Difficulty: Medium

Average Score: 50%

Which of the following is the most appropriate way to help students understand that 12 + 2/3 is equal to 18?

Rationale

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

This method effectively demonstrates the concept of addition with fractions by visually representing how 12 can be divided into segments of two-thirds, making the mathematical relationship clear.

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

While this choice involves fractions and can provide a hands-on activity, it does not directly illustrate how 12 plus two-thirds equals 18. The folding and cutting process may confuse the concept of addition, as it focuses more on division than on combining quantities.

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

This choice clearly shows how many two-thirds fit into 12, effectively demonstrating that 12 + 2/3 results in 18. It allows students to visualize the addition of whole numbers and fractions in a tangible way, reinforcing their understanding of the operation.

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

This option introduces unnecessary complexity by involving division and multiplication rules rather than focusing on addition. The 'invert and multiply' rule applies to division of fractions and does not help students grasp the straightforward addition of 12 and two-thirds.

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

This method complicates the understanding of the problem by introducing a different unit of measurement (inches) and performing a division that is unrelated to the original question. It detracts from the goal of adding 12 and two-thirds directly.

Conclusion

Visual aids and practical examples greatly enhance comprehension of mathematical concepts. By using 12 cups of sand to represent the addition of 12 and two-thirds, students can gain a clearer understanding of how to combine whole numbers with fractions, leading to a correct total of 18. Other methods either misrepresent the operation or complicate the explanation, hindering effective learning.

Related Questions

View all