---

Day 1: Introduction to Partial Quotients

Standards

• CCSS.MATH.CONTENT.5.NBT.B.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, including partial quotients.
• CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
• CCSS.MATH.PRACTICE.MP7: Look for and make use of structure.

Learning Objectives (I Can Statements)

• I can explain what a partial quotient is.
• I can use partial quotients to divide a four-digit number by a two-digit number.
• I can break down division problems into easier parts using place value.

Success Criteria

• I correctly identify place values in a division problem.
• I record partial quotients step-by-step to find the exact quotient.
• I check my work by multiplying my quotient by the divisor.

Materials Needed

• Whiteboard and markers
• Chart paper with example problems
• Student math journals or notebooks
• Base-ten blocks or place value charts
• Exit ticket handouts

Lesson Activities

Time	Activity Description
0-10 min	Engage: Start with a math talk: pose a division word problem like “There are 1,236 beads shared equally among 12 children. How many beads does each child get?” Ask students how they might solve this. Introduce the idea of partial quotients as an easier strategy compared to traditional long division. Use base-ten blocks to model breaking down the dividend.
10-25 min	Explore: Demonstrate division using partial quotients on the whiteboard. Choose a 3-4 digit dividend divided by a two-digit divisor. Show how to subtract chunks of multiples (e.g., subtract 100 lots of the divisor, then 20 lots, and so on). Emphasize writing partial quotients as you go.
25-40 min	Guided Practice: Students work in pairs with printed problems using partial quotients (e.g., 824 ÷ 23, 1,156 ÷ 14). Circulate and scaffold – prompt students to estimate multiples and write partial quotients clearly. Encourage use of place value strategies.
40-50 min	Reflection and Discussion: Volunteers explain their process. Discuss why partial quotients method helps with understanding place value and division. Highlight connections to multiplication facts and estimation.
50-60 min	Exit Ticket: Students solve one division problem independently using partial quotients. Collect to assess understanding.

Differentiation

• For Struggling Learners: Use smaller numbers for practice; provide place value charts and manipulatives; allow partner collaboration.
• For Advanced Learners: Challenge with 4-digit dividends divided by 2-digit divisors with remainders; encourage them to write word problems based on partial quotients.

Extension

• Students create a comic strip explaining partial quotients in their own words and illustrations.
• Begin exploring how partial quotients relate to decimal division in later lessons.

---

Day 2: Practicing Partial Quotients with Real-World Problems

Standards

• CCSS.MATH.CONTENT.5.NBT.B.6 (continued)
• CCSS.MATH.PRACTICE.MP4: Model with mathematics.
• CCSS.MATH.PRACTICE.MP6: Attend to precision.

Learning Objectives (I Can Statements)

• I can solve real-world division problems using the partial quotients method.
• I can estimate and check my answers for accuracy.
• I can explain each step I take in solving division problems.

Success Criteria

• I write clear and correct partial quotients for word problems.
• I verify my solution by multiplying the quotient with the divisor and comparing to the dividend.
• I use estimation to decide if my answer is reasonable.

Materials Needed

• Math journals/notebooks
• Word problem handouts with varying difficulty
• Calculators (for checking solutions only)
• Chart paper for group recording

Lesson Activities

Time	Activity Description
0-10 min	Review: Briefly revisit Day 1’s partial quotients method with an example problem as a warm-up. Ask students what they remember about the place value strategy.
10-30 min	Guided Group Work: Present 3-4 real-life word problems (e.g., dividing money, items in groups, data distribution) requiring partial quotients. Assign groups of 4 students 1 problem each to solve collaboratively. Groups record steps and partial quotients on chart paper.
30-45 min	Gallery Walk: Groups display their chart papers around the room. Students rotate and review each problem-solving strategy used by their classmates.
45-55 min	Class Discussion: Compare strategies noticed during gallery walk. Highlight diverse ways to estimate partial quotients and how groups checked accuracy.
55-60 min	Exit Reflection: Students write in journals: “How does partial quotient strategy help me solve division problems better?”

Differentiation

• For Struggling Learners: Provide word problems with smaller numbers or simpler contexts; allow use of base-ten blocks during group work.
• For Advanced Learners: Extend problems to multi-step word problems requiring division and addition/subtraction, asking them to write mixed number or decimal quotients.

Extension

• Create and solve your own real-world division problems using partial quotients with a partner.

---

Day 3: Mastering Partial Quotients & Assessment

Standards

• CCSS.MATH.CONTENT.5.NBT.B.6
• CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
• CCSS.MATH.PRACTICE.MP5: Use appropriate tools strategically.

Learning Objectives (I Can Statements)

• I can independently solve division problems using partial quotients accurately.
• I can explain and justify my process to peers.
• I can use tools and strategies to check my answers.

Success Criteria

• I solve division equations with 4-digit dividends and 2-digit divisors using partial quotients correctly without assistance.
• I explain each step with clear reasoning.
• I identify errors and correct my work when needed.

Materials Needed

• Paper and pencils
• Math assessment sheet
• Whiteboard for peer teaching
• Place value manipulatives (optional)

Lesson Activities

Time	Activity Description
0-10 min	Mini Review: Quick Q&A on key partial quotient strategies from previous lessons. Address common misconceptions or questions.
10-35 min	Independent Practice & Formative Assessment: Students complete a set of 5 division problems to demonstrate mastery. Problems increase gradually in difficulty, including some with remainders.
35-50 min	Peer Teaching: In pairs, students explain their solutions to each other, using precise language and partial quotients steps. Partners ask clarifying questions.
50-60 min	Reflection & Self-Assessment: Students complete a self-check rubric assessing their confidence with partial quotients and write an “I can…” statement reflection on what they learned.

Differentiation

• For Struggling Learners: Provide guided prompts on assessment sheet to scaffold writing partial quotients. Allow use of calculators for checking.
• For Advanced Learners: Include an optional challenge problem requiring mixed numbers or converting remainders into decimals.

Extension

• Present a small group mini-lesson on applying partial quotients to division with decimals, previewing future grade concepts.

---

Teacher Notes

• Grouping: Use flexible groups during activities to allow peer support.
• Classroom Tools: Encourage use of whiteboards, base-ten blocks, and calculators at strategic points.
• Assessment: The exit tickets and Day 3 assessments provide formative and summative data for student understanding.
• Engagement: Incorporate number talks and real-world contexts to keep students motivated and relate math to their lives.
• Feedback: Provide immediate feedback during pair work to correct misunderstandings.

This 3-day plan integrates the Common Core emphasis on place value understanding, story problem solving, and mathematical reasoning using the partial quotients strategy for division, providing scaffolded and engaging instruction for all learners in grade 5.