Lesson 16 — Scaled Graphs & Our Data Celebration

Summary

The unit’s capstone: learners ask a real question, collect data, and draw a scaled picture graph and a scaled bar graph — where one symbol or one square stands for two or more answers — then use multiplication, division, and comparison to read what the data say. They present one finding in a data celebration, gathering everything the unit made possible.

Objectives

• Draw scaled picture and bar graphs and use them to solve problems and make comparisons. (D05.S4.03.02)
• Solve two-step word problems using the four operations and explain the relationship between addition and subtraction or multiplication and division. (D05.S2.03.02)

Connection

This unit you have counted to a thousand, multiplied and divided, seen patterns, solved two-step stories, measured area and perimeter, and weighed and poured real things — and now it all comes together. A class that wants to plan a celebration asks “how will we get there?” and graphs the answers; a village counts its water jars; a family tallies its favorite meals. When there are many answers, one mark for each is too many marks — so people use a scale: one symbol stands for two, or five, or ten. The math you know — multiplying, dividing, comparing — is exactly how you read a scaled graph. Today you do what data-keepers do everywhere: ask, collect, scale, graph, and share.

Materials

• A survey question and a way to record answers (per group)
• Paper, grid paper, and a drawing tool
• Small objects or marks for a picture graph

Preparation

• Help each group choose one respectful question with no “right” answer.
• Prepare recording sheets, grid paper, and a data wall or sharing circle.
• Plan a worked example of a scale (one symbol = 2 people).

Facilitator note

This lesson is written to the learner (“you”). It is the unit’s capstone, weaving together the whole unit. The one new skill is the scale — drawing a graph where one symbol or square stands for two, five, or ten answers — and using multiplication and division to read it. Teach with a worked example (philosophy §13) if needed, but let the groups drive. The celebration is a festival of mastery, not a competition: every graph is honored, every finding is real, and every answer counts exactly once (egalitarianism). No one’s graph is “better”; a clear, honest graph is the goal, and every learner’s contribution matters. For learners who are Deaf or hard of hearing, present findings in sign and point to the bars; for learners who are blind or low-vision, build a tactile graph and present by counting aloud. A learner who does not speak presents by pointing to symbols and holding up the number. Celebrate every group.

Procedure

1. Gather — the big question (5 min). Today is our data celebration. With a partner or small group, choose a real question to ask everyone (favorite fruit, how we get to school, a game we like, hours we sleep).
2. Collect the data (12 min). Ask your question and tally the answers — one mark for each person, so everyone counts exactly once. Keep your tally neat, like a data-keeper.
3. Choose a scale (8 min). If your counts are big, choose a scale: one symbol or one square stands for 2 (or 5) people. Show your scale in a key so anyone can read your graph.
4. Graph it two ways (15 min). Draw your data as a scaled picture graph and a scaled bar graph, each with a title and a key. Check that both show the same counts — multiply to check (3 symbols × 2 people each = 6 people).
5. Read and compare (12 min). Read your graphs. Which has the most? The fewest? Now answer “how many more or less” — multiply by the scale, then subtract. Write one finding as a sentence, using the operations of this unit.
6. Present at the celebration (8 min). Each group shares one finding, pointing to the symbols and bars. Listeners ask kind questions. Every graph is part of the celebration.

Differentiation

• Support: Use a two- or three-answer question and a scale of one symbol = 2; present one finding aloud with a partner.
• Support (motor): Have a partner draw while the learner tallies and counts.
• Extension: Write two findings, or combine two groups’ data and compare them, or predict what a bigger group would answer and say why.

Assessment

• Summative (portfolio): The learner’s scaled picture graph and scaled bar graph, kept as the unit’s data artifact.
• Observation: Can the learner collect data, draw it to a scale, and use multiplication, division, and comparison to answer “how many more or less”?
• Peer: Can the learner present a finding clearly and respond kindly to a classmate’s graph?

Home connection

At home, run a mini data celebration: ask your family a question, graph the answers with a scale (one symbol = 2 people), and present one finding to them.

Resources

• National Research Council. (2009). Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. The National Academies Press. (Collecting, representing, and reasoning about data with graphs, including scaling.)