Question

part a
which expression best describes the model below?
image of green square, rod, and unit models
\\( 2 \times 244 \\)
\\( 4 \times (100 + 3) \\)
\\( 3 \times (100 + 4) \\)
\\( 3 \times 144 \\)

part b
what are the partial products shown in the array in part a?
\\( 400 + 80 + 8 = 488 \\)
\\( 300 + 120 + 12 = 432 \\)
\\( 400 + 12 = 412 \\)
\\( 800 + 160 + 16 = 976 \\)

Explanation:

Part A

Step1: Analyze the model

Each row has 1 large square (100), 4 columns of 10 (4×10 = 40), and 4 single units. So each row is \(100 + 40+ 4=144\). There are 3 rows.

Step2: Check the options

• \(2\times244\): Incorrect, as there are 3 rows, not 2.
• \(4\times(100 + 3)\): Incorrect, the non - 100 part is 40 + 4, not 3.
• \(3\times(100 + 4)\): Incorrect, the non - 100 part is 40+4, not 4.
• \(3\times144\): Correct, since each row is 144 and there are 3 rows.

Step1: Recall the model from Part A

We have 3 groups of 144. Using the distributive property, \(3\times144=3\times(100 + 40+4)\).

Step2: Calculate partial products

• Partial product for 100: \(3\times100 = 300\)
• Partial product for 40: \(3\times40=120\)
• Partial product for 4: \(3\times4 = 12\)
• Sum: \(300+120 + 12=432\)

Answer:

D. \(3\times144\) (assuming the options are labeled A - D with D being \(3\times144\))

Part B