Fractions - Improper to mixed numbers (Cubes) - Presentation

In the third lesson of a series on fractions, students delve into the conversion of improper fractions to mixed numbers. The lesson begins with a discussion aimed at defining 'improper fraction' and 'mixed number.' An improper fraction is one where the numerator (the top number) is larger than the denominator (the bottom number), resulting in a value greater than one. A mixed number, on the other hand, combines a whole number with a proper fraction, representing a value greater than one but with the fraction part being less than one. The class is encouraged to explore these concepts and come up with their own definitions, setting the stage for a deeper understanding of the mathematical conversion process.

Throughout the lesson, various activities are designed to reinforce the concept of converting improper fractions to mixed numbers. One such activity involves a practical approach where Kate groups cubes to visually demonstrate the conversion process. For example, she takes the improper fraction 15/4 and groups the cubes into sets of 4, with 3 cubes left over, illustrating that 15/4 is the same as 3 whole sets plus 3/4, hence the mixed number 3 3/4. Students then apply this method to other fractions, such as 13/2, 13/3, 13/4, and 13/5, converting them into mixed numbers. Another activity uses bar models to aid in the conversion process, as demonstrated by Malachi with the fraction 30/7. The lesson also includes reasoning challenges where students are encouraged to spot mistakes in given conversions and to correct them, fostering critical thinking and a deeper comprehension of the relationship between improper fractions and mixed numbers.