Mathematics · Grade 1 · Geometry and Spatial Reasoning · Term 3

Attributes of 2D Shapes

Distinguishing between defining attributes (e.g., number of sides, vertices) and non-defining attributes (e.g., color, size, orientation) of 2D shapes.

• Ontario Curriculum Expectations
• 1.G.A.1

About This Topic

Composing and decomposing shapes is the geometric equivalent of addition and subtraction. In Ontario's Grade 1 curriculum, students learn how smaller shapes can be combined to create new, larger shapes (composition) and how larger shapes can be broken down into smaller ones (decomposition). This skill is vital for developing spatial reasoning and understanding how parts relate to a whole.

Using tools like pattern blocks or tangrams, students can explore how two triangles can form a square or how six triangles can make a hexagon. This also introduces the early concepts of fractions, as students see shapes being divided into equal parts. This topic is most effectively taught through collaborative investigations where students work together to solve 'shape puzzles' or create composite designs that reflect their multicultural environment.

Key Questions

1. Justify why we categorize shapes based on their corners and sides instead of their size or color.
2. Compare a square and a rhombus; what are their defining attributes?
3. Analyze how changing the orientation of a shape does not change its name.

Learning Objectives

• Identify the defining attributes (number of sides, number of vertices) of common 2D shapes.
• Classify 2D shapes based on their defining attributes.
• Compare and contrast 2D shapes by analyzing their defining attributes.
• Explain why non-defining attributes like color or size do not change a shape's classification.
• Analyze how changing the orientation of a 2D shape does not alter its defining attributes.

Before You Start

Identifying Basic 2D Shapes

Why: Students need to be able to recognize and name common 2D shapes before they can analyze their attributes.

Counting

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

Key Vocabulary

2D Shape	A flat shape that has length and width, but no depth. Examples include circles, squares, and triangles.
Attribute	A characteristic or feature of a shape, such as its number of sides or corners.
Defining Attribute	A characteristic that is essential to identify a shape, like the number of sides or vertices.
Non-Defining Attribute	A characteristic that does not change the identity of a shape, such as its color, size, or how it is turned.
Vertex	A corner or point where two or more lines or edges meet. Plural is vertices.
Side	A straight line segment that forms part of the boundary of a 2D shape.

Watch Out for These Misconceptions

Common Misconception

Students may think that when you cut a shape, the pieces are no longer related to the original.

What to Teach Instead

Use the term 'composed of' frequently. Have students physically put the pieces back together like a puzzle to show that the area remains the same. Active 'surgery' with paper shapes makes this relationship clear.

Common Misconception

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

What to Teach Instead

Use transparent pattern blocks or overlays. Peer discussion where one student 'traces' the hidden shape for another helps develop the 'spatial eye' needed to see sub-shapes within a whole.

Active Learning Ideas

Inquiry Circle: Pattern Block Murals

Small groups are given a large outline of an animal or object. They must work together to fill the entire space using pattern blocks, then count how many of each smaller shape they used to 'compose' the larger image.

30 min·Small Groups

Peer Teaching: Shape Surgeons

Students are given paper shapes (rectangles, squares) and must 'perform surgery' by cutting them into smaller shapes. They then challenge a partner to put the pieces back together to form the original whole.

20 min·Pairs

Stations Rotation: Tangram Challenges

Set up stations with different tangram puzzles. At one station, students compose a specific shape; at another, they decompose a complex shape into its basic parts. They rotate and compare their methods.

25 min·Small Groups

Real-World Connections

• Architects and designers use their understanding of 2D shape attributes to create blueprints for buildings and design furniture. They must ensure shapes fit together correctly, regardless of their color or size.
• Toy manufacturers create puzzles and building blocks based on specific 2D shapes. For example, a square block is always a square, no matter its color or how it is oriented, because it consistently has four equal sides and four vertices.
• Cartographers use precise geometric shapes when drawing maps. They rely on consistent attributes like the number of sides and vertices to represent different land features accurately, even if the map is rotated.

Assessment Ideas

Quick Check

Present students with various 2D shapes (e.g., a red square, a blue square, a large green triangle, a small green triangle). Ask: 'Point to two shapes that are the same kind of shape. Explain why they are the same kind of shape, using the words 'sides' and 'vertices'.

Exit Ticket

Give each student a card with a picture of a 2D shape. Ask them to write down two defining attributes of that shape and one non-defining attribute. For example, for a square: 'Defining attributes: 4 sides, 4 vertices. Non-defining attribute: blue color'.

Discussion Prompt

Show students a square and a rhombus that are the same size. Ask: 'How are these shapes the same? How are they different? Which of these are defining attributes and which are not? Why do we call them by different names if they have the same number of sides and vertices?'

Frequently Asked Questions

How does composing shapes help with later math skills?

It builds the foundation for understanding area, perimeter, and fractions. It also develops spatial visualization, which is a key predictor of success in higher-level STEM subjects.

What are the best manipulatives for this topic?

Pattern blocks are the gold standard because their angles and side lengths are designed to fit together perfectly. Tangrams and geoboards are also excellent for exploring how shapes can be divided and combined.

How can I connect this to Indigenous perspectives?

Look at traditional beadwork or quilt patterns. Many Indigenous designs use repeated geometric shapes to create complex, beautiful compositions. Discussing the 'parts' that make up these 'wholes' is a great way to integrate culture and math.

How can active learning help students understand composing and decomposing shapes?

Active learning through 'Shape Puzzles' or 'Pattern Block Murals' turns geometry into a tactile experience. When students physically manipulate shapes to see how they fit, they are developing spatial reasoning in a way that looking at a worksheet cannot provide. The trial-and-error process of active learning is essential for this topic.