Mathematics · 3rd Grade · Deepening Number Sense: Fractions and Place Value · Weeks 28-36

Reviewing Place Value to 1000

Reinforcing understanding of place value for whole numbers up to 1000, including reading, writing, and comparing numbers.

• Common Core State Standards
• CCSS.Math.Content.3.NBT.A.2

About This Topic

Place value to 1,000 is one of the organizing ideas of third-grade mathematics in the US Common Core framework. By the end of third grade, students are expected to fluently add and subtract within 1,000 using strategies based on place value (CCSS.Math.Content.3.NBT.A.2), which means the conceptual foundation built in this review unit matters enormously. Students who understand that the digit 4 in 847 represents 40 are equipped to reason through computation flexibly rather than relying solely on the standard algorithm.

This topic revisits reading, writing, and comparing three-digit numbers through a conceptual lens. Students practice expanded form, compare numbers using symbols, and build numbers from component values. These tasks prepare them for rounding and multi-digit operations in fourth grade, and they surface persistent gaps that can undermine fluency if left unaddressed.

Active learning makes place value review more than a repeat performance. When students build numbers with base-ten blocks, debate which of two numbers is greater, and explain their reasoning to classmates, they deepen understanding rather than simply refreshing surface-level recall.

Key Questions

1. Explain how the position of a digit determines its value in a three-digit number.
2. Compare two three-digit numbers using place value understanding.
3. Construct a number using given digits and justify its value based on place.

Learning Objectives

• Explain how the position of a digit in a three-digit number determines its value.
• Compare two three-digit numbers using place value concepts and appropriate symbols (<, >, =).
• Construct a three-digit number given its value in hundreds, tens, and ones, and justify the construction.
• Write a three-digit number in expanded form and standard form, and vice versa.
• Identify the value of each digit within a three-digit number.

Before You Start

Understanding Place Value to 100

Why: Students need a foundational understanding of tens and ones before extending their knowledge to hundreds.

Reading and Writing Numbers to 100

Why: Familiarity with reading and writing numbers up to 100 is essential for building the skill with larger numbers.

Key Vocabulary

Place Value	The value of a digit based on its position within a number. For example, in the number 345, the digit 4 is in the tens place, representing 40.
Digit	A single symbol used to write numbers. In the base-ten system, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Hundreds	The place value representing groups of 100. A digit in the hundreds place indicates how many hundreds are in the number.
Tens	The place value representing groups of 10. A digit in the tens place indicates how many tens are in the number.
Ones	The place value representing individual units. A digit in the ones place indicates how many individual units are in the number.
Expanded Form	Writing a number to show the value of each digit. For example, 345 in expanded form is 300 + 40 + 5.

Watch Out for These Misconceptions

Common Misconception

Students read multi-digit numbers by saying each digit separately, for example reading 405 as "four zero five" instead of "four hundred five."

What to Teach Instead

Consistently pair standard form with expanded form and base-ten block models. When students explain numbers in all three representations during partner work, digit-by-digit reading surfaces quickly and gets corrected through peer discussion.

Common Misconception

When comparing numbers, students focus only on the number of digits rather than the value of the leading digit.

What to Teach Instead

Use base-ten blocks to physically compare two numbers side by side. Starting the comparison at the hundreds place and working right becomes intuitive when students see that more hundreds always means a larger number regardless of tens or ones.

Active Learning Ideas

Inquiry Circle: Build My Number

One student draws a number card and describes it using only place value language (hundreds, tens, ones) while a partner builds it with base-ten blocks. Partners check the built number against the card, then switch roles. The debrief focuses on which clues were most helpful.

20 min·Pairs

Think-Pair-Share: Which Number Is Greater?

Display two three-digit numbers and ask students to independently determine which is greater and explain why using place value language. Students share reasoning with a partner before the class discusses. Rotating through several number pairs builds flexibility.

15 min·Pairs

Gallery Walk: True or False Number Statements

Post large cards around the room, each showing a place value statement (e.g., "5 hundreds + 3 ones = 530") that is either true or false. Groups rotate with markers to circle their answer and write a one-sentence justification before moving to the next card.

20 min·Small Groups

Real-World Connections

• Librarians use place value to organize books on shelves, ensuring that books with similar call numbers, like 513.1 and 513.2, are shelved close together for easy retrieval.
• Cashiers use place value when making change. If a customer pays with a $10 bill for an item costing $7.35, the cashier counts up using place value: $7.35, $7.40 (tens), $8.00 (hundreds), $9.00, $10.00 (thousands).

Assessment Ideas

Exit Ticket

Provide students with a card showing a three-digit number, such as 729. Ask them to write the value of each digit (700, 20, 9) and then write the number in expanded form (700 + 20 + 9).

Quick Check

Write two three-digit numbers on the board, e.g., 456 and 465. Ask students to hold up a card with '<', '>', or '=' to show the relationship between the two numbers. Follow up by asking a few students to explain their reasoning using place value.

Discussion Prompt

Present students with a scenario: 'I have 5 hundreds, 12 tens, and 3 ones. What number do I have?' Allow students time to work individually or in pairs, then facilitate a class discussion where students share their answers and explain how they used place value to solve the problem.

Frequently Asked Questions

How can active learning strategies make place value review more effective for 3rd graders?

Place value review can feel repetitive if it is only worksheet-based. Active approaches like building numbers with base-ten blocks in pairs or debating place value statements in a gallery walk require students to explain reasoning aloud. This verbalization catches misconceptions and builds the flexible number sense that supports fluent addition and subtraction within 1,000.

What does CCSS.Math.Content.3.NBT.A.2 expect students to be able to do?

The standard requires students to fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction. A strong grasp of place value structure is the prerequisite that makes this fluency possible.

What is expanded form and why is it important in 3rd grade?

Expanded form breaks a number into the sum of its place values, for example 743 = 700 + 40 + 3. It is important because it makes explicit the value contributed by each digit. Writing numbers in expanded form helps students understand why addition and subtraction algorithms work, preparing them for multi-digit computation.

How do students compare three-digit numbers using place value?

Students compare starting from the highest place value. If hundreds digits differ, the number with more hundreds is greater. If those are equal, they move to the tens, then the ones. Third graders record comparisons using the symbols >, <, and =. This left-to-right process works the same way for all larger numbers they encounter in later grades.