Expanding Numbers

Overview

In this 10-minute lesson, you will practise expanding 2- and 3-digit numbers into place value parts (e.g., 342 = 300 + 40 + 2). This builds the strategies students need for addition and subtraction using mental and written methods with at least 1000.

Learning intentions

Students will be able to:

• expand 2- and 3-digit numbers using place value (hundreds, tens, ones)
• use expanded form to understand what each digit represents
• check their work by recombining parts to return to the original number

Success criteria

Students can:

• correctly write a number in expanded form using + between place value parts
• match digits to the correct value (e.g., the 4 in 342 represents 40)
• recombine expanded form to get back the original number

Curriculum links

• MA2-RN-01 — represent numbers using place value and the role of zero
• MA2-AR-01 — select and use mental and written strategies for addition and subtraction involving 2- and 3-digit numbers (place value helps regrouping later)
• MA2-AR-02 — complete number sentences with unknowns (expanded form supports finding missing parts)

Lesson structure (10 minutes)

1. 0–2 min · Warm-up (place value prompt). Teacher writes: “What does the 5 mean in 5? and in 52?” and asks the learner to explain where the 5 sits. Students respond by stating the value of the digit based on its position.

2. 2–4 min · Direct teach (expanding form model). Teacher demonstrates with an example on the board: “342 = 300 + 40 + 2” and “405 = 400 + 0 + 5 (or 400 + 5)”. Students watch and answer quick checks: “Why is the tens part 40?” and “Where does zero fit?”

3. 4–7 min · Guided practice (one worked example + try). Teacher works through another number together: “527 = 500 + 20 + 7”. Then teacher asks the learner to complete expanding for one number (teacher says it aloud). Example: “306” → learner writes “300 + 0 + 6” (or “300 + 6” if the learner prefers).

4. 7–10 min · Worksheet task (expanding numbers form). Teacher gives the worksheet “Expanding Numbers Form”. Students complete all questions, then do a quick self-check: they circle the ones where they can recombine to confirm the original number.

Resources

• “Expanding Numbers Form” worksheet (printed)
• pencil and eraser
• place value chart (hundreds/tens/ones) or quick grid on board
• small set of number cards (optional: 2- and 3-digit numbers for teacher call-out)

Assessment

• Formative during guided practice: listen for correct digit-to-place mapping and correct handling of zero
• Worksheet check: accuracy of expanded form and whether recombination matches the original number
• Quick end-of-lesson question: “Show me one number’s expanded form and point to the digit that matches each part”

Differentiation

• Support: Provide sentence starters on the worksheet such as “The number 3 __ is 300 + …” and allow recombining using a calculator if available for checking only.
• Support for zero: Accept “400 + 0 + 5” or “400 + 5” as long as the learner shows understanding that zero contributes nothing.
• Extension (only if finished early): Ask the learner to write the original number from an expanded form like “600 + 30 + 4”.
• EAL/SEN: Keep numbers and instructions short; teacher can read questions aloud and confirm the place of each digit using a place value chart.

Worksheet: Expanding Numbers Form

Name: ____________________ Date: ____________________

Directions: Expand each number into hundreds + tens + ones. Then recombine to check.

1. 246 Expanded form: _________________________________ Check (recombine): ____________________________

2. 530 Expanded form: _________________________________ Check (recombine): ____________________________

3. 708 Expanded form: _________________________________ Check (recombine): ____________________________

4. 915 Expanded form: _________________________________ Check (recombine): ____________________________

5. 402 Expanded form: _________________________________ Check (recombine): ____________________________

Recombination rule (for your checking): hundreds + tens + ones = original number

Final check: Circle your answers you are sure about. Number(s): ____________________