KGB4 About the Math, Learning Targets, and Opportunities for Enrichment

Kindergarten Mathematics Geometry

K.G.B.4

About the Math

Full Standard

Analyze and compare two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and /"corners") and other attributes (e.g., having sides of equal length).

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**Kindergarten Students Learning Kindergarten Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
			Report Card Measurement Topic: Reason about shapes and their attributes.

About the Math

Skills and concepts below are learning goals for this standard.

Describe a shape by telling things like the number of sides, number of vertices (corners), and other special qualities.
Describe two-dimensional shapes (circles, triangles, rectangles, and squares) by the number of sides and corners.
Describe why square is a special kind of rectangle.
Compare two-dimensional shapes and describe their similarities and differences.
Compare three-dimensional shapes and describe their similarities and differences.

Geometry instruction at the kindergarten level should devote plenty of time to sorting and classifying, with a primary focus on helping students see how shapes are alike and different. Initial descriptions of attributes include non-defining attributes such as colors or size before students learn defining attributes.

Due to inaccurate or inappropriate materials (e.g., books, toys, games, apps), children are often introduced to shapes in rigid ways, such as equilateral triangles or rectangles that are horizontal, elongated shapes that are twice as long as they are wide. Thus, children tend only to see typical forms of each shape, or exemplars, and are given limited opportunities to explore, see, and discuss variant examples. This confusion includes the common assumption by children that by turning a shape it changes name or that squares and rectangles belong in separate categories.

Children's ideas stabilize as early as 6 years of age, and experiences and instruction play a large role in shaping children's knowledge of geometry. Varied examples and nonexamples should be provided to help children understand attributes of shapes that are mathematically relevant as well as those that are not. Showing nonexamples and comparing them to similar examples helps focus children's attention on the critical attributes of shapes and prompts discussion as to why a shape belongs to a certain category (such as why a square is a special type of rectangle or that an isosceles triangle with two long, skinny sides and one short side is still a triangle because it has 3 straight sides).

Common Misconceptions

Some students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for counting and should be tagged with a different count word, the student uses the original count word. For example, a student counts four geometric figures: triangle, square, circle and rectangle with the count words: one, two, three, four. If these items are rearranged as rectangle, triangle, circle and square and counted, the student says these count words: four, one, three, two.

Progression of Standard within Kindergarten

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
			Describe a shape by telling things like the number of sides, number of vertices (corners), and other special qualities. Compare two-dimensional shapes and describe their similarities and differences. Compare three-dimensional shapes and describe their similarities and differences.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 1
Defining attributes vs non-defining attributes (1.G.1)

Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Give each student two different shapes (flat or solid). Allow students to have a minute to explore their shapes. Tell students that you are looking for a shape and if they have that shape, they should hold it up. Describe the type of shape you are looking for and when students hold up shape that matches the statement, discuss what students notice. Statement examples: I am looking for a shape with three sides. I am looking for a shape that is a solid. I am looking for a shape that has square faces.
Use 20 small popsicle sticks to make three shapes. None of the shapes can use the same number of popsicle sticks. Describe your shapes.
Student reaches into a bag and feels the hidden three-dimensional shape. Student describes the hidden shape using defining attributes.
I am a three-dimensional shape. I have two square faces and 4 faces that are rectangles. What shape am I?
Display a cube and a rectangular prism. How are they alike and how are they different?
Create a picture using less than 15 pattern blocks. Record your picture and the number of each shape used.
What is the relationship between a square and a rectangle? Is a square always a rectangle? Is a rectangle always a square?

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 14 • 2D and 3D Figure

Analyze and Compare Attributes of 2D and 3D Figures:

Additional Tasks

These links provide instructional ideas connected to this standard.

Alike or Different Game Links to an external site. (Illustrative Mathematics)

Squares are Special Rectangles Links to an external site. NCTM Illuminations (NCTM membership required for lesson access)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

All kindergarten teams have been provided with the resources listed below.

Print Resources
Book Thumbnail	Title	Reference
	Hands-On Standards published by: Learning Resources	Lesson 2, Attribute of Plane Shapes, p. 66 Lesson 4, Exploring Shape Attributes, p. 70 Lesson 5, Shape Attribute Riddles, p. 72 Lesson 6, Cubes and Spheres, p. 74
	Teaching Student-Centered Mathematics by: John A. Van de Walle and Lou Ann H. Lovin	Activity 7.1, p. 194 Activity 7.2, p. 195 Activity 7.6, p. 207 Activity 7.18, p. 217

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/corners) and other attributes (e.g., having sides of equal length).

Tasks Connected to Literature

Suggested titles to support the standard can be found in the table below. Check your school library or Howard County Library System for availability, or purchase using Materials of Instruction (MOI) funds. When available, select links to view activities aligned to each title.

Shapes, Shapes, Shapes

by Tana Hoban

Changes, Changes

by Pat Hutchins

Perfect Square

by Michael Hall

Shape by Shape

by Suse MacDonald

Centers and Practice

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Shapely Sentences Download Shapely Sentences
(HCPSS-adapted resource)
Guess My Shape Download Guess My Shape
(HCPSS-adapted resource)

PRACTICE/ASSESSMENT

These materials can be used for independent practice and/or for assessment purposes. These tasks align with the learning goals for the standard.

Assessment and Instructional Tasks

Assessment

Full Standard

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

Kindergarten Students Learning Kindergarten Standards by Measurement Topic

Reason about shapes and their attributes

Quarter 4

Analyze and compare two- and three-dimensional shapes using attributes (number of sides, number of vertices/corners, or other special qualities).

KG4 Anecdotal Data Collection Tool Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf) Links to an external site.

Exemplars for this standard (if available)

These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.

TASK	MEETS EXPECTATIONS	MAKING PROGRESS	MAKING LIMITED/NO PROGRESS
Show student 2D shapes one at a time and prompt the student to name the shape and explain how they know. (circle, square, triangle- not equilateral, rectangle, hexagon)	Student names all shapes correctly and uses attributes (i.e. no straight edges, 3 sides, 4 angles) to explain how they know. 1-2 minor errors are acceptable.	Student names 3-4 shapes and can use some attributes to explain what they know. There may be several errors in identifying shapes and/or attributes (i.e confuses square and rectangle, can not identify a hexagon).	Student names 0-2 shapes, or misidentifies 4-5 shapes. Student is unable to describe attributes of given shapes.