Add and Subtract Strategically

Overview

In this second lesson of “Build, Model, Solve,” students connect concrete and visual models to the standard algorithms for multi-digit addition and subtraction. They use estimation to judge whether answers are reasonable and apply their strategies to real-world problems in small groups.

Learning intentions

Students will be able to:

• Model multi-digit addition and subtraction with base-ten blocks, place-value charts, and open number lines.
• Connect models to the standard addition and subtraction algorithms.
• Estimate sums and differences by rounding to an appropriate place.
• Solve and explain multi-step real-world problems collaboratively.

Success criteria

• I can represent a multi-digit addition or subtraction problem in more than one way.
• I can use the standard algorithm accurately and explain what regrouping means.
• I can estimate before or after solving and decide whether my answer is reasonable.
• I can explain my strategy and listen to my group members’ ideas.

Curriculum links

• Read, write, compare, and interpret multi-digit whole numbers using place-value understanding.
• Round multi-digit whole numbers to estimate and check reasonableness.
• Fluently add and subtract multi-digit whole numbers using the standard algorithms.
• Use place-value strategies and properties of operations to connect models, equations, and explanations.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Open with the hook and retrieval slides and display the question: “A school says it collected 4,982 cans one week and 2,167 the next. Is 7,149 a reasonable total?” Students estimate mentally, share a possible method with a partner, and identify what they already know about regrouping.

2. 7–18 min · Model addition. Use the addition modeling slides to demonstrate 2,468 + 1,753 with base-ten blocks and a place-value chart, exchanging 10 ones for 1 ten and 10 tens for 1 hundred. Students build the numbers with blocks, record the expanded-form addition, and connect each exchange to the standard algorithm on the modeling and problem-solving worksheet.

3. 18–29 min · Model subtraction. Demonstrate 5,203 − 2,786 with blocks, a place-value chart, and an open number line, emphasizing that regrouping may move across a zero. Students represent the problem, discuss why a hundred or thousand must be decomposed, and complete the corresponding subtraction model on the modeling and problem-solving worksheet. Check understanding by asking students to point to the place where each exchange occurs.

4. 29–35 min · Estimate and check. Present 6,384 − 2,917 and 3,782 + 2,146 using the estimation and reasonableness slides. Students round each number to the nearest hundred, predict a reasonable range, solve one problem with the standard algorithm, and compare the exact answer with the estimate. Invite students to explain why an answer that is far from the estimate signals an error.

5. 35–52 min · Collaborative problem solving. Place students in groups of four and assign roles using the group role cards. Distribute the modeling and problem-solving worksheet and direct groups to solve three real-world problems, such as comparing library collections, finding the total attendance at two events, and determining how many items remain after a donation. Each group must estimate, choose a model, solve using the standard algorithm, and write an explanation. Circulate, asking: “What does this digit represent?” and “How does your model prove your answer?”

6. 52–57 min · Share and compare strategies. Return to the discussion and strategy comparison slides. Select two groups to show different representations for the same problem. Students compare the models and algorithms, then complete the sentence: “Both strategies work because…”

7. 57–60 min · Exit check. Finish with the success criteria exit ticket slips. Students solve 4,506 + 2,789, estimate first by rounding to the nearest hundred, and write one sentence explaining how they know the answer is reasonable.

Resources

• the Add and Subtract Strategically slide deck
• the modeling and problem-solving worksheet
• the group role cards
• the success criteria exit ticket slips
• Base-ten blocks for each group
• Place-value charts
• Open number-line strips
• Pencils, erasers, and chart paper
• Document camera or interactive whiteboard

Assessment

• Listen for accurate place-value language and observe whether students exchange units correctly during modeling.
• Use questioning and the group worksheet to check estimation, algorithm accuracy, and explanations; record students needing support with regrouping across zeros.
• Review the exit ticket for correct estimation, computation, and justification. Reteach using blocks or a place-value chart if students cannot connect the model to the algorithm.

Differentiation

• Support students with preprinted place-value charts, color-coded blocks, an open number line, and sentence frames such as “I decomposed ___ because…” and “My estimate is reasonable because…”
• Provide numbers with fewer digits or no regrouping initially, then move students toward problems requiring regrouping across zeros. Pair students strategically and read problem text aloud as needed.
• For multilingual learners, preview terms such as estimate, regroup, exchange, difference, and reasonable with gestures and visual examples; allow students to explain orally before writing.
• Extend ready students by asking them to create a second real-world problem with the same solution, solve it in two representations, and explain which method is most efficient.