Budding Scientists: ABC's of Applied Mathematics for Kids

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ABC's of Applied Mathematics: Let's Play with Shapes and Polygons!

Suitable for 4 to 6 years old children


Squares, triangles, and rectangles are shapes that can be found in the world around us. There are also many other interesting shapes such as pentagons, hexagons, and octagons. Let us enter the wonderful world of polygons and discover the shapes that are around us!

Let us have some fun learning about the concept of shapes and polygons with books and art materials!


Tuning-in Song: We are Shapes


Repeat this song with other shapes such as circles, rectangles and triangles and ask your child if they can notice and name any differences between their characteristics!

The full song lyrics can be found here: Full Song Lyrics for We Are Shapes

Tips for Parents:

The repetitive nature of the song helps with pattern recognition and rhythm synchronisation. The catchy rhythm helps your child remember what they are learning, and they will be singing about the different properties of shapes in no time!



What Can I Be?
By: Ann Rand Ingrid Fiksdahl King
Publisher: New York : Princeton Architectural Press, [2016]

Tips for Parents:

Asking open-ended questions is an important way to guide a child’s exploration. It can also introduce new vocabulary to them when you ask questions that require them to make simple comparisons between objects that they observe in their immediate environment.

Questions to spark discussion with your child:

1. Which is your favourite shape? Why do you like that shape?

2. How are these shapes similar and different? Can you list down the characteristics for me?

3. What other objects do you think these shapes could be?



What are Polygons?

A polygon is a flat, two-dimensional (2D) shape with straight sides that are fully closed (all the sides are joined up).

The sides must be straight.

Polygons may have any number of sides.

Definition of a Polygon
The School Run. (2022). What is a polygon? TheSchoolRun. Retrieved April 30, 2022, from

What are Polygons

Discuss with your child if they can tell you which of the following three shapes above our polygons and their reasons why they chose that shape. Ask them if they can relate their decision to the characteristics they had learnt above.

Polygons are named by the number of their shapes, and you can find them all around you!

Download the flash cards at: Polygon Worksheet Part 1 and Polygon Worksheet Part 2 to go through the names and properties of some well-known polygons with your child, as well as common objects that have the same shapes.

It may be a mouthful, but squares and rectangles are also known as Quadrilaterals, a name that refers to their four sides! Here are some flashcards to help them retain this fun fact: Fun Facts of Quadrilaterals

Tips for Parents:

Ask your child to observe their surroundings around them. Have them point out to you shapes and polygons that they can see around them. Make it into a fun game! It can be a variation of "I Spy." For example, "I spy...a circle!" Whoever is guessing needs to find as many circle-shaped objects they can find.

Lets learn about Shapes and Polygons 1

What are 3D Shapes?

Once your child understands 2D shapes, i.e. flat shapes, you can slowly start introducing them to 3D shapes!

To differentiate between 2D and 3D Shapes, let us look at a triangle and pyramid side by side!



The most important differences between a 2D shape and a 3D shape are the below:

- A 2D shape is flat while a 3D shape can be physically held.

- A 2D shape has only one face while a 3D shape has multiple faces.

Can your child identify and name 3D shapes? Download the flash cards here: 3D Shapes Worksheet Part 1 and 3D Shapes Worksheet Part 2 to go through the names and properties of some well-known 3-D shapes with your child, as well as common objects that have the same shapes.

Teach them on the different characteristics of cubes, cuboids, pyramids, and cones with this simple set of flashcards: Differences Between 3D Shapes

Tips for Parents:

Linking theory to the physical environment is the best way for children to learn about scientific concepts as they can then better understand the relevance of these concepts in their lives. If you notice any 2D and 3D shapes around, point them out to your child or ask them if they recognise these shapes and if they remember how their properties differ. For example, you could play ball with your children and pause for a while to ask them if they recognise the shape of the ball.


Let Us Make Some Collage Robots!

Time to have some fun! Let us get creative and make robots out of polygons. Here is what you will need:

Materials Needed


1. Select one sheet of colouring paper to be the base. This is where you will stick the parts to make your robot.

2. Draw out the shapes you want to use to make your robot! To challenge yourself, try to have at least 1 of each polygon. I.e., 1 triangle, 1 square, 1 rectangle, 1 pentagon, 1 hexagon and 1 octagon. Do ensure your shapes are small enough to fit onto your base!


3. Time to cut them out! Get Mommy or Daddy to help you with this part.

4. Feel free to cut out more in any colour and size for extra parts and decorations!

5. Paste your shapes onto your base paper to form a robot, in any way that you like! Use markers to scribble on any additional touches.

6. Ta-da! You have your very own robot collage! Check out mine below!

Complete Robot Collage

His name is Turturo, and he is a turtle-bird robot! He has parts that help him fly and swim, and his hobbies include trimming tree branches and diving for pearls to adorn his body.

Can you count and identify the different shapes and colours I used to make him?

Tips for Parents:

Encourage your child to share with you their creations! Engaging them to communicate their creative processes through language is a great way to build up their speaking, thinking and cognitive skills.


Here are some fun downloadable activity sheets below for you and your child to have fun completing together!

Perfect Pyramids 1

The most possibly famous 3-D shape we can see is the Pyramid! Have you seen these great structures in books, cartoons, or documentaries? Fill in the right vowels in the blanks in this sheet to unlock some fun facts about pyramids!

Click: The Perfect Pyramids to download and print out your activity sheet!

Search for Shapes

Uh oh! Looks like the shapes have gone into hiding! Can you find them in this wordsearch? Try looking up, down, left, and right as well as diagonally.

Click: Search for Shapes to download and print out the word search!

Click: Search for Shapes Answer Key to download and print out the answer key!



Let us give Science an artistic twist! Origami is a fun, family-oriented activity to keep the concepts of shapes and polygons fresh in your child’s mind! Try out the easy crafts below with your child!

Origami Fox
How to fold a very easy origami Fox. (2018, May 14). Retrieved April 19, 2022, from

Origami Fox1

Origami Fox2

Craft Instructions (with Pictures)

Origami Ice Cream
How to make an easy origami ice cream cone. (2018, May 16). Retrieved April 19, 2022, from

Origami Ice Cream1

Origami Ice Cream2

Craft Instructions (with Pictures)

After making these lovely creations, ask your child the questions below to keep interesting conversations going about geometrical concepts!

1. What shapes do you notice as you make your origami creation?

2. How many sides does your origami creation have?

3. Can your origami stand upright or lie flat? What does that tell you?


Unwind with your child with these helpful videos in understanding geometry, the study of the sizes, shapes, positions angles and dimensions of things. Geometry itself is a word that you can teach your children!

Polygon Song

Video Thumbnail 1

Have Fun Teaching (2013, 16 April). Polygon Song. YouTube.
Let's dance our way into learning about polygons! This fun 4-minute song about polygons and their properties will have your child recognising these interesting shapes in no time.

The Singing Walrus - English Songs for Kids. (2017, 17 April). 3D Shapes Song | Shapes for kids | The Singing Walrus. YouTube.
Take it a step further and let us look at 3D shapes as well! Spheres, cones, cylinders, and pyramids, oh my!


Shapes at the Park

Shapes at the Park
By: Christianne C. Jones
Publisher: North Mankato, Minnesota : Pebble, a Capstone imprint, [2022]

Amazing Shapes

Amazing Shapes: Lift and Learn
By: Hélène Hilton (Editor)
Publisher: London : Dorling Kindersley Limited, [2020]

Drawing a Bear with Squares

Drawing a Bear with Squares
By: Jo Marie Anderson
Publisher: New York : PowerKids Press, 2019

I Spy Shapes

I Spy Shapes
By: Marie Roesser
Publisher: New York : Gareth Stevens Publishing, 2022

The copyright to all book covers belongs to the relevant publishers or illustrators.

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