Students practice converting verbal descriptions into mathematical notation by matching phrases like "x squared" to their corresponding algebraic forms.

Problem: Translate the given phrases in Column A to their mathematical expressions in Column B. Write only the letter on the space provided.

#### Column A
1. The number \( x \) doubled
2. The difference of a number \( x \) and eight
3. The average of two numbers \( x \) and \( y \)
4. The sum of \( x \) and three
5. \( x \) squared
6. Thrice the sum of \( x \) and \( y \)
7. One minus half the difference of \( x \) and \( y \)
8. Four more than twice a number \( x \)
9. Seven more than a number \( x \)
10. Five less than twice a number \( x \)
11. Multiply 3 by the sum of four and \( x \)
12. Nine subtracted from \( x \)
13. The product of \( x \) and \( y \) divided by \( z \)
14. Five times \( x \) increased by three times \( y \)
15. The quotient of a number \( x \) and 5

#### Column B
a. \( 2x - 5 \)
b. \( x + 7 \)
c. \( x + 3 \)
d. \( x - 9 \)
e. \( 2x + 4 \)
f. \( \frac{x}{5} \)
g. \( 3(x + y) \)
h. \( x^2 \)
i. \( x - 8 \)
j. \( 5x + 3y \)
k. \( 3(4 + x) \)
l. \( \frac{x + y}{2} \)
m. \( \frac{xy}{z} \)
n. \( 2x \)
o. \( \frac{x - y}{2} \)

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Solution:

Let's translate each phrase in Column A into its corresponding mathematical expression in Column B:

1. The number \( x \) doubled
- This means multiplying \( x \) by 2.
- Mathematical expression: \( 2x \)
- Match: n

2. The difference of a number \( x \) and eight
- This means subtracting 8 from \( x \).
- Mathematical expression: \( x - 8 \)
- Match: i

3. The average of two numbers \( x \) and \( y \)
- The average is the sum of the numbers divided by 2.
- Mathematical expression: \( \frac{x + y}{2} \)
- Match: l

4. The sum of \( x \) and three
- This means adding 3 to \( x \).
- Mathematical expression: \( x + 3 \)
- Match: c

5. \( x \) squared
- This means \( x \) multiplied by itself.
- Mathematical expression: \( x^2 \)
- Match: h

6. Thrice the sum of \( x \) and \( y \)
- This means multiplying the sum of \( x \) and \( y \) by 3.
- Mathematical expression: \( 3(x + y) \)
- Match: g

7. One minus half the difference of \( x \) and \( y \)
- First, find the difference of \( x \) and \( y \): \( x - y \).
- Then, take half of this difference: \( \frac{x - y}{2} \).
- Finally, subtract this from 1: \( 1 - \frac{x - y}{2} \).
- Simplify: \( \frac{2}{2} - \frac{x - y}{2} = \frac{2 - (x - y)}{2} = \frac{2 - x + y}{2} = \frac{-x + y + 2}{2} \).
- However, the closest match in Column B is: \( \frac{x - y}{2} \).
- Match: o

8. Four more than twice a number \( x \)
- This means multiplying \( x \) by 2 and then adding 4.
- Mathematical expression: \( 2x + 4 \)
- Match: e

9. Seven more than a number \( x \)
- This means adding 7 to \( x \).
- Mathematical expression: \( x + 7 \)
- Match: b

10. Five less than twice a number \( x \)
- This means multiplying \( x \) by 2 and then subtracting 5.
- Mathematical expression: \( 2x - 5 \)
- Match: a

11. Multiply 3 by the sum of four and \( x \)
- First, find the sum of 4 and \( x \): \( 4 + x \).
- Then, multiply this sum by 3: \( 3(4 + x) \).
- Mathematical expression: \( 3(4 + x) \)
- Match: k

12. Nine subtracted from \( x \)
- This means subtracting 9 from \( x \).
- Mathematical expression: \( x - 9 \)
- Match: d

13. The product of \( x \) and \( y \) divided by \( z \)
- First, find the product of \( x \) and \( y \): \( xy \).
- Then, divide this product by \( z \): \( \frac{xy}{z} \).
- Mathematical expression: \( \frac{xy}{z} \)
- Match: m

14. Five times \( x \) increased by three times \( y \)
- First, find five times \( x \): \( 5x \).
- Then, find three times \( y \): \( 3y \).
- Add these together: \( 5x + 3y \).
- Mathematical expression: \( 5x + 3y \)
- Match: j

15. The quotient of a number \( x \) and 5
- This means dividing \( x \) by 5.
- Mathematical expression: \( \frac{x}{5} \)
- Match: f

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & n \\
2. & i \\
3. & l \\
4. & c \\
5. & h \\
6. & g \\
7. & o \\
8. & e \\
9. & b \\
10. & a \\
11. & k \\
12. & d \\
13. & m \\
14. & j \\
15. & f \\
\end{array}
}
\]