A short lesson on improper fractions and mixed numbers in three sheets. The first shows that they are two names for the same amount and how to change one into the other. The second is guided practice with the steps laid out. The third is practice on its own, ending with a word problem and a mistake to explain.
Bar models, a number line with both names, and a worked example in each direction.
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Sixteen problems that start with pictures and lay out each step of the conversion. Includes answer key.
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Conversions both ways, whole-number answers, a word problem, and one mistake to explain. Includes answer key.
Download PDFAn improper fraction is a fraction whose top number is as big as or bigger than its bottom number, such as 7/4. A mixed number is a whole number and a fraction written together, such as 1 3/4. They are two ways of writing the same amount. Seven fourths is one whole and three more fourths.
The How It Works sheet shows that first with shaded bars and then on a number line where every point past 1 carries both names. Only after that does it give the two procedures: divide to go from an improper fraction to a mixed number, and multiply then add to go back.
Each procedure is tied to the picture. Dividing 11 by 4 asks how many groups of four fourths fit in eleven fourths. Multiplying the whole number by the bottom turns the wholes into pieces, so two wholes become ten fifths before the extra fifths are added on.
The guided practice sheet lays those steps out with boxes to fill in. The independent practice sheet drops the boxes and adds fractions that come out to whole numbers. Earlier lessons in this series are equivalent fractions and comparing fractions, and more practice is on the fractions worksheets page.