Place value and number senseGrades 2–3
Pictograph worksheets with scaled keys
Each sheet has one pictograph with five categories, a key, and six questions on totals, most, fewest and differences. Choose what each picture stands for and whether half pictures appear, then print with an answer key.
- Fresh problems every time
- Answer key on its own page
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Reading data from pictures
A pictograph shows data with small symbols instead of numbers. It is one of the first graphs children see, because counting symbols feels natural. The new idea comes when one symbol stands for more than one thing. Then the key becomes essential, and the student has to multiply or skip count to read each row. Second graders begin with a key of 1 or 2, and third graders work with larger and less friendly scales.
Every sheet shows one graph with five rows. The topic changes with each new set of problems: weather, favorite sports, cars in a parking lot, and so on. A one-line story at the top sets the scene, and a circle with an equals sign below the graph gives the key.
Settings
- Each picture stands for. Choose 1, 2, 5 or 10. With 1, the graph is a plain tally. With 2 and 5, the student skip counts. With 10, the counts reach the dozens.
- Use half pictures. When on, a row may end in a half circle that stands for half the key value. Halves only make sense for a key that splits evenly, so the option appears for a key of 2 or 10. With a key of 1 or 5, the sheet prints whole pictures only.
There is no problem count here, because the sheet is built around one graph. Each page asks six questions: two "how many" questions for named categories, which has the most, which has the fewest, how many more the most has than the fewest, and the total. The answers are in the key, which prints in color next to each blank when you turn it on.
Use new problems to cycle through topics; the numbers and categories both change.
Worked example: a key of 2 with half pictures
Imagine the key reads: one circle = 2, half a circle = 1. A graph of favorite sports shows these counts after reading each row:
- Soccer: 4 full circles and a half, which is 4 × 2 + 1 = 9
- Basketball: 3 full circles, so 3 × 2 = 6
- Swimming: 2 full circles, so 4
- Baseball: 5 full circles and a half, so 5 × 2 + 1 = 11
- Tennis: 3 full circles and a half, so 7
Now answer the six questions.
- How many for Soccer? 9
- How many for Swimming? 4
- Which has the most? Baseball, with 11
- Which has the fewest? Swimming, with 4
- How many more Baseball than Swimming? 11 − 4 = 7
- How many in all? 9 + 6 + 4 + 11 + 7 = 37
For the total, add in pairs that are easy: 9 + 11 = 20, 6 + 4 = 10, 20 + 10 + 7 = 37 again.
Errors to watch for
- Counting pictures instead of values. A student who writes 5 for the Soccer row counted four whole circles and a half as five pictures. The answer is 9 because each picture is worth 2.
- Ignoring the half. Forgetting the half circle leaves the count one short. The key line reminds students what half a picture is worth.
- Answering with the category. For "which has the most," the answer is a name, not a number.
- Mixing up "how many more." This question asks for a difference, so the answer is a subtraction, not the larger count.
Extending the lesson
After finishing the sheet, ask students to invent a question of their own about the graph, or to redraw the same data with a key of 1. Skipping a beat at the half pictures gives lots of useful conversation. Students who find the skip counting slow can warm up with the skip counting worksheets. For the larger idea of reading data on a line, try the number line worksheet, and for adding and subtracting the numbers that come out of a graph, see the 2-digit addition without regrouping page.