Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Students are able to…
- Recognize that a word problem requires division based on the context of the problem.
- Model and solve a variety of division problems involving deciding what to do with the remainder.
- Explain their thinking for interpreting the remainder as a fraction.
- Explain that a fraction is a type of division problem.
Students are able to…because teachers:
- Provide students with a variety of division problems to model interpreting the remainder as a fraction.
- Provide students with opportunities to model division problems and decide what to do with the remainder.
- Facilitate classroom discussions about the meaning of the remainder and why a fraction remainder makes sense depending on the situation.
- Facilitate discussion where students explain their thinking and the meaning of their solutions given the context of the problem and provide means for students to communicate their thinking.
Questions to ask students:
When you have a division problem and a remainder, what might you do with the remainder? (could show student several similar division scenarios and ask them to describe what to do with the remainder)
- Sample answer that indicates understanding: Sometimes the remainder is the answer. Other times you drop the remainder because it isn’t important in the situation. Sometimes we write the remainder as a fraction. Sometimes we need to add one to the quotient and drop the remainder.
- Sample answer that indicates an incomplete understanding or a misconception: Write R for remainder and write the amount left over.
How are division and fractions related?
- Sample answer that indicates understanding: Fractions and division are the same thing. Division is breaking things up into equal groups. The divisor tells us how many groups. In fractions the denominator tells us how many pieces we are breaking something up into.
- Sample answer that indicates an incomplete understanding or a misconception: Division and fractions are not similar. Fractions are less than a whole.
How can you divide a smaller number by a larger number?
- Sample answer that indicates understanding: If you divide a smaller number by a larger number your answer will be a fraction. The divisor will be the denominator and the dividend will be the numerator.
- Sample answer that indicates an incomplete understanding or a misconception: You cannot do that. You can only divide a larger number by a smaller number.
Cognitive Complexity Level: Level 2: Basic Application of Skills & Concepts
Achievement Level Descriptions:
Level 2: rewrites a fraction as a division problem (a/b = a ÷ b ); uses manipulatives or visual models to solve problems involving division of whole numbers, leading to answers in the form of fractions or mixed numbers
Level 3: interprets and solves word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers
Level 4: interprets a fraction greater than 1, presented as a mixed number, as division of the numerator by the denominator (a/b = a ÷ b ); identifies a context involving division of whole numbers, leading to answers in the form of fractions or mixed numbers
Level 5: creates a context involving division of whole numbers, leading to answers in the form of fractions or mixed numbers
- Quotients in division items may not be equivalent to a whole number.
- Items may contain fractions greater than 1.
- Items may not use the terms “simplify” or “lowest terms.”
- Only use whole numbers for the divisor and dividend of a fraction.
- For given fractions in items, denominators are limited to 1‐20.
Sample Formative Assessment Tasks:
Mr. Clarke has a rope that is 11 inches long that he needs to cut into 6 equal parts to share with the 6 students in his after-school program for a knot-tying project.
Draw a model to show how the rope can be equally shared.
What fraction of the rope will each student receive?
Write a sentence to explain how you know that you are correct.
Joe has a board that is 6 feet long. He needs to cut the board into 15 equal‐length pieces.
How many feet long should each piece of the board be?
James was preparing boxes of school supplies to send to a school in another country. Thirty-two packs of paper were donated for the boxes. This paper had to be shared equally with the 6 boxes being prepared.
Draw a model to show how James can divide the paper equally among the 6 boxes.
What fractional part of the paper did James put in each box?
Create a division equation and label what numbers represent the numerator and denominator in this problem.
Resources/Task to Support Your Child at Home
- Learn Zillion -Fractions Represented as Division http://tinyurl.com/zv5n2nd
- Real World Situation: Sharing objects with people; sharing 3 cookies among 4 people and asking what amount of cookies each person will get.
- Real World Example: There are 253 students waiting for a van to go on a field trip. If each van holds 8 students, what fraction of the last van is full?
- Math is Fun: Division and Remainders – https://goo.gl/P45T7B