Place Value Decomposition

Overview

Students will compose and decompose whole numbers up to 10 000 using place value to explain what digits mean in everyday contexts. They will move from concrete base-ten materials to pictorial place-value charts to symbolic expanded form.

Learning intentions

• WALT decompose whole numbers up to 10 000 into thousands, hundreds, tens, and ones.
• WALT represent a number in different forms (standard form and expanded form).
• WALT explain how place value helps describe numbers in real-life situations.
• WALT use base-ten blocks and place-value charts to justify answers.

Success criteria

• I can break a number (up to 10 000) into thousands, hundreds, tens, and ones.
• I can show a number using base-ten blocks and a place-value chart.
• I can write expanded form for a number using place value parts.
• I can explain my thinking using place value language (thousands, hundreds, tens, ones).

Curriculum links

• Students develop number sense for whole numbers up to 10 000 using place value.
• Students represent and explain whole numbers using expanded form and base-ten models.
• Students solve problems and communicate reasoning using mathematical language and representations.

Lesson structure (40 minutes)

1. 0–5 min | Minds On (ticket number) Show a photo of a ticket stub with attendance of 3 847. Ask: “What does this number tell us? How many different ways could we write it?” Chart student wonderings and key terms (thousands, hundreds, tens, ones).

2. 5–12 min | Connect to place value Tell students we can understand any number by breaking it into place value parts. Write “3 847” and ask what each digit might represent. Link answers to the idea of thousands, hundreds, tens, and ones.

3. 12–25 min | Concrete → Pictorial → Symbolic (model together) Use the real scenario: A school library has 2 546 books.

• 12–16 min | Concrete: Build 2 546 with base-ten blocks: 2 thousands cubes, 5 hundreds flats, 4 tens rods, 6 ones units. Pause after each group and ask how many each part is.
• 16–20 min | Pictorial: Draw a place-value chart with labeled columns: thousands | hundreds | tens | ones, and fill in 2 | 5 | 4 | 6. Point out that the chart matches the blocks.
• 20–25 min | Symbolic: Write expanded form: 2 546 = 2000 + 500 + 40 + 6. Model a second decomposition too (for example, 1000 + 1000 + 500 + 40 + 6). Ask students to notice that it’s still the same total.

4. 25–33 min | Guided practice (student number) Give each student a number to represent (example: 4 321). Students first build it with base-ten blocks (or virtual manipulatives) and then complete a place-value chart. As they work, circulate with prompts:

• “How many thousands do you have?”
• “What does the 3 represent in 4 321?”
• “Write the expanded form you would explain to someone.”

5. 33–37 min | Consolidation (think-pair-share) Prompt: “How would you explain decomposing a number to someone at home?” Students share in pairs, using sentence frames such as: “I decomposed 4 321 into…” and “The digit 4 means…”

6. 37–40 min | Exit ticket Students independently write 3 789 in expanded form. Collect for quick check.

Resources

• Photo of a ticket stub showing attendance of 3 847
• Base-ten blocks (thousands cubes, hundreds flats, tens rods, ones units) or virtual manipulatives
• Large place-value chart template (thousands | hundreds | tens | ones)
• Student number cards (e.g., 4 321 and other close options if desired)
• Paper for place-value charts and expanded form
• Markers/whiteboard and projector/screen for charting wonderings
• Exit ticket slips with: “Write 3 789 in expanded form.”
• Visual sentence frames for explanations

Assessment

• Teacher observation during the concrete → pictorial → symbolic example and guided practice (use place-value prompts).
• Checklist of success criteria: correct place-value partitioning and correct expanded form for the student number.
• Exit ticket: expanded form for 3 789 (evidence of understanding thousands, hundreds, tens, ones).

Differentiation

• Support: Provide a partially filled place-value chart and/or a small example number worked as a class reminder (digits matched to columns). Offer base-ten block count guides (e.g., “Thousands: __”).
• Support for SEN: Allow use of manipulatives longer and encourage verbal counting (thousands, then hundreds, then tens, then ones).
• Extension: Give a second decomposition task: “Write 4 321 as a sum using two different ways” (e.g., 3000 + 1000 + 300 + 20 + 1 style if appropriate).
• EAL: Use sentence frames and word banks with thousands, hundreds, tens, ones, and expanded form. Encourage students to point to parts on the chart and blocks while speaking.