Question

1. first, sort the cards that show ways the model can be represented.

equivalent not equivalent
200 × 6 206 × 0.01
206 tenths 206 hundredths

Explanation:

To solve this, we analyze each expression/card by relating to the model (two full blue grids and a grid with 6 blue hundredths, representing \(2 + 0.06=2.06\) or \(206\times0.01\) since each grid is 10x10=100 hundredths, two grids are 200 hundredths and 6 hundredths is 206 hundredths).

Step 1: Analyze \(200\times6\)

\(200\times6 = 1200\), which is not equal to \(2.06\). So this is Not Equivalent.

Step 2: Analyze \(206\times0.01\)

\(206\times0.01=\frac{206}{100}=2.06\), which matches the model (2 full grids + 6 hundredths). So this is Equivalent.

Step 3: Analyze "206 tenths"

206 tenths \(=206\times\frac{1}{10}=20.6\), which is not equal to \(2.06\). So this is Not Equivalent.

Step 4: Analyze "206 hundredths"

206 hundredths \(=206\times\frac{1}{100}=2.06\), which matches the model. So this is Equivalent.

Sorting:

• Equivalent: \(206\times0.01\), 206 hundredths
• Not Equivalent: \(200\times6\), 206 tenths

Answer:

• Equivalent: \(206 \times 0.01\), 206 hundredths
• Not Equivalent: \(200 \times 6\), 206 tenths