L3 · A fraction is a number of unit fractions; one whole (a/a)

Learning goal

“I can build any fraction by counting unit fractions - 3/4 is three one-fourths - and I can recognize exactly one whole, written with the same numerator and denominator.”

Compose — to build up by putting parts together: 3/4 is composed of three 1/4s.

Unit fraction — one equal part of a whole (from L1): 1/4, 1/8, 1/12.

One whole — all the parts together: 4/4 is one whole, because all 4 parts of the whole are counted.

Worked example

A strip is split into 4 equal parts. Each part is the unit fraction 1/4. Shade the parts one at a time and count: 1/4 ... two parts is 1/4 + 1/4, named 2/4 ... three parts is 1/4 + 1/4 + 1/4, named 3/4. So a fraction is a NUMBER OF unit fractions. The numerator is the count; the unit fraction is what is being counted. 3/4 is not a mystery symbol - it is three one-fourths, the way 3 apples is three of one apple-kind. Count by unit fractions the same way you count by ones: 1/5, 2/5, 3/5, 4/5, 5/5.

Check yourself — explain it

What is being counted when we say 3/4?

Paired problem — example still visible

Write 5/6 as a count of unit fractions: 5/6 = 1/6 + 1/6 + ___ -> three more 1/6s (five 1/6s in all)

Faded completion — last step is yours

"Four one-eighths make ___." -> 4/8

Ready to practise?

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

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