# 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.

### Grade 2

**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

### Grade 3

**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}/_{2}s, 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?"

### Grade 4

**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.

- Check answer for reasonableness.

### Grade 5

- 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.