A scaled pictograph shows books read by students. The key says: each 📚 = 4 books. Kenji's row shows 3 full book symbols and one half-symbol. How many books did Kenji read?
A3 — there are 3 full symbols in his row
B7 — add 3 full symbols plus 1 half-symbol
C14 — multiply 3.5 symbols × 4 books per symbol
D12 — multiply only the 3 full symbols by 4, ignoring the half-symbol
Each full symbol = 4 books; a half-symbol = 2 books (half of 4). So: 3 × 4 = 12 books from the full symbols, plus 2 books from the half-symbol = 14 total. Option D is the common error of ignoring the half-symbol. Option A ignores the scale entirely — that mistake is the same as reading a scaled pictograph like a one-to-one pictograph.
Question 2 Multiple Choice
A teacher has data: Soccer: 20 students, Basketball: 15, Swimming: 10. Which scale makes the cleanest scaled pictograph?
AEach symbol = 3 students — 20 ÷ 3 and 15 ÷ 3 don't divide evenly
BEach symbol = 4 students — 15 ÷ 4 doesn't divide evenly
DEach symbol = 6 students — none of the values divide evenly by 6
The best scale divides evenly into all data values to avoid partial or broken symbols. 5 divides cleanly into 20, 15, and 10 — producing exactly 4, 3, and 2 whole symbols. The other scales produce remainders, which require awkward partial symbols that are hard to draw accurately and hard to interpret.
Question 3 True / False
In a scaled pictograph where each symbol = 5 items, a row with 6 symbols means there are 6 items in that category.
TTrue
FFalse
Answer: False
In a scaled pictograph, you must multiply the number of symbols by the scale value. 6 symbols × 5 items per symbol = 30 items — not 6. Reading the symbol count directly as the data value is the most common error when working with scaled pictographs; it treats the graph as if it were a one-to-one pictograph.
Question 4 True / False
You must read the key (legend) of a scaled pictograph before interpreting any data in the graph.
TTrue
FFalse
Answer: True
Without the key, you don't know what each symbol represents. Every calculation you make — reading individual values, comparing categories, finding totals — depends entirely on the scale defined in the key. A pictograph without its key is uninterpretable: the same row of symbols could mean 6 items, 12 items, 30 items, or any other value depending on the scale.
Question 5 Short Answer
Explain why pictographs use a scale (where each symbol represents more than one item) and what goes wrong if you forget to apply the scale when reading one.
Think about your answer, then reveal below.
Model answer: We use a scale so that large data values can be shown with fewer symbols — drawing 80 individual symbols for a category would be tedious and hard to read. A scale of 10 reduces 80 symbols to just 8. If you forget to apply the scale, you read the symbol count as the data value and get the wrong answer. For example, if each symbol = 10 and a row has 7 symbols, you'd misread 7 instead of the correct 70.
The scale is the key difference between a one-to-one pictograph and a scaled one. In a one-to-one graph, you just count symbols. In a scaled graph, counting symbols gives you only the intermediate step — you must then multiply by the scale value. Forgetting this step produces answers that are off by exactly the scale factor.