Division Types
In this type of division problem, the number of groups is known and the size of each group is unknown.
What is partitive (fair share) division?
The total number of equal parts in a whole.
What is the denominator?
Solving 24 ÷ 6 by repeatedly subtracting 6.
What is repeated subtraction?
Thinking “6 × 4 = 24” to solve 24 ÷ 6.
What is understanding the relationship between multiplication and division?
The fraction piece that represents the entire strip in a fraction kit.
What is one whole?
In this type of division problem, the size of each group is known but the number of groups is unknown.
What is quotative (measurement) division?
The fraction that represents 5 things shared by 8 people.
What is 5/8?
Counting “3, 6, 9, 12, 15” to solve 15 ÷ 3.
What is skip counting with tracking?
The property that allows students to use 3 × 5 to help solve 3 × 6.
What is the distributive property?
What fraction kits help students see when combining pieces to make a whole.
What is fraction equivalence?
15 ÷ 3 = ? (How many groups of 3?)
What is an example of quotative division?
The top number in a fraction that tells how many parts are being considered.
What is the numerator?
Splitting items in half repeatedly and coordinating shares at the end.
What is repeated halving with coordination at the end?
A quantity that represents the “per” amount in multiplication or division.
What is an intensive quantity?
The mathematical idea students explore when they cover one whole with combinations like 1/2 + 1/4 + 1/4.
What is composition of fractions?
56 cookies shared equally among 8 children.
What is an example of a partitive division question?
Fractions should initially be introduced through this type of context.
What are equal sharing situations?
Partitioning each item into the number of sharers from the beginning.
What is additive coordination (one item at a time)?
The pedagogical purpose of anticipating multiple strategies for the same problem.
What is understanding students’ thinking and planning questioning?
Students replace two 1/8 pieces with one 1/4 piece because they take up the same space.
What is unitizing and equivalence?
The feature that distinguishes quotative and partitive division.
What is which quantity is unknown (number of groups vs. amount per group)?
Two recommended changes in fraction language.
What are saying fraction names like “one fourth” and no longer referring to fractions as improper fractions?
Coordinating the relationship between sharers and shares without partitioning each item.
What is transitional multiplicative coordination?
The strategy showing a shift toward multiplicative reasoning.
What is using known multiplication facts to solve division?
According to Marilyn Burns in The Fraction Kit Guide, this is a key benefit of using a fraction kit in instruction: it allows students to see fractions as equal parts of a whole and explore equivalence through hands-on reasoning.
What is using fraction kits to help students explore fraction equivalence and equal parts through hands-on reasoning?