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Examples
A triangle can be compared to a rectangle by stating that they both have straight sides, but a triangle has 3 sides and vertices, and a rectangle has 4 sides and vertices.Clarifications
Clarification 1: Instruction includes exploring figures in a variety of sizes and orientations.Clarification 2: Instruction focuses on using informal language to describe relative positions and the similarities or differences between figures when comparing and sorting.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Circle
- Rectangle
- Square
- Triangle
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to build on their understanding of classification of two-dimensional figures by finding similarities and differences between shapes (MTR.5.1).- Instruction includes opportunities for students to sort images based on various criteria, such as same number of sides, and figures with all straight sides (MTR.2.1, MTR.5.1).
- Instruction includes helping students describe objects based on relative positions. Relative position refers to students identifying left/right, in front of/behind, apart and above/below. When comparing figures students should understand that relative position can change even though the other features of the figures stay the same.
- Instruction includes figures of various sizes and orientations, and may include figures that are not triangles, circles, rectangles or squares (MTR.2.1).
- Instruction includes examples of squares when discussing rectangles.
- Right angles are technically not addressed until grade 4, but it is appropriate to discuss “square corners” and corners that are not square in an informal way in Kindergarten.
Common Misconceptions or Errors
- Students may not understand that all squares are also classified as rectangles; however, only specific rectangles (with sides that are the same length) are also classified as squares.
- Students may sort figures separately because of orientation and/or size rather than the identified attributes of the figures.
Strategies to Support Tiered Instruction
- Teacher provides plane shapes (circles, squares, triangles, rectangles) for students to
sort.
- For example, instruction includes sorting shapes by how they are the same or by how they are different. The teacher asks follow up questions such as, “How did you decide to sort the shapes? How many sides does this group have?”
- Teacher provides the following plane figures in multiple sizes: squares, circles, triangles, rectangles. Shapes are scattered in the workspace. Students work to match the squares with the squares, the circles with the circles, etc., until all shapes are grouped. The focus is on students recognizing that shapes of different sizes go in the same group (i.e., all circles large and small should be together).
- Teacher provides instruction by doing a “Shape Show.” The teacher shows and names a large rectangle. Walk fingers around its perimeter, describing and exaggerating the actions (straight side...turn, straight side...turn, straight side...turn, straight side...stop), while asking students how many sides the rectangle has and count the sides with him or her. Repeat the actions for a large square, drawing connections between the similarities. The teacher explains that squares are a special kind of rectangle.
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.4.1)
Using the figures below, create sorting cards for students. Provide each student in a group with their own set of figures to sort. Ask each student to sort the figures in any way they choose. Once students have sorted their figures, give each student time to share about their choices, and explain how they sorted their figures (by shape, straight sides and circles, filled and not filled or number of sides). Once students have shared, ask them to sort their figures in a new way. Give time for sorting and sharing again. Repeat the task as needed.
Instructional Task 2
Identify which of the figures below are rectangles and describe their relative positions.
Instructional Items
Instructional Item 1
Circle all of the figures that have 4 sides.
Instructional Item 2
How many figures have straight sides?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
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Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
MFAS Formative Assessments
Students compare a triangle to a rectangle based on attributes of these figures.
Original Student Tutorials Mathematics - Grades K-5
Learn how to identify the similarities and differences in the number of sides of two-dimensional shapes in this interactive tutorial.
Relative positions include up and down, top and bottom, over, on, and under, and above and below. Learn different types of up and down positions to rescue eight chicks in this farm-themed, interactive tutorial.
Identify and name rectangles and squares based on their defining attributes, even if they have different sizes or positions. Join King Geo and his scout, Quad, as they search for rectangles and squares in this interactive tutorial.
This is part of a series on the defining attributes of shapes. Click the links below.
- "The Search for Shapes: Tracking Triangles"
- The Search for Shapes: Recognizing Rectangles and Squares"
Track down triangles based on their defining attributes for King Geo in this interactive tutorial. Learn what makes a triangle a triangle.
This is part of a series on the defining attributes of shapes. Click the links below.
- "The Search for Shapes: Tracking Triangles"
- The Search for Shapes: Recognizing Rectangles and Squares"
Student Resources
Original Student Tutorials
Relative positions include up and down, top and bottom, over, on, and under, and above and below. Learn different types of up and down positions to rescue eight chicks in this farm-themed, interactive tutorial.
Type: Original Student Tutorial
Identify and name rectangles and squares based on their defining attributes, even if they have different sizes or positions. Join King Geo and his scout, Quad, as they search for rectangles and squares in this interactive tutorial.
This is part of a series on the defining attributes of shapes. Click the links below.
- "The Search for Shapes: Tracking Triangles"
- The Search for Shapes: Recognizing Rectangles and Squares"
Type: Original Student Tutorial
Track down triangles based on their defining attributes for King Geo in this interactive tutorial. Learn what makes a triangle a triangle.
This is part of a series on the defining attributes of shapes. Click the links below.
- "The Search for Shapes: Tracking Triangles"
- The Search for Shapes: Recognizing Rectangles and Squares"
Type: Original Student Tutorial
Learn how to identify the similarities and differences in the number of sides of two-dimensional shapes in this interactive tutorial.
Type: Original Student Tutorial
