K-6 Geometry Progression
In Practice
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

To explore the K-5 Geometry
Standards for Mathematics
To experience a math activity that focuses on deeper understanding of the classification of shapes.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License 3

Geometry Learning
Progression
K 1
2-D and 3-D
Shapes
Compose and
Decompose
2
Compose and
Decompose
Precise
Terminology
Properties and Attributes
Sides and
Angles

Geometry Learning
Progression
3
Area
4
Definitions
Fractions
Parallel,
Perpendicular,
Right, Acute,
Obtuse angles,
Line segments,
Ray, Symmetry
5
Volume
Coordinate System
Categorize Shapes

Read Geometry Progressions Overview Page 2-5
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

• Shapes, components, properties and categorization based on properties
• Compose and decompose shapes
• Spatial relationships and structuring
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Visual
• Students recognize shapes.
• A rectangle “looks like a door”.
Descriptive
• Students perceive properties of shapes.
• A rectangle has four sides, all of its sides are straight, opposite sides have equal length.
Analytic
• Students characterize shapes by their properties.
• A rectangle has opposite sides of equal length and four right angles.
Abstract
• Students understand that a rectangle is a parallelogram because it has all the properties of parallelograms.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

“From Kindergarten on, students experience all of the properties of shapes that they will study in Grades K –7, recognizing and working with these properties in increasingly sophisticated ways .”
K-6 Geometry Progressions
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Let’s do some math!
 Start with one post-it note.
 Fold the note in half on the diagonal.
 Cut along the fold.
 What new shapes have we created?
 Explore the shapes you can make with two triangles.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

These follow my rule
These don’t follow my rule
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

The Four Triangle Problem
 Cut another post-it on the diagonal.
 Use 4 triangles to compose a shape that follows my rule and tape it together.
 Is your shape the same or different from your teammates shapes?
 How do you know? What makes a shape unique?
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Shape Search
 With your team find all possible unique shapes using four triangles.
 Consider only congruence – not color or position.
 Tape each composite shape together.
 Persevere until you have found them all… how many do you think there are?
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Shape Sort
 What attributes could you use to sort the shapes?
 Sort the shapes using this attribute.
 Display the results of your sort on a piece of chart paper.
 Be ready to share your sort.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Connect to Geometry
Progression
• Look at a grade level progression.
• How could you use the Four Triangle
Problem at the grade level you teach?
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Connect to Geometry Standards
• Align this to a grade-level content standard.
• Align this to at least one practice standard.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

“It is important to vary the examples in many ways so that students do not learn limited concepts that they must later unlearn.”
K-6 Geometry Progressions

Reflection
• How has the geometry domain changed since previous standards?
• How will this effect your teaching and planning?
• What resources/tools do you need to be able to implement the geometry domain in your classroom?

The Four Triangle Problem was written by
Cheryl Rectanus and can be found in the book
Math By All Means
Geometry Grades 3 – 4
A Marilyn Burns
Replacement Unit
Copyright 1994 by
Math Solutions
Publications