L1 · Improper fractions and mixed numbers

Learning goal

“I can count in unit fractions past 1 whole, and I can read a model two ways - as an improper fraction and as a mixed number - because both name the same amount.”

Unit fraction — one equal part of a whole: 1/4 is one quarter-part. Counting unit fractions is how all fractions are built.

Improper fraction — a fraction whose numerator is greater than its denominator, like 7/4. It names an amount bigger than 1 whole. (When the numerator equals the denominator, the fraction is exactly 1 whole.)

Mixed number — a whole number and a fraction written together, like 1 3/4. It names one amount: 1 whole and 3 quarter-parts more.

Whole — one complete unit: 4/4, 5/5, 6/6 each make exactly 1 whole.

Worked example

Count in quarters. One pizza is cut into 4 equal quarters. Count the quarters as they are served: 1/4, 2/4, 3/4, 4/4. Stop and name it: 4 quarters rebuild the whole pizza, so 4/4 = 1. But the count does not stop - a second pizza is being served. Keep counting: 5/4, 6/4, 7/4, 8/4. 8/4 = 2 wholes. Name the new kind of number: in 5/4 the numerator (5) is greater than the denominator (4). 5/4 is an improper fraction, and it is a perfectly good number: 5/4 = 4/4 + 1/4 = 1 1/4. Model both ways, side by side: two pizza bars in quarters with 5 quarters shaded in total, AND a 0-2 number line marked in quarters with 5/4 sitting one quarter-step past 1. Same count, two pictures - and past 1, the quarters keep the same size.

Check yourself — explain it

Why doesn't the count stop at 4/4?

Paired problem — example still visible

Count in thirds: 1/3, 2/3, 3/3 = 1, then the next two counts -> 4/3, 5/3

Faded completion — last step is yours

"In sixths: 5/6, 6/6 = 1, ___, 8/6. The missing count is ___ sixths in total, which is 1 whole and ___ sixth." -> 7/6; 7; 1 (7/6 = 1 1/6.)

Ready to practise?

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

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