Real-life examples show us how the things we learn at school display their presence and application in the little things that surround us. While it’s easier to appreciate the use of concepts we learn in science and geography in daily life, it is not the same with math. Geometrical concepts like triangles are difficult to understand in the context of the real world. To support our curious learners, we have come up with this article where we will mention some of the most common real-life examples of the isosceles triangle, the triangle with two equal sides.

How is an isosceles triangle different from other triangles?

Like other triangles, the isosceles triangle is also a three-sided closed polygon. What sets it apart from other triangles is that it has two sides of the same length. The two same-length sides are called the “legs” of the triangle, and the third unequal side is known as its “base.” A few other properties of an isosceles triangle are:

1. An isosceles triangle has two equal base angles as the two angles opposite to the equal sides are congruent. 

2. The third angle, known as the apex angle, is not equal to the two base angles.

3. A line drawn straight from the apex to the base splits the base into two equal parts. 

4. The apex angle can either be an acute angle or an obtuse angle.

5. The sum of all sides of an isosceles triangle gives its perimeter.

6. The sum of all angles of an isosceles triangle is 180 degrees. 

Spotting isosceles triangles around us: 10 real-world examples

1. A slice of pizza 

Who doesn’t love a slice (or more!) of pizza for dinner? This mouth-watering circular delicacy is traditionally divided into triangular portions before serving so that it’s easy to eat and share. The next time you eat pizza, observe carefully, and you will notice that each slice resembles an isosceles triangle. Yes, we know its base isn’t a straight line, but its overall shape is similar to an isosceles triangle with two sides of the same size.

2. A pair of earrings

Contemporary style earrings are so fashionable. Some of them are designed in geometrical shapes like squares, circles, and even triangles! A jewelry section in a store will probably showcase a few triangular earrings as well. The ones with two long equal sides and a small base will look just like isosceles triangles. Who knew geometrical shapes could find a place in jewelry design and work so well in enhancing a person’s personality? 

3. Church spire

Many churches have this beautiful architectural feature on the top known as the steeple. The steeple gives a long look to the buildings. The topmost part of the steeple is called the spire, and this is what looks like an isosceles triangle. When you look at this tall conical shape, it appears as a triangle with two long sides and a comparatively smaller base. A spire has a religious symbolism and is very common in Gothic architecture. 

4. Tepee

Tepee or tipi is a type of tent made by North American Indians residing in the Great Lakes regions and the Plains. These conical-shaped tents are constructed by tying poles together at the top and spreading them at the bottom to form a conical shape. This structure is then covered with animal skins or canvas to turn it into a comfortable living space. The tepee is an excellent example of an isosceles triangle, as the adjacent poles of the tepee form quite a few of them with the base.

5. A flying flock of birds 

Ever noticed how a flock of birds, especially the migratory ones, fly from one place to the other? They form a classic V-shape during their flight. While we are not here to discuss why they prefer this form of movement, we have surely noticed that this V-shape does resemble an isosceles triangle if we draw an imaginary line over it. The two lanes of birds form the equal sides of the triangle with a fictional base of shorter or longer length. 

6. Tripod stand

Spread the legs of a tripod stand and see how it looks. Do you see anything familiar? Yes, the adjacent legs of a tripod also make an isosceles triangle. Some tripods come with foldable legs. You can stretch them to open up and increase the height of the tripod. No matter what height you choose, you will always observe three isosceles triangles forming in the tripod.

7. Truss bridge

A bridge with a truss, a superstructure that bears the load, is also a great example of a real-world isosceles triangle. A truss bridge has not just one but several triangular units. The metal triangles form a durable structure that can bear large amounts of loads. Truss bridges are commonly used to build railroad and military bridges because they need less material for construction and can support a considerable amount of weight on it. 

8. A Rooftop

Look at the rooftop of houses. Don’t you think these slanting structures also look like isosceles triangles? If not, see again! A rooftop has two slanting sides of equal lengths, and the sides are connected to each other at the base of a different length. Since houses come in varied sizes, the rooftops, or if we may say, the isosceles triangles, also vary in size. 

9. Hangers

Hangers are a very common household item, and guess what! It also resembles an isosceles triangle. Don’t believe us? Pick a hanger out of the closet and use a ruler to check its dimensions. You will see that the two sides of the hanger and its base follow the basic properties of the triangle in discussion. At the store, you may find steel, plastic, or wood hangers. They may even differ in size. But they all hold the shape of an isosceles triangle. 

10. Arrowheads

A bow and an arrow were powerful weapons used in ancient times for self-defense and hunting. Arrows used in them were made of a wooden shaft that had a feathered tail at one end. On the other end was an arrowhead made of materials like metal and stone so it could be sharp enough to serve its purpose. Interestingly, a classic arrowhead was also designed in the shape of an isosceles triangle. Arrowsmiths preferred this shape because it had a pointy apex with a strong base, capable of creating a solid impact and penetrating deep into the target. 

Concluding thoughts

Though not as common as an equilateral triangle, isosceles triangles are also a commonly found shape in the real world. Once students know the difference between this triangle with two equal sides and other triangles, it gets easier for them to spot it in their surroundings. Real-world examples like those of the isosceles triangle, right angle triangle, and others help build a connection between what students are learning and what they see outside the classroom. This connection fosters critical thinking and engages students much better. So, use these examples as a teaching strategy to see how they spark interest in the classroom and make learning more meaningful for your students.  

Priyanka Sonkushre

I am Priyanka Sonkushre, a writer and blogger. I am the person behind “One Loving Mama,” a mom blog. Equipped with a Bachelor’s degree along with an MBA, my healthcare background helps me deeply understand learning difficulties. I know how challenging it can be for parents to find the right resources to help their children excel in life. So, here I am to blend my healthcare expertise with my parenting experience to create valuable and helpful resources for parents and teachers supporting children with learning differences. If you wish, you can follow me on Facebook and LinkedIn.

onelovingmama.com

The post 10 Examples Of Isosceles Triangles Around Us appeared first on Number Dyslexia.

One common example is the construction of buildings and other structures. The triangular shape of an equilateral triangle is very strong and stable, making it an ideal choice for use in support beams and other structural elements.

Equilateral triangles also appear in nature, such as in the shape of certain crystals, and the markings on the shells of certain species of turtles. In addition to their practical uses, equilateral triangles also have a rich history in mathematics and geometry. They have been studied for centuries and have many interesting properties that make them an important subject of study.

This post includes vital and common examples of an equilateral triangle in real life that is crucial to know about.

Equilateral triangle real-life examples to comprehend the tricky topic better

Just like many other shapes, from cones to spheres, equilateral triangles, too, can be found in many real-life situations and have several important properties that make them useful in various applications. Some examples of the importance of equilateral triangles in real life include:

1. Traffic signs

Many traffic signs are shaped like equilateral triangles, such as yield and stop signs. The triangle shape is used for traffic signs because it is easily recognizable and can be quickly identified from a distance. The bright colors and bold lines of the triangle also help to grab the attention of drivers and pedestrians. In addition, the triangle is a very stable shape, which means that it can withstand strong winds and other forces without tipping over.

2.  The Great Pyramid of Giza

The Great Pyramid of Giza is one of the Seven Wonders of the Ancient World and is located in Giza, Egypt. It is a pyramid with a base that is an equilateral triangle, with each side measuring about 230 meters (755 feet) in length. The Great Pyramid was built around 2550 BC and is the oldest and largest of the three pyramids in the Giza Necropolis. It is also the only surviving ancient wonder of the world.

3. The Mercedes-Benz logo

The logo for Mercedes-Benz features a silver equilateral triangle with a circle in the center. The triangle represents the brand’s mission to create engines that are powerful, efficient, and reliable, while the circle represents the brand’s commitment to innovation and perfection. The logo has evolved over time, but the triangle and circle have remained a constant element of the design. 

4. Quilts

Quilts are blankets that are made up of layers of fabric that are stitched together. Quilts often feature equilateral triangles as part of their design, as the triangle is a versatile and balanced shape that can be pieced together to create complex patterns and shapes. Quilts are often made by hand, and the use of triangles in their design allows for a wide range of creative possibilities.

5. The Triforce

The Triforce is a symbol from the popular video game series “The Legend of Zelda.” It is made up of three equilateral triangles that are interlocked, with each triangle representing one of the three virtues of the series: wisdom, power, and courage. The Triforce is a powerful and important symbol in the “Legend of Zelda” universe, and it is often featured prominently in the games and related media.

6. Kites

Kites are flying objects that are propelled by the wind and are typically made of lightweight materials, such as paper or fabric. Many kite shapes are based on equilateral triangles, as they provide a stable and balanced structure for the kite to fly. The use of triangles in kite design helps to distribute the weight of the kite evenly, which allows it to stay aloft and maintain its shape while in the air.

7.  The flag of Cuba

It features an equilateral triangle on the left side of the flag, with a white star superimposed on the red field inside the triangle. The use of the equilateral triangle in the flag is a reference to the Masonic symbol of the Great Architect of the Universe, which is commonly seen as an equilateral triangle with an eye inside. It also references the concept of the three Masonic tenants, which are brotherhood, truth, and relief. Additionally, the red field and white star within the triangle are symbolic of the bloodshed and pure ideals of the Cuban Revolution.

8.  Nachos

Nachos are a great example of an equilateral triangle in real life. An equilateral triangle is a type of triangle with three congruent (equal) sides. In the case of nachos, the three sides of the equilateral triangle are represented by the tortilla chips, the cheese, and the toppings. It’s a perfect example of how in real life, geometry can be found in food and cooking.

9. Fire trucks

Fire trucks are vehicles that are used by fire departments to respond to emergencies and extinguish fires. They often feature flashing lights in the shape of an equilateral triangle, which helps to alert other drivers to the presence of the truck and to signal that the truck is on an emergency call. The triangle shape is used for the flashing lights because it is easily recognizable and can be seen from a distance, which helps to ensure the safety of the fire truck and its crew as they respond to emergencies.

10. Pool table rack

If you have played pool before, you might have seen the pool table rack, where all the balls are placed before the player targets them with the cue stick. This pool table rack is an equilateral triangle if you closely see it. The reason behind this is that balls in the rack are placed in a way that the first ball is on the top, and the number of balls increases slowly and gradually in every line.

Equilateral triangles: All around us?

Equilateral triangles can be found in many everyday objects which can be useful for helping children understand and remember the concept of equilateral triangles. Here are a few ways that equilateral triangles can be incorporated into lessons to help children learn about this type of triangle:

1.   Piece of paper: Children can be encouraged to create triangles of the same length and then cut them out with the help of scissors. They will be able to experiment with the formation of an equilateral triangle while also learning how to do it.

2.   A three-legged stool: It creates an equilateral triangle with the three legs forming the sides. This is because all three legs are the same length, and when they are connected at the top, they form a triangle with three equal sides.

3.   A triangular-shaped wedge pillow: It also creates an equilateral triangle with all sides equal in length. This is because the pillow is designed with three sides of equal length, forming an equilateral triangle.

4.   Stop Sign: A stop sign is an example of an equilateral triangle. It is a familiar object that students can see in their daily lives, making it easy for them to understand the concept of an equilateral triangle.

5.   Sports: The center circle of a soccer field and a volleyball court is also an example of an equilateral triangle, with the three corner points of the center circle having equal distance from the center.

Overall, equilateral triangles can be found all around us in various shapes and forms, and these five examples are just a few of the many ways in which we can see and demonstrate this type of triangle in our everyday lives.

Conclusion

In conclusion, to help students understand the concept of an equilateral triangle, it may be helpful to connect the mathematical definition to real-life examples. This can be done by highlighting the properties of an equilateral triangle, such as all sides having an equal length and all angles having a measure of 60 degrees, and pointing out how these properties can be observed in real-world objects and situations. Additionally, providing hands-on activities or interactive demonstrations like DIYs can help students visualize and apply the concept in a tangible way.

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 Equilateral Triangles Around Us appeared first on Number Dyslexia.

If your students or kids look at this symbol and think someone put some toothpaste on an equality sign, they are not alone.

Using statements and some simple set of rules to find whether two triangles will completely coincide when put above each other or not is definitely an interesting application of math. 

But it isn’t always the easiest one. 

Teaching the same concept by including various interactive components like competitions, and arts and crafts that encourage hands-on learning can certainly help make it much more simpler and fun. This blog enlists several activities that will enable the students to prove congruence in interesting and exciting ways.

Learning triangle congruency through activities

Just like many triangle games and manipulatives, make learning enjoyable and the conceptual knowledge of congruence palatable, here’s a list of a few activities that you can do and learn with your class.

1. Cut and match 

For this activity, this educator will have to draw differently shaped, unaligned, and randomly placed triangles on a sheet. This can be done digitally as well and then the sheets can be printed out such that each student gets one. The educator will also need to arrange several student-friendly scissors or other safe paper-cutting instruments. 

The goal of the students in this activity would be to cut the different triangles and see which one completely overlaps with another. They will then be given certain properties about the triangles that will further help them prove which triangles are congruent with one another.

This activity will help students in understanding the basics of the principle of congruence and what it means as well as how to prove it.   

2. Designer page

For this activity as well, the educator needs to arrange some student-friendly paper-cutting and pasting instruments. 

Here, soon after the students are done learning about a new condition for finding congruence, they will be asked to represent the same in their notebooks. They will do so by cutting, folding, and pasting the page right after their notes about that particular condition end. For example, for the RHS condition, the students will cut the page and fold it to make two congruent right-angled triangles. 

Not just pictorially but physically engaging in the activity of making congruent triangles will help the students better understand and remember the various conditions for congruence. 

3. Prove it 

For this activity, the educator will have to make a bowl full of triangles with various properties written on them like their angles, length of their sides, etc.

The class will be divided into 4-5 teams. One student from each team will go up one by one and pick out two triangles at random. They will be given time to assess the triangles. Their task, as a team, will be to come up with proof and present the same on the board proving or disproving the congruence of two triangles based on their properties. The team that correctly proves the most number of assertions will be declared the winner.

This activity will involve group learning and team participation to help analyze various properties of the triangles and arrive at the correct proof while backing it all up with evidence.

4. Jigsaw with a twist

For this activity, the educator will need to write down the proof of congruence based on different conditions for four pairs of triangles. Then they will have to cut this proof up step by step into chits and mix the chits up in two bowls. This should be done in such a way that each bowl has mixed-up chits with steps written for two proofs.

The class will be divided into two teams with an equal number of students in each. They will each be given the bowls with steps and the four sets of triangles will be drawn on the board. Here the task of the students will be to look at the sets of triangles and arrange the steps of the proof such that it proves two pairs represented on the board are congruent. The first team to figure out which triangles’ proof they have and correctly arrange it will win.

This game will introduce competitiveness to learning, making it more fun and engaging for students. They will have to reconstruct the proof step by step which will require a fair amount of exercise of their deductive skills and congruent conceptual knowledge.

5. Mix and match

For this activity, the educator will have to make congruent triangles in pairs with different conditions of congruence. They will then have to put various sets of these triangles in a bowl.

The task of the students here will be to walk up to the bowl and pick a pair at random. The properties of the triangles that helped prove that they are congruent will be mentioned in the triangles. Based on what is mentioned, the students will then place the pair of triangles depending on the condition that proves their congruence. 

For example, if the pair of triangles the student picked has two equal sides and the angle between those sides for both the triangles is 40 degrees, this means the triangles are congruent based on the Side-Angle-Side condition and will be placed in the SAS pile by the student. 

This activity will help students in understanding, learning, and applying various conditions of congruence without even needing a pen and paper to write it all down to prove it.

6. Under my seat

For this activity, the educator will have to prepare several pairs of congruent triangles. These triangles should then be mixed together and randomly placed under the seats of the students. 

The task of the students here will be to pick the triangle placed under their seat and find it’s congruent among their classmates. 

They will have to go around seeing the properties of the triangles of various classmates to see if they are congruent with their triangles under any condition of congruence. The first three pairs to successfully find their congruent partners should be awarded.

This activity will also require the students to use their knowledge of various conditions of congruence to eliminate the triangles that don’t meet any as fast as possible and find their congruent partner in a limited time.

7. Similarity or congruence? 

For this activity, the educator will need to prepare several pairs of triangles with different properties mentioned and a screen to present these triangles on.

The class will be divided into two teams with equal students on each team. Turn by turn, the teams will be shown a pair of triangles and their task will be to tell if they are similar or congruent and under which condition. For example, two triangles having three angles of 80 degrees, 50 degrees, and 50 degrees will be similar under the Angle-Angle-Angle condition. In the end, the team with the highest number of correct answers will win.

This game will encourage the students to learn the difference between similarity and congruence as well as various conditions that prove them.

8. Who am I?

For this game, the educator will have to prepare cards with various conditions of congruence written on them.

The class will be divided into two teams with equal students in each. One member from each team will go pick a card and without seeing what it is, hold it up against their forehead so that the class can see the condition of congruence mentioned. Then, the task of the team members would be to describe a pair of triangles and their properties to help their team members guess the condition they are holding. The team to successfully guess it first will get the point and the team with the highest points will win.

For understanding the condition they are holding against their forehead based on the triangles described by their team, the student will have to mentally figure out what condition of congruence fits these triangles. This activity will require quite a bit of teamwork as well as sound congruence condition knowledge.

9. Color me mine 

For this activity, the educator will have to design a coloring sheet full of abstract figures, including scattered triangles. This can be made digitally after which the educator can take printouts to give to each student. The educator will also have to arrange a set of colors for every student. 

Every congruence condition will have its own assigned color. The task of the students here will be to fill in the colors based on the congruence condition a pair of triangles fulfills. 

This activity will make assessing students on their understanding of different conditions of congruence and their application a lot more enjoyable.

10. Give me a reason 

For this activity, the educator will have to prepare a series of assertions and reasons. For example, the assertion could be that Triangle ABC is congruent to Triangle PQR. One of the many possible correct reasons for this assertion could be that Side AB=PQ, Side BC=QR, and Side CA=RP. This will prove that Triangle ABC is congruent to Triangle PQR under the Side-Side-Side condition. This will then need to be jumbled up and digitally presented to students on a screen.

The class will be divided into 5 teams with an equal number of students in each. The task of the students here will be to buzz whenever they see a match between the presented reasons and assertions. The first team to buzz will get to answer one match. If they match it correctly, they’ll get a point and if not, the chance to answer will be passed on to the team that buzzed second. At the end of the game, the team with the highest points will win.

This game will make the task of learning how to successfully prove a claim and back one’s assertions with reason more challenging yet interesting.

Conclusion

Congruence can be a tricky concept to understand and learn with all its different conditions and whatnot. But, learning can always be made fun using some simple but exciting games and activities. 

The games that have been mentioned above do exactly that by including various components of arts, and crafts, competitions, quizzes, and much more, to make learning more hands-on and interactive.

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 Fun Triangle Congruent Games and Activities For Classroom appeared first on Number Dyslexia.

That’s why I always try to use art and craft activities at home to strengthen school learning. Recently, my daughter learnt about the different types of triangles in school. To build up on her learnings at school, I decided to do an interesting craft activity at home. 

I am going to share the details with you here in this blog. If you wish to try it out with your kiddo, you’re more than welcome. So, let’s begin!

Fun craft activity with different types of triangles 

Things You’ll Need:

• “Types of triangles” print out
• Choice of colors – crayons, oil pastels, etc.
• Black marker
• Glue
• Scissors (Disclaimer: Adult supervision is required. Please be vigilant while your kid is using a scissor for this craft.)

Instructions: 

Take a print of our “Types of triangles” pdf. You can print as many copies as you would like. I printed two copies for this activity so I have an extra print in case things go wrong with the first one. 

Review the various types of triangles with your kid and explain how each one is different from the others. 

Now let your child use their choice of coloring medium to color all the triangles given on the sheet. 

My daughter used crayons for this activity, but your child can also use oil pastels, water colors, marker pens, etc.

When all the triangles are colored, it’s time to cut them out. If your child is older and is comfortable using scissors, you can let them do it. Or else, give them a helping hand to cut out the shapes. 

These are pairs of different types of triangles that we cut out. Each type of triangle is colored with a specific color for easy differentiation. For example, the green triangles are isosceles triangles, the red ones are obtuse triangles, the pink ones are scalene triangles, and so on. 

Now use these triangles to make the craft. We decided to club this triangle craft with different types of emotions and called it the “Emotion Triangles.” Have a look at the video shared below to see how I and my little one together made this colorful fun craft.

And here is the final look! Isn’t it cute? As kids love emojis, I thought it would be a good idea to incorporate them into this activity. We gave our triangles different expressions with tiny little hands and legs to complete their look. The best part of this activity was that I could teach the types of triangles to my daughter and make something fun out of them. 

And here is a closer look, in case you and your child wish to draw the same expressions on triangles. You can also do a quick search on the internet to find emojis with different expressions and use them in the craft. 

Wrapping up,

Learning triangles and their types can be confusing for kids as these are differentiated based on the length of the sides or their angles. This activity is a great way of helping kids grasp these concepts in a fun engaging way. I hope you and your kid enjoy this activity as much as we did. If you do, don’t forget to let us know!

In case you’re looking for more ideas to engage with children at home, do browse through our arts and crafts section where you’ll find activities like DIY geoboard, DIY Tangrams, DIY Flashcards, and more.

Happy Crafting!

Priyanka Sonkushre

I am Priyanka Sonkushre, a writer and blogger. I am the person behind “One Loving Mama,” a mom blog. Equipped with a Bachelor’s degree along with an MBA, my healthcare background helps me deeply understand learning difficulties. I know how challenging it can be for parents to find the right resources to help their children excel in life. So, here I am to blend my healthcare expertise with my parenting experience to create valuable and helpful resources for parents and teachers supporting children with learning differences. If you wish, you can follow me on Facebook and LinkedIn.

onelovingmama.com

The post DIY: Types Of Triangle Craft appeared first on Number Dyslexia.

Children possess very dynamic learning capabilities, and their world evolves every day with new data to the knowledge bank. Once the child is familiar with basic shapes, it helps to understand more complex structures in the future.

Introducing the triangle shape to kids can be made facile and effortless with the help of a few manipulatives, activities, and games. These can help them identify and use forms through fun-filled learning experiences. 

Games for introducing triangles to little aspirants

1. Spot the triangle

Elementary math involves learning basic shapes and counting. These concepts are tested in this game. The game provides the child with different tasks in each round, namely counting the number of triangles, identifying its color, or even picking the triangle from two figures displayed. 

The game is highly interactive and is designed for the beginner. It helps the child to get familiar with shapes, colors, and even counting. The appearance of the triangle in every round of the game ensures that the child retains the concept through repetition. 

2. Draw the triangle

Through this game, the child is introduced to the next level of learning shapes, which is drawing them. The game focuses on drawing triangles only. A game is designed intelligently for multiplayer; it offers children a competitive spirit along with an enriched learning experience. 

Dots are displayed on the screen. The children join two dots at a time with a straight line. The goal is to form a triangle. The player who completes a triangle first scores a point. The game continues till all options to create triangles are exhausted. 

The game tests the power of reasoning and keen observation; it will keep the child engaged while keeping the learning process going. 

3. Paint along

Drawing enhances the child’s motor activities along with making the learning experience highly enjoyable. Kids love to color, and this game uses this fact as an advantage.

This game has various options that a child can choose from. From drawing and painting shapes to different figures, the child can pick one pattern, one drawing tool, and the various other options to draw the perfect triangle and all triangle-related objects. 

The child proceeds to draw as per the process on the left side of the screen and once this is done accurately, earns a rock as a point. The games test the child’s power of observation and help in learning to draw a shape. 

4. Scavenger hunt

Learning is always fun with friends, especially when it is subsumed into a game. Scavenger Hunt is a popular game that can be played in a lot of variations. One such variation can be integrating the triangle shape so that the child better understand the shape and its properties. 

The educator or the parent needs to put different triangle-shaped objects in different corners of the room. The child now has to find all the objects which look like a triangle. These can be a particular triangle-shaped cushion or a nacho, and even an upside-down kept umbrella.

To make the activity even more thrilling, the child can be given a target. For example, find 5 items in 5 minutes. This activity can also be conducted for a group of students. This way, the student who collects the maximum triangle-shaped objects wins the game. 

Learning through playing in a group with the help of activities like the Scavenger hunt helps the child understand concepts in an easier way and offers the freedom even to turn mistakes into lessons. Moreover, playing together in a group fosters the spirit of sportsmanship along with a healthy learning atmosphere. 

5. Triangles with paper strips

This is a fun activity that will no doubt have messy hands but will also impart clarity of concepts.

The educator or the adult cuts strips out of coloured craft paper or cardstock and demonstrates how to glue them at corners to obtain a triangle. It is then the turn of the children to try the same. 

The game can be made competitive by asking them to make triangles of a particular colour by choosing from a large mix of them. Children get acquainted with colours and also create triangles, thus helping them with their motor activity too. 

To make the activity even more challenging, the children can be given a time limit. For example, whoever colours and pastes the maximum number of triangles in the next 20 minutes wins the game. 

6. Playdoh and buttons

This game uses play-doh and some colored triangle buttons. One can easily get triangle buttons from a nearby utility store or e-commerce. Give the children playdoh of various colours. It may be a good idea to wear aprons lest they mess up their clothes. Ask the children to roll out small flat cakes from the play-doh. Give them all buttons and demonstrate how triangles are made by arranging the buttons on them in the form of a triangle. 

The game can be made more challenging by instructing them to choose particular colors or make triangles of various sizes. 

This would enhance their knowledge of colors and size comparison too. 

7. Identify types of triangles

This game is for the slightly older lot. In this game, the players would be asked different questions on the types of triangles. For example, a question could be, which triangle has a right angle?

Other questions could be, what is the main unique property of a scalene triangle? The knowledge of kids with respect to the different types of triangles would be put to test in this game. Students of 3rd grade and higher can play this game to evaluate their understanding of the concepts.

This is a fun game that can be incorporated as a classroom activity and can be used by educators to evaluate the students. Moreover, this just does not test the knowledge but also builds up the understanding level of the students when it comes to the types of triangles. The game provides a score, where students can monitor their performance. 

8. Block Triangle Puzzle

Every kid loves a good jigsaw puzzle, but have you tried and indulged them in a game wherein they have to arrange sets of triangles in a big piece of the triangle while making sure that there are no empty gaps?

This game revolves around the same concept. There is a big triangle, which needs to be filled up with small pieces that are given as an option. The player needs to choose which piece would fit where assuming that no piece can be left, all are to be used and no gaps should be there in the bigger triangle.

Not only teaching about triangles, but this game also stimulates the brain to think harder and make place for all the parts that are given as an option. 

9. Triangle

This is a fun mind and eye coordination game, where the bars are falling, and there is a tri-coloured triangle that needs to be rotated according to the bar of the colour to smash it. Basically, if a red bar is falling, the player needs to rotate the triangle to keep the red part on the top so that the same colour as the bar is able to smash it.

If the player is late or is not able to do so, the game is over! But the catch in the game is that the bar is swiftly falling, so the player must be super quick in rotating the triangle. This triangle game not only involves the learning of triangles but also develops reflexes as the player is encouraged to think and act promptly. 

10. Recognizing Triangles

This game is perfect for a little learner who is still learning to recognize and identify a triangle. With multiple shapes given as options, the player needs to choose the triangle from all of the shapes like circle, rectangle, and square. To make the game more thrilling, in many levels, triangle objects are given which depict a triangle, for example, a signboard, and even at some levels, a nacho!

This way, the student not only learns to recognize a triangle but is also able to relate the many real-life figures that are triangle-shaped. Moreover, a lot of times, the game asks for a particular triangle, which helps in building differentiation skills in children. Apart from this, they are able to differentiate between the various kinds of triangles. 

Let’s talk science: A Triangle is a strong shape

Ever wondered why a lot of buildings, roofs, and bridges are triangle in shape? Well, to your surprise it is because out of all the shapes, the triangle is a solid, robust, and strong shape^[1]. 

When engineers build structures, they wish to construct something that can hold a lot of weight. Imagine hundreds of cars on one single bridge; it would have to be solid to bear the weight of all those cars, plus the humans in the cars. Therefore, they need a structure that doesn’t fall down when too much force is applied to it. 

Therefore, construction architects and engineers choose a triangle shape^[2] because it transfers force or the load in a way in which it can endure it fully. Basically, when the load is applied to any of the corners of the triangle, it gets distributed on each of the sides equally. This way, the two sides of the triangle are squeezed, which can also be called compression.

This is the reason why architects, builders, and civil engineers trust the triangle shape in plenty of bulky projects. Some of them are:

1. Bridges: 

To build a bridge, multiple triangles are combined together so that they can apply load and tension at different places. This way, the compression or the load happens on the outer sides, and the tension happens on the inner and the bottom of the triangle. The bridge is thus able to hold tons of kilos of weight and does not get ruptured for a long time.

2. Roofs: 

We often see roofs at snowy areas to be triangular, and roofs at plains to be flat. Ever wondered why is that? Well, when it snows, a lot of weight is collected on the roof, which can be easily carried by no other shape, but a triangle. When it snows, the load of the snow is divided equally into both sides, so that the top of the roof does not have to bear the weight. This way, the houses are safe when it snows. The biggest reason here too is because a triangle is considered to be a strong shape!

3. Buildings:

With modern architecture going to new heights, we often see a lot of buildings being triangular in shape. Most of us think of it being an architect’s creation, but there is a lot more to it than design. Architects and engineers create buildings that are triangle in shape so that they can lift the weight of people and things inside. Apart from looking great, it is a smart solution to create long-lasting buildings which can endure the weight and bulk easily. 

To conclude

Helping a child to recognize a shape and identify it from the surroundings is a great task. But a few games and activities can make the whole learning experience a delight, as it brings knowledge along, which can be grasped during play-time and can be retained for a longer time. 

In addition, it is a good means of connecting with the child and understanding their perception. At the same time, the parents and educators need to be encouraging and motivating so that learning never stops for the little ones. Always remember that motivation and help go a long way in building self-esteem for the child. 

Moreover, at early stages, a helping hand in learning and education can build a strong base in further education.  

References:

1. World’s Strongest Shape. (2012). Archer Defterios.
2. Why is a Triangle a Strong Shape? (2020, August 17). Let’s Talk Science.

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 Fun Games For Introducing Triangles To Little Learners appeared first on Number Dyslexia.

How right triangles are used in real-life?

What exactly is a right triangle? If you visualize elaborately, a right triangle is two line segments placed at 90^o angle to each other and their free ends are joined by a diagonally oriented segment. This is a shape that we may locate quite effortlessly around us. Staircases when observed from the side may give you an impression of several right angles juxtaposed to each other. Apart from this common example locatable in homes, listed here are the other real-life uses of the right triangles.

• Shadow cast by a tall object: A tree forms right angle to the land. Its top and the open end of the shadow form the hypotenuse allowing you to visualize the right triangle structure.

• A climbing ladder leaning to the wall: A slanting ladder to the wall forms right triangle shape where hypotenuse corresponds to the ladder.

• Angles for placing a slab: Wall mounted shelves are placed on right triangular holding points.

• A person standing at a tower and locating a ball on the land : The gaze of a person standing on the tower forms the hypotenuse of the right triangle shape whose two vertical and horizontal arms are height of the tower and distance between the tower and ball.

Solving right triangle and its application in various professions

Right triangles fit various spheres of our lives like a glove. These geometrical figures have an entire branch of math dedicated to it. We all know it by the name of ‘trigonometry’. Various relationships between the two from the three sides of the right triangle (trigonometric functions) help solve real-life problems various professionals face^[1]. Let’s take a look at those.

1. Carpentry

Carpenters need to ascertain that the walls are perfectly straight and corners are squares to fit in the elements as a part of the interior designing process. They may apply the Pythagorean theorem that relates the sides of the right triangle to find the required measurements.

2. Finding height or length

In architecture, the experts solve right triangle problems to find the required height or length of any structure. This calculation is needed to assure compliance with the building plan.

3. Navigation

In navigation, finding the distance of the ship from the shore, or between two ships or other objects can help in finding the probable duration of the tour. It may also help find the safe speed and the suitable maneuvering angles to keep the vessel protected from hits or accidents.

4. Surveying

Surveyor uses the trigonometry functions or solves right triangle based problems to estimate the height of a building. Using a total station theodolite (TST), the surveyor finds the exact angle of elevation from a chosen distance.

5. Astronomy

Several astronomical calculations like estimating the radius of the Earth or the movement of certain objects in a particular period can be found using the principles and functions of trigonometry. The study of distances between the two astral bodies becomes possible to do by treating the distance as one arm of the right triangle and applying trigonometry principles.

6. Astronauts and space scientists

Astronauts, during their expedition to space, need to find the characteristics of weather, soil, air pressure, etc. of the places where they cannot visit physically. They use tools like robotic arms for such purposes. With the help of right triangles-based calculations, they can find the correct angle and orientation for maneuvering the robotic arm or other similar tools.

Teaching right triangles the activity way

All the examples mentioned above indicate the possibility of teaching right triangles by using activities. High school students have to hone their trigonometry basic skills. Just solving equations and mugging up values of cos, tan and sine may not produce the required outcomes. Better learning is achieved when they get to apply the concepts. Activities based on right triangles help learn by doing.

A few activities that involve solving right triangles’ variables are:

1. Estimating heights of objects using Lego Robot kit

Lego Robot Kit act as a portable counterpart of the things students may see around. They apply trigonometry principles to estimate the height of various objects given in the kit. On scaling up the measurements received, they can apply the learning to find the heights of buildings, towers, poles, etc.

2. Estimating boundaries of a plot

Prepare the model of a landscape with dummy hills, buildings, empty land, etc. Assign a few values to the objects’ distance from each other and contours of the land. By making hypothetical right triangles from the top of the dummy hill, building, etc., students can learn about how to find values of various variables like height, speed, distance, etc.

3. Parallax activity to guess the distance between stars and sun

Parallax means the difference in the position of an object when viewed from different points of view. This displacement can create an angle of view, and two arms that resemble a triangle. By using calculators and trigonometric functions’ tables, they can get the idea of the distance between astronomical objects. Moving forth, the distance between two landmarks can also be estimated.

Conclusion

Studying right triangles can help students understand how the geometric and trigonometric principles can be applied to solve real-life problems. It is this practical knowledge attained that helps blur the line between bookish knowledge and applied science. So, next time you are done mugging up the definitions and functions’ values, start making hypothetical models and apply various combinations of values to strengthen your learning. It brings fun into the learning hour and makes the study of mathematical concepts more interesting.

References:

1. Libretexts. (2021, January 2). 1.3: Applications and Solving Right Triangles. Mathematics LibreTexts. https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Elementary_Trigonometry_(Corral)/01%3A_Right_Triangle_Trigonometry_Angles/1.03%3A_Applications_and_Solving_Right_Triangles

Pratiksha Bhatt

I am Pratiksha Bhatt, Bachelor of Life Science, and Masters in Management Studies. I have done certification courses in early education counseling. I am a writer, a mother of a child with spelling difficulties which drove me to alternative resources of education like manipulatives and participatory activities. My areas of expertise are learning difficulties, alternative learning methods, and activity-based learning.

The post Real Life Applications Of Right Angle Triangle appeared first on Number Dyslexia.

For this purpose, educators can use activities to create an appealing bond between students and the triangle shape. In this post, we will look at 8 such activities that would be advantageous for a preschooler learning to identify and draw a triangle. 

Learning based activities to teach triangles to preshcoolers

1. Using Triangle Shaped Stamps 

Educators can make triangles out of cardboard, thermocols, etc. Little learners can use these pieces as stamps in a very simple manner for some extra fun educational playtime. Apart from this, you can also use triangle-shaped erasers, sponges, and even utensil boxes as stamps.

All you have to do is take the stamps and dip them in the colours of your toddler‘s choice. You can paste them in any pattern on a plain sheet of paper. Better yet, get your toddler to do all the work by themselves. This can be a great learning experience that does not get that messy either. 

2. Draw Those Triangles

While drawing can be an everyday activity for a pre-schooler, it is also essential as it is a big step for a child to use crayons or pencils to form a shape. By helping them create an outline, the kids can trace over the outline and draw a perfect triangle! Other than this, educators or parents can also place three dots in the form of a triangle. Later, the child can connect these dots, which will challenge them to use their spatial perception, and they will have to figure out how to get from one point to another. Start with small to medium-sized triangles and increase the size.

3. Gum it Up!

Take out a large construction paper and draw some triangles of different sizes, but just the outline. Now cut out triangular shapes of the same size from another thick paper or cardboard that you have drawn on the paper. Get the child to paste the correct sizes in the correct positions. Educators and parents can also use post-its for this activity. This will teach them how to fit things within the lines. Try to face the triangles in different directions and get them to paste it correctly. This will prove to be quite a challenging and fun exercise for your preschool child.

4. Rainbows and Triangles

This is a fun activity that will teach them the importance of differences in size. What you can do to make this a better experience is to get them to colour each triangle based on the size. Draw outlines of 5-6 triangles. Make sure that at least two of them are of the same size. Now instruct the child to colour the biggest triangle using one colour and the smallest using another. Also, ask them to colour similarly sized triangles using the same colours. 

5. Play-Doh, Say no more!

While this game might be a little messier; however, the fun that comes along with this one would make you not regret the plight. Get at least 3 to 4 differently coloured Play-Dohs to help you with this activity. You might want to get a pair of gloves as well and start working on the clay to get those triangular shapes going. Prepare an outline on a sheet over which you can get the child to place the triangles that they create. Again, mix and match the colours and have as much fun as you can.

To make things even more entertaining, kids can make triangles of different sizes and colours, and later, educators and parents can jumble them up and ask the little learners to arrange them according to their colour or size. This would help them establish differentiation skills and teach them much more about colours, sizes and triangles altogether.

6. Figures with Triangles

Learning the triangle shape is just not about drawing it. It is also crucial that kids understand and are able to identify a triangle-shaped object once they see it. Educators and parents can carry out this activity to give the student an old book or a newspaper and find all the triangle-shaped images they see like advertisements of pizzas, cheese, sandwiches, roadsigns, house roofs, etc. 

You can also ask the child to identify at least 5 such triangle-shaped images and then circle them with different colors. This would not only help them understand the shape better but also comprehend its practical usage. Moreover, they would build a skill to identify the shape easily.

7. What Objects Are Triangle Shaped?

Much like the activity ‘figures with triangles,’ this one is different as in this activity, kids need to draw out objects which are triangles in shape. For example- a pizza slice, the top of a hut, a mountain, etc. To make it more exciting, you can ask the children to make certain figures out of triangle cutouts. For example, making a man out of triangles– the kids can use triangles to make a face and the body. This activity is unique and would keep the little learners entertained. Moreover, since the activity triggers creativity, this would also help them build creativity, along with critical thinking skills. 

8. Make Triangle Shaped Snacks

While we wouldn’t recommend putting out Doritos and hoping that your toddler recognizes that to be a triangle, it is not a bad idea to involve tasty treats as part of the learning exercise. Many things can be shaped to be a triangle. You can slice apples, carrots, potatoes, nuggets, and many other snacks in the form of triangles of different sizes.

To make it further interesting, you can cut out various other shapes such as circles, squares, and rectangles, out of food items such as bananas (for circles), cakes (for rectangles and squares), etc. Now, you can encourage the little one to identify which snack is shaped like a triangle amongst the other-shaped snacks.

Why learning based activities matter in preschool education ?

1. Create a long-lasting impression 

When you think back and ponder upon your own learning experiences, you will note that when you are actively involved in the learning process, you absorb information that stays with you for a long time. Children are in a similar position when they are introduced to fun activities as opposed to classroom learning. Shapes are fundamental things that must be learned about at a young age. It is quite difficult to make anything fun for a toddler and grasp their attention for long enough. This is why such activities become important.

2. Improve their skill set and perception

During preschool, kids are at such an age where they can be moulded easily. This means that they are quick to absorb things and develop their perception about what they learn. It is important to introduce engaging activities to keep their minds occupied and active. They will learn to use their senses better and understand the world around them. You can also incorporate knowledge of other things such as safety, using different objects, cleaning up messes, etc.

3. Establish a positive student-teacher relationship

It is proven that high-quality teacher-student relationships facilitate learning and improve engagement in any game or activity that the preschooler participates in. When preschoolers have an established and positive relationship with their teachers, it fulfils their developmental need for a connection, thus, enhancing learning^[1].

With facilitated learning, the preschooler may feel more enthusiastic and engaged in what the teacher encourages them to do, i.e., activities and games in this reference. An enthusiastic preschooler (or a student of any age) should be better at grasping concepts and the aim of the activity because of the increased willingness to participate.

4. Reinforces Positive Learning Memories

Playing activities to introduce preschoolers to a concept in learning can help reinforce positive learning memories. It may be possible that while playing these activities, kids can associate them with happy memories that they create while playing these activities. 

For example, when you teach a student how triangles look using a slice of pizza, it is possible that when the child sees a pizza again, they immediately trace back to the time of the activity, simultaneously associating it to happy memories they created while playing the activity.

Conclusion

Getting your toddler to recognise a triangle as a triangle is in itself a big deal. Try to make this a fun and very stress-free experience for the preschooler who is just learning to learn. You can use these activities as an excellent way to connect with the child as a person and understand how they perceive the world. 

Positive reinforcement goes a long way at this age. Appreciate everything that they do and make sure that you show them that their work is important. You can stick the crafts onto the refrigerator or take pictures for memories.

References:

1. Rimm-Kaufman, S. (2010, April 19). Improving students’ relationships with teachers. American Psychological Association. http://www.apa.org/education-career/k12/relationships2.

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 8 Fun Triangle Shape Activities For Preschoolers appeared first on Number Dyslexia.

Triangle is one of the unique geometrical shapes which requires in-depth study. A whole branch of maths called trigonometry is based on triangles; it is that important a figure. Teaching concepts based on triangles may require more than reading books. Especially, when elementary knowledge building is a concern, activity-based learning helps. One of the pedagogical tools that ease teaching through activities is manipulatives. How triangles are taught through manipulatives and what are various triangle manipulatives available to try, let’s explore!

Manipulatives for teaching triangles – What to expect

Teaching triangles at an early age to students is important as it allows them more time to practice. But, we cannot expect them to be comfortable with terms like angles, sides, median, etc. The first job while teaching kids about triangles is to befriend them with this novel concept. Manipulatives allow teachers to familiarize kids with triangles by the way of maneuvering and acquaint them with triangles in a readily absorbable manner.

Manipulatives help generate intellectual curiosity among kids. These work as ice-breakers and encourage kids to put forth learning-directed questions. Teachers can solve a variety of queries by giving heads-up at the start of doing activities with triangle manipulatives.

Most importantly, manipulatives promote a multisensory learning approach. All kids have different paces of learning. By creating an activity-based learning environment with the use of manipulatives, kids can learn triangles by the senses of vision, touch, kinesthetics, etc. Thus, they can adjust easily to the enriching repertoire of topics that focus on their overall development.

Keeping these facts in mind, we have curated here the 6 most engaging manipulatives that can help young learners adopt activity-based learning to internalize triangles’ basics.

Engaging triangle manipulatives for young learners

1. GeoStix

Geostix basic set comprises 80 sticks in color-coded lengths, a collection of activity cards, and protractors. Kids can dispense the measuring part as the sticks are provided in cms. They can learn several concepts of triangles by doing activities based on the Pythagoras theorem, congruence concept, principles of intersecting lines, etc. These geostix have ridged appearance that allows easy moving and adjusting of the sticks over one another without hassles. The easy set-up allows kids to devote more time to do activities and learn.

It is the engagement quotient that sets this manipulative aside from various counterparts. The multisensory approach comes into play when kids actually join the sticks and create figures given in activity cards. Help your young learner get into quick yet sustainable learning mode by doing collaborative activities with Geosticks set. Concepts based on spatial relationships of triangles become easy to grasp with this activity set.

2. Tile Set

Triangle is an important part of geometry. Like many other shapes, triangles are a shape as well. You can find triangular shapes embedded in various structures around. Impart a tangible introduction of such structures by asking kids to make figures by using this tileset. This manipulative set contains 8 acute triangles and 10 right-angle triangles among other geometric shapes. Thus, you can give an idea of how triangles can fill in the space or add to the structures by playing with these tiles.

This learning material offers several benefits. It allows involving a multisensory approach to be conversant with triangle-based facts. Fine motor skills can get better too, as the tiles are joined to make structures. One can also be familiar with right-angle triangles’ physical characteristics and related theorems by doing activities with this play-based learning material.

3. Stacking blocks

Stacking blocks allow easy concept retrieval as kids append these to make structures. It is a manipulative fit for toddlers who need to develop shape-based reasoning. These blocks come with holes and the pegs fit on those only when the right structure is chosen. It is just the start! Further, you can engage kids in making structures by taking cues from the activity cards. The learners can refine the color recognition, and also have a firsthand introduction to triangles.

Employ these stacking blocks to teach the idea of balance, height, and width and show how triangles can be integrated to form several shapes. In the higher classes, you can introduce right-angle triangles, angles and corners, and several congruency rules with the help of these blocks.

4. Geoboard

Geoboard offers tactile learning support for kids who want to study shapes and their characteristics. This wooden board with pegs and latex bands can work as your fun-filled learning tool to be conversant with 2D shapes including triangles. All pegs are placed one cm apart. Hence, you can create triangles on this board as per measurements provided as cues. This activity tool combines the learning of fine motor skills, triangle concepts, and 2D imagery and eases the elementary learning of geometrical figures.

Driving kids into learning by reading books becomes tough due to their monotonous nature. Manipulatives offer supplementary resources to explore topics and encourage them to internalize abstract learning. Introduce types of triangles to kids by asking them to create triangles with equal sides or only two equal sides, etc. Activity-based learning promotes deeper interest and kids try to explore more by trying to highlight the use of geometrical shapes in the structures they see around.

5. Pattern Blocks

Knowledge of patterns develops from sequential memory build-up. It is possible to arrange triangles of different sizes and shapes in several patterns to create new, composite figures. Young learners can appreciate the practical use of learning triangles by making patterns with triangular, flat blocks. Activity cues are provided along with the pattern blocks in this set to drive kids into constructive thinking.

Pattern blocks help grasp the relationships between triangles and other shapes. When trying to know about the properties such as balance and stability of triangles, this manipulative can provide the requisite learning support. Teachers can offer two-dimensional puzzles based on the concept of tangram. Skills of perceptual reasoning and visual-spatial awareness find seamless augmentation on experimenting with these 7-piece puzzles.

Multi-utility element of triangle manipulatives

The learning support is quite evident from the way manipulatives boost critical, spatial, and visual thinking. Apart from the learning support, manipulatives can offer several other utilities, such as:

• Tool for developing social skills: When you employ manipulatives in a group activity, the learners build social skills like responsibility, cooperation, and problem-solving (Moch,2008). Their mind engaged in an activity tends to become more focused and disciplined.
• Support for fine motor skills development: All manipulatives useful for learning triangles require grip, balance and small muscular movements. It, therefore, amounts to development of fine motor skills.
• A result-oriented playful activity tool: It takes a lot of effort to engage kids in doing some constructive activity. Manipulatives with their intriguing colors and styles can easily attract young brains and divert their mind to solve problems. The sense of achievement fills kids with pride and they are driven to try harder.

Conclusion

The use of alternative methods of teaching proves effective in keeping all kids at comparative levels of proficiency. Manipulatives serve as alternative teaching tools to manage all challenges associated with imparting newer skills. Concepts like triangles tend to stay with early learners for long by learning in an activity-based manner. Thus, the most pronounced impact is seen in the development of foundational skills which augment smooth transitioning to higher proficiency levels.

Pratiksha Bhatt

I am Pratiksha Bhatt, Bachelor of Life Science, and Masters in Management Studies. I have done certification courses in early education counseling. I am a writer, a mother of a child with spelling difficulties which drove me to alternative resources of education like manipulatives and participatory activities. My areas of expertise are learning difficulties, alternative learning methods, and activity-based learning.

The post 6 Best Manipulatives For Learning Triangles appeared first on Number Dyslexia.