# Middle School Program Samples

The curriculum samples shown here represent critical topics we address at each grade level. An asterisk (*) indicates program elements covered at Mathnasium that are not typically covered in most school programs.

### 6^{th} Grade

**Percent**

- Find 0, 10, 25, 33
^{1}/_{3}, 50, 66^{2}/_{3}, 75, 100, 200, and 250 percent of selected numbers. - Find "7% of 300" for multiples and sub–multiples of 100 mentally.

**Properties of Numbers**

- Explain how the identity for multiplication ["Every number times one (1) equals itself."] is used in renaming fractions.
- Explain how the identity for division ["Every number divided by one (1) equals itself."] is used in reducing fractions.
- Explain why division by zero (0) is not allowed.

**Fractional Parts**

- Knowing that "a quarter of" and "one-fourth of" mean the same thing
- Find half and a quarter of all whole numbers up to 100.
- Find three–quarters, one–third, and two–thirds of selected whole numbers and fractions.
- Count by
^{1}/_{2}s,^{1}/_{4}s,^{3}/_{4}s,^{1}/_{3}s,^{2}/_{3}s, 11/2s, 21/2s. - Count by 0.1s.
- "Half of what number is …?" for whole numbers and appropriate fractions
- "A quarter of what number is …?" for whole numbers and appropriate fractions
- Find "
^{2}/_{3}of 12" for appropriate fractions and whole numbers.

### 7^{th} and 8^{th} Grades

**Fractional Parts**

- Find the part when the fractional part and whole are given.
- "
^{2}/_{3}of 24 equals what number?"

- "
- Find the whole when the fractional part and part are given.
- "
^{3}/_{4}of what number equals 9?"

- "
- Find the fractional part when the whole and part are given.
- "8 is what part of 12?"

**Proportional Thinking**

- "The distance around the Earth is about 24,000 miles. At 3 inches for every 500 miles, about how many inches would it take to represent the distance around the Earth?"

**Rational Numbers**

- The meaning of rational numbers
- Comparing and ordering rational numbers
- Locating rational numbers on the number line
- Computation (addition, subtraction, multiplication, division)
- Negative exponents
- Word problems

**The Language of Algebra**

- Symbols
- Variables
- Terms and expressions
- Mathematical sentences
- Open sentences
- Equations and inequalities