Elementary 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.

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

Counting

• 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, 11/2s, 21/2s.
• "How many 20s/25s/50s are there in 200?"
• "How many 11/2s are there in 6? How many 21/2s are there in 71/2?" 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 15/8 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.

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

Ordering

• 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.