L5 · Equivalence on the number line: clinic

Learning goal

“I can use the number line to rename, simplify, compare, and switch fractions to decimals - because equivalent fractions are the same point, no matter which name I use.”

Point — the exact spot a number lives on the number line; equivalent fractions share one point.

Name — any of the many ways to write the same number (fraction, simplest form, or decimal).

Worked example

Find every name for the halfway point. Step 1: On the 0-2 line, mark 1/2. Now re-mark the same line in quarters: the point is also 2/4. Step 2: Re-mark in tenths: the point is also 5/10. Re-mark in hundredths: also 50/100. Step 3: As a decimal, the point is 0.5. Five names - 1/2, 2/4, 5/10, 50/100, 0.5 - one point, one amount. Model both ways, side by side: a bar shaded to half in halves, quarters, and tenths (shading identical each time) AND the line with all the names stacked at the single halfway point. Say it plainly: renaming never moves the point. If a "new name" lands somewhere else on the line, it is not a rename - it is a different number.

Check yourself — explain it

How can you test whether two fractions are really equivalent?

Paired problem — example still visible

Name the point 3/4 in eighths, and again in twelfths. -> 3/4 = 6/8 = 9/12

Faded completion — last step is yours

"The point 2/5 in tenths: 2/5 = ___/10, and as a decimal it is ___." -> 4/10; 0.4

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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