Place Value and Rounding

Overview

Students will use base-ten place value to read, write, compare, and round whole numbers up to one million. They will also practice constructing arguments by explaining why a rounding choice and comparison result make sense.

Learning intentions

• Students will be able to explain place value relationships in multi-digit whole numbers up to one million.
• Students will be able to read and write whole numbers using numerals, number names, and expanded form.
• Students will be able to compare two whole numbers using place value and the symbols >, =, and <.
• Students will be able to round whole numbers to any place value (including within the one-million range).
• Students will be able to construct an argument by justifying comparisons and rounding using place value.

Success criteria

• I can identify what each digit means in a number (for example, thousands vs. tens).
• I can compare two numbers correctly and explain which digit-place controls the result.
• I can round a number to a given place correctly.
• I can explain my thinking clearly using place value language (ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions).

Curriculum links

• Number — place value understanding (Grade 4, Cluster A): digit value in one place is ten times the value to the right.
• Number — read and write multi-digit whole numbers and compare using digit meanings (Grade 4, Cluster A).
• Number — use place value understanding to round multi-digit whole numbers to any place (Grade 4, Cluster A).
• Mathematics — explain reasoning for number comparisons and rounding using clear arguments based on place value (connected to Cluster A expectations).

Lesson structure (30 minutes)

1. 0–4 min · Warm-up: Number Detective. Teacher displays three number cards (e.g., 483,269; 483,296; 483,269 written as expanded form), asks: “What does the 4 mean in each?” Students turn and talk, then one pair shares a place-value explanation.
2. 4–9 min · Mini-teach: Reading, writing, comparing. Teacher models converting 526,407 into number name and expanded form, then compares it to 526,470 using place value; teacher says: “The deciding place is the tens of ones/tens place.” Students complete a quick guided check: compare 371,905 and 371,950 and write the correct symbol.
3. 9–16 min · Guided practice: Construct arguments with comparisons. Teacher gives two comparison prompts on the board:

• 642,381 ___ 642,318
• 905,000 ___ 905,099 Teacher prompts: “Which digit-place decides? What is the digit there in each number?” Students work in pairs to choose >, <, or = and write a one-sentence justification starting with “I know because…”.

4. 16–24 min · Guided practice: Rounding within one million. Teacher teaches a rounding routine with place value language:

• Step 1: Identify the place to round (e.g., nearest thousand).
• Step 2: Look at the digit to the right (the “rounding digit”).
• Step 3: Round up if it is 5–9; round down if it is 0–4; keep earlier places the same; replace later digits with zeros. Teacher models rounding 738,542 to the nearest thousand and explains the decision using the hundreds digit (5). Students do two rounds independently:
• Round 204,639 to the nearest hundred
• Round 815,275 to the nearest ten thousand

5. 24–28 min · Argument share: Explain your rounding. Teacher selects two student responses (one correct, one common error such as rounding the wrong place). Students use a sentence stem to argue:

• “My answer is correct because the digit in the rounding place is ___ and the next digit is ___.” Teacher leads a brief whole-class discussion to connect reasoning to place value.

6. 28–30 min · Exit ticket (quick check). Students answer:

• Compare: 560,204 ___ 560,240 (write symbol)
• Round: 93,785 to the nearest hundred

Resources

• Number cards (up to one-million range)
• Board/markers or projector slides showing worked examples
• Rounding routine poster (place to round, look right digit, round up/down)
• Student recording sheets for expanded form and justifications
• Two-color sticky notes (green = correct choice, yellow = needs explanation)
• Digital timer or clock for pacing
• Optional: base-ten blocks or place value chart template (hundreds of thousands to ones)

Assessment

• Teacher listens during Step 1 and Step 3 for correct use of place value language (ones, tens, hundreds, thousands).
• During Step 4, teacher checks student rounding for correct target place and correct up/down decision.
• Exit ticket: compare two numbers and round to the nearest hundred; score for accuracy and place-value justification in the student work if included.

Differentiation

• Support: Provide sentence starters for arguments (“I know because the ___ place has the same/different digit, so…”). Offer a place value chart with labeled columns for hundreds of thousands to ones.
• Support: For students who struggle with rounding, require them to underline the target place and circle the rounding digit before choosing up/down.
• Extension: Challenge students to round the same number to two different places (nearest hundred and nearest thousand) and write a claim about how the digits change and why.
• EAL/SEN: Use consistent language routines (target place, next digit, round up/down). Allow oral explanation with teacher prompting before writing.

Extension

• N/A