Mathematics · Kindergarten · The Language of Shapes · Weeks 19-27

Describing Shapes by Attributes

Using names of shapes to describe objects in the environment and identifying attributes like number of sides and vertices.

• Common Core State Standards
• CCSS.Math.Content.K.G.B.4

About This Topic

Creating new shapes involves composing simple geometric figures to build more complex ones. Kindergarteners learn that two triangles can make a square, or six triangles can make a hexagon. This is a vital step in spatial reasoning and problem-solving, as it requires students to visualize how parts fit together to form a whole. The Common Core standards focus on this 'composing' of shapes to develop an early understanding of area and symmetry.

This topic is inherently creative and hands-on. It is much more effective for students to discover these combinations through trial and error with pattern blocks than to be told the answers. This topic comes alive when students can physically model the patterns and see how one shape can be 'hidden' inside another through collaborative building.

Key Questions

1. How can we describe a shape to someone using only its attributes?
2. Differentiate between a side and a corner (vertex) of a shape.
3. Justify why a circle has no corners.

Learning Objectives

• Identify the number of sides and vertices for common 2D shapes (circle, square, triangle, rectangle, hexagon).
• Compare and contrast attributes of different 2D shapes, such as the number of sides and corners.
• Classify objects in the classroom based on their geometric shape and attributes.
• Explain why a circle does not have vertices or sides.

Before You Start

Recognizing Basic Shapes

Why: Students need to be able to name basic 2D shapes (circle, square, triangle) before they can describe their attributes.

Counting to 10

Why: Students must be able to count the number of sides and vertices accurately.

Key Vocabulary

side	A straight line segment that forms part of the boundary of a 2D shape.
vertex	A corner where two sides of a 2D shape meet. Plural is vertices.
circle	A shape with no straight sides and no corners, where all points on the edge are the same distance from the center.
square	A shape with four equal sides and four square corners (vertices).
triangle	A shape with three sides and three corners (vertices).

Watch Out for These Misconceptions

Common Misconception

Students may think a shape can only be made of one kind of smaller shape.

What to Teach Instead

They might think a hexagon can only be made of triangles. Use a collaborative 'Shape Swap' where they try to replace two triangles with one rhombus to see that multiple combinations work.

Common Misconception

Students might struggle to see the 'hidden' shapes within a larger design.

What to Teach Instead

Use transparent pattern blocks on a light table or overhead. This allows students to physically overlay shapes, making the composition visible and helping them 'see' the parts within the whole.

Active Learning Ideas

Inquiry Circle: Shape Puzzles

Give small groups a large outline of a shape (like a giant hexagon). They must work together to fill the entire space using different combinations of smaller pattern blocks and record their 'recipe'.

25 min·Small Groups

Peer Teaching: Mirror Me

One student builds a simple design with 3-4 shapes. Their partner must try to build the exact same design, then they discuss which shapes they used and how they fit together.

20 min·Pairs

Think-Pair-Share: The Triangle Challenge

Ask students: 'How many different things can you build using only four triangles?' Students build individually, then share their creations with a partner to see if they made the same things.

15 min·Pairs

Real-World Connections

• Architects and designers use their understanding of shapes and their attributes to create blueprints for buildings and design furniture. They must consider how shapes fit together and their stability.
• Toy manufacturers create blocks and puzzles that often feature basic geometric shapes. Children learn about shapes and their properties by playing with these toys, like stacking blocks or fitting shapes into corresponding holes.

Assessment Ideas

Exit Ticket

Give each student a card with a picture of a common object (e.g., a clock, a book, a slice of pizza). Ask them to write the name of the shape that best describes the object and list the number of sides and vertices it has.

Discussion Prompt

Hold up two different shapes, for example, a square and a hexagon. Ask students: 'How are these shapes the same? How are they different?' Guide them to use vocabulary like 'sides' and 'corners' in their answers.

Quick Check

During a classroom scavenger hunt, ask students to find three objects that have at least four sides. Have them point to the sides and count them as a class or in small groups.

Frequently Asked Questions

What are pattern blocks and why are they used for this?

Pattern blocks are a set of six geometric shapes (hexagon, trapezoid, square, triangle, and two types of rhombi) designed so their sides and angles are related. This allows them to fit together perfectly, making them the ideal tool for exploring shape composition and decomposition.

How can active learning help students understand creating new shapes?

Active learning encourages experimentation. In a student-centered environment, children are free to flip, turn, and slide blocks until they fit. This 'productive struggle' is where the learning happens. By working in pairs or groups to solve shape puzzles, they also have to verbalize their spatial thinking, which solidifies their understanding of how shapes relate to one another.

How does this topic prepare students for later math?

Composing shapes is the precursor to understanding fractions (parts of a whole) and area (the space inside a shape). It also builds the fine motor skills and visual-spatial intelligence needed for geometry and engineering.

What if a student just wants to build 'towers' instead of flat designs?

That's a great opportunity to talk about 3D composition! Ask them which 3D shapes (like cubes) stack well and which (like spheres) do not. This naturally bridges the gap between 2D and 3D geometry.