Modeling Sharing with Shares Greater Than One
When sharing more items than people (a > b in a division problem), each person receives more than one whole item, which can be found by first distributing whole items and then splitting the remainder as fractions, as covered in Illustrative Mathematics Grade 5, Chapter 2: Fractions as Quotients and Fraction Multiplication. For example, sharing 5 sandwiches among 3 people gives each person 1 + 2/3 = 1 2/3 sandwiches.
Key Concepts
When sharing $a$ items among $b$ people where $a b$, each person's share will be greater than 1. The total share can be found by first distributing whole items, and then partitioning the remaining items equally.
Common Questions
What happens when you share more items than people?
When there are more items to share than people, each person receives at least one whole item, and the remainder is split into fractions; the result is expressed as a mixed number.
How do you model sharing 5 sandwiches among 3 people?
First give each person 1 whole sandwich (using 3), leaving 2; divide the remaining 2 sandwiches into thirds, giving each person 2/3 more; total per person is 1 + 2/3 = 1 2/3 sandwiches.
Why does this kind of sharing result in a mixed number?
When the total items exceed the number of people, the result of division is greater than 1 but not a whole number; expressing it as a mixed number (whole part plus fraction) captures both parts of each person share.
How is this related to improper fractions?
The mixed number result (like 1 2/3) is the same as the improper fraction 5/3; both represent the same amount, but the mixed number is easier to visualize as a real-world quantity.
What grade level is this skill for?
This skill on modeling sharing with shares greater than one is covered in Grade 5 mathematics, specifically in the unit on fractions as quotients and fraction multiplication in Illustrative Mathematics.