Addition with Place Value

Overview

This is Lesson 10 of 18 in the unit “Math in Our World.” Students use base-ten blocks, place-value disks, drawings, and a vertical algorithm to add numbers within 10,000, with particular attention to aligning places and regrouping.

Learning intentions

Students will be able to:

• Add numbers within 10,000 using place-value understanding.
• Model addition with base-ten blocks or place-value disks.
• Align ones, tens, hundreds, and thousands when using a vertical algorithm.
• Explain when and why regrouping is needed.

Success criteria

• I can align the digits by place value.
• I can combine the numbers in each place.
• I can regroup 10 of one unit for 1 of the next unit.
• I can check that my sum is reasonable.

Curriculum links

• Grade 3 number and operations: use place value to compose, decompose, and add multi-digit whole numbers.
• Mathematical reasoning: represent, explain, and check addition using concrete models, drawings, and equations.
• Measurement and Data — area models and the distributive property: connect careful alignment and combining parts to reasoning about quantities represented in parts.
• Georgia Standards of Excellence, Common Core-aligned expectations for Grade 3 computation and place-value reasoning.

Lesson structure (30 minutes)

1. 0–3 min · Hook and learning intention. Teacher displays a vertical addition problem with misaligned digits, such as 246 + 132, using the opening place-value puzzle slide, and asks, “What mistake might happen here?” State: “I can add numbers within 10,000 using place value.” Students identify the alignment problem and briefly explain where each digit belongs.

2. 3–15 min · I do: model the strategy. Teacher uses base-ten blocks to model 247 + 186, building each number in separate place-value columns and emphasizing that ones combine with ones, tens with tens, and hundreds with hundreds; then record the same work with a vertical algorithm on the teacher modeling slides. Students watch, explain each step, and help identify when 10 ones are exchanged for 1 ten and when 10 tens are exchanged for 1 hundred.

Model the language: “I start with the ones. I have 13 ones, so I write 3 ones and regroup 1 ten. Next, I combine the tens, including the regrouped ten.” Use the terms add, sum, ones, regroup, and carry. Clarify that “carry” is a quick way to record a regrouped unit.

3. 15–19 min · We do: guided regrouping. Teacher places disks for 368 + 257 on the Smartboard and invites students to direct the regrouping, using the guided place-value disk slides. Students take turns moving or describing disks, solve each place together, and explain why 10 units can be exchanged for 1 unit in the next place.

4. 19–25 min · You do: supported practice. Teacher distributes the place-value addition practice and assessment sheet and assigns the four practice problems. Students solve using blocks, drawings, or the lined place-value organizer, then compare one answer with a partner. Circulate among the five students, checking alignment before students calculate and prompting, “Which place will you add first?” Include three-digit problems first, followed by a four-digit problem for students ready for extension.

5. 25–29 min · Individual assessment. Teacher directs students to complete the five three-choice questions on the worksheet independently: include examples without regrouping and with regrouping, and ask students to select the correct sum rather than copy lengthy explanations. Students show work with a model, drawing, or vertical algorithm and circle one answer choice for each question.

6. 29–30 min · Share and close. Teacher revisits the success criteria and closing prompt slide and asks students to complete the sentence aloud: “I know my addition is organized when…” Students self-check whether they aligned places, combined each place, and regrouped when needed.

Resources

• the place-value addition slide deck
• the place-value addition practice and assessment sheet
• Base-ten blocks
• Place-value disks
• Smartboard or interactive display
• Lined place-value templates
• Pencils and erasers
• Color markers or crayons
• Regrouping guide
• Large-print number cards

Assessment

• During modeling and guided practice, listen for students’ explanations of why 10 ones make 1 ten and check that they align digits by place.
• Review the four practice problems for correct models, alignment, regrouping, and sums; provide immediate feedback before the independent assessment.
• Use the five three-choice assessment questions to identify whether each student can add without regrouping, regroup across one place, and apply the vertical algorithm.

Differentiation

• Support students by beginning with three-digit numbers, using color-coded columns for ones, tens, hundreds, and thousands, and providing a regrouping guide with visual exchange steps.
• Allow students to solve with base-ten blocks, place-value disks, drawings, or the organizer before requiring the vertical algorithm. Work beside students who need repeated modeling, using one problem at a time.
• For students ready for more challenge, provide four-digit addition problems, including regrouping across more than one place, and ask them to explain how they know the sum is reasonable.
• For dyslexia-friendly access, use lined place-value templates, large numerals, uncluttered pages, high-contrast printing, and minimal copying. Read each problem aloud, allow students to answer orally while pointing to their work, and avoid requiring students to read dense directions independently.