options: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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?

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students draw and shade rectangles with a unit fraction side length and a whole number side length. Then they find the areas of the shaded regions. The tactile experience of drawing and shading encourages students to count the number of shaded parts and then either reason about their size or think about moving them to make full unit squares. They also consider a diagram where not all of the unit squares are shown. Students estimate how many of the unit squares are hidden. This helps to highlight that finding the total area can be done with multiplication where one factor is the area of each shaded part and the other factor is the total number of shaded parts (MP7).
Required Materials
Materials to Copy
Grid Paper 5
Launch
Groups of 2
Give students grid paper.
Activity
5–7 minutes: independent work time
5 minutes: partner work time
Monitor for students who:
use the grid structure on the paper to draw their rectangles
count the number of unit squares that might be hidden under the yellow rectangle
Student Facing
Represent each rectangle on grid paper:
\(\frac{1}{2}\)
unit by 1 unit
\(\frac{1}{2}\)
unit by 2 units
\(\frac{1}{2}\)
unit by 3 units
\(\frac{1}{2}\)
unit by 4 units
Find the area of each rectangle that you drew.
What information do you need to find the area of the shaded region?
[IMG]
What might the area of the shaded region be? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students do not draw the rectangles correctly, show them the shaded region from the previous activity with side lengths 6 units and
\(\frac{1}{2}\)
unit and ask “How could you adapt this diagram to show a rectangle that is 4 units by
\(\frac{1}{2}\)
unit?”
Activity Synthesis
Display a student generated image of the
\(\frac{1}{2}\)
unit by 4 unit rectangle.
Ask previously selected students to describe how they drew they 4 by
\(\frac{1}{2}\)
rectangle.
Display image from student workbook of the rectangle that is partly covered.
“What do you need to know to determine the area of the shaded region?” (We need to know how many unit squares are under the yellow rectangle.)
“How many unit squares do you think make up the rectangle?” (6 or 7)
“How did you use the number of these unit squares to make an estimate for the shaded region?” (I know that each shaded blue rectangle is
\(\frac{1}{2}\)
of a square so if there are 6 or 7 of those, that would be
\(\frac{6}{2}\)
or
\(\frac{7}{2}\)
square units.)


correct_option_index: 2