Expanded Form

Overview

In this third lesson of the “Math in Our World” unit, students decompose whole numbers by place value and write each number in expanded form. Building on prior work with thousands, hundreds, tens, and ones, students use color-coded place-value disks, value cards, drawings, and equations to connect each digit with its value.

Learning intentions

Students will be able to:

• I can decompose a number by place value.
• I can write a number in expanded form.
• I can explain the value of every nonzero digit.
• I can use blocks, cards, or a drawing to prove my answer.

Success criteria

• I can show the thousands, hundreds, tens, and ones in a number.
• I can write one addend for each nonzero digit.
• I can check that my expanded form has the same value as the original number.
• I can explain what a zero means in a place-value position.

Curriculum links

• Georgia Standards of Excellence, Grade 3 Number and Operations: represent whole numbers by place value and explain the value of digits.
• Mathematical reasoning: use concrete models, drawings, and equations to represent and justify thinking.
• Operations and Algebraic Thinking: use equations to represent quantities and unknown addends.
• Measurement and Data connections: organize and interpret quantities using clear mathematical representations.

Lesson structure (30 minutes)

1. 0–3 min · Hook and goal. Teacher displays 3,482 and asks, “What does each digit contribute to this number?” using the opening number puzzle slide; students make a quick estimate, then share one digit’s value with a partner.

2. 3–15 min · I do: model expanded form. Teacher introduces the words expanded form, value, thousands, hundreds, tens, and ones, then models 3,482 with color-coded place-value disks: 3 thousands, 4 hundreds, 8 tens, and 2 ones. Teacher writes one equation per line:

3,000

• 400
• 80
• 2 = 3,482

Teacher emphasizes that the expanded form shows the value of every nonzero digit and that a zero place contributes no addend. Students echo-read the vocabulary, identify each digit’s value, and explain why the equation equals 3,482. Refer to the color-coded modeling slides throughout the demonstration.

3. 15–20 min · We do: match and explain. Teacher gives pairs of numeral cards and value cards, then displays examples and prompts students to move cards to match each numeral with its expanded form. Students work together to match a numeral, its addends, and a visual equation, explaining their choices aloud. Use the partner matching directions and discussion prompts to show one example and remind students to check every place.

4. 20–26 min · You do: independent practice. Teacher distributes the expanded-form practice and assessment worksheet and provides place-value mats and disks as needed. Students represent three numbers in expanded form using blocks, cards, or drawings before recording equations. The teacher conferences briefly with each student, asking, “What is the value of this digit?” and “How do you know your equation matches the numeral?”

5. 26–29 min · Five-question check. Students complete the worksheet’s five three-choice questions independently: identify the expanded form of 2,314, match the expanded form of 5,060, find a missing addend, interpret a zero in the tens or hundreds place, and explain which equation represents a given numeral. Teacher reads choices aloud, pauses between questions, and accepts pointing or verbal responses when writing is a barrier.

6. 29–30 min · Plenary and self-check. Teacher displays the final review and exit prompt and asks students to complete the sentence, “Expanded form shows…” Students share one strategy, then indicate with fingers 1–3 how confident they feel: 1 = need help, 2 = almost there, 3 = can explain it.

Resources

• the expanded-form mini-lesson deck
• the expanded-form practice and assessment worksheet
• Color-coded place-value disks or base-ten blocks
• Place-value mats labeled thousands, hundreds, tens, and ones
• Numeral cards and value cards
• Whiteboards and dry-erase markers
• Pencils and colored pencils
• Large-print vocabulary and equation examples

Assessment

• During the model, ask students to identify the value of each digit in 3,482 and explain why each addend is included.
• During partner work and practice, check whether students match each digit to its correct value and write one addend per nonzero place.
• Use the five three-choice questions to identify misconceptions, especially confusing a digit with its value or adding an unnecessary zero-place term. Review errors individually or in the next small-group lesson.

Differentiation

• Support students with two- or three-digit numbers first, a place-value mat, color-coded disks, and a completed example beside the task. Gradually include four-digit numbers when ready.
• Provide sentence starters: “The ___ is worth ___ because it is in the ___ place” and “The expanded form is ___ because…”
• For dyslexia-friendly access, use a clear sans-serif font, large symbols, strong color coding, one equation per line, reduced visual clutter, and teacher-read directions and answer choices. Allow students to respond orally, by pointing, or with manipulatives.
• Challenge students to represent numbers through 10,000, including numbers with zero places, and explain why a zero does not create an addend in expanded form.