Subtract Using Place Value

Overview

In Lesson 21 of 30 in Building Mathematical Thinking, students subtract two-digit numbers by separating tens and ones. They build on place-value understanding and addition/subtraction within 100, then model, solve, and check subtraction problems using concrete tools, drawings, and equations.

Learning intentions

Students will be able to:

• I can subtract two-digit numbers using place value.
• I can model subtraction with base-ten blocks, a number line, or an expanded-form equation.
• I can explain how I solved a subtraction problem.
• I can check whether my answer makes sense.

Success criteria

• I can subtract the ones and tens in the correct place-value columns.
• I can show my thinking with a model, drawing, or expanded form.
• I can solve and record a subtraction equation accurately.
• I can check my answer using addition or a second strategy.

Curriculum links

• Place value and addition/subtraction within 100: students add and subtract by working with tens and ones.
• Number and Operations in Base Ten: students fluently subtract within 100 using place-value strategies.
• Place-value reasoning: students explain how digits represent tens and ones and use the relationship between addition and subtraction.
• Grade 4 mathematical practice connection: students represent and explain multiplication and related operations with equations, arrays, and area models; here, students develop the same habit of connecting models to written equations.

Lesson structure (30 minutes)

1. 0–4 min · Hook and review. Teacher opens the subtraction hook and place-value review slides and displays 54 − 20, asking, “What changes when we take away two tens?” Students use fingers, quick drawings, or a place-value chart to show that 54 becomes 34, then share how they know.

2. 4–10 min · Teacher modeling. Teacher models 63 − 21 with base-ten blocks and a place-value mat: subtract 1 one from 3 ones and 2 tens from 6 tens, recording 60 + 3 − 20 − 1 = 40 + 2 = 42. Students watch, name the tens and ones being subtracted, and help connect the blocks to the written equation using the worked-example slides.

3. 10–15 min · Guided practice. Teacher solves 78 − 34 with students, pausing after each step and asking, “What do we subtract first?” and “How can we check?” Students work with a partner using base-ten blocks or a number line, then record a model, equation, and check on the place-value subtraction practice sheet.

4. 15–23 min · Supported partner practice. Teacher assigns each pair two or three non-regrouping problems from the worksheet, circulating to prompt, “Show the tens,” “Show the ones,” and “Tell your partner why your answer is reasonable.” Students choose a base-ten model, open number line, or expanded form, solve, and check each answer with addition.

5. 23–27 min · Explain and compare. Teacher displays 86 − 42 and invites two students to show different strategies using the strategy-sharing slides. Students compare the models and complete the sentence, “Both strategies work because ___ tens and ___ ones are being subtracted.”

6. 27–30 min · Exit check and close. Teacher gives the final problem on the exit problem and self-check section: 75 − 32. Students solve independently, show one model or expanded form, and check with addition; they circle one statement: “I can do this,” “I need more practice,” or “I need help.”

Resources

• the complete subtraction slide deck
• the place-value subtraction practice sheet
• Base-ten blocks
• Place-value mats
• Open number-line strips
• Pencils, crayons, and erasers
• Large-print digit cards
• Step cards showing model, subtract ones, subtract tens, solve, and check
• Individual whiteboards or scratch paper

Assessment

• During modeling and guided practice, check whether students identify tens and ones correctly and subtract within the correct place-value column.
• During partner practice, listen for explanations connecting the model, expanded form, and equation; note whether students check with addition.
• Use the exit problem to identify students ready for regrouping, students needing more non-regrouping practice, and students needing concrete support.

Differentiation

• Support: Provide base-ten blocks, a place-value mat, and an open number line. Begin with problems without regrouping, such as 68 − 25, and reduce the number of problems while maintaining repeated practice.
• Dyslexia-friendly options: Use large, clearly aligned digits; high-contrast, uncluttered pages; short step cards; tactile blocks; and verbal directions paired with visual models. Allow students to explain orally instead of writing a full explanation.
• Language and communication support: Use sentence frames such as “I subtracted ___ ones from ___ ones,” “I subtracted ___ tens from ___ tens,” and “I checked by adding ___ and ___.”
• Advanced learners: Provide regrouping problems such as 52 − 28 and 71 − 46. Ask students to exchange one ten for ten ones, draw the exchange, solve, and explain why the answer remains equivalent.

Extension

• Solve a regrouping problem and explain the exchange using blocks, a drawing, and an equation.
• Create a two-digit subtraction problem with an answer between 20 and 40, then trade with a partner to solve and check.