In elementary school, children must master their number facts and develop numerical fluency. They begin with computation and problem solving using whole numbers, and then move on to computation and problem solving with rational numbers (fractions, decimals, percents, negative numbers). This foundation is essential for pre-algebra and algebra, which they will encounter in middle school.




Students engage, one on one, in a unique combination of mental, verbal, visual, tactile, and written exercises (click here to learn more) that cover and surpass state math standards as well as the recommendations of the National Council of Teachers of Mathematics and the new Common Core State Standards. Basic math skills are blended with a program specifically designed to help students build number sense by showing them how numbers work.

Each student is evaluated with a written and verbal assessment unique to Mathnasium. Based on their assessment results, we assemble a tailored program just for them designed to close any educational gaps that they may have and jump ahead when they are ready for advanced math challenges. Mental math is emphasized.

We also help students with their regular school homework as part of the session, and prepare them for school tests and standardized tests such as the ISEE and middle school entrance exams.



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.




Place Value

  • Count by 10s, 100s, and 1,000s.
  • Say, "23 ones is the same as 2 tens and 3 ones," for all whole numbers to 1,000.
  • Identify ones, tens, hundreds, and thousands place.
  • Read and write whole numbers up to 1,000 in standard form.
  • Rounding off: "Is 271 closer to 200 or to 300?" for appropriate numbers.
  • "How many 10s are there in 120?"

Proportional Thinking

  • "If two pieces of candy cost five cents, how much will six pieces of candy cost?"
  • "Recyclers pay 5¢ for every 2 cans.
  • How many cans are needed to get 25¢?
  • How much are 8 cans worth?"

Algorithm for Subtraction of Whole Numbers

  • One–digit number minus one–digit number, column and vertical format
  • Up to three–digit number minus three–digit number, with and without "borrowing" ("regrouping," "trading"), column format





  • Count by 2, 3, 4, 5, 10, 11, 15, 20, 25, and 50 (first 13 multiples of each number starting at 0).
  • Count by 6, 7, 8, 9, 12 (first 13 multiples of each number starting at 0).
  • Count by 15, 20, 25, and 50 (first 13 multiples of each number).
  • Count by 1/2s, 1/4s, 1/3s, 1 1/2s, 2 1/2s.
  • "How many 20s/25s/50s are there in 200?"
  • "How many 1 1/2s are there in 6? How many 2 1/2s are there in 7 1/2?" for appropriate numbers

Subtraction Facts for Whole Numbers

  • Single–digit minus single–digit, positive answer
  • Double–digit minus single–digit, difference equal to or greater than 10
  • Double–digit minus single–digit, difference less than 10
  • "15 minus what number is 9?" for numbers up to 20
  • Explain the concept and use of fact families in subtraction.
  • Subtract 10 from any number up to 1,000.
  • A multiple of 10 minus a double–digit number (30 – 14; 70 – 26) mentally
  • Single–digit minus single–digit, negative answer

Fraction Concepts

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

Proportional Thinking

  • "If three candies cost 25¢, how many candies can you buy for $1.00?"
  • "If three candies cost 25¢, how much does it cost to buy a total of 18 candies?"




Rounding off

  • Round off any whole number to any place up to millions.
  • "Is 1 5/8 closer to 1 or to 2?" for appropriate numbers
  • "Is 2.07 closer to 2 or to 3?" for appropriate numbers

Find the missing numbers... (seeing patterns)

  • 1, 2, 4, 7, 11, ___, ___, ___
  • * 1, 2, 4, 8, 16, ___, ___, ___
  •  0, 1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___

Problem Solving

  • State and understand that:
  • "The whole is equal to the sum of its parts."
  • "Any part equals the whole minus the other parts."
  • Solve two- and three- step word problems using two or more operations.
  • Use various techniques in problem solving:
  • Break down the problem into simpler parts.
  • Apply the "easier number" method.
  • Draw a picture.
  • Use mental math.
  • Check answer for reasonableness.




Proportional Thinking

  • "On a certain map, 3 inches represents 500 miles. How many miles does 18 inches represent?"


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

Common Fraction Concepts

  • Find least common multiple (LCM).
  • Find greatest common factor (GCF).
  • Reduce fractions to lowest terms.
  • Rewrite improper fractions as mixed numbers.
  • Rewrite mixed numbers as improper fractions.