L4 · Fractions on the number line: clinic

Learning goal

“I can place fractions, improper fractions, and mixed numbers on a number line, read a point's value in both forms, count along the line past whole numbers, and use positions on the line to compare.”

Interval — the space between two neighbouring marks on a number line; in this unit each interval is one unit fraction.

Position — the exact mark where a number lives on the line. Equivalent numbers share one position.

Benchmark — a known number used as a measuring post: on the line, 0, 1/2, 1, 2, and 3 are the posts. (Review from L3.)

Worked example

Placing: place 11/4 on a number line marked in quarters, running from 0 to 3. Count quarter marks from 0: 4/4 = 1, 8/4 = 2, and 11/4 is the 11th mark - three quarter-steps past 2. So 11/4 sits between 2 and 3, at the same position as 2 3/4. Reading: a point P is marked at the 13th sixth on a line marked in sixths. As a fraction, P = 13/6. Group the sixths: 12/6 = 2 wholes, with 1 sixth left over, so P = 2 1/6 as a mixed number. One position, two names - the bar model agrees: two full bars in sixths plus 1 shaded sixth.

Check yourself — explain it

Why do 11/4 and 2 3/4 share one position on the line?

Paired problem — example still visible

Place 7/3 on a line marked in thirds from 0 to 3: which mark, and between which wholes? -> The 7th third mark; between 2 and 3 (7/3 = 2 1/3)

Faded completion — last step is yours

"On a line in fifths, the mark at 2 2/5 is the ___th fifth mark, because 2 wholes = ___ fifths and 2 more fifths make ___." -> 12; 10; 12 (2 2/5 = 12/5)

Ready to practise?

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

Start practice →Take the unit quiz