Miles incorrectly gave the product of 7 × 2.6 as 14.42. Use a place value chart or an area model to help Miles understand his mistake.

We prepare two columns of ones and tenths separated by dots.
In the ones column, place two dots on each row until it reaches 7 rows. This means 7 times 2 equal to 14 dots.
In the tenth column, place six dots on each row until it reaches 7 rows. This means 7 times 0.6.
In the tenth column, every time it reaches 10 dots, it becomes 1 ones which are added to the dots in the ones column.
There are 4 additional dots in the ones column as a result of each 10 dots in the tenth column. We add 14 dots with 4 dots and the result is 18 ones.
The remaining dots in the tenth column will be added with all the dots in the ones column. There are two dots left so that it becomes 2 tenths.

[tex]\boxed{ \ 7 \times 2.6 = 18 \ ones \ plus \ 2 \ tenths = \boxed{ \ 18.2 \ } \ }[/tex]

Area Model

7 x 2.6 is the same as 7 multiplied by 2 ones and 6 tenths.

Let 2 ones and 6 tenths as the length and 7 as the width of a rectangle.
7 x 2 ones = 14 ones or 14.
7 x 6 tenths = 42 tenths or 4.2.
The area of the rectangle is 14 ones plus 42 tenths, or 14 plus 4.2.

[tex]\boxed{ \ 7 \times 2.6 = 14 + 4.2 = \boxed{ \ 18.2 \ } \ }[/tex]

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