Unit 2 Fractions as Quotients and Fraction Multiplication (Family Materials)
In this unit, students solve problems involving division of whole numbers with answers that are fractions (which could be in the form of mixed numbers). They develop an understanding of fractions as the division of the numerator by the denominator, that is
Near the end of the unit, ask your student the following questions:
Write as many expressions as you can that represent this diagram:
- What is the area of the following rectangle?
Questions that may be helpful as they work:
How are the two problems similar? How are they different?
How does your expression represent the diagram?
How did you break up the rectangle to help you solve for the entire area?
What are the side lengths of the rectangle?
Section A Fractions as Quotients
In this section, students learn that fractions are quotients and can be interpreted as division of the numerator by the denominator. Students draw and analyze tape diagrams that represent sharing situations. Through the context of first sharing 1, then sharing more than 1, then sharing a number of things with increasingly more people, students notice patterns and begin to understand that in general
Section B Fractions of Whole Numbers
In this section, students make connections between multiplication and division and use visual representations that can show both operations. For example, the diagram above can also represent 4 groups of
Section C Area and Fractional Side Lengths
In this section, students use what they know about the area of rectangles with whole number side lengths to find the area of rectangles that have one whole number side length and one fractional side length.
In the same way,
In addition, students see that the expressions
Students analyze diagrams where one side length is a mixed number, for example a rectangle that is 2 by
To find the area represented by this diagram, students may see two rectangles: a rectangle that is 2 units by 3 units and a rectangle that is 2 units by