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Vertical Topic Study (K-6 Progression)

Objective:

Explore how a core math concept develops and is scaffolded across the K–6 continuum, highlighting developmental shifts and pedagogical implications.

Requirements:

  • Choose a foundational topic (e.g., multiplication, fractions, number lines, early algebra, decimals).
  • Trace the concept from kindergarten to grade 6 using:
  • NYS Standards
  • Common Core Progressions
  • EngageNY/Eureka Math or other curriculum samples
  • Create a visual “learning progression map” showing when and how the topic evolves.
  • Discuss instructional strategies, common misconceptions, and suggestions for cross-grade consistency.

Deliverables:

  • Written report or infographic
  • Short reflection on implications for curriculum planning or support for struggling learners
  • Fifteen minute presentation to your classmates. 

📈 Vertical Topic Study (K–6 Progression) – Project Instructions

Objective:
Explore how a core math concept develops across grades K–6, emphasizing developmental shifts, instructional strategies, and implications for curriculum planning.

✅ Project Requirements:

  1. Select a Foundational Math Topic
    Choose one core topic that appears across multiple grades. Examples include:

  1. Trace the Topic Through Grades K–6
    Use the following resources to analyze how the topic is introduced, expanded, and deepened from kindergarten to grade 6:

  1. Create a Visual “Learning Progression Map”
    Design a clear visual representation showing:

  1. You may use tables, flowcharts, timelines, diagrams, or a structured infographic.

  2. Write a Commentary or Summary Report
    Your written reflection (approx. 1–2 pages) should include:

  1. Reflection Paragraph
    Write a short reflection (1 paragraph) on the implications of this work for:

📝 Deliverables:

Vertical Topic Study (K–6 Progression) Rubric

Criteria

Excellent (4)

Proficient (3)

Developing (2)

Beginning (1)

Topic Selection & Focus

Clearly selects a foundational math topic with strong relevance and focus throughout the study.

Selects a relevant foundational topic with mostly clear focus.

Topic chosen is somewhat relevant but lacks clear focus.

Topic is unclear or not foundational to K–6 math.

Standards Alignment

Thoroughly traces the concept through NYS Standards, Common Core Progressions, and curriculum samples with detailed references.

Adequately traces the concept with appropriate references to standards and curriculum.

Provides limited or inconsistent alignment to standards and curriculum.

Minimal or no alignment to standards and curriculum.

Learning Progression Map

Creates a clear, accurate, and visually effective map showing concept development K–6.

Map shows concept progression with some clarity and visual organization.

Map is incomplete or lacks clarity in progression or visuals.

Map is missing, unclear, or inaccurate.

Instructional Strategies

Insightfully discusses instructional strategies, addressing developmental needs and misconceptions.

Discusses instructional strategies with some attention to developmental needs and misconceptions.

Mentions instructional strategies but lacks depth or clarity.

Omits or poorly addresses instructional strategies.

Misconceptions & Consistency

Clearly identifies common misconceptions and provides thoughtful suggestions for cross-grade consistency.

Identifies some misconceptions and offers basic suggestions for consistency.

Mentions misconceptions or consistency but lacks detail or relevance.

Does not address misconceptions or cross-grade consistency.

Reflection on Implications

Provides a thoughtful, well-articulated reflection on curriculum planning and support for struggling learners.

Reflection addresses implications with reasonable insight.

Reflection is superficial or only partially addresses implications.

Reflection is missing or unrelated.

Presentation & Clarity

Report or infographic is well-organized, professional, and easy to follow; free of errors.

Presentation is mostly clear and organized with minor errors.

Presentation is somewhat unclear or disorganized; several errors.

Presentation is confusing, incomplete, or error-filled.

Example

1. Topic Overview

Fractions are fundamental to understanding parts of a whole and rational numbers. This study traces how fraction concepts develop from informal partitioning in Kindergarten to operations with fractions and ratios by Grade 6. Understanding this progression supports effective scaffolding and instructional alignment across grades.

2. Standards Alignment

Grade Level

NYS Standards (Selected)

Common Core Progressions Highlights

Curriculum Samples (Eureka Math/EngageNY)

Kindergarten

K.G.A.3: Partition circles and rectangles into halves and quarters

Introduce equal shares (halves, quarters) as foundational concept

EngageNY K Module 5: Partition shapes into equal parts

Grade 1

1.G.A.3: Partition circles and rectangles into equal shares

Recognize and name halves, fourths as equal parts

Eureka Math 1st Grade Module 5: Fractions as equal shares

Grade 2

2.G.A.3: Partition shapes into halves, thirds, and fourths

Fractions as numbers on number line; understanding unit fractions

EngageNY 2nd Grade Module 6: Fractions on number lines

Grade 3

3.NF.A.1-3: Understand fractions as numbers

Connect fractions with division, number line placement

Eureka Math Module 4: Equivalent fractions, fraction comparison

Grade 4

4.NF.A.1-3: Extend fraction equivalence, ordering

Develop multiplication of fractions and decimals

EngageNY Module 5: Multiplying fractions

Grade 5

5.NF.A.1-7: Add, subtract fractions with unlike denominators

Operations with fractions and decimals

Eureka Math Module 3: Adding and subtracting fractions

Grade 6

6.RP.A.1-3: Apply ratio concepts using fractions

Division of fractions, complex fraction problems

EngageNY Module 5: Dividing fractions and ratio problems

3. Learning Progression Map

Grade

Concept Focus

Key Skills & Activities

Curriculum Example

–1

Partitioning shapes into halves and quarters

Use concrete shapes to partition; identify halves, quarters

EngageNY K Module 5: Partitioning shapes

2–3

Fractions as numbers on number lines

Represent fractions on number lines; identify unit fractions

Eureka Math 2nd Grade Module 6: Fraction number lines

3

Understanding equivalence and comparison

Use visual models and number lines to compare fractions

EngageNY Module 4: Equivalent fractions

4–5

Adding, subtracting, multiplying fractions

Add/subtract with like and unlike denominators; multiply fractions

Eureka Math Module 5: Fraction operations

6

Dividing fractions and applying ratios

Divide fractions; solve real-world ratio problems

EngageNY Module 5: Dividing fractions

4. Instructional Strategies, Misconceptions & Cross-Grade Consistency

Instructional Strategies:

Common Misconceptions:

Suggestions for Cross-Grade Consistency:

5. Reflection on Implications for Curriculum Planning and Support for Struggling Learners

This progression study highlights that fraction understanding builds incrementally, starting with concrete experiences in early grades and advancing to abstract operations by grade 6. Curriculum planners should ensure a smooth transition from tactile, visual learning to symbolic manipulation, with ample opportunities to revisit key concepts.

For struggling learners, targeted interventions using manipulatives and visual fraction models are critical. Emphasizing conceptual understanding rather than rote procedures can reduce common errors and deepen comprehension. Teachers should also use formative assessments to identify misconceptions early and provide timely support.

Cross-grade collaboration among teachers can foster consistent terminology and instructional approaches, minimizing student confusion as they progress through grades.