Unit 4 — Reason with Shapes and Their Attributes
Description
Students distinguish between defining and non-defining attributes of two-dimensional shapes (squares, triangles, rectangles, regular hexagons) and three-dimensional shapes (cubes, right rectangular prisms, right circular cones, cylinders). They build and draw shapes when given defining attributes, recognizing that shapes can appear in different orientations and sizes. Students compose two-dimensional and three-dimensional shapes to create composite shapes and then compose new shapes from composite shapes, developing understanding of part-whole relationships. Students partition circles and rectangles into two and four equal shares, using vocabulary of halves, fourths, quarters, and the phrases half of, fourth of, quarter of. They understand that decomposing a whole into more equal shares creates smaller shares. Addition and subtraction within 20 and place value concepts are integrated throughout shape work.
Essential Questions
- What are attributes?
- How can shapes be sorted?
- How are shapes used in our world?
- What makes shapes different from each other?
- How can I create a shape?
- How do shapes fit together and come apart?
- What is a 2-dimensional shape?
- What is a 3-dimensional shape?
- How are shapes alike and different?
- How can we divide shapes into equal parts?
- How do we know when parts are equal?
Learning Objectives
- Name the attributes of a given two-dimensional shape (square, triangle, rectangle, regular hexagon), distinguishing between defining and non-defining attributes.
- Build and draw shapes when given defining attributes.
- Create a composite shape by composing 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), and compose new shapes from the composite shape.
- Partition circles and rectangles into two or four equal shares, describing the shares using halves, fourths, and quarters and use the phrases half of, fourth of, and quarter of; describe the whole circle (or rectangle) partitioned into two or four equal shares as two of, or four of the shares.
- Understand that decomposing a whole into a greater number of equal shares creates smaller shares.
- Use addition and subtraction within 20 to solve problems, including word problems.
- Add and subtract whole numbers within 20 using various strategies.
- Count to 120 orally, read and write numerals, and write numerals to represent the number of objects (up to 120).
- Add a 2-digit and a 1-digit number using concrete models and drawings with a place value strategy; explain or show how the model relates to the strategy (sums within 100).
- Add a 2-digit number and a multiple of 10, using concrete models and drawings with a place value strategy; explain or show how the model relates to the strategy (sums within 100).
Supplemental Resources
- Pattern blocks or geometric shape sets (cardboard or plastic) in various colors and sizes
- Geoboards with rubber bands for creating two-dimensional shapes
- Dot paper for copying and drawing shapes
- Paper circles and rectangles for folding activities to explore equal shares
- Tangram pieces or composite shape puzzles for shape exploration
Geometry
Number and Operations in Base Ten
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to mathematical terms, utilize reading comprehension skills by acting out or drawing the order of important events in story problems, and create mathematical stories using numbers, pictures, and words through interactive student notebooks and read-alouds.
Students work with data and make calculations involving measurements and other data across all mathematical modules, engaging in investigations and observations related to patterns and phenomena.
Students connect money as a means for helping people buy things they need or want and complete independent or partner projects to plan and market a good or service, exploring economic concepts and community responsibilities.
Formative Assessments
- Shape sorting activities distinguishing defining and non-defining attributes
- Individual and group shape composition and decomposition tasks
- Drawing activities representing shapes with different attributes in different orientations
- Partitioning activities with circles and rectangles into equal shares
- Exit tickets assessing shape identification and attribute naming
- Hands-on problem-solving tasks combining shapes and addition/subtraction
Summative Assessment
Unit 4 chapter tests and performance tasks assessing shape attribute identification, composition/decomposition understanding, equal partitioning skills, and integration of addition and subtraction with geometric thinking.
Benchmark Assessment
Benchmark assessment within adopted programs and alternative assessments measuring spatial reasoning and geometric understanding.
Alternative Assessment
Students may demonstrate understanding of shape attributes through a teacher-led sorting activity or verbal description of shapes rather than independent written or drawn responses. Manipulatives, shape outlines, or labeled visual aids may be provided to support identification and composition of shapes.
IEP (Individualized Education Program)
During shape identification and attribute work, provide physical manipulatives such as shape tiles and three-dimensional solids so students can touch and handle examples while building understanding of defining versus non-defining attributes. Offer picture-supported vocabulary cards that pair shape names with labeled diagrams showing key attributes, and allow students to respond orally or by pointing rather than requiring written output. When working with partitioning, use pre-drawn circles and rectangles so students can focus on the equal-shares concept rather than the drawing task, and break multi-step directions into single numbered steps with visual cues at each stage.
Section 504
Provide preferential seating near direct instruction during shape-sorting and partitioning lessons to minimize distraction and support visual focus on demonstrations. Allow extended time on tasks that require drawing or labeling shapes and their attributes, and provide a quiet space or reduced-distraction setting during any individual assessment of shape identification or equal-shares work.
ELL / MLL
Introduce and consistently display a visual word wall featuring shape names alongside pictures and labeled diagrams of defining attributes in both English and students' home languages where possible. Use physical shape manipulatives and gestures during instruction so that understanding of concepts like 'equal shares,' 'halves,' and 'fourths' is grounded in concrete, visual experience before language demands are introduced. Give directions for sorting, building, and partitioning tasks in short, simple sentences, and invite students to demonstrate understanding through hands-on action before requiring verbal or written responses.
At Risk (RTI)
Begin instruction by connecting new shape vocabulary to familiar real-world objects — such as recognizing rectangles in a door or a book — so students can anchor abstract attribute language to prior experience. Reduce the number of shapes addressed at one time and provide sorting tasks that offer a clear visual model of success before asking students to work independently. During partitioning activities, use concrete folding or cutting of paper shapes so students build the concept of equal shares through direct physical action before moving to symbolic or pictorial representations.
Gifted & Talented
Challenge students to investigate how the defining attributes of two-dimensional shapes relate to one another — for example, exploring why a square can also be considered a rectangle and what that implies about attribute hierarchies. Encourage students to design their own composite shape creations and articulate in writing or oral explanation exactly which shapes were used and why they fit together, extending into early geometric reasoning. When exploring equal partitioning, invite students to investigate what happens when a shape is divided into three or eight equal shares, connecting their observations about share size to foundational ideas about fractions beyond halves and fourths.