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. Part A Which student correctly models the problem 1.25 + 0.4. Type your answer in the box. Part B What is the correct answer for 1.25 + 0.4? Part C Explain the errors made by the incorrect student. Refer back to the models and use equations to support your explanation.

Answer 1

To answer your questions, let’s analyze the addition of the decimal numbers 1.25 and 0.4, and identify the errors made by the students, Sophia and Aiden.

Part A: Correct Modeling of 1.25 + 0.4

To decide which student correctly models the problem, we need to look at how both students represent the numbers on their grids.

1. Sophia’s Work: She should show:

   • A representation of 1.25, which is 1 whole (10 tenths), 2 tenths, and 5 hundredths.
   • A representation of 0.4, which is 0 whole and 4 tenths (or 4 tenths in hundredths: 40 hundredths).

2. Aiden’s Work: If he models it as:

   • 1 whole (10 tenths) and 2 tenths for 1.25, plus 0.4 as 4 tenths, he’ll be combining tenths correctly.
   • He could also have misrepresented the decimal places, which would lead to errors.

To determine which student correctly models the problem, you would compare how they placed and added these values on their grids. If one student constructs the grids correctly reflecting the total counts of tenths and hundredths, that student would be correct.

Part B: Correct Answer for 1.25 + 0.4

To calculate 1.25 + 0.4 as a decimal:

• Convert 0.4 to hundredths: 0.4 = 0.40.

Now, add them:

• 1.25
• • 0.40

• ---

• 1.65

Thus, the correct answer to 1.25 + 0.4 is 1.65.

Part C: Explanation of Errors Made by the Incorrect Student

Let's assume Sophia is the incorrect student. Here's how to discuss her errors:

1. Addition of Decimal Values: If Sophia did not align the decimal points properly when stacking her numbers on the grid, this could lead to an inaccurate total. For example, if she added 1.25 (1 whole, 2 tenths, 5 hundredths) and 0.4 (4 tenths) without aligning them by decimal places (not adding 0.40 correctly), she could miscount the tenths and hundredths.

2. Counting Errors: If Sophia miscounted the grids (e.g., incorrectly representing 0.4 as being equal to a number of hundredths rather than tenths), she could result in a total that is lower than 1.65.

3. Mathematical Principles: To illustrate mathematically:

   • Properly combined, the tenths should be calculated as 2 tenths + 4 tenths = 6 tenths, and the hundredths remain as 5 (from 1.25).
   • Hence, 1 (1 whole), 6 (combined tenths), and 5 (remaining hundredths) yield a new total of 1.65.

In conclusion, we assume that aligning decimals and properly counting values on the grids is crucial for accuracy in addition. Misalignment or counting errors can lead to incorrect answers.