Geometry is a subset of mathematics that deals with the shapes of objects, including size, shapes, angles, and dimensions. It is one of the oldest branches of math because it helps to describe the shapes we see all around us!

To prepare children for future work with geometry, we present them with the geometry cabinet, which introduces the child to over 40 different shapes. This cabinet contains six drawers, each holding wooden shapes the child can feel, hold, and manipulate so that he or she can learn to distinguish between the different shapes. The various figures are grouped by similar shapes: Circles, Rectangles, Triangles (there are seven types!), Quadrilaterals (such as a rhombus and a parallelogram), Curved figures (including an oval and an ellipse), and Regular Polygons (such as pentagons and hexagons).

At school, we introduce your children to the cabinet and invite them to explore through lots of hands-on experiences. They trace the shapes, play games with them, and search the classroom for their favorite shapes too. Later we give children the language of the shapes using the three-period lesson.

Three Period Lessons

Three-period lessons are the primary way Montessori teachers introduce children to new vocabulary. These lessons are given every day in the primary classroom. They are quick, simple, fun! And follow a simple formula that I will share with you today.

But first, allow me to share a bit of history. Three-period lessons were originally developed by the French physician Edouard Seguin. Seguin was a psychiatrist who developed methods for helping children with learning differences more easily associate objects and their names. Dr. Montessori was inspired by his work and adopted his approach for her classrooms. Fun fact: Edouard Seguin also developed the geometry cabinet!

To better illustrate the lessons, we can use the presentation tray of the geometry cabinet as an example. We use this tray to introduce the youngest of primary children to the names triangle, circle, and square.

1^{st} Period: Introduction

We begin by picking up the shape and giving its precise name of the shape, repeating for emphasis:

“This is a square. Square; This is a circle. Circle; This is a triangle. Triangle.”

2^{nd} Period: Recognition

This phase helps the child recognize the shape by name when it is given. Starting with the last object introduced, we use active commands that require the child to physically manipulate the objects as a way to reinforce their association between the name and the shape.

“Touch the triangle. Pick up the circle. Hand me the square. Put the circle at the top of the table.”

Your children are smart, so after a few commands, rotate the order of the objects before continuing. Be careful not to use your eyes to give the child clues as you work through the second period. The second period is the longest stage of the game and should be played until the child is readily identifying the shapes without needing verbal or non-verbal cues from the adult.

***Only move to the third period when you know the child will answer correctly!***

If the second period has gone on for a while, and the child does not appear confident with the names, smile, and let your child know you will work with them again tomorrow. They mustn't feel as if they have failed in any way. Instead, they are having fun manipulating the shapes. If you are unable to move to the third period, try again on a different day.

3^{rd} Period: The “Test.”

During the third and last phase, we ask the child to recall the name of each shape. If the child does remember, the test should be short and sweet:

“What is this?” The child should respond, “a square!”

That’s it! On a different day, we will review the names of shapes the child already knows and introduce the names of new shapes.

Now you can try offering these types of lessons at home! Are you ready?

Geometry Activities:

Circle Activities

Over 2300 years ago, the renowned mathematician Euclid defined a circle as:

“…a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal.”

Circles are one of the most recognizable geometric shapes. Children are typically introduced to the circle very early on in childhood and arrive in the primary community with the ability to identify this curved figure quite easily. Yet, we still include work with this shape as we introduce the geometry cabinet. Why?

By offering six different circles (each increasing in diameter from 5 cm to 10 cm), we help the child learn to discriminate subtle differences in shape. We also help the child become more aware of this familiar shape in his or her everyday environment. Once children notice circles in the classroom, around the house, and in nature, their awareness of shapes overall becomes heightened, and they become eager to learn about the other shapes as well.

Circle Comparisons ages 3 to 4

Directions: Print out the six circles that are similar to the ones found in the geometry cabinet. Invite your child to color them. Help your child cut out the circles and use them to play a comparison game. Use the directions in the Circle Comparisons PDF to guide you through the game.

Circle Ladybug Collage ages 3 to 6 ½

Directions: Color the circles and half-circles using crayons or colored pencils. Cut out the shapes and arrange them on a large sheet of paper to create a ladybug. Use glue or tape to keep the pieces in place.

Circle Scavenger Hunt ages 3 to 6 ½

Directions: Explore your home and look for items that are circular in shape.

ages 3-4 Bring the objects to a table or collect them in a safe place on the floor.

ages 4 ½ to 6 ½ Draw pictures of the circular items and write the names below.

Fun with Circles ages 5 and up

Directions: Use colored pencils to fill in as many different circles as possible. Count the number of circles on the page and record the number.

Rectangle and Square Activities

Rectangles and squares are the two most common quadrilaterals, or four sided plane figures. We introduce the children to the geometry cabinet’s rectangle drawer that contains six different shapes (each increasing in width from 5 cm to 10 cm). Through hands-on exploration, children will experience that rectangles have two pairs of sides that are the same. Some may even discover that the largest rectangle (with four sides of equal length) is actually a square. Since children are quite familiar with these shapes, many of the activities we introduce highlight these shapes in art!

Rectangle and Square Coloring ages 3 to 3 ½

Directions: Print out the six shapes that are similar to the ones found in the rectangle drawer of the geometry cabinet. Invite your child to color them. Help your child cut out the shapes and lay them out from thinnest to thickest. Use them to go on a scavenger hunt for rectangles and squares in your home.

Albers-Inspired Collage ages 3 to 6 ½

Directions: Josef Albers was a famous painter who is well-known for creating over 100 prints and paintings in a series entitled “Homage to the Square.” Print out the attached PDF for instructions on how to create your own version of this square tribute through collage.

Piet Mondrian Coloring Activity ages 3 to 6 ½

Directions: Take a moment to read the cultural story about Piet Mondrian, an artist who featured squares and rectangles in his abstract art. Then, print out the Mondrian coloring sheet and complete the picture using primary colors (yellow, blue, and red) in the style Piet Mondrian used many years ago.

Fun with Rectangles ages 5 ½ and up

Directions: Read the instructions and fill in the rectangle drawing as indicated. Use your counting skills and your geometry skills at the same time!

Triangle Activities

We introduce the children to the seven types of triangles using the Geometry Cabinet. The triangle drawer of the cabinet contains six triangles that are named according to their angles(acute or obtuse) and their sides(isosceles/two sides are the same and scalene/all three sides are different). The presentation tray holds the equilateral triangle whose angles and sides are all equivalent.

Just as with the other shapes in the cabinet, the child’s first experiences with the triangles is hands-on. They trace the shapes, match them to form cards, play distance games with them, and search the classroom for objects that match the triangles in the drawer. All of these activities help develop the child’s ability to tell the difference between a right angled scalene triangle and a right angled isosceles triangle. This refined ability to visually discriminate between two shapes will directly translate into the child’s capability to discern between “b and d” or “p and q” when they embark upon reading later on.

After lots of manipulation and exploration with the triangles, we give children the language of the triangles using the three period lesson. We introduce the children to the full name of each triangle without bringing attention to the details regarding angles or sides. Primary children are hungry for rich vocabulary and are able to recall the names and associate them with the triangle’s form alone. We bring attention to the angles and sides as children are transitioning to the lower elementary program where these concepts are explored in much greater detail.

Three Period Lessons with Triangles ages 3 ½ and up

Directions: Print out the geometry cabinet triangle cards from the “Three Period Lessons with Triangles” document attached. Choose three contrasting shapes to introduce to your child using a three period lesson. Over time, you will introduce the child to other triangles (and shapes in general) in the same manner.

Triangle Fish Collage ages 3 and up

Directions: Color the triangles using crayons or colored pencils. Cut out the shapes and arrange them on a large sheet of paper to create a fish. Use glue or tape to keep the pieces in place. (see example below)

Fun with Triangles 1 and 2 ages 5 and up

Directions: Read the instructions and fill in the triangle drawing as indicated. Use your counting skills and your geometry skills at the same time!

Triangle 3 Part Cards ages 5 and up

Directions: Print and cut the three part cards. Each triangle will have a classified card, a printed slip and a control card (depicting the classified card and its associated slip). Mix up the classified cards and slips. Use your knowledge of the triangles to match the slips to the triangles. Check your work with the control card.

Three Period Lessons with Curved Figures ages 3 and up, as needed

Directions: Print out the geometry cabinet cards from the “Activities with Curved Figures” document. Choose three contrasting shapes to introduce to your child using a three-period lesson. Over time, you will introduce the child to other shapes in the same manner.

Curved Figures Collage ages 3 ½ and up

Directions: Color the curvilinear shapes using crayons and colored pencils. Cut out the shapes and arrange them on a large sheet of paper. With permission, use glue or tape to create a collage using the curved figures.

Labeling Curved Figures ages 4 ½ and up

Directions: Color the curvilinear shapes using crayons or colored pencils. For an extra challenge, use up and down lines as you would with metal insets. Write the names of the shapes below using cursive writing.

Curved Figure 3 Part Cards ages 5 and up

Directions: Print and cut the three-part cards. Each curved figure will have a classified card, a printed slip, and a control card (depicting the classified card and its associated slip). Mix up the classified cards and slips. Use your knowledge of curved figures to match the slips to the shapes. Check your work with the control card.

Quadrilateral Activities

Quadrilaterals are plane figures that have four sides. The word "quadrilateral" is derived from the Latin words quadri, a variant of the number four, and latus, meaning "side." Quadrilaterals can also be classified as polygons (as we shared last week). The children are already familiar with the most common quadrilaterals: squares and rectangles. To build upon their knowledge of shapes, we also introduce children to the six quadrilaterals in the geometry cabinet, including the rhombus, parallelogram, right-angled trapezoid, isosceles trapezoid, kite, and chevron.

Three Period Lessons with Quadrilaterals ages 3 ½ and up

Directions: Print out the geometry cabinet quadrilateral cards. Choose three shapes to introduce to your child using a three-period lesson. Later, introduce the child to the other quadrilaterals (and geometry cabinet shapes in general) in the same manner.

Sidewalk Stained Glass ages 3 and up

Directions: This activity has become quite popular! Transform your sidewalk or driveway into a work of art with this fun outdoor activity. Print out the activity sheet for supplies, instructions, and photos. As you create your design, count to see how many quadrilaterals you can include!

Quadrilateral 3 Part Cards ages 5 and up

Directions: Print and cut the three-part cards. Each quadrilateral will have a classified card, a printed slip, and a control card (depicting the classified card and its associated slip). Mix up the classified cards and slips. Use your knowledge of the quadrilaterals to match the slips to the shapes. Check your work with the control card.

Polygon Activities

Polygons are two dimensional (plane) figures that have at least three straight sides. In fact, polygons are named based upon their number of sides. Triangles, rectangles, and squares are polygons that are very familiar to the children. To expand their knowledge of shapes, we also introduce children to the six regular (all sides are the same) polygons housed in the Geometry Cabinet. The polygon drawer of the cabinet contains a pentagon, hexagon, heptagon, octagon, nonagon, and a decagon.

The child’s first experiences with polygons involve hands-on manipulation and comparison between the various shapes. Most children immediately recognize the “stop sign” in this drawer! We encourage lots of tracing and work with the geometric form cards, which helps the child see the subtle differences between a six-sided figure and a seven-sided shape. Lastly, we offer the children the language of the polygons using the three-period lesson. Older children begin to make associations between the names of the shapes and the number of sides it has. They discover that heptagons have seven sides, and decagons have ten sides. In lower elementary, the children will be introduced to the Greek origins of the prefixes used in the polygon naming system.

Three Period Lessons with Polygons ages 3 ½ and up

Directions: Print out the geometry cabinet polygons cards from the “Three Period Lessons with Polygons” document. Choose three shapes to introduce to your child using a three-period lesson. Over time, you will introduce the child to the other three polygons (and geometry cabinet shapes in general) in the same manner.

Hexagon Coloring Activity ages 3 and up

Directions: Color the shapes to create an interesting design!

Polygon 3 Part Cards ages 5 and up

Directions: Print and cut the three-part cards. Each polygon will have a classified card, a printed slip, and a control card (depicting the classified card and its associated slip). Mix up the classified cards and slips. Use your knowledge of the polygon to match the slips to the shapes. Check your work with the control card.