Overview

This five-day unit guides 5th graders through mastering division strategies using place value patterns, mental math, and models. The lessons align with the South Carolina standard 5.PARF.1.2 and connect explicitly with Common Core State Standards for Mathematics, particularly 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, the properties of operations, and the relationship between multiplication and division).

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Week-at-a-Glance

Day	Focus	Duration	Format	Key Activity
1	Using Place Value Patterns to Divide	60 min	Whole/Small grp	Mental math & place value pattern exploration
2	Estimating Quotients with Place Value	60 min	Whole/Small grp	Estimation strategies & number talk
3	Using Models to Find Quotients	60 min	Whole/Small grp	Base-ten blocks and area model division
4	Review & Small Group Intervention	60 min	Small groups	Practice & differentiated support
5	Assessment & Reflection	60 min	Individual	Formal assessment & self-assessment

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Day 1: Place Value Patterns

I Can

• I can use place value patterns to mentally find quotients of division problems with up to four-digit dividends and two-digit divisors.

Success Criteria

• I identify place value patterns in numbers
• I use mental math strategies to break down dividends using place value
• I explain my thinking using place value concepts

Standards Addressed

• CCSS.MATH.CONTENT.5.NBT.B.6
• SC Math Standard 5.PARF.1.2

Materials

• Whiteboards & markers
• Place value charts
• Sample division problems on cards

Activities

1. Warm-up (10 min):

   • Quick number talk: Breaking down 3,468 into thousands, hundreds, tens, ones
   • Discuss how numbers break into place values

2. Modeling (15 min):

   • Teacher demonstrates dividing 3,468 ÷ 12 using place value decomposition
   • Think aloud: breaking down 3,468 as 3,000 + 400 + 60 + 8, estimating partial quotients mentally

3. Guided Practice (15 min):

   • Students work in pairs to try similar problems on whiteboards
   • Use place value charts to support decomposition

4. Small Groups (15 min):

   • Advanced learners: Challenge with larger dividends or missing digits problems
   • Intervention: Hands-on charts plus scaffolded questions on smaller numbers (e.g., 452 ÷ 14)

5. Closure (5 min):

   • Students share strategies used, emphasizing place value use

Differentiation Strategies

• Use visual place value charts for visual learners
• Provide step-by-step sentence stems for ELL and struggling learners (“First, I broke 3,000 into…”)

Extension

• Create your own division problem using place value decomposition and challenge a peer.

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Day 2: Estimating Quotients

I Can

• I can use place value patterns to estimate quotients before calculating the exact answer.

Success Criteria

• I round numbers to nearest hundreds or tens to estimate quotients
• I explain why my estimate makes sense
• I check estimates against exact answers

Standards Addressed

• CCSS.MATH.CONTENT.5.NBT.B.6
• SC Math Standard 5.PARF.1.2

Materials

• Number lines
• Estimation anchor charts
• Problem cards for estimating quotients

Activities

1. Warm-up (10 min):

   • Review rounding rules and place value terms
   • Practice rounding numbers to nearest ten and hundred

2. Introduction/Demo (10 min):

   • Teacher models estimating 1,234 ÷ 23 by rounding 1,234 to 1,200 and 23 to 20
   • Estimate quotient and discuss reasonableness

3. Guided Practice (20 min):

   • Students estimate quotients in pairs using problem cards
   • Use number lines to visualize rounding and division estimates

4. Small Groups (15 min):

   • Intervention: Focus on rounding strategies and using benchmarks such as 10, 100
   • Advanced: Challenge estimating with larger digits and decimals (preview topic)

5. Closure (5 min):

   • Share and discuss estimation strategies and how place value helps

Differentiation Strategies

• Graphic organizers to map rounding steps for learners needing support
• Encourage peer explanations to solidify understanding

Extension

• Create a poster explaining how to estimate division problems using place value rounding.

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Day 3: Models for Division

I Can

• I can use base-ten blocks and area models to find quotients.

Success Criteria

• I represent division problems using models
• I explain how models show the quotient
• I use models to verify mental math and estimation answers

Standards Addressed

• CCSS.MATH.CONTENT.5.NBT.B.6
• SC Math Standard 5.PARF.1.2

Materials

• Base-ten blocks sets
• Grid paper for area models
• Problem cards

Activities

1. Warm-up (5 min):

   • Review place value and estimation from prior days

2. Model Demonstration (15 min):

   • Teacher models 432 ÷ 12 using base-ten blocks: grouping thousands, hundreds, and tens
   • Demonstrate area model method by drawing rectangle grids representing dividend and divisor

3. Hands-on Practice (25 min):

   • Students work in pairs with blocks and grid paper to solve assigned division problems
   • Rotate among groups to support and encourage explanation

4. Small Group (10 min):

   • Intervention: Simplify problems to smaller dividends and divisors, support block manipulation
   • Advanced: Use mixed model methods (base-ten + partial quotient area models)

5. Closure (5 min):

   • Students reflect in journals on which model helped them understand division best

Differentiation Strategies

• Use tactile manipulatives for kinesthetic learners
• Visual step-by-step modelling for ELLs and learners needing clarity

Extension

• Design your own area model for a division problem you create and present it.

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Day 4: Review & Intervention

I Can

• I can apply place value patterns, estimation, and models to divide effectively.

Success Criteria

• I solve division problems using at least two different strategies
• I explain my reasoning clearly
• I receive support when needed to improve my understanding

Activities

1. Warm-up (10 min):

   • Quick quiz game re-capping core skills from days 1-3

2. Small Groups (40 min):

   • Groups by skill level:
     • Intervention group focuses on foundational skills with targeted scaffolding and manipulatives
     • Core group practices full problems and connects strategies
     • Advanced group applies skills to multi-step real world division problems

3. Group sharing (10 min):

   • Groups present one strategy they learned or improved on

Differentiation Strategies

• Scaffold tasks, provide visual aids and sentence starters for interventions
• Encourage peer mentoring and independent problem solving for advanced learners

Extension

• Challenge: Create a division word problem that requires estimation and place value to solve.

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Day 5: Assessment & Reflection

I Can

• I can demonstrate my understanding of division using place value, estimation, and models.

Success Criteria

• I complete the assessment using the skills I have learned
• I reflect on my strengths and areas for growth
• I set a goal to improve further in division

Materials

• Paper-based assessment
• Reflection journals

Activities

1. Assessment (40 min):

   • Students complete a multi-part division assessment:
     • Part 1: Mental division problems using place value patterns
     • Part 2: Estimation questions
     • Part 3: Model-based division problems

2. Reflection (15 min):

   • Students journal about their learning journey, including "I can" statements and success criteria they met
   • Teacher facilitates goal setting for division skills improvement

3. Closure (5 min):

   • Class discussion about progress and excitement for future math challenges

Differentiation Strategies

• Provide extra time or quiet space for students who need it
• Allow use of place value charts or models during assessment if appropriate (per IEP or 504)

Extension

• Create a personalized division strategy guide summarizing what worked best for you.

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Final Notes for Teachers

• Grouping: Flexible small groups allow fair intervention without stigma and challenge advanced learners.
• Formative Feedback: Collect exit tickets daily during warm-ups to inform next day’s small groups.
• Materials Prep: Prepare manipulatives and problem cards prior to class to streamline transitions.
• Family Engagement: Send home a one-page summary of division strategies with "I can" statements for family practice support.

This detailed, varied, and scaffolded unit places 5th graders firmly on the path to mastering reliable division strategies with a strong conceptual foundation aligned with Common Core expectations.