Unit 4 — Reason with Shapes and Represent Data
Description
Unit 4 concludes the year by focusing on geometric reasoning and data representation. Students recognize and draw shapes with specified attributes such as number of angles or equal faces, identifying triangles, quadrilaterals, pentagons, hexagons, and cubes. They partition circles and rectangles into equal shares using language like halves, thirds, and fourths, recognizing that equal shares of identical wholes need not have the same shape. Students solve word problems involving money (dollar bills, quarters, dimes, nickels, and pennies), generate measurement data by measuring lengths to the nearest whole unit, and represent data using line plots and bar graphs. They draw picture and bar graphs with up to four categories and solve problems using the information presented in graphs. The unit reinforces addition and subtraction skills in practical contexts while developing geometric and data literacy.
Essential Questions
- How can I keep track of an amount?
- How can I learn to quickly calculate sums in my head?
- How can I use a number line to add or subtract?
- How can I use data to help me understand the answers to the questions posed?
- How can we use a picture graph, bar graph, chart, or table to organize data and answer questions?
- How do we know if we have enough money to buy something?
Learning Objectives
- Draw shapes having specified attributes and identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
- Partition circles and rectangles into equal shares and describe using fractional language.
- Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies.
- Generate measurement data by measuring lengths to the nearest whole unit.
- Represent measurement data using line plots with whole-number units on horizontal scale.
- Draw picture graphs and bar graphs with single-unit scale for up to four categories.
- Solve put-together, take-apart, and compare problems using information from graphs.
- Fluently add and subtract within 20 using mental strategies.
- Fluently add and subtract within 100 using strategies based on place value and operations.
Supplemental Resources
- Shape templates and geometric models (pattern blocks, 3-D solids)
- Play money (dollar bills, quarters, dimes, nickels, pennies)
- Measuring tools for data collection activities
- Chart paper and graphing templates for creating large graphs
- Index cards or sticky notes for data points in line plots
Digital Literacy
Geometry
Measurement
Number and Operations in Base Ten
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to strengthen understanding of mathematical terms through conversations and reading. Students utilize reading comprehension skills by acting out or drawing the order of important events in story problems. Students read and write stories to represent addition and subtraction, create mathematical stories using numbers, pictures and words, and participate in interactive student notebooks and read-alouds.
Students work with data and make calculations involving measurements and other data across all units. Students practice data collection, organization, and analysis as part of scientific inquiry.
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, connecting mathematics to economics and financial literacy.
Formative Assessments
- Shape recognition and drawing activities checking attribute understanding
- Exit tickets assessing money problems and fractional partitioning
- Classwork on data collection and graph creation
- Whiteboards for quick checks on addition and subtraction in contexts
- Peer discussions analyzing graphs and data representations
Summative Assessment
Chapter tests on shapes, money, and data; performance tasks requiring students to collect data, create representations, and answer questions using graphs; extended projects applying shape understanding and data skills.
Benchmark Assessment
Benchmark tests within adoption materials; state assessment items on geometry and data; Renaissance/STAR testing
Alternative Assessment
Students may demonstrate shape recognition and drawing through sorting activities, matching shapes to attribute cards, or pointing to correct shapes in response to spoken descriptions instead of independent drawing. For money and fractional partitioning tasks, manipulatives such as coin models or fraction pieces may be provided, and responses may be given orally or through gesture rather than written form.
IEP (Individualized Education Program)
Students with IEPs may benefit from manipulatives such as pattern blocks, attribute shapes, and coin sets to support hands-on exploration of geometric attributes and money concepts. Providing graphic organizers that visually organize shape attributes or graph categories can reduce processing demands while keeping the focus on mathematical reasoning. For money and data tasks, breaking multi-step word problems into smaller numbered steps and allowing oral or whiteboard responses in place of written work supports access without lowering expectations. Teachers should also provide a reference card with shape names, coin values, and fractional vocabulary so students can focus cognitive effort on applying concepts rather than recalling terminology.
Section 504
Students with 504 plans should be given extended time on money problem-solving tasks and graph-based assessments, as these require sustained attention across multiple steps. Preferential seating near instructional materials and reduced visual clutter on worksheets—such as fewer problems per page on shape or data tasks—can help students maintain focus. Providing printed copies of any graphs or data displays shown on the board ensures consistent access without requiring students to copy information under time pressure.
ELL / MLL
Multilingual learners benefit from a visual word wall or illustrated reference card that pairs key unit vocabulary—such as halves, thirds, quadrilateral, bar graph, and coin names—with pictures and, where possible, home language translations. Teachers should use physical objects, visual models, and gesture-supported demonstrations when introducing shape attributes, fractional partitioning, and graph types to make meaning accessible across language proficiency levels. Simplified, step-by-step directions for data collection and graphing tasks, paired with a visual model of a completed graph, help students understand the task structure before attempting independent work.
At Risk (RTI)
Students who need additional support should begin shape, money, and graphing work with concrete materials and visual models before moving to representational or abstract tasks, ensuring a strong foundation in the unit's core concepts. Connecting coin values and shape attributes to real-world, familiar contexts can help activate prior knowledge and make abstract ideas feel approachable. Reducing the number of categories or data points required in graphing tasks allows students to build confidence and accuracy before encountering greater complexity, and frequent brief check-ins during classwork help identify and address confusion early.
Gifted & Talented
Students who have demonstrated strong grasp of the unit's foundational skills can be invited to investigate more complex geometric relationships, such as exploring how shapes can be subdivided or combined and whether equal shares of a whole must always look the same. In data contexts, these students may design their own surveys, determine appropriate graph types, and draw analytical conclusions that go beyond reading a single graph—comparing multiple data sets or identifying patterns across representations. Extending money reasoning to multi-step scenarios involving making change or comparing purchasing options challenges students to apply flexible arithmetic thinking in realistic contexts.