Lesson 15 — Picture Graphs and Bar Graphs

Summary

Learners turn the same data into two graphs — a picture graph and a bar graph — and read both: which answer has the most, which the fewest, and how many more or less. They discover that a bar graph is just a picture graph with bars instead of pictures.

Objectives

• Draw and interpret picture graphs and bar graphs and answer questions about how many more or less. (D05.S4.02.02)

Connection

A class wants to know which fruit to bring for a celebration; a village wants to know how many homes have a garden; a family wants to know each person’s favorite game. When you ask everyone the same question and draw the answers, you make a graph — and the answer jumps out at you. Graphs are how people turn many voices into one clear picture, so decisions are fair and everyone is counted.

Materials

• A survey question and a way to record answers
• One small object, mark, or drawn picture per learner
• Paper or slate and a drawing tool

Preparation

• Choose one question everyone can answer.
• Prepare a chart with a row for each answer.
• Give each learner one object or mark to place.

Facilitator note

This lesson is written to the learner (“you”). It builds on Grade 1’s picture graphs and adds the bar graph — the new skill is drawing bars and answering “how many more or less.” Teach with a worked example (philosophy §13): build the picture graph, then draw a bar the same height and show the two are the same data. The powerful ideas are one mark per answer, bars that match the count, and how many more or less as a subtraction question. Frame graphs as fairness tools: every answer counts once, and no answer is more important than another (egalitarianism). Choose a question that is respectful and has no “right” answer. For learners who are Deaf or hard of hearing, pose the question in sign or pictures and count bars with fingers; for learners who are blind or low-vision, build a tactile graph with objects in rows the hands can count. A learner who does not speak places an object or points. Every answer is one mark, and every mark matters equally.

Procedure

1. Gather — a question for everyone (5 min). Today we ask one question of everyone and draw the answers two ways. Here is our question: ___ (for example, “Which fruit do you like best?”).
2. Worked example — build the picture graph (10 min). Each learner places one object in the row for their answer — one object for one person. Count each row. Which has the most? Which the fewest?
3. Draw the bar graph (12 min). Now draw the same data as a bar graph: for each answer, draw a bar as tall as its count (one square per person). Give the graph a title. A bar graph is the same as a picture graph — bars instead of pictures.
4. Read “how many more or less” (10 min). Compare two bars. How many more people chose the top answer than the bottom one? Count the difference, or subtract. How many less chose one than another? Say and write the answers.
5. Ask new questions (8 min). What else can the graph tell us? How many people answered in all? Are any bars the same? Wonder about it together.
6. Close (5 min). You asked a question, collected answers, and drew them two ways. A graph turns many voices into one fair picture — and “how many more” is a question you can now answer.

Differentiation

• Support: Use only two or three answer choices and count bars together, touching each square.
• Support (blind/low-vision): Build the graph with objects in rows and read it by feeling and counting each row.
• Extension: Write a sentence about the graph (“six chose mango, three chose apple, so three more chose mango”), or draw the graph with a scale of one square per person.

Assessment

• Formative (observation): Can the learner draw a picture graph and a bar graph and answer questions about most, fewest, and how many more or less?
• Artifact (portfolio): The learner’s bar graph (or a drawing of it), kept as a record of data work.

Home connection

At home, ask everyone the same question (“which color do you like best?”), draw the answers as a bar graph, and tell a grown-up which has the most and how many more.

Resources

• National Research Council. (2009). Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. The National Academies Press. (Representing data with picture and bar graphs and comparing quantities.)