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Combine two-dimensional figures to form a given composite figure. Figures used to form a composite shape are limited to triangles, rectangles and squares.
Examples
Two triangles can be used to form a given rectangle.Clarifications
Clarification 1: This benchmark is intended to develop the understanding of spatial relationships.General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: K
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
- There are no direct connections outside of this standard; however, teachers are encouraged to find possible indirect connections.
Terms from the K-12 Glossary
- Composite Figures
- Rectangles
- Squares
- Triangle
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to allow students opportunities to discover further connections and patterns with two-dimensional figures. Students should have an opportunity to investigate combining figures in a variety of sizes and orientations (MTR.2.1, MTR.5.1).- Instruction includes composite figures that may be named based on previous benchmarks,
as well as those not included in previous benchmarks, though there is no expectation of a
formal name for new composite shapes outside of previously named figures.
- For example, a triangle and square forming a pentagon, may not need to be formally identified as a pentagon. Two triangles that form a rectangle can be formally identified as a rectangle.
- Exploring with figures of different sizes and orientations allows students to continue to develop an understanding of spatial reasoning (MTR.2.1).
Common Misconceptions or Errors
- Students may attempt to compose figures without regard to aligning sides or vertices. The overlap may cause difficulty in naming or describing the new composite figures.
- Students may avoid lining the edges of two figures if the sides aren’t the same length.
- For example, it could be appropriate to join several rectangles of various sizes to make a figure that looks like a building with towers.
Strategies to Support Tiered Instruction
- Instruction includes providing opportunities to compose shapes using pattern blocks.
Begin by having students compose rectangles using squares.
- Example:
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- Teacher provides opportunities for students to explore what happens when they compose shapes.
- For example, teacher provides right triangles, squares, and rectangles in the middle of the workspace. The teacher may ask, “What shapes can you combine to make a square?” and places the square in front of the student.
- To differentiate this activity, the teacher may place a different shape in front of each student.
- Teacher provides a set of tangram pieces for the students to explore how they can compose shapes to create a larger figure. If tangram pieces are not available to the teacher, the teacher may use a search engine to print a set of tangram pieces to copy.
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.4.1, MTR.5.1, MTR.7.1)
Provide each student in a group or whole class with a plethora of rectangles, squares and triangles in a variety of shapes and sizes (be intentional in assuring that various sides are congruent for the purpose of composing new figures). Ask students, “can you make a new figure using two of the figures I have given you?” Give students time to explore, then opportunities to share. Record the findings, focusing on what may be considered “key” compositions (two squares making a rectangle, two triangles making a rectangle, a “house” from a rectangle and triangle, or an octagon from triangles).
Instructional Items
Instructional Item 1
Jamie says that you cannot make a rectangle using the 2 triangles below. Is she correct? Justify your answer.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
This benchmark is part of these courses.
5012020: Grade Kindergarten Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712015: Access Mathematics - Grade Kindergarten (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
MA.K.GR.1.AP.5: Recognize that a different figure can be formed by combining two smaller two-dimensional figures. Figures used to form a composite shape are limited to triangles, rectangles and squares.
Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
Formative Assessments
Lesson Plan
Perspectives Video: Teaching Idea
MFAS Formative Assessments
Compose a Square:
Students join small squares together to compose a larger square and then justify the new shape.
Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
