Question 11

Putting 12 cups of sand into piles, each containing two-thirds of a cup of sand effectively illustrates that 12 + 2/3 equals 18.

This method clearly demonstrates the concept of addition by visually representing the total amount when 12 cups are combined with additional smaller units of two-thirds.

A) Folding a 12-inch ribbon in half and then cutting the folded ribbon into thirds

This option does not effectively represent the addition of 12 and 2/3, as it focuses on manipulating a single ribbon rather than illustrating the total quantity of 12 cups plus additional fractions. The process described does not yield a clear understanding of how to combine these two values.

B) Putting 12 cups of sand into piles, each containing two-thirds of a cup of sand

This choice is the most appropriate because it allows students to physically see how 12 cups can be augmented by smaller fractional parts. By creating piles of two-thirds, students can grasp the idea that these fractions contribute to the overall total, leading to a better comprehension of the equation.

C) Using the rule 'invert and multiply' to divide 12 by 2 and then to multiply 6 by 3

This option incorrectly applies mathematical operations that are not relevant to the addition of whole numbers and fractions. It introduces unnecessary complexity and does not aid in visualizing how 12 and 2/3 combine to create a total.

D) Counting the number of one-half inches in 12 inches on a ruler and then dividing the count by 3

This method does not accurately address the addition of 12 and 2/3 and instead focuses on measuring lengths, which may confuse students regarding the concept of combining whole numbers and fractions. It does not provide a straightforward connection to the operation needed.

Conclusion

The choice of putting 12 cups of sand into piles, each containing two-thirds of a cup, effectively illustrates the addition of 12 and 2/3 by providing a tangible representation of the quantities involved. Other options either misrepresent the mathematical operation needed or complicate the understanding of how to combine whole numbers with fractions, ultimately failing to convey the correct concept.