Math Unit – Four Operations is a homeschool math curriculum for ages 9–11 that develops addition, subtraction, multiplication, and division with multi-digit whole numbers and decimals. Students review standard algorithms, factors and prime factorization, long division, and decimal operations before moving into numerical expressions, exponents, and the order of operations. Activities such as “Cross Number Puzzle,” “Hiking at Green Park,” “Money Matters,” and the “PEMDAS Dice Game” combine computation with problem-solving and interactive practice.

At a Glance

Age Range: Ages 9–11 (usually 5th grade)
Estimated Time Commitment: 21 lessons, approximately 45 minutes each
Prerequisites: Ability to calculate with whole numbers, use long division, understand place value, prime numbers, and powers of ten
Student Independence: Designed for students to work independently, with parent support as needed
Includes: Student-directed lessons, parent guidance, student activity pages, answer keys, and linked online practice activities
Required items: Math Materials Kit, and any required math literature sold separately

This unit is part of the age 9-11 full year math program, which covers all fifth-grade math standards.

Key Features

• Multi-Digit Operations: Students add and subtract numbers through seven digits, extend multiplication to larger factors, and use the standard long-division process with two-digit divisors. “Long Division Steps” gives students an Interactive Notebook reference for the sequence Divide, Multiply, Subtract, Bring down, Repeat.
• Decimal Operations: Students extend all four operations to decimals using place-value reasoning, models, algorithms, and reference pages. “Hiking at Green Park” applies decimal addition to trail distances, while later lessons use base-10 blocks and structured steps to develop decimal multiplication and division.
• Real-World Problem-Solving: Students choose and combine operations in situations involving money, measurements, rates, and purchases. In “Money Matters,” they compare weekly earnings, calculate donut costs, and determine which tomato-sauce jar has the best price per ounce.
• Expression and PEMDAS Reasoning: Students translate written situations into expressions, use grouping symbols and exponents, and evaluate multi-step expressions with PEMDAS. Practice includes “Working With Exponents,” “Unlocking the Safe,” and the “PEMDAS Dice Game,” where students use logic and trial and error to reach target values.
• Project-Based Explanation: For the final project, students choose three skills from decimal operations and order of operations, create real-world examples when appropriate, write solution steps and spoken scripts, and film or present three 1–2 minute lessons.

Learning Outcomes

By the end of this unit, students will be able to:

• Add and subtract multi-digit whole numbers using standard algorithms.
• Multiply multi-digit whole numbers using partial products and the standard algorithm.
• Divide whole numbers using long division with two-digit divisors.
• Add, subtract, multiply, and divide decimals.
• Apply the four operations to real-world problems involving money, measurements, rates, and quantities.
• Identify factors and prime factors and express repeated prime factors with exponents.
• Translate written mathematical situations into numerical expressions.
• Evaluate expressions using exponents, grouping symbols, and the order of operations.

Math Unit – Four Operations connects computational procedures with place-value reasoning, visual models, applied problems, and mathematical explanation. Through whole-number and decimal operations, Interactive Notebook references, PEMDAS practice, and a teaching project, students use arithmetic skills in both written and real-world contexts.

This item includes free online access to Beyond the Page Online for 18 months. This includes Learning Gates, Portfolio and any curriculum or student activity pages that you have purchased.