Unit 4 — Place Value and Geometric Shapes
Description
Unit 4 consolidates place value understanding and deepens geometric reasoning. Students count to 100 by ones and tens, achieving the full counting sequence. Fluency with addition and subtraction within 5 is expected by year's end. Students analyze and compare two- and three-dimensional shapes, identifying similarities and differences in attributes such as sides and corners. Students build shapes from components and compose larger shapes from smaller ones. Place value concepts culminate in composing and decomposing numbers 11-19. The unit strengthens mathematical communication as students use informal language to describe shape properties and relationships.
Essential Questions
- Can patterns be found in numbers?
- Can you describe the patterns you find?
- How can I show numbers beyond 10?
- What makes shapes different from each other?
- How can shapes be sorted?
- Where can we find shapes in the real world?
Learning Objectives
- Count to 100 by ones and by tens
- Fluently add and subtract within 5
- Analyze and compare two- and three-dimensional shapes in different sizes and orientations
- Describe similarities, differences, parts, and other attributes of shapes using informal language
- Model shapes in the world by building and drawing shapes
- Compose simple shapes to form larger shapes
- Compose and decompose numbers 11-19 into ten ones and further ones
- Record compositions and decompositions using drawings and equations
Supplemental Resources
- Pattern blocks for shape composition activities
- Number charts 1-100 for reference during counting
- Markers or colored pencils for drawing and recording shapes
- Rulers for drawing straight lines in shapes
- Graphic organizers for comparing shape attributes
Counting and Cardinality
Geometry
Number and Operations in Base Ten
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to strengthen understanding of mathematical terms. Students utilize reading comprehension skills by acting out or drawing the order of important events in story problems. Students create mathematical stories using numbers, pictures, and words in interactive student notebooks and read alouds.
Students work with data and make calculations involving measurements and other data across all modules. Students develop understanding through observing patterns and analyzing information related to physical and natural phenomena.
Students connect money as a means for helping people buy things they need or want. Students complete independent and partner projects to plan and market a good or service, developing economic literacy.
Formative Assessments
- Classwork on counting by ones and tens to 100
- Exit tickets comparing shapes and identifying attributes
- Whiteboards for quick addition and subtraction within 5
- Individual and group shape building activities
- Math journals documenting shape compositions
Summative Assessment
Chapter tests on counting to 100, addition and subtraction fluency within 5, analyzing and comparing shapes, modeling shapes, and composing/decomposing teen numbers
Benchmark Assessment
Benchmark tests on fluency with addition and subtraction within 5, counting to 100, and shape properties
Alternative Assessment
Students may demonstrate understanding of counting sequences and shape attributes through one-on-one oral counting practice with manipulatives or visual number lines, and through pointing to or physically sorting shapes rather than writing or drawing comparisons. Simplified answer choices or pre-made shape cards may be provided to reduce task complexity while assessing the same concepts.
IEP (Individualized Education Program)
Students may benefit from concrete manipulatives such as linking cubes, shape tiles, and ten-frames to support place value and geometric reasoning, reducing reliance on abstract representation. Oral responses and pointing to answers should be accepted in place of written work when recording equations or describing shape attributes. Directions for multi-step tasks like composing shapes or decomposing teen numbers should be broken into small, numbered steps with visual anchors. Frequent check-ins and immediate corrective feedback during counting sequences and addition and subtraction practice will help reinforce emerging fluency.
Section 504
Students should be seated close to instruction during shape analysis and counting activities to minimize distraction and support focus. Extended time should be provided on chapter assessments and any written recording tasks, such as drawing or labeling shape compositions. A visual number line or ten-frame reference card taped to the desk can support access during addition, subtraction, and place value work without altering expectations.
ELL / MLL
Visual supports such as labeled shape posters, illustrated number charts, and picture-supported anchor charts connecting informal shape vocabulary to visual examples will help students access both the geometric and place value content. Teachers should introduce and preview key terms — such as corner, side, flat, solid, and ten — using real objects and gestures before embedding them in instruction. Simplified, repeated directions paired with physical demonstration support participation in shape-building and counting activities, and students should be encouraged to use their home language alongside English when explaining mathematical thinking.
At Risk (RTI)
Students who need additional entry points may benefit from starting counting sequences from a familiar number before extending to 100, and from working with smaller sets of shapes before comparing multiple attributes at once. Hands-on building and sorting activities provide a concrete foundation for both geometric reasoning and teen number decomposition, allowing students to develop understanding before moving to drawn or symbolic representations. Connecting new shape and place value concepts to familiar objects in the classroom helps activate prior knowledge and supports meaningful engagement with the content.
Gifted & Talented
Students who have demonstrated mastery of counting to 100 and basic shape identification can be invited to explore patterns within the counting sequence, such as reasoning about what changes and what stays the same when counting by tens. In geometry, students can be challenged to investigate how many different ways smaller shapes can be composed to form the same larger shape, or to describe and classify shapes using increasingly precise attribute language. For place value, extending thinking to numbers beyond 19 and exploring how the ten-and-some-more structure continues encourages deeper conceptual understanding rather than simple repetition of mastered skills.