2.G.A.1 - About the Math, Learning Targets, and Increasing Rigor

Grade 2 Geometry

2.G.A.1

About the Math

Full Standard

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes (Note: 1.G.A.2 explores solid figures including cubes, right rectangular prisms, right circular cones, and right circular cylinders. Second graders should also be comfortable with these figures.)

 

Measurement Topic

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

2nd Grade Students Learning 2nd Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

   Report Card Measurement Topic: Demonstrates understanding of geometry concepts.
1st Grade Students Learning 2nd Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

   Report Card Measurement Topic: Reasons about shapes and attributes

 

About the Math

 Skills and concepts below are learning goals for this standard.

  • Identify important attributes of a shape (sides, faces, angles/vertices/corners).
  • Use important attributes to name shapes (triangles, quadrilaterals, pentagons, hexagons, cubes, right rectangular prisms, right rectangular cones, and right circular cylinders).
  • Draw a shape when given its attributes.

Spatial sense is an important component of geometry. Spatial sense is an intuition about shapes and the relationships among shapes. Rich experiences with shape and spatial relationships help develop students' spatial sense. Students begin this experience by working with two and three dimensional shapes. As students look at how shapes are alike and different, they begin to see the properties of shapes. Students need to see shapes in different sizes and orientations. Triangles should be more than equilateral and not always show the vertex at the top. Students need to sort shapes based on their similar characteristics. Students need to experiment with composing and decomposing shapes so they can see how to form larger shapes from smaller shapes. A rectangle can be made up of two triangles. Essential vocabulary for this standard includes: rectangle, row, column, angle, face, triangle, quadrilaterals, pentagons, hexagons, and cube.

 


2-D shapes for instructional focus include squares, rectangles, triangles, and circles. Students should understand the difference between closed and open figures. They should understand that number/type of sides and angles are defining attributes (though they do not necessarily need to specifically state "defining attribute"). They should understand that color, pattern-fill, size, and orientation for example are not defining attributes. Students should be comfortable with these shapes in any orientation and/or size. The standard can be extended to other polygons as needed. Students DO NOT need to memorize/recite the following definitions.  These definitions are provided for accurate teacher understanding for the discussion of defining attributes and/or creation of anchor charts.

  • polygon: a closed, two dimensional shape with three or more straight sides
  • triangle: a polygon with three sides and three angles
  • quadrilateral: a polygon with four sides and four angles
  • rectangle: a polygon with two pairs of parallel sides and four right angles **Note: the definition of a rectangle is NOT two long sides and two short sides.  A square is a rectangle. Please use provided definition**
  • rhombus: a quadrilateral with two pairs of parallel sides and all sides are the same length, a square is rhombus
  • square: a quadrilateral with two pairs of parallel sides, all sides are the same length and four right angles
  • trapezoid: a quadrilateral with one set of parallel lines
  • pentagon: a polygon with five sides and five angles
  • hexagon: a polygon with six sides and six angles
  • octagon: a polygon with eight sides and eight angles

 

3-D shapes for instructional focus include spheres, cones, prisms (including cubes), cylinders, and pyramids. Students do not need to distinguish between rectangular and triangular prisms or pyramids though that may be a needed extension for some students. Students should be able to recognize defining attributes including faces and edges. Note: Cylinders have no edges as edges are line segments joining polygon faces. There is standard definition for faces. Therefore, cones and cylinders can be considered to have 1 and 2 circular faces respectively. Essential vocabulary for this standard includes: defining attributes, non-defining attributes, sides, angles, and faces (online dictionary Links to an external site., HCPSS vocabulary cards can be found on the Additional Resources page)

  • Construct and draw a shape when given defining attributes.

Students leverage their understanding of shares to create examples of those shapes. Keep in mind that student work may be imprecise. Even so, we should be able to recognize the shape. In some cases, it makes good sense to ask students to describe their created shape and its attributes to us. 

IMPORTANT NOTE: This standard is not intended to be an exercise in memorization of vocabulary and definitions/attributes. Students should recognize these shapes/figures in their world. They should talk about shapes relative to their given name. We can restate shape/figure names when students are inaccurate or imprecise. Use of graphic organizers, including Frayer models, are wise for making connections among shapes/figures.

 

Progression of Standard within Grade 2

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


  • Identify important attributes of a shape (sides, faces, angles/vertices/corners).
  • Use important attributes to name shapes (triangles, quadrilaterals, pentagons, hexagons, cubes, right rectangular prisms, right rectangular cones, and right circular cylinders).
  • Draw a shape when given its attributes.
(Note: 1.G.A.2 explores solid figures including cubes, right rectangular prisms, right circular cones, and right circular cylinders. Second graders should also be comfortable with these figures.)

 

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 Grade 3
  • Distinguish between defining and non-defining attributes (1.G.1)
  • Understand that shapes in different categories may share attributes (3.G.1)

 

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Instructional Tasks

TASKS

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

  • Distribute pattern blocks to a group of students. Pose questions such as what do you notice about your shapes? How would you describe your shapes? What are the names of the shapes? If the vocabulary words of a corner (vertex) and side do not come up naturally in conversation, expose students to these vocabulary words.
  • Distribute geoboards to students. Have students create a triangle. Share out different triangles students made. Be sure to point out that triangles can look differently but they need to have three sides and three corners. Have students use four rubber bands to create different quadrilaterals and share out the different types of quadrilaterals that were made. Continue to create different pentagons and hexagons.
  • Use AngLegs to create different shapes. Students can create a table in their journal. As they build shapes, they can record the name of the shape, the number of corners, and the number of sides.
  • You can play What shape am I? When you read through some clues, students can either build the shape with a geoboard or AngLegs.
  • Distribute snap cubes to students. Have students each create rectangular prisms using multiple snap cubes. Group students into triads and pose questions such as how many faces does a rectangular prism have? How many edges does a rectangular prims have? How many corners does a rectangular prism have?  Did anyone create a cube? How are a cube and a rectangular prism different? How are they the same?
  • Distribute a bag of 2-D and 3-D shapes. Pose questions such as what do you notice about the shapes? How are they similar? How are they different? Have students sort the shapes into two or more groups. As a class, reflect on how students sorted the shapes.
  • Walk around the inside of the building and outside Have students record where they see triangles, quadrilaterals, pentagons, hexagons, cubes, rectangular prisms, cones, and cylinders.
  • What shapes can you make with 2 identical short straws and 2 identical long straws?
  • Draw 2 different quadrilaterals. Compare them. What is same/different about them?
  • Is a rectangle always a square? Is a square always a rectangle?
  • I have six faces, what solid shape might I be?
  • Can a shape have 4 sides and 3 angles? Explain your thinking.

 

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 • Geometry

Identify Polygons:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to lessons.] 

 

 

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. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics K-3 207 (Mystery Definition, Activity 7.6)
217 (Shape Hunts, Activity 7.18)

Hands-On Standards

 

 1-2 52-53 (Decomposing Numbers)
40-41 (Exploring Place Value)

Brain Compatible Activities for Mathematics

 2-3 112-113 (Name My Shape)
118-121 (Shape-y Shake-y)
134-137 (Shape Sort)

Brain Compatible Activities for Mathematics

 K-1 70-71 (Feel the Shapes)
90-93 (Smart Shapes)

SuperSource: Pattern Blocks

SuperSource: Tangrams

SuperSource: Geoboards

K-2

K-2

K-2

62-65

50-53

86-89

20 Thinking Questions for Shapes and Sizes Attribute Pieces

1-3

6-9 (What is the Mystery Shape?)
10-13 (How are the shapes alike/different?)
30-33 (What Could the Shape Be?)
34-37 (Can You Sort Your Shapes?)
42-45 (Where Does Your Shape Belong?)
46 (How Many Shapes are Diff in 1 Way?)
58 (Can You Find Shapes Different in 2 Ways?)
69 (Can You Find Shapes Different in 3 Ways?)

Math In Practice

Teaching Second-Grade Math

2

Module 14

 

 

 

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Independent Work

Centers

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

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

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Assessment

Full Standard

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes (Note: 1.G.A.2 explores solid figures including cubes, right rectangular prisms, right circular cones, and right circular cylinders. Second graders should also be comfortable with these figures.)

 

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.

 

2nd Grade Students Learning 2nd Grade Standards by Measurement Topic

Demonstrates understanding of measurement and geometry concepts

Quarter 4

  • Recognize and draw shapes accurately based on given attributes.
  • Use defining attributes to name shapes such as triangles, quadrilaterals, pentagons, hexagons, cubes, right rectangular prisms, right rectangular cones, and right circular cylinders.

 

1st Grade Students Learning 2nd Grade Standards by Measurement Topic

Reasons about shapes and attributes

Quarter 4

  • Recognize and draw shapes accurately based on given attributes.
  • Use defining attributes to name shapes such as triangles, quadrilaterals, pentagons, hexagons, cubes, right rectangular prisms, right rectangular cones, and right circular cylinders.

 

2G1 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).

Screenshot 2023-06-12 104305.png

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.

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.