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

The Mathnasium curriculum takes into account The Standards of the National Council of Teachers of Mathematics (1989), The California Mathematics Content Standards (1997), as well as the 30 years of teaching experience of its creator, Larry Martinek.


Place Value

a. Count by 10s, 100s, and 1,000s.
b. Say, “23 ones is the same as 2 tens and 3 ones,” for all wholes numbers to 1,000.
c. Identify ones, tens, hundreds, and thousands place.
d. Read and write wholes numbers up to 1,000 in Standard Form.
e. Rounding–off: Answer: “Is 271 closer to 200 or to 300?” for appropriate numbers.
f. Answer: “How many 10s are there in 120?”

Proportional Thinking

*a. Answer: “If two pieces of candy cost five cents, how much will six pieces of candy cost?”
*b. Answer: “If two pieces of candy cost five cents, how many pieces can you buy for a quarter?”

Algorithm for Subtraction of Whole Numbers

a. One–digit number minus one–digit number, column and vertical format.
b. Up to three–digit number minus three–digit number, with and without “borrowing” (“regrouping,” “trading”), column format.


a. Count by 2, 3, 4, 5, 10, 11, 15, 20, 25, and 50 (first 13 multiples of each number).
b. Count by 6, 7, 8, 9, 12 (first 13 multiples of each number).
*c. 15, 20, 25, and 50 (first 13 multiples of each number).
*d. Count by 1/2s, 1/4s, 1/3s, 11/2s, 21/2s.
*e. Answer: “How many 20s/25s/50s are there in 200?”
*f. How many 11/2s are there in 6? How many 21/2s are there in 71/2?” for appropriate numbers.

Subtraction of Whole Numbers Facts

a. Single–digit minus single–digit, positive answer.
b. Double–digit minus single–digit, difference equal to or greater than 10.
c. Double–digit minus single–digit, difference less than 10.
d. Answer: “15 minus what number is 9?” for numbers up to 20.
e. Explain the concept and use of “Fact Families” in subtraction.
f. Subtract 10 from any number up to 1,000.
*g. A multiple of 10 minus a double–digit number (“30 – 14, ” “70 – 26”) mentally.
*h. Single–digit minus single–digit, negative answer.

Fraction Concepts

*a. Tell whether a given proper fraction is greater than, less than, or equal to 1/2.
*b. Tell whether a given proper or improper fraction is greater than, less than, or equal to one whole (1).
c. Explain why 1/2 and 2/4 are the same amount, and draw pictures demonstrating knowledge of Equivalent Fractions in general.
d. Draw and interpret pictures of given proper and improper fractions and mixed numbers.


a. Round–off any whole number to any place up to millions.
*b. Answer: “Is 15/8 closer to 1 or to 2?” for appropriate numbers.
*c. Answer: “Is 2.07 closer to 2 or to 3?” for appropriate numbers.

Find the missing numbers…(Patterns)

a. 1, 2, 4, 7, 11, ___, ___, ___
*b. 1, 2, 4, 8, 16, ___, ___, ___
*c. 0, 1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___

Problem Solving

*a. State: “The whole is equal to the sum of its parts,” and, “Any part equals the whole minus all of the other parts.”
b. Solve two and three step word problems using two or more operations.
c. Use various techniques in Problem Solving:

1. break–down the problem into simpler parts,
2. apply the “easier number” method,
3. draw a picture,
4. make a table,
5. mental math.

d. Check answer for reasonableness.

Proportional Thinking

a. Answer: “On a certain map, 3 inches represents 500 miles. How many miles does 18 inches represent ?”
b. Answer: “On a certain map, 3 inches represents 500 miles. How one foot represent ?”
c. Answer: “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?”


a. Arrange a group of whole numbers from 0 to 1,000 in order.
b. Arrange a group of fractions containing 0, 1, 1/2, 1/4, 3/4, 5/8, 3/8, 9/10.
c. Arrange a group of fractions containing 0.3, 1, 0, 0.09, 1.2, 0.67.

Common Fraction Concepts

a. Find Least Common Multiple (LCM).
b. Find Greatest Common Factor (GCF).
c. Reduce fractions to lowest terms.
d. Rewrite improper fractions as mixed numbers.
e. Rewrite mixed numbers as improper fractions.


a) Find 0, 10, 25, 331/3, 50, 662/3, 75, 100, 200, and 250 percent of selected numbers.
*b) Find “7% of 300” for multiples and sub–multiples of 100 mentally.

Properties of Numbers

a. Explain how the Identity for Multiplication [“Every number times one (1) equals itself.”] is used in renaming fractions.
b. Explain how the Identity for Divison [“Every number divided one (1) equals itself.”] is used in reducing fractions.
*c. Explain why “division by zero (0)” is not allowed.

Fractional Parts

a. Knows that “a quarter of” and “a one–fourth of” mean the same thing.
b. Find half and quarter of all whole numbers up to 100.
c. Find three–quarters, one–third, and two–thirds of selected whole numbers and fractions.
*d. Count by 1/2s, 1/4s, 3/4s, 1/3s, 2/3s, 11/2s, 21/2s.
*e. Count by 0.1s.
*f. Answer “Half of what number is…?” for whole numbers and half–numbers from 0 to 100.
*g. Answer “A quarter of what number is…?” for whole numbers and quarter–numbers from 0 to 100.
h. Find “2/3 of 12” for appropriate fractions and whole numbers.

7th and 8th GRADES
Fractional Parts

a. Find the part when the fractional part and whole are given
(2/3 of 24 equals what number?)
b. Find the whole when the fractional part and part are given
(3/4 of what number 9?)
c. Find the fractional part when the whole and part are given
(8 is what part 12?)

Rational Numbers

a. The meaning of rational numbers
b. Comparing and ordering rational numbers
c. Locating rational numbers on the number line
d. Computation (addition, subtraction, multiplication, division
e. Negative exponents
f. Word problems

The Language of Algebra

a. Symbols
b. Variables
c. Terms and expressions
d. Mathematical sentences

• open sentences
• equations
• inequalities


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