Grade 1: Identifying, Composing, and Partitioning Shapes


5 apple rating


Reason with shapes and their attributes.

CCSS.MATH.CONTENT.1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

CCSS.MATH.CONTENT.1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)

CCSS.MATH.CONTENT.1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Tell and write time and money.

CCSS.MATH.CONTENT.1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Recognize and identify coins, their names, and their values.


MP.1 Make sense of problems and persevere in solving them.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.


This Grade 1 unit titled “Identifying, Composing, and Partitioning Shapes” from is intended to be completed in 15 sessions. The emphasis of instruction is to have students consider part-whole relationships through a geometric lens. In the opening activities, students identify the defining parts (or attributes) of two- and three-dimensional shapes, building on their experiences in kindergarten where they sorted, analyzed, compared and created various two- and three-dimensional shapes and objects. During daily lessons, students combine shapes to create a new whole, relate geometric figures to equal parts, and apply their understanding of halves to tell time. Students also practice addition and subtraction during daily fluency activities. An end-of-unit assessment consists of nine constructed-response questions that are designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted standards.


Connecticut teachers should be cautioned that teacher notes and preparation materials are extensive and will require familiarity to be used effectively. Due to new and key geometry vocabulary, extra time and scaffolded activities may be needed to provide students ample opportunities to learn and relate to pictorial representations and concepts, especially for English language learners (ELLs). A pictorial word wall in the classroom could include the following: circle, hexagon, rectangle, rhombus, square, trapezoid, triangle, cone, cube, cylinder, rectangular prism, and sphere. The unit authors note that for Content Standard 1.MD.3, only telling and writing time in hours and half-hours using analog and digital clocks are addressed in this module. Recognizing and identifying coins, their names, and their values are addressed in Module 6.


This unit is an exemplary example of a progression of learning where concepts and skills advance and deepen over time. Instruction reflects evidence of the keys shifts required by the CCSS. Standards for Mathematical Practice are identified, handled in a grade-appropriate way, and are well connected to the content being addressed. Activities engage students in a productive struggle through thought-provoking questions and tasks that stimulate interest and elicit mathematical thinking. The instructional plan targets the major work of the grade and allows time for students to develop their conceptual understanding through “hands-on” tasks and partner opportunities. Lessons are designed to gradually remove supports, requiring students to demonstrate their mathematical understanding independently. Instruction builds on previous learning, and where appropriate, provides ways for students to connect knowledge and skills within or across clusters, domains, and learning progressions. Teachers may use this curriculum as presented or integrate parts into a related, pre-existing curriculum. An aligned rubric for scoring the end-of-unit assessment is included. Materials have been translated and are available in Arabic, Bengali, Spanish, and Traditional Chinese.

Supplementary Materials:

  • How to Implement A Story of UnitsThis resource provides details about EngageNY’s sequenced educational mathematics program for grades pre-K-5 with a strong emphasis on differentiating instruction, meaningful assessment, and data-driven instruction.

  • Scaffolding Instruction for English Language Learners Resource Guides for ELA and Mathematics—These guides provide guidance to educators on how to take the curriculum materials on EngageNY and provide additional scaffolds for ELLs.