Maysa made an error in her work on the following problem

Question

3.5 - 2.46 = 1.16
Describe Maysa's error. Explain how you would use a model or place - value concepts to help Maysa build understanding. Give the correct answer in your explanation.

Answer 1

Maysa's calculation of \( 3.5 - 2.46 = 1.16 \) is incorrect. To describe her error, let's break down the subtraction step by step.

When we align the numbers vertically for easier subtraction, we have:

  3.50
- 2.46
-------

1. Starting from the rightmost digits, we first subtract \( 6 \) from \( 0 \). Since \( 0 \) is less than \( 6 \), we cannot subtract directly, so we need to borrow from the next column, which is \( 5 \) in the tenths place. This \( 5 \) becomes \( 4 \), and \( 0 \) becomes \( 10 \).
2. Now we perform the subtraction in the hundredths place: \( 10 - 6 = 4 \).
3. Moving to the tenths place, we subtract \( 4 \) from \( 4 \): \( 4 - 4 = 0 \).
4. Finally, in the ones place, we have \( 3 - 2 = 1 \).

Putting it all together, the answer is:

  3.50
- 2.46
-------
  1.04

Thus, the correct answer to \( 3.5 - 2.46 \) is \( 1.04 \).

Helping Maysa Build Understanding

To help Maysa understand her error, I would use a model such as base-ten blocks or a place-value chart. Here's how:

1. Place-Value Chart: Create a place-value chart showing the numbers clearly in their respective columns (hundreds, tens, units, tenths, hundredths). Then, explicitly display how borrowing works:

   • Show that \( 3.50 \) has \( 0 \) in the hundredths and needs to borrow from the tenths.
   • Demonstrate how borrowing converts \( 5 \) into \( 4 \) and adds \( 10 \) to \( 0 \).

2. Base-Ten Blocks: Use physical or drawn base-ten blocks to represent the numbers. For instance:

   • Represent \( 3.50 \) with 3 whole blocks and 5 tenths blocks.
   • Show \( 2.46 \) with 2 whole blocks, 4 tenths, and 6 hundredths.
   • Use the blocks to visually subtract \( 2 \) whole blocks, \( 4 \) tenths, and \( 6 \) hundredths from \( 3.50 \).

3. Practice Problems: Together with Maysa, practice similar problems, slowly ensuring she understands the process of borrowing and how it impacts the values in each column, reinforcing the place-value concept.

By emphasizing the importance of each digit's position and how borrowing affects the numbers, Maysa will gain a clearer understanding of the subtraction process and avoid similar errors in the future.