options: 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.

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.)
problem_activity: Stage 4: Whole Number and Fraction Factors
Required Preparation
Materials to Gather
Colored pencils, crayons, or markers
Number cubes
Paper clips
Materials to Copy
Blackline Masters
Rectangle Rumble Stage 4 Spinner
Rectangle Rumble Stage 4 Grid

Narrative
Students generate factors with a number cube and a spinner with fractions with denominators of 3, 6, or 12. Students use a
\(24 \times 24\)
grid that represents 16 square units.
Additional Information
Each group of students need a paper clip, a number cube, and two different color writing utensils.


correct_option_index: 0