Question
Maysa made an error in her work on the following problem.
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.
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.
Answers
GPT-4o mini
To identify Maysa's error in the calculation \( 3.5 - 2.46 = 1.16 \), we start by performing the subtraction correctly.
First, let's rewrite the numbers with the same number of decimal places for clarity:
- \( 3.5 \) can be expressed as \( 3.50 \)
- \( 2.46 \) already has two decimal places.
Now we can perform the subtraction step by step:
\[
\begin{array}{r}
3.50 \\
- 2.46 \\
\hline
\end{array}
\]
Starting with the hundredths place, we have \( 0 - 6 \). Since we can't subtract 6 from 0, we need to borrow. We borrow 1 from the tenths place (3 becomes 2), making the hundredths place 10:
\[
10 - 6 = 4
\]
Now moving to the tenths place, we now have \( 2 - 4 \). Again, since we can't subtract 4 from 2, we need to borrow from the units place (3 becomes 2):
\[
12 - 4 = 8
\]
Now, in the units place, we have \( 2 - 2 = 0 \).
Putting it all together, we have:
\[
\begin{array}{r}
3.50 \\
- 2.46 \\
\hline
1.04 \\
\end{array}
\]
Thus, the correct answer is \( 1.04 \).
### Maysa's Error:
Maysa's error likely occurred in the borrowing process during subtraction or possibly an oversight in handling decimal places. It appears she miscalculated, leading her to arrive at \( 1.16 \) instead of the correct \( 1.04 \).
### Using a Model or Place-Value Concepts:
To help Maysa understand where she went wrong, we can use place-value blocks or a visual model:
1. **Place-Value Chart**: Draw a place-value chart that clearly represents the units, tenths, and hundredths. Show her what \( 3.50 \) and \( 2.46 \) look like in terms of these values:
- \( 3.50 = 3 \) units and \( 5 \) tenths and \( 0 \) hundredths
- \( 2.46 = 2 \) units and \( 4 \) tenths and \( 6 \) hundredths
2. **Visual Subtraction**: Use blocks to represent each digit, showing Maysa how you can’t subtract from a smaller number (0 from 6, for example) without borrowing appropriately.
3. **Step-by-Step Guide**: Walk Maysa through the borrowing process with clear steps, emphasizing why borrowing is necessary and how it affects each place value.
By using these methods, Maysa can develop a stronger understanding of decimal subtraction and the importance of careful borrowing, ultimately leading her to the correct answer of \( 1.04 \).
First, let's rewrite the numbers with the same number of decimal places for clarity:
- \( 3.5 \) can be expressed as \( 3.50 \)
- \( 2.46 \) already has two decimal places.
Now we can perform the subtraction step by step:
\[
\begin{array}{r}
3.50 \\
- 2.46 \\
\hline
\end{array}
\]
Starting with the hundredths place, we have \( 0 - 6 \). Since we can't subtract 6 from 0, we need to borrow. We borrow 1 from the tenths place (3 becomes 2), making the hundredths place 10:
\[
10 - 6 = 4
\]
Now moving to the tenths place, we now have \( 2 - 4 \). Again, since we can't subtract 4 from 2, we need to borrow from the units place (3 becomes 2):
\[
12 - 4 = 8
\]
Now, in the units place, we have \( 2 - 2 = 0 \).
Putting it all together, we have:
\[
\begin{array}{r}
3.50 \\
- 2.46 \\
\hline
1.04 \\
\end{array}
\]
Thus, the correct answer is \( 1.04 \).
### Maysa's Error:
Maysa's error likely occurred in the borrowing process during subtraction or possibly an oversight in handling decimal places. It appears she miscalculated, leading her to arrive at \( 1.16 \) instead of the correct \( 1.04 \).
### Using a Model or Place-Value Concepts:
To help Maysa understand where she went wrong, we can use place-value blocks or a visual model:
1. **Place-Value Chart**: Draw a place-value chart that clearly represents the units, tenths, and hundredths. Show her what \( 3.50 \) and \( 2.46 \) look like in terms of these values:
- \( 3.50 = 3 \) units and \( 5 \) tenths and \( 0 \) hundredths
- \( 2.46 = 2 \) units and \( 4 \) tenths and \( 6 \) hundredths
2. **Visual Subtraction**: Use blocks to represent each digit, showing Maysa how you can’t subtract from a smaller number (0 from 6, for example) without borrowing appropriately.
3. **Step-by-Step Guide**: Walk Maysa through the borrowing process with clear steps, emphasizing why borrowing is necessary and how it affects each place value.
By using these methods, Maysa can develop a stronger understanding of decimal subtraction and the importance of careful borrowing, ultimately leading her to the correct answer of \( 1.04 \).