are dependent on each other for various mathematical calculations.

• Algebraic equations are used in graphs to find answers to difficult word problems.
• Ample algebraic skills and lessons are related to finding the area of missing dimensions of geometrical shapes.
• Pythagoras theorem is a classic example where angle triangles represent geometry while equations represent Algebra.
• Arithmetic geometrics is yet another field of math that focuses on number fields, polynomial equations, and height functions with the inclusion of algebraic varieties.
• The basic modes of operations of Arithmetic are nearly used in most branches of math for calculating distance, time, and numbers used for algebraic expressions as well as geometry.

Table of comparison: Algebra, Geometry, and Arithmetic 

Summing up..

The differences between Algebra, Geometry, and Arithmetic can be tricky to teach and learn. However, a basic understanding of differences leads to a better grasp of several mathematical concepts. As mentioned, these branches are interrelated and knowledge of each is prominent to solve real word problems. After a thorough understanding, parents, teachers, and adults can use different math worksheets, online games, applications, and manipulatives to polish the concepts. It is always an added advantage when individuals actively practice the concept through practical learning.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post Algebra vs Geometry vs Arithmetic: ELI5 The Difference Between These appeared first on Number Dyslexia.

Many people essentially don’t have a particular liking for math and its concepts. Geometry, being a part of it, may fall under the same category of dislike for many students. However, if taught through viable ways like educational apps, following responsive websites, podcasts, using the right manipulatives, teaching approaches, etc; even a subject like geometry can become a favorite to many.

Manipulatives, being an integral part of learning geometry are of various types and sorts that can be used to teach angles. Therefore, in this post, we will be discussing the apt manipulatives to teach angles to students and how to benefit from them. Read more below.

Manipulatives to teach angles: How will it change the class environment

Manipulatives are of multiple types. Some of these are physical objects, while others are digital or online tools. Let’s have a look at them and undermine how these manipulatives can change the air of learning geometry in the classroom.

1. Physical Manipulatives

Physical manipulatives can be used to help students visualize and understand angles. Some common physical manipulatives that can be used to teach angles include protractors, rulers, and compasses.

2. Digital and Online Manipulatives

There are also a number of digital and online manipulatives that can be used to teach angles. These manipulatives can be found on websites, in apps, and even in video games. Some popular digital and online manipulatives for teaching angles include angle finders, angle measures, and angle games.

Way to use manipulatives to teach angles

When using manipulatives to teach angles, it is important to provide students with opportunities to explore and experiment. Students should be encouraged to try different manipulatives and to use them in different ways. It is also important to provide guidance and support as needed.

Here are some ideas for using manipulatives to teach angles:

• Have students use a ruler and a compass to draw angles of different sizes.
• Have students use an angle finder or measure to identify the angles in everyday objects (e.g., doorways, windows, furniture).
• Play an angle game with students and challenge them to identify angles of different sizes.
• Use a digital or online manipulative to help students visualize and understand angles.
• Have students create their own angles using physical manipulatives.

With a variety of manipulatives available, there are many ways to teach angles. By providing opportunities for exploration and experimentation, students can learn about this important topic in a fun and engaging way.

Manipulatives to teach angles concepts to little learners

There are 8 interesting manipulatives that can help students who are on the quest to learn this vast, yet inevitable topic of angles.

1. Geoboard

Geoboard is a manipulative used by teachers to help students understand geometric concepts. They can be used to teach a variety of topics, including angles, area, perimeter, and fractions.

Geoboard is an important geometry manipulative because it allows students to physically manipulate objects and see the results of their actions. This kinesthetic learning style can be beneficial for students who struggle with abstract concepts.

It is also versatile and can be used to teach a variety of topics. When teaching angles, for example, students can use geoboards to measure angles, create angle bisectors, and compare acute, obtuse, and right angles.

2. Angle Sticks

There are many ways to teach angles, but one of the most effective is through the use of angle sticks. Angle sticks are simply two sticks that are placed together at one end to form an angle. By manipulating the angle sticks, students can easily visualize and understand various concepts related to angles.

Some of the key concepts that can be taught with angle sticks include:

• Angles can be measured in degrees.
• The size of an angle is determined by the amount of rotation needed to close the angle.
• Angles can be classified as acute, obtuse, or right angles based on their size.
• Complementary and supplementary angles have a special relationship.
• Angles can be added and subtracted.

Angle sticks are a versatile and essential geometry manipulative that every teacher should have in their classroom. With a little creativity, they can be used to teach a wide variety of concepts related to angles.

3. Cuisenaire rods

Using these rods of different sizes helps in learning angles in a much simpler fashion. These rods, when put together, can make any two-dimensional shape. These rods have different size and colors to distinguish them easily. 

To teach angles using Cuisenaire rods,

• start by introducing the concept of angles and explaining that they are measured in degrees.
• Next, demonstrate how to measure angles using a protractor.
• Finally, have students use Cuisenaire rods to create angles of their own and then measure them.

When introducing the concept of angles, be sure to explain that they are formed when two lines intersect.

4. K’NEX models

These versatile tools teach angles in an easy manner. Primarily, it is used to familiarize students with common angles such as 45, 90, 120, 180, and 360 degrees. These angles are prominently used in all geometry problems. K’NEX models comprise two straight thin rods and a connector.

The connector has 10 different joints where the rods can be fixed. In doing so, students can make any type of angle using the rods as turning mediums. For example, both the rods are right angle to each other and would make a 90 degrees angle. Similarly, when placed straight in a line, they form a 180 degrees angle.

5. Masking Tape

All you need is a long whiteboard, some tape, and different color sketch pens for this activity. Using the tape, you can create intersecting lines on the whiteboard and mark the angles on the points when the lines cross each other. This would allow students to understand many angles in one place. 

Draw straight lines on the board, dividing it into many sections. Use different colored sketch pens to mark the angles at each intersection of the lines. For example, mark all the 90 degrees angles with red and all the 180-degree angles with blue. Then ask the students to use the tape to mark more lines on the board and calculate complex angles.

The primary objective of this activity is to make students understand different types of angles, such as acute, obtuse, opposite, and corresponding. They would also have a thorough knowledge of reinforcing angles on a straight line that would always add up to 180 degrees. Simultaneously, all the angles around a single point on the board would add up to make 360 degrees angles.

6. Teaching Clocks

Large or mini clocks help teach angles in the classrooms. The hands of the clock form these angles. It teaches students the concept of time and the measurement of angles between the needles of the clock.

Every clock is divided into 12 equal intervals. The center at which both the needles are connected makes a 360-degree angle. The measure of each interval is 30 degrees. Place a clock at every table in the classroom.

Ask students to change the time of the clock period and calculate the angle between the clock’s needles. To simplify it, tell the students to place the clock’s needles at 180 degrees to each other and ask them the time. Similarly, you can ask them what angle the needles make when the time is 3:15 or 3:30.

How can effective ways of using manipulatives can change the class environment?

Studies indicate that the use of manipulatives has a direct effect on the students’ learning. They don’t have to hold as much information in their working memory while using these techniques. This allows them to focus on the task more wherein the learning outcomes are result-driven. Here’s how manipulatives can change a class’s environment if taught effectively.

• The use of manipulatives improves students’ mathematical reasoning and problem-solving skills.
• Manipulatives help make abstract mathematical ideas concrete and easy to grasp.
• These allow students to explore using a developmentally appropriate hands-on approach. 
• Manipulatives help students to understand geometry and the different variants of angles conceptually. 
• Through different tools, students receive knowledge and gain the confidence to raise questions in the practical learning session.
• Thus, it provides students the concrete awareness of angles and the hands-on experience of actually touching and feeling manipulatives. Rather than looking at the angles symbolically on paper. 

Conclusion

There are a variety of ways to teach angles using manipulatives. By using new ways and techniques, one can easily explore and use objects, and they can develop a deeper understanding of angle measurement. Some common manipulatives that can be used to teach angles include protractors, compasses, triangles, and rulers.

When using these manipulatives, it is important to provide clear instructions and demonstrations. Students should also be given opportunities to practice measuring angles on their own. With some guidance and practice, one can merrily develop the skills needed to accurately measure angles.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 6 Manipulatives For Teaching Angles And Its Related Concepts appeared first on Number Dyslexia.

If we look closely, geometry is an integral part of our daily lives. Geometry is, with arithmetic, one of the oldest branches of mathematics. It is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. 

With so much to learn and retain, it would make the process fun to have quotes introduced while teaching Geometry. It also helps the educator communicate more efficiently with the students and keep them attentive during class. 

Funny and quirky quotes on the use of geometry

1. The shortest distance between two points is under construction. – Bill Sanderson

2. Geometry is the science of correct reasoning on incorrect figures. – George Polya

3. It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry.– E. W. Howe

4. Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree.-  Benoit Mandelbrot

5. I may not be great at geometry but I know one theorem. The longest distance between two points is you and your parents.-  Jane Wagner

6. The first test of potential in mathematics is whether you can get anything out of geometry.- John Edensor Littlewood

7. There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.-  Martin Gardner

8. How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!.-Archimedes

9. I write rhymes with addition and algebra, and mental geometry.- Ice T

10. Geometry is the knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them.– Rudolf Steiner

11. Geometry is not true, it is advantageous. – Henri Poincare

12. Geometry in every proposition speaks a language which experience never dares to utter, and indeed of which she but halfway comprehends the meaning. – William Whewell

13. Our civil rights have no dependence upon our religious opinions more than our opinions in physics or geometry. – Thomas Jefferson

14. There is geometry in the humming of the strings, there is music in the spacing of the spheres. – Pythagoras

15. I think the universe is pure geometry – basically, a beautiful shape twisting around and dancing over space-time. – Antony Garrett Lisi

16. There is no royal road to geometry. – Euclid

17. I love the simplicity of the Cube because it’s a very clear geometrical shape, and I love geometry because it’s the study of how the whole universe is structured. – Erno Rubik

18. You can’t criticize geometry. It’s never wrong. – Paul Rand

19. One geometry cannot be more true than another; it can only be more convenient. – Robert M. Pirsig

20. As astronomy is the daughter of idleness, geometry is the daughter of property.– Bernard le Bovier de Fontenelle

Can quotes help us realize the gravity of geometry?

Quotes help look at things differently, prompting one to look in a different direction. Geometry is an essential part of our lives, and quotes draw attention to it. The quotes shed light on the role geometry plays in objects and concepts we use every day, through humor too. It also highlights the importance of Math and geometry in other related subjects. 

Quotes do help us shift our attention to things that were not in the picture earlier. Thereby helping us realize its value of it. Maths and geometry are taken as a challenge by children due to the complex concepts involved. Usage of quotes in the classroom by the educator helps in making communication easier, therefore, helping in the learning process too.

Geometry is basically all about shapes and the way we look at them. It also plays an important role in our daily activities like culinary arts, computer games, and objects like medical equipment and even cars. These are areas where we don’t even realize the use of geometry. Quotes can highlight aspects like this and make us appreciate the role played by this subject in the world around us.

Quotes also capture and appeal to the subconscious mind. This stimulates creativity. This can immediately change the thought process and direct the attention to a particular path.  

So usage of quotes or anecdotes does help one in realizing the importance and gravity of the subject. 

Summing up,

Geometry affects us even in the most basic areas of our life. Irrespective of the form it helps us understand specific concepts and improve our quality of life. Buildings, vehicles, equipment, machinery, animations, all these, and more use geometry. Quotes are an enjoyable way to have the class participate in learning and to make the experience memorable Gaining knowledge must not be cumbersome. Funny quotes help to ease the atmosphere and have the attention of the learner. Witty words and well-phrased sentences help to retain the concept in memory easily. 

The creative element of the students is activated through the usage of quotes by helping them look at things in a different perspective. They learn to identify and appreciate where the subject has been put to use around them. So go ahead and add a few laughs to learning.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 20 Funny Quotes For Geometry Class appeared first on Number Dyslexia.

From the buildings to the technology used in real life, this is a concept that just doesn’t have a bookish meaning, as it is used quite often practically too. Explaining to the kids how geometry as a concept is used in real life can help them become more proficient in the topic, and can make them inquisitive to learn it further.

In this post, we will talk about the various geometry examples in real life that can give insights as to why this topic becomes a must-learn for little learners. 

Geometry: Some real-life instances 

Simply observing the entities and activities around us can give us a better understanding of the practicality of geometry. Geometry plays a major role in determining lengths, areas, and volumes in almost everything we do. Here are ten real-life instances where geometry is widely present.

1. Nature

Look around outside – this is where geometry is greatly present. We are likely to see various geometrical shapes and patterns in different sizes and symmetries if we look closely at flowers, leaves, stems, roots, and many more. From fruits and vegetables to even a small honeycomb, a lot of natural things around us have the perfect geometrical shape. Looking at a small plant, you can observe the shape of the leaves and how different geometrical shapes are formed within just one plant. 

2. Living Spaces 

Geometry can be everywhere inside a home, from doors to windows to chairs to rugs of different sizes. Various patterns are imprinted on carpets and curtains to make them aesthetically pleasing. Keepsakes and paintings that decorate living spaces also come in different geometrical shapes. In fact, each and everything in our homes has a particular geometrical figure and shape. At the same time, a lot of those things are kept at various angles, which can teach us the essence of learning the concept. 

3. Technology 

Technology is another area where you can find the most uses for geometry. From computers to robotics to video games, geometry is present in all their underlying concepts. The concepts of geometry are what help computer programmers to work creatively. Geometric computations are a crucial part of the designs and graphics of computer games. Raycasting, a rendering technique in computer graphics, uses a two-dimensional map to create a three-dimensional world in video gaming. 

4. Sports 

Sports is where making use of geometrical angles and shapes is most enjoyed by children and adults in daily life. From skating rinks being round, to cricket grounds being spherical, geometry is everywhere in sports, even a bat and a ball are geometrical figures which means that geometry is a crucial part of sports too. Another important aspect while playing games is angles- players are careful about certain angles to enhance their performance and score points.

5. Medicine 

Geometry-related techniques are closely associated with medical technology such as in Magnetic Resonance Imaging, X-rays, and ultrasounds. They are all about reconstructing the shapes of internal organs, bones, and tumors for diagnosis and treatment. Geometric features also help greatly to define the image in digital grids. Another vital thing to talk about is bisecting angle techniques, which are central in radiology. 

6. Architecture 

The establishment of buildings and monuments is greatly associated with geometry in all aspects – it includes the different aspects of geometry, such as shapes, sizes, angles, and volume of materials used. It is present right from the stages of creating structural blueprints. The theories related to symmetries and proportions are used to make fixed aspects of every building. The carvings of all architectural marvels incorporate some form of geometry into their designs. From the famous leaning tower of Pisa tilted at a particular angle, to the Eiffel tower has a triangular, rectangular, and spherical shape in between, looking closely at the seven wonders also gives us an insight about how geometry is used in architecture around us. 

7. Designing

The field of designing uses geometric aspects in almost everything, from drawing the designs on paper to creating animated figures. Most design elements are entangled with geometrical proportions, which help convey a concept quite easily. Geometric principles are applied while composing the layout of manuscript illumination and miniature paintings. Take the example of calligraphy- so much attention is given while writing individual letters using calligraphic techniques. 

8. Plotting 

The exact calculation of physical distances is made easier with geometry. Many geometry techniques are used in astronomy to study the distances between different planets and stars. Apart from deciding the movement relationship between various bodies, geometry also plays a crucial role in surveying, where the area of the land is determined by the correct determination of shape of the land. When a builder, architect, and contractor work together to build a house on a plot, they use geometry extensively from dividing the plot to making the house and even doing the interiors. 

9. Artforms

Art is about shapes, figures, patterns, and measurements employed in either a two-dimensional or three-dimensional plane. Geometry is closely related to art in all forms, as the creation of any shape results from using several geometrical forms such as circles, rectangles, squares, or even mandalas. The choice and shape of frames affect a painting, and principles of projective geometry are used in most paintings. 

10. Global positioning system (GPS)

The GPS of satellites make use of geometrical principles to determine their position. Employing coordinate geometry in GPS help fetch precise information about location and time. Similar employment helps track many transportation accidents and to carry out rescue operations at many places. It also helps improve flight security, weather forecasting, military operations, environmental protection, and earthquake monitoring. 

How to learn geometry effectively?

Many students face difficulty in school while grasping the concepts of geometry. Not to worry, here are some great ways to teach geometry better. 

1. Read Geometry Books 

Children need to develop cognitive intelligence to boost mathematical awareness in them. Reading geometry-related books will help children identify shapes and patterns in detail. Books discuss many geometrical concepts in detail, like the relationship of sides with angles, effects of changes in measurements, etc. Such books are helpful for both children and adults to develop a learning-centered attitude. Geometry books for high school students help to learn a lot of unexplored new things in detail. 

2. Use Math Manipulatives 

Children are usually taught the basic concepts of geometry, which mostly stick just with shapes and solids. Developing visual and applicable skills is the next step of learning. 

It is where math manipulatives come into play. Practicing math manipulatives regularly will help children develop their curiosity in learning the aspects of geometry without getting bored. Having a hands-on experience with manipulatives helps children construct several physical models and learn about them. Here is a guide that discusses the top five manipulatives to learn geometry interestingly.

3. Play Geometry-Related Games 

The geometric skills of a child should not be limited to solving equations and playing with shapes. They need to understand all the big and small concepts related to geometry to develop shape intelligence, structural thinking, and collaborative learning. Geometry-related games help children understand the importance of related concepts in their daily lives. 

5. Following Math Blogs 

Math blogs play a great role in updating people with new information and real experiences. It is always joyful to learn from experts from the instance they sight in their daily lives. Educators recommend many math assistance blogs for children and teachers to read to stay updated and grasp the concepts and principles of geometry in a relaxed way. Blogs familiarize everyone with new techniques that they can apply in day-to-day lives more confidently. 

6. Playing Board Games 

Playing board games helps you understand angles and shapes in detail. Ameliorating geometrical knowledge gets easier through engaging in interesting activities such as board games. Playing board games helps to comprehend directions, improve focus, and improve geometrical intelligence that you can employ in day-to-day life. 

Before we conclude 

On top of sighting plenty of geometry-related instances in our daily life, we are most likely to apply geometry concepts in most areas of our life. Improving geometry skills is crucial to grasping concepts quickly and solving issues where it is applicable.

Resorting on interesting activities, games, and math blogs will always be a game changer for everyone who is finding it hard to cultivate an interest in geometrical concepts. All of us will learn and, at the same time, enjoy the process thoroughly without really thinking about it.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 10 Examples Of Geometry In Real Life To Understand It Better appeared first on Number Dyslexia.

Apart from classroom assessments, offline practices are often effective in cultivating crucial concepts in the learner, ensuring the real-life essence in them.  Monopoly, for instance, is a game of business and money transactions. Not only for this, some board games may ensure to ameliorate selected skills like geometry too. 

Being the theory of shapes and their attributes, these may be better grasped with pragmatic practices. For this reason, students or mentors may choose to employ manipulatives or games and can also implant the practice of geometry board games 

While you may find a number of board games, which of them are fitting for angles and shapes? To answer these queries,  here we mentioned a list of selected games that we believe may ameliorate geometrical knowledge in players.

Geometry board games: A smart mathematical tool?

An enjoyable math game usually includes clear rules, objectives, and competition—either against the clock or against other players. Clear norms and objectives are essential because they inform children of their responsibilities. Competition is important because it provides a challenge for children.

The finest geometry games offer exactly the perfect amount of difficulty. As they play, children must pick and employ strategies to get things done faster. They are required to solve problems and make judgments. No matter if they win or not, games often add to the thrill besides offering multiple edges. Below are the ways in which Geometry board games help children.

1. Comprehend and Following Directions: Following directions is an important life skill for both home and school, whether your child has just begun school or is going up to secondary school. Children must listen to instructions, absorb them, and then figure out what to do when playing board games. They learn to deal with limitations and constraints and discover methods to work around them.

2. Enhancing Insights and Teamwork: Board games are often inspired from real life scenarios. Monopoly for example is a clear example of trade and business. This way evidently valuable insights are learned. Further, these games are often played in groups- at least with two players. This teamwork is often addressed, thereby may ensure these as a  fun way to engage kids of all ages to collaborate.

3. Improved Focus: When played without interruptions, board games can enhance a child’s attention span. When people focus on one thing all the time, it becomes second nature to them. Playing these games will make them habitual to give attention to one activity for a long period of time. 

4. Ameliorates Mathematical Intelligence: Along with geometrical abilities, these board games aid in the development of numerous visual, perceptual, cognitive, and thinking skills. These skills help in the development of overall mathematical intelligence. 

Board games for Geometry: Our eminent choices 

Board games can have a wide variety of play strategies, here are our suggestions to learn and travel with geometry enticingly:

1. Coogam Wooden Hexagon puzzle

Being a set of Hexagon pieces on board, there are a variety of methods to put the pieces together to finish the puzzle. Players get a chance to discover new combinations, thereby ensuring exhilaration. 

This game may be effective for kids to work on their hand-eye coordination, geometry, visual-motor abilities, and fine motor skills. Playing with the wooden preschool educational toys improves finger flexibility, stimulates children’s interest in understanding and learning about the world, and improves sensory abilities.

This recreation encourages the youngster to understand spatial relationships between pieces to arrange them. Further, varying colors and combinations may indulge them to learn geometry in multiple dimensions.

2.  Volume victory

Volume Victory is a board game that lets children practice calculating the volume of rectangular, triangular, pyramidal, cylinder, and cone prisms. There is a printed and a digital version of this resource. Students must calculate the volume of various numbers in order to progress across the game board.

The complexity of the problems in Volume Victory varies. The complexity of the task is proportional to the number of places they will be able to move if it is solved successfully.

3. Learning Advantage: Fence in it

Out of the box, this game comes with a board, pieces of tiles and a few cards with shapes on them.  In this recreation, Hands-on activities, problem-solving, and a three-level card game are used to teach area and perimeter principles. 

To start with, each player gets a shape card, which they may need to create on the board with the areas and dimensions given on it. Tiles may be considered as unit areas. This way, players can employ these tiles along with rulers to determine areas effortlessly. With these manipulatives, the shapes are created. Now the perimeter and area is measured once again to compare it with that asked in their cards. These insights and gameplay make it a noteworthy pick for revision attributes of shapes. 

9 double-sided work cards, rulers, square tiles, and 50 cards are included in this set which makes it suitable for 1-4 players. It assists  children to discover how area and perimeter are used in real-life situations and makes use of measurement equipment and mental math abilities.

4. Geoboards

Geoboards help learners understand the principles of geometric forms in an entertaining way. Children can make 2D shapes and compete with each other as to who is the first one to calculate the area or perimeter of that game. They can draw in shapes like squares, triangles, rhombus, etc.

Playing this game, they will be in a better position to calculate the area and perimeter of various shapes. Their speed may also increase as they will be constantly competing to complete the calculations first. 

5. Ice cool board game

With the four white fish tokens, this game secures the five-game board boxes together. The player needs to collect a penguin of certain color along with a reminder card, ID card, and three fish tokens to start with. Now, one learner shuffles the cards and piles them up. The fish tokens may now be connected to the entrance of the hall monitors. 

The goal of the game is for each player to carefully flick a gaming piece such that their opponents fall over. Each flick symbolizes a different perspective. Children might be encouraged to estimate the magnitude of the angle utilized to flick a piece by their parents. They can also teach their children how to name the many types of angles. 

In addition, parents can demonstrate to high school students the relationship between angles and projectile motion in Physics. However, children aged 6 to 10 years old are more likely to find this game intriguing.

6. Three sticks

An enticing game with a board and building sticks; this family board game may entice children’s interest in the wonders of geometry. Sticks of three different lengths – 3, 4, and 5 units are used in the game. The players need to make geometric forms using these. They may gain points based on the size and formation they made. . At a multiplayer level, the game becomes further challenging with one player attacking others.

To begin with, you do not get to pick the sticks; they are chosen at random. Second, each turn only allows you to use two sticks! It’s difficult to make a form using only two sticks. As a result, you must use both of your sticks, as well as any others that the other players may have put on the board. 

This is when the game becomes quite creative. This recreation helps children to learn about new shapes. When they will be making shapes themselves by playing a game, it is even easier for them to learn.

7. Learning Resources Crosstown coordinate

It comes with 150 location cards, pawns, checklists, a 19″ square gaming board, and a handbook. Coordinate cards tell players where they should go in the community. They need to flip to check whether they moved the cards correctly by flipping them over. For more complex play, the game board has positive coordinates on one side and both positive and negative coordinates on the other.

It is a  simple and enjoyable method of teaching and reinforcing the concept of coordinates. The picture is made in the form of a graph where all the coordinate points are made. Children have to play on these coordinates on the X and Y-axis. Joining the coordinates, they make various shapes on the graph.

8. Azul Board game

Azul is a tile-placing game in which players take on the role of artists charged with making the most beautiful tile mosaics possible. You must draw tiles from a central market and arrange them in rows on your boards in this game. Collecting sets of the same color tile and making specific patterns will earn you extra points. 

Every time you claim has an impact on what your opponents can do next. To win massive scores while disturbing your opponents’ intentions, prepare wisely. You’ll have to make decisions that benefit you while not benefiting them.

This game will require a lot of strategy and understanding of various shapes and patterns. This way, indulging in the game may implicitly stipulate the learner practice geometry implicitly. 

9. OjO Shape Factory

Out of the box, the players can access a building area (board), a sand timer, cards depicting an object and shapes of varying colors along with an instruction manual. All these are sturdy and reliable enough to be handled by young learners. 

To start with, the pile of cards is shuffled and one random piece is picked. Now, the student looks at the card and places it on the board. They need to observe the image given on the card and start to fabricate the same on the board.  They may make use of various shapes like squares, rhombus, triangles to ensure proper output. 

This simple game may be suitable for all learners expediting through shapes and geometry concepts. With hands-on practice, the learners may better understand how these shapes are implemented in real life.  

10. Khet Laser

Out of the box, you may get to see a chess-like board with 7*10 grids along with transparent pieces to play with. At the first glimpse, this game may often seem similar to laser version of chess, nonetheless, the shape of pieces and gameplay is distinct. 

What makes this unique is that after every move, the player presses a laser beam to analyze the future movie. The laser passes through the pieces and deflects based on their positions, making it enticing to play. 

With around a game time of 20 minutes, it involves various geometric concepts like rotation, angles, reflection, and refraction. This way, a gameplay may let the learners to ensure a proper geometric practice as well. 

Concluding thoughts 

While math games are often entertaining while they review and practise ideas. Playing math games with your child can also help you gain a better understanding of their strengths and areas to boost. These often let step the little one out of paper inferences and feel the shapes pragmatically. Consequently, try these fun geometry board games with your child to upskill their geometry. They will learn and, at the same time, enjoy the learning process.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 10 Cool Board Games That’ll Make Geometry Interesting For You appeared first on Number Dyslexia.

Being a crucial wing of math, geometry deals with the study and properties of points, lines, surfaces, and other multidimensional objects. Dealing with real-life objects, the concept can be enticing for some pupils, some students may find it taxing to visualize and discern complex queries. That being the case, the ability of special students in such skills is not perfectly discerned. For those with math learning compromise, is geometry a stumbling block?

Suitably, here we traverse through relevant insights to arrive at conclusions. To comprehend the effect of Dyscalculia on learning geometry, we evaluate applicable traits in such individuals so that befitting strategies can be set on later, finally finishing off with verdicts. 

Entailing traits for geometry learning- Evaluating these in dyscalculics

Geometry is one of the most crucial yet taxing notions for students as they may need to visualize. Skills like describing the picture, drawing and comprehending a figure may require a few attributes. Here we explore these in Dyscalculia to evaluate their status:

1. Creative and drawing skills- A clear Edge!

Stipulating the need to learn various symbols, geometry needs creativity. Being more than just creative, Dyscalculics can have clear benefits with this trait. They often like being trained creatively employing games, activities, and real-life learning. Thus, geometry can be an enticing concept. 

Chapters like angles, triangles, and other shapes often precede geometry. Mastering these notions can make learning geometry facile. Accordingly, Nathalie Sinclair^[1] studied how to forge ways of including drawing as part of the teaching and learning of geometry. He outlined that new ways of thinking and thereby ensuring creativity may nurture young learners with spatial geometric reasoning. These results imply the importance of drawing and creativity in such notions. 

2. Spatial Intelligence- The Need of Thrust

Comprise in comprehending what the notions are and thereby where these are actually applicable may be evident in few individuals, these can also reflect in notions like geometry as well. 

Also known as visuospatial ability, spatial intelligence can be grasped as the ability of the individual to retain, retrieve and make obligatory transformations of well-designed visual images. While concepts like geometry are all about two-dimensional figures, it often needs spatial abilities. Nova Riastuti^[2] and the team made a research study to describe the students’ geometry skills in resolving geometry problems viewed from spatial intelligence. The results indicate that there was a correlation between students’ spatial intelligence with geometric skills. Students had different geometric skills in each category of spatial intelligence, although there were similarities in some geometry skill indicators.

Further Nova also found that students with low spatial intelligence had fewer geometry skills, thus needing special attention from teachers. Here, we can conclude that individuals with Dyscalculia who may need to work on spatial abilities, can be aided with specialized surveillance.  

3. Logical thinking- Can be Grasped

The ability to solve a problem with sensible notions needs logical thinking. While a few would learn the procedural aspects, pragmatic applications of the same may not be grasped. These factors may affect geometrical skills. 

Logical thinking, as we know, is the ability to analyze the situation and come up with a befitting and sensible solution. Learners of Geometry may design appropriate solutions by looking at the questions, implicitly requiring logical thinking abilities. Accordingly, Nazan Sezen^[3] Studied logical thinking as a crucial cognitive ability and its effects on math. It concludes that the importance of visual perception and multidimensional thinking is undeniable in geometry. 

Kinga Morsanyi^[4] studied the pattern of logical thinking in Developmental Dyscalculics and high math performing students. The results found that children with Developmental Dyscalculia had some noteworthy compromises in logical reasoning skills, especially in math notions. These inferences depict the need for special care to develop logical skills. 

4. Reasoning skills- Not merely a Catch!

Evaluating, analyzing, and then synthesizing are indeed needed for notions like geometry while coming into sensible inferences. For that reason, Berna Canturk Gunhan^[5] investigated reasoning skills in geometry. Geometry problems given to 6 random 8th-grade students showed differences in their reasoning skills. These inferences outline that the reasoning skills are related to conceptualization which plays a noteworthy role in geometry practice.  

Some individuals may feel it taxing to analyze the query and evaluate it.  Despite being creative, compromise in spatial inferences may make comprehending the problem further arduous. Accordingly, practicing or solving the geometry sums may be taxing for Dyscalculics.  In the book Reasoning Skills in Individuals with Mathematics Difficulties, Kinga Morsanyi studied the reasoning skill in individuals with math difficulties and found that cognitive abilities and resources might be affected in dyscalculia, as reasoning skills rely heavily on cognitive resources. Thereby, these individuals should focus on refining reasoning skills. 

5. Applied Skills

Some individuals may feel it is taxing to manage and interact in the classroom to brainstorm about various notions. This may retain some doubts. Interaction, collaboration, and managing may be learned in the classroom over time. These learning attributes turn handy in various notions like Geometry. Subsequently, Nova Riastuti also mentioned the need for applied skills to reinforce students with geometry along with other attributes like spatial intelligence. Relative pedagogies and techniques can aid Dyscalculics to grasp applied skills. Consequently, applied skills can be learned and often are not a snag.

Geometry skills in dyscalculia- Schemes to refine productively

Going through various traits that need to be thrusted to master geometry, here are a few simple yet working strategies to comeover geometry hitches:

• Draw to learn: Having a clear edge with creative and drawing abilities, students can draw the notions to learn.  For instance, if the pupil needs to learn triangles, they may draw a rough figure on paper and then look into its attribute to derive a sensible solution.
• Learn Formulas: Formulae are often crucial to learning chapters of geometry. Learning these can make solving questions facile. Flashcards can be befitting manipulative to assist in grasping these rules, as they ensure repeated learning.
• Make use of tools and Hacks: Geometry is often all about implementation of employing tools like protractor and compass. Apprehending to use them perfectly can ameliorate geometry skills.  Further, knowing rules and a few hacks can save on time on solving. For instance, if the student identifies that two angles add up to become 180 degrees, they can use supplementary angles regulation to prove effortlessly. 

• Practice More : Applied skills are crucial; woefully, the value is lesser-known.Ensuring frequent Practice  can improve coordination and thus cognition. By this, the learner can improve their abilities with time.
• Transpire out of Assumptions : Being creative can bring about some assumptions; nonetheless, cross-checking whether they are valid can bring the learner out of complications—geometry deals with diagrams and shapes, where assumptions can turn crucial. To prove the same, a valid rule or regulation is crucial.  

Can dyscalculics master geometry? 

As a first impression, math compromises may have an effect on any math-related notion, including geometry. Nevertheless, evaluating various traits needed for geometry, the inferences may be midway. Getting indulged in activities like puzzles, legos, and other three-dimensional activities can boost spatial intelligence. Ensuring the same may moderately assist in ameliorating logical, reasoning, applied skills as well. 

While being creative is a clear edge, other attributes like reasoning, logical thinking, and applied skills can be grasped with some additional thrust. For that reason, it is not fair to derive generalized manifestations; geometry may be managed with additional efforts.

Concluding thoughts

Challenges in discerning numbers are evident in some kids, aversion to geometry may not be the case with all of them. While a few may feel it arduous, the world has witnessed successful mathematicians who have math compromise. Subsequently, emanating from general and baseless assumptions, it is crucial to evaluate at a personal level to determine which strategy and trait need attention. Traverse through the above-mentioned insights and strategies to make be-fitting decisions. 

References:

1. Learning Through and from Drawing in Early Years Geometry. (2018). Nathalie Sinclai.
2. Analysis of students geometry skills viewed from spatial intelligence. (2017, December). Nova Riastuti.
3. A scale on logical thinking abilities. (2011). Nazan Sezen. https://doi.org/10.1016/j.sbspro.2011.04.131
4. The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children. (2013, March). Kinga Morsanyi. https://doi.org/10.1111/desc.12048
5. Gunhan, B. C. (2014). A case study on the investigation of reasoning skills in geometry. South African Journal of Education, 34(2), 1-19.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post How Learning Geometry Is Affected By Dyscalculia? appeared first on Number Dyslexia.