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Scaled Picture and Bar Graphs

A 50-minute Grade 3 lesson on drawing and reading picture and bar graphs where one symbol or one square stands for more than one, and on answering how-many-more questions from them.

Scaled Picture and Bar Graphs is a free 50-minute Grade 3 math lesson plan for Common Core standard 3.MD.B.3 — draw and read picture graphs and bar graphs where one picture or one square stands for more than one. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 3
Length:
50 minutes
Standard:
3.MD.B.3

Grade 3 · Measurement & Data

3.MD.B.3

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.

Objective

Students will be able to draw a scaled picture graph and a scaled bar graph from a data set, and solve one- and two-step 'how many more' and 'how many fewer' problems from a scaled bar graph.

Students are successful when they can

  • Reads the key or the scale before reading any bar or row of symbols.
  • Draws a graph with a scale that fits the data, including a half symbol or a bar between gridlines.
  • Solves a two-step comparison, such as how many more two categories have together than a third.

What you need

  • Grid paper and rulers
  • A class data set with four categories
  • Star stickers or stamps for picture graphs
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — what does one star mean?

6 min
  1. Show a picture graph with 6 stars in a row and a key saying each star is 2 students. Ask how many students.
  2. Some will say 6. Ask them to read the key aloud, then answer again. 12.

Teach — the key is part of every answer

15 min
  1. Use the data set: apples 12, bananas 8, grapes 14, pears 6.
  2. Draw a picture graph with one star for 2. Apples get 6 stars, bananas 4, grapes 7 and pears 3. Ask why one star for 1 would be a worse choice — 14 stars is a lot to draw and read.
  3. Redraw with one star for 4. Apples are 3 stars, bananas 2, grapes 3½ and pears 1½. A half star stands for 2, and the half is part of the graph, not a mistake.
  4. Draw a bar graph of the same data with a scale counting by 2s. Bars end on gridlines, and the scale is labeled every 2.
  5. Ask how many more students chose grapes than pears. 14 − 6 = 8. Show it on the graph as the part of the grapes bar above the top of the pears bar.
  6. Ask a two-step question: how many more chose apples and bananas together than grapes? 12 + 8 = 20, and 20 − 14 = 6.
“Read the key before you count anything. Each picture, or each square, stands for the number in the key, not for one.”

Guided practice — draw it, then ask it

14 min
  1. Pairs draw a scaled bar graph for a four-category data set, choosing a scale of 2 or 5 and saying why it fits.
  2. They write one 'how many more' and one 'how many fewer' question, and one two-step question, for another pair.
  3. The other pair answers them and checks each answer against the original data.

Independent practice

12 min
  1. Students complete a scaled graphs page.
  2. Answers that are exactly a half or a fifth of the right number are the key-not-applied error and show up across every question at once.

Close

3 min
  1. Show a bar that ends halfway between 10 and 12 on a scale of 2, and ask what it shows.
  2. 11. Reading between gridlines uses the scale as a measuring line, which is where the line plots come in next.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Counts the symbols in a row and gives that as the answer, ignoring the key.

Why: Every picture graph met before had one symbol for one thing, so the key has never changed an answer and has stopped being read.

Fix: Make the first written line of every answer the key itself: '1 star = 2'. Then count the stars and multiply, so the key cannot be skipped.

Answers 'how many more apples than pears' with the number of squares between the bars, not their value.

Why: The difference has been found correctly on the grid but in squares, because the scale was applied to the bar heights and not to the gap.

Fix: Read both bars as numbers from the scale first, then subtract the numbers. The difference is always a number of students, never a number of squares.

Solves a two-step question in one step, subtracting the first two numbers it mentions.

Why: The question is being matched to a single operation by its key word, 'more', so the 'together' part is missed.

Fix: Ask what the question compares before calculating: apples and bananas together, against grapes. Writing the two groups down shows that the total has to be found first.

If they are not there yet

  • Start with a key of one symbol for 2 and data sets of even numbers only, so no half symbols are needed.
  • Write the value beside each symbol as it is counted: 2, 4, 6, 8.

If they finish early

  • Draw the same data with a key of 1 symbol for 5 and decide how to show 12.
  • Compare two bar graphs of the same data with different scales and say which is easier to read and why.
  • Write a question whose answer needs three steps, and solve it.

Exit ticket

On a bar graph where each square is 5 students, red has 7 squares and blue has 4. How many more chose red than blue? How many chose red and blue altogether?

What to look for: 15 more and 55 altogether. Answers of 3 and 11 mean the scale was not applied; 15 with a total of 11 means the scale is being used for comparisons but not yet for totals.

Printable practice for 3.MD.B.3

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Scaled Picture and Bar Graphs

How long does the Scaled Picture and Bar Graphs lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Scaled Picture and Bar Graphs teach?

CCSS.MATH.CONTENT.3.MD.B.3 — 3.MD.B.3, Measurement & Data for Grade 3: “Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.” In plain terms, draw and read picture graphs and bar graphs where one picture or one square stands for more than one.

What do I need to teach this lesson?

Grid paper and rulers, a class data set with four categories, star stickers or stamps for picture graphs and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: counts the symbols in a row and gives that as the answer, ignoring the key; answers 'how many more apples than pears' with the number of squares between the bars, not their value and solves a two-step question in one step, subtracting the first two numbers it mentions. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “On a bar graph where each square is 5 students, red has 7 squares and blue has 4. How many more chose red than blue? How many chose red and blue altogether?.” 15 more and 55 altogether. Answers of 3 and 11 mean the scale was not applied; 15 with a total of 11 means the scale is being used for comparisons but not yet for totals. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Scaled Picture and Bar Graphs?

Yes — 1 printable 3.MD.B.3 worksheet, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Scaled Picture and Bar Graphs free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on October 22, 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-10-22. Aligned to 3.MD.B.3 of the Common Core State Standards for Mathematics.