L2 · Many-to-One Correspondence: Choosing a Scale

Learning goal

“I can use many-to-one correspondence: read the key to learn what ONE symbol stands for, use multiplication and division with the key to move between symbols and real counts, handle half symbols, and choose a sensible key or axis scale for big counts.”

Many-to-one correspondence — when ONE symbol or ONE step on a graph stands for MANY things. One symbol, many books.

Scale — the pattern of numbers a graph counts by: a key that says each symbol = 10, or an axis labelled 0, 10, 20, 30.

Key — the note beside a pictograph that tells what each symbol stands for. No key, no reading the graph.

Symbol — the little picture in a pictograph row. Its value comes from the key, never from the picture itself.

Worked example

Four classes counted the books they read in one month: Maple 40, Birch 30, Cedar 50, Pine 20. Step 1: A one-to-one pictograph would need 50 symbols in the Cedar row - slow to draw and easy to miscount. Too many symbols is a real problem. Step 2: Choose a KEY: each symbol = 10 books. Now divide each count by 10 to get rows: Maple 40 / 10 = 4 symbols; Birch 3; Cedar 5; Pine 2. Step 3: Read it back with multiplication: a row of 5 symbols x 10 books each = 50 books. The total is 40 + 30 + 50 + 20 = 140 books. Say it plainly: the KEY is the exchange rate between symbols and real things. Symbols -> real: multiply by the key. Real -> symbols: divide by the key. And a graph without a key cannot be read at all.

Check yourself — explain it

Why did the class choose a key of 10 instead of drawing all 140 books one by one?

Paired problem — example still visible

A new class, Aspen, read 60 books. With the same key (each symbol = 10 books), how many symbols go in Aspen's row? -> 6 symbols (60 / 10)

Faded completion — last step is yours

"A row in this pictograph has 4 symbols. Real books = 4 x 10 = ___ books. The class with that row is ___." -> 40 books; Maple

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