Unit 4 — Representing Data
Description
Unit 4 focuses on collecting, organizing, and representing data using picture graphs, bar graphs, and line plots. Students draw scaled picture graphs and bar graphs where each symbol or unit represents more than one object, solving one- and two-step comparison problems. They measure lengths using rulers marked with halves and fourths of an inch and display measurement data on line plots with appropriate scales. The unit reinforces fluent multiplication and division within 100 as students analyze scaled graphs. Two-step word problems using all four operations are solved with equations and unknowns. Addition and subtraction within 1000 continue to develop automaticity. Area of rectilinear figures is determined by decomposing into non-overlapping rectangles, connecting earlier geometry and measurement learning. By year's end, students have mastered foundational skills in operations, fractions, measurement, and data representation.
Essential Questions
- How are tables, bar graphs, and line plot graphs useful ways to display data?
- How can you use graphs to answer a question?
- How can surveys be used to collect and gather information?
- How can graphs be used to display data gathered from a survey?
Learning Objectives
- Draw scaled picture graphs and scaled bar graphs to represent data with several categories.
- Solve one- and two-step comparison problems using information from scaled bar graphs.
- Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
- Display measurement data on line plots with scales marked in whole numbers, halves, or quarters.
- Fluently multiply and divide within 100 using strategies.
- Solve two-step word problems using all four operations and assess reasonableness.
- Fluently add and subtract within 1000.
- Solve real-world problems involving areas of rectilinear figures by decomposing and adding.
Supplemental Resources
- Chart paper and markers for creating large-scale graphs
- Graph templates for picture graphs and bar graphs with different scales
- Rulers marked with halves and quarter inches for measurement
- Sticky notes for data collection and organization activities
- Grid paper for creating line plots with appropriate scales
- Index cards for recording measurement data points
Digital Literacy
Measurement
Number and Operations in Base Ten
Operations and Algebraic Thinking
Students use reading comprehension skills to problem solve and explain mathematical thinking in written form using mathematical terms. Students connect everyday vocabulary to strengthen their understanding of mathematical concepts.
Students collect and analyze data and make calculations involving measurements across life science, physical science, and earth science modules. Students represent data in tables and graphical displays to describe observations and patterns.
Formative Assessments
- Exit tickets checking understanding of scaled graphs and data interpretation
- Classwork drawing and interpreting picture graphs and bar graphs
- Individual work measuring and creating line plots
- Math journals recording data collection and representation strategies
- Group activities comparing data across different graph types
- Whiteboard activities solving comparison problems from graphs
Summative Assessment
Chapter tests on data representation and interpretation; performance tasks requiring students to collect, organize, and represent survey data; extended projects analyzing real-world data using multiple graph types.
Benchmark Assessment
Benchmark assessments within Go Math, Eureka Math, and iReady; PARCC released items and practice tests; state testing results.
Alternative Assessment
Students may demonstrate understanding through oral explanation of graph data while viewing a completed graph, or by selecting correct answers from multiple-choice options about scaled graphs and comparison problems. Simplified graphs with fewer categories, pre-made graph templates, or number lines may be provided as support.
IEP (Individualized Education Program)
Students may benefit from having graph templates pre-structured with labeled axes and scaled intervals to reduce the organizational demand of setting up graphs independently, allowing focus on data interpretation and comparison. Providing a reference card with multiplication and division fact strategies supports fluency work without interrupting problem-solving momentum. For two-step word problems, breaking the problem into sequenced steps with visual cues or graphic organizers helps students process each operation separately. Output modes such as oral explanation, pointing to responses on a model graph, or dictating reasoning to a scribe should be accepted alongside written work.
Section 504
Students should be provided extended time during graph-drawing and measurement tasks, as precision work with rulers and scaled intervals can require additional processing time. Preferential seating near the teacher during instruction on interpreting scaled bar graphs and line plots supports focus when multiple data representations are being compared. A reduced-distraction environment is especially helpful during assessments involving multi-step problems with graphs, where visual complexity may be a barrier.
ELL / MLL
Visual supports such as labeled example graphs, color-coded scales, and illustrated vocabulary cards for key terms — including scale, interval, data, half-inch, and quarter-inch — help students connect language to the mathematical concepts in this unit. Directions for measurement tasks and graph construction should be simplified and paired with a visual model showing the expected process or product. Where possible, connecting graph topics to contexts familiar from students' home cultures or communities can make data collection tasks more accessible and meaningful.
At Risk (RTI)
Connecting new graphing work to students' prior experience with simple picture graphs or tally charts provides a meaningful entry point before introducing scaled representations. Reducing the number of categories or data points in initial graph tasks allows students to build confidence with the process before increasing complexity. Using hands-on tools such as physical rulers and concrete graph-building materials supports understanding of both measurement and data display, and frequent brief check-ins during problem-solving help catch and correct misunderstandings before they compound across multi-step tasks.
Gifted & Talented
Students can be challenged to design and conduct their own multi-category data collection projects, choosing appropriate graph types and justifying their scale decisions with mathematical reasoning. Exploring how changes to the scale of a graph affect its visual interpretation encourages critical thinking about data representation and potential bias. Connecting area decomposition to real-world design contexts — such as analyzing floor plans or map regions — and asking students to create and solve their own two-step problems using self-generated data sets deepens engagement and extends thinking well beyond procedural fluency.