Questions: Problem Solving Performance The students in Ms. Lowell's class wrote a thousandths decimal chart on the board. Some of the numbers got erased. 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.8 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.015 0.021 0.022 0.023 0.024 0.025 0.026 0.027 0.28 0.039 0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.038 0.03 5. Use Patterns and Structure Describe the pattern for moving across a row from left to right. Each row is increasing by 0.001. 6. Communicate and Justify How does the pattern change in the last square of each row? Explain. The decimal in the last square of each row is always one less than the row number. 7. Use Patterns and Structure Describe the pattern for moving down a column.

Problem Solving Performance

The students in Ms. Lowell's class wrote a thousandths decimal chart on the board. Some of the numbers got erased.

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.8
0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.015
0.021 0.022 0.023 0.024 0.025 0.026 0.027 0.28 0.039
0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.038 0.03

5. Use Patterns and Structure Describe the pattern for moving across a row from left to right. Each row is increasing by 0.001.

6. Communicate and Justify How does the pattern change in the last square of each row? Explain. The decimal in the last square of each row is always one less than the row number.

7. Use Patterns and Structure Describe the pattern for moving down a column.

Transcript text: Problem Solving Performance The students in Ms. Lowell's class wrote a thousandths decimal chart on the board. Some of the numbers got erased. \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline 0.001 & 0.002 & 0.003 & 0.004 & 0.005 & 0.006 & 0.007 & 0.008 & 0.8 \\ \hline 0.011 & 0.012 & 0.013 & 0.014 & 0.015 & 0.016 & 0.017 & 0.018 & 0.015 \\ \hline 0.021 & 0.022 & 0.023 & 0.024 & 0.025 & 0.026 & 0.027 & 0.28 & 0.039 \\ \hline 0.031 & 0.032 & 0.033 & 0.034 & 0.035 & 0.036 & 0.037 & 0.038 & 0.03 \\ \hline \end{tabular} 5. Use Patterns and Structure Describe the pattern for moving across a row from left to right. Each row is increasing by $0.001$. 6. Communicate and Justify How does the pattern change in the last square of each row? Explain. The decimal in the last square of each row is always one less than the row number. 7. Use Patterns and Structure Describe the pattern for moving down a column.

Solution

Solution Steps

Solution Approach

Pattern Across Rows: The pattern for moving across a row from left to right is that each number increases by 0.001, except for the last number in each row which seems to be incorrect or follows a different pattern.
Pattern in Last Square: The last square of each row does not follow the same pattern as the rest of the row. It appears to be an anomaly or error in the chart.
Pattern Down Columns: The pattern for moving down a column is not explicitly given, but it can be inferred that the numbers should increase by a consistent value, possibly 0.01, based on the structure of the chart.

Step 1: Analyze the Pattern Across Rows

The pattern across each row is that the numbers increase by $0.001$ from left to right, except for the last number in each row. The differences between consecutive numbers in each row are as follows:

Row 1: $[0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.792]$
Row 2: $[0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, -0.003]$
Row 3: $[0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.253, -0.241]$
Row 4: $[0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, -0.008]$

The last number in each row does not follow the pattern of increasing by $0.001$.

Step 2: Analyze the Pattern Down Columns

The pattern down each column is that the numbers increase by $0.01$ from top to bottom, except for the last two columns. The differences between consecutive numbers in each column are as follows:

Columns 1 to 7: $[0.01, 0.01, 0.01]$
Column 8: $[0.01, 0.262, -0.242]$
Column 9: $[-0.785, 0.024, -0.009]$

The last two columns do not follow the consistent pattern of increasing by $0.01$.