Subtract With Place Value

Overview

This is lesson 11 of 18 in the unit “Math in Our World.” Students use place-value disks to subtract numbers within 10,000, including regrouping when a place does not have enough units. They connect concrete models to written methods and check whether their differences are reasonable.

Learning intentions

Students will be able to:

• I can subtract numbers within 10,000 using place value.
• I can align digits by place value.
• I can regroup by trading one unit for ten smaller units.
• I can explain how I know my difference is reasonable.

Success criteria

• I can align the ones, tens, hundreds, and thousands correctly.
• I can regroup correctly when I do not have enough units to subtract.
• I can subtract accurately and label the difference.
• I can estimate or use addition to check that my answer is reasonable.

Curriculum links

• Georgia Standards of Excellence/Common Core-aligned Grade 3 place-value reasoning and multi-digit addition and subtraction.
• Number and Operations—Fractions: representing quantities as equal parts and using unit fractions, supporting precise use of mathematical units and representations.
• Measurement and Data: using area models and decomposition to represent mathematical reasoning, supporting the use of visual models and breaking complex problems into parts.
• Mathematical Practices: represent problems, use tools strategically, explain reasoning, and check solutions.

Lesson structure (30 minutes)

1. 0–3 min · Hook and readiness. Teacher opens the place-value subtraction introduction with the question, “How can we take away 126 when there are only 3 ones?” and briefly reviews the value of ones, tens, hundreds, and thousands. Students identify each digit’s value and orally use the words subtract, difference, regroup, borrow, and take away.

2. 3–15 min · I do: model with disks. Teacher displays 463 minus 128 using place-value disks, models aligning the minuend and subtrahend, and thinks aloud: “I cannot take away 8 ones from 3 ones, so I trade one ten for ten ones”; teacher then removes the subtrahend and records the written steps on the regrouping model and worked example. Students watch, explain each trade, and point to the place being changed; they compare the concrete disks with the written algorithm.

3. 15–19 min · We do: Smartboard practice. Teacher uses the interactive drag-and-trade practice to show two problems, such as 752 − 236 and 1,204 − 587, pausing before each regrouping decision. Students take turns dragging disks, trading pieces, and removing the subtrahend on the Smartboard while classmates signal whether the move is correct and explain why.

4. 19–26 min · You do: independent practice. Teacher distributes the place-value subtraction practice sheet and reminds students to use the four-step organizer: align, trade, subtract, check. Students solve four problems with and without regrouping, using disks, a number line, or drawings as needed. The teacher conferences briefly with each student, asking, “Which place needs regrouping?” and “How can you check?”

5. 26–29 min · Five-question assessment. Teacher directs students to the assessment section of the place-value subtraction practice sheet and presents one item at a time, reading directions aloud and displaying the corresponding problem on the assessment and checking slides. Students answer five three-choice questions involving subtraction with and without regrouping, including one problem with zeros in the minuend; they may respond by circling, pointing, or stating an answer.

6. 29–30 min · Plenary and self-check. Teacher displays the final success-criteria check and asks, “What does regrouping change, and what stays the same?” Students share one strategy or point to the criterion they met, then hand in the worksheet for review.

Resources

• the place-value subtraction slide deck
• the place-value subtraction practice sheet
• Place-value disks or base-ten blocks for ones, tens, hundreds, and thousands
• Smartboard or interactive display
• Dry-erase boards and markers
• Pencils and erasers
• Optional number lines
• High-contrast place-value columns or enlarged teacher model

Assessment

• During modeling and Smartboard practice, check whether students align places, identify when regrouping is needed, and trade one unit for ten smaller units correctly.
• Review the four practice problems for accurate organization, regrouping, subtraction, and a reasonable check. Record brief notes for each of the five students.
• Use the five three-choice assessment questions as the exit measure. A student demonstrating at least four correct answers and explaining or modeling regrouping is ready for continued work within 10,000; provide targeted reteaching for errors involving place alignment or trading.

Differentiation

• Support: Provide disks, smaller numbers, enlarged high-contrast columns, and the step checklist: 1) align, 2) trade, 3) subtract, 4) check. Work one problem at a time and keep the minuend and subtrahend visually separated.
• Language and diverse learners: Pair each action with gestures and repeated vocabulary. Offer sentence frames such as “I traded ___ because ___” and “The difference is reasonable because ___.”
• Dyslexia-friendly access: Use a clear sans-serif font, generous spacing, dark text on a light background, minimal visual clutter, and one problem per viewing area. Read all directions aloud and allow verbal, pointing, or oral responses.
• Extension: Invite students to solve a problem containing zeros in the minuend, such as 3,002 − 1,458, and explain each trade using disks, a drawing, or addition to check.