Question

1. owen spent $1.24 on a pen and $0.37 on an eraser at the school store.

a. (2pts) what is wrong with the model to find the sum of the pen and eraser?
□ = 1 □ = 1/10 □ = 1/100
=

b. (1pt) circle true or false
when modeling adding two decimals, model both numbers.

Explanation:

Part A

Step1: Analyze the value of each shape

The square represents \(1\), the rectangle (vertical bar) represents \(\frac{1}{10}=0.1\), and the small square represents \(\frac{1}{100} = 0.01\).
The first number \(1.24\) should be \(1\) square (for the unit), \(2\) rectangles (for \(0.2\)) and \(4\) small - squares (for \(0.04\)). The second number \(0.37\) should be \(0\) squares, \(3\) rectangles and \(7\) small - squares.

Step2: Check the addition process

When adding decimals using the model, we need to add the like - place values (units with units, tenths with tenths, hundredths with hundredths). In the given model, the tenths (rectangles) are not grouped and added correctly. Also, when the sum of the hundredths (small - squares) is \(4 + 7=11\) small - squares (\(0.11\)), we should convert \(10\) of the hundredths (\(0.10\)) into \(1\) tenth (\(0.1\)).

Part B

Step1: Recall the decimal addition model concept

When modeling the addition of two decimals (e.g., using base - ten blocks), we need to represent each decimal (both numbers) using the appropriate place - value blocks (units, tenths, hundredths etc.) and then combine the like - place value blocks.

Answer:

Part A

The error in the model is that the tenths (rectangles) are not grouped and added correctly and there is no conversion of \(10\) hundredths into \(1\) tenth when the sum of the hundredths is \(11\) (since \(4 + 7 = 11\) hundredths).

Part B

TRUE. When modeling adding two decimals, we need to model BOTH numbers so that we can combine the like - place value components (units with units, tenths with tenths, hundredths with hundredths) to find the sum.