Standard #: MA.K.GR.1.5

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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.


Two triangles can be used to form a given rectangle.


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
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: 

  • Teacher provides pattern block fill-in puzzles and has students join shapes together to compose new shapes using triangles, rectangles and squares.


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.

two triangles


*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

Course Number1111 Course Title222
5012020: Grade Kindergarten Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 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 and beyond (current))

Related Access Points

Access Point Number Access Point Title
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

Formative Assessments

Name Description
Compose a Rectangle

Students join two right triangles together to compose a rectangle.

Can You Make a Rectangle?

Students are asked to make a rectangle using only squares.

Compose a Square

Students join small squares together to compose a larger square and then justify the new shape.

Lesson Plan

Name Description

In this hands-on lesson, students will be challenged to demonstrate their understanding of shapes to combine smaller two-dimensional shapes to form larger composite shapes. The lesson culminates with students using triangles, rectangles, and squares to form a "robot".

Perspectives Video: Teaching Idea

Name Description
Connecting Geometry to Numbers

Unlock an effective teaching strategy for connecting geometry and numbers in order to build number sense in this Teacher Perspectives video for educators.

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