Use the hundredth grids below to answer the questions. The first two hundredth grids show Sophia's work. The second two hundredth grids show Aiden's work.

Question

This image shows Sophia's work. One whole 10-by-10 grid and 2 columns and 5 squares on a second grid are shaded blue. On the second grid, the remaining 5 squares in the third column, 3 more columns, and 5 more squares are shaded brown.

This image shows Aiden's work. One whole 10-by-10 grid and 2 columns and 5 squares on a second grid are shaded blue. On the second grid, 4 squares in the third column are shaded brown.

(1 point)
Part A

Which student correctly models the problem 1.25 + 0.4. Type your answer in the box.

Question 2
(1 point)
Part B

Answer 1

To determine which student correctly models the problem 1.25 + 0.4 using the hundredths grid, we need to analyze the shading in both Sophia's and Aiden's works.

1. Understanding the Problem

   • 1.25 can be represented as 1 whole (10x10 grid) and an additional 25 hundredths, which means we fill 25 squares on the second grid.
   • 0.4 can be represented as 40 hundredths, which means we need to fill an additional 40 squares.

2. Add the Values Together

   • When combining 1.25 and 0.4:
     • 1.25 = 100 + 25 = 125 hundredths
     • 0.4 = 40 hundredths
     • Total = 125 + 40 = 165 hundredths

3. Comparing Sophia's Work

   • Sophia shaded 1 whole grid (100 squares) and 2 columns plus 5 squares, which gives us:
     • 100 + (2 columns * 10 squares/column) + 5 squares = 100 + 20 + 5 = 125 squares.
   • On the second grid, she shaded 5 squares in the third column, 3 more columns (each with 10 squares), and 5 more squares, making:
     • Shaded squares from the second grid = (5 columns * 10) + 5 = 30 + 5 = 35 squares.
   • Total shaded by Sophia = 125 + 35 = 160 squares (or hundredths).

4. Comparing Aiden's Work

   • Aiden shaded 1 whole grid (100 squares) and similar to Sophia, an additional 25 squares:
     • 100 + (2 columns * 10 squares/column) + 5 squares = 125 squares.
   • On the second grid, he shaded 4 squares in the third column, totaling:
     • Total from second grid = 4 squares.
   • Thus, Total shaded by Aiden = 125 + 4 = 129 squares (or hundredths).

5. Conclusion

   • Neither modeled the problem correctly, but Sophia was closer with 160 squares because it accounted for 1.25 + 0.4 = 165.
   • Based on shading, Sophia effectively modeled the problem better than Aiden, but both are inaccurate since total should be 165.

So, my answer for Part A is Sophia as she shaded more of the correct total than Aiden.

If you have Part B or any more questions, please provide more context!