Math Unit – Place Value is a homeschool math curriculum for ages 9–11 that reviews and extends place-value understanding from whole numbers through the millions place to decimals through the thousandths place. Students read, write, compare, order, and represent numbers in multiple forms while examining how digit values change across the base-10 system. Activities such as “Big Numbers in Different Forms,” “Beat My Number!,” “Decimal Sort,” and “One-Mile Run” combine number sense with comparison, rounding, expanded notation, and decimal reasoning.

At a Glance

Age Range: Ages 9–11 (usually 5th grade)
Estimated Time Commitment: 16 lessons, approximately 45 minutes each
Prerequisites: Ability to read, write, and compare whole numbers; understand place value and decimals through hundredths
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

• Place-Value Reasoning: Students identify digit values, read large numbers, and represent numbers in number form, word form, expanded form, and expanded notation. In “Digit Values,” they examine the rule that a digit is worth 10 times as much as the same digit one place to its right and one-tenth as much as it is one place to its left.
• Number Comparison and Problem-Solving: Students use place value to compare, order, and construct large numbers. In “Beat My Number!,” they place drawn digit cards into seven-digit numbers and compare their results, while “Mystery Numbers” asks them to use place-value clues to identify whole and decimal values.
• Decimal and Powers-of-10 Reasoning: Students extend place value through thousandths using decimal grids and place-value charts, then represent decimals in fraction and decimal expanded forms. “Powers of 10” connects these relationships to multiplication and division, while “One-Mile Run” combines decimal comparison, ordering, rounding, and expanded forms.
• Real-World Number Application: Students read On Beyond a Million by David M. Schwartz and create a “Did You Know?” fact sheet using numbers greater than one million. In the final project, they collect 12 real-world numbers, show each in at least three forms, create trading cards, and order them from smallest to greatest.
• Multiple Representations and Interactive Practice: Interactive Notebook activities reinforce connections among number forms. Students create a “Number Forms” foldable, complete a “Decimal Sort,” and use laminated place-value charts to compare decimals through thousandths.

Learning Outcomes

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

• Read and write whole numbers through the millions place in multiple forms.
• Identify the value of digits and explain relationships between adjacent places.
• Compare and order large whole numbers and decimals.
• Represent decimals through thousandths using standard, word, fraction, and expanded forms.
• Apply powers-of-10 relationships when multiplying and dividing whole numbers and decimals.
• Round whole numbers and decimal values.
• Use place-value clues to construct and identify numbers.
• Apply place-value concepts to real-world numbers and data.

Math Unit – Place Value connects whole-number and decimal place value through the consistent structure of the base-10 system. Through games, visual models, Interactive Notebook activities, large-number research, and a real-world trading-card project, students use place value to represent, compare, construct, and interpret numbers in several forms.

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.