Lecture 7 Powerpoint

Session Overview

Currins 520: Developing Mathematical Thinking in Early Childhood Ensure to gather nametags, handouts, and supply boxes at the beginning of the session to create an organized and focused learning environment for participants.

Agenda

Topics Covered:

• Number Relationships: Understanding the concepts of 1 More, 1 Less, 2 More, 2 Less, crucial for developing early number sense.

• Homework Check-in: Review and discuss homework assignments related to number relationships to reinforce learning and provide feedback.

• Anchoring Concepts to 5 and 10: Strategies for helping children anchor their understanding of numbers, enhancing their ability to make quick calculations and comparisons.

• Part-Part Whole Relationships: Exploring how numbers can be viewed as parts of a whole, essential for addition and subtraction.

• Midterm Announcement: Inform students about upcoming midterm examinations, emphasizing the importance of review and preparation.

• Homework Discussion: Collaborative sharing of strategies and solutions regarding homework.

Learning Goals

Focus on the following:

• Deepening Understanding of Number Relationships: Emphasis on concepts like 1 more, 2 more, 1 less, and 2 less to build a strong foundation in number fluency.

• Anchoring to 5 and 10: Developing skills to confidently reference these numbers in various mathematical concepts.

• Part-Part Whole Relationships: Understanding how to recognize and use part-part-whole structures to develop number sense more holistically.

Key Concepts in Early Math Development

1. Early Counting and Addition/Subtraction: Introduce strategies for early counting, utilizing both tangible and representative objects.

2. Fundamental Number Relationships: Overview of key relationships, including:

   • Verbal Count Sequence: Mastering counting verbally in a sequential manner.

   • One-to-One Correspondence: Understanding that each object counted corresponds to one number.

   • Cardinality: Grasping that the last number counted represents the total amount.

3. Fluency Expectations:

   • Kindergarten (K.OA.5): Students should be able to count up to 5.

   • 1st Grade (1.OA.6): Students should extend their counting skills to 10.

   • 2nd Grade (2.OA.2): Aim to count up to 20 effectively.

4. Subitizing: Recognizing quantities without counting, fostering quick visual recognition of small amounts.

Types of Number Relationships

Four Key Relationships

• One More: Incrementally adding to a number.

• Two More: Progressing in larger increments.

• One Less: Understanding the concept of subtraction or reduction.

• Two Less: Further understanding reduction through larger decrements.

Benchmarks for Understanding

• Anchors to 5 and 10: These benchmarks serve as essential reference points for students as they explore more complex number relationships.

• Part-Part Whole Concept: A critical foundational concept that aids in developing a robust understanding of how numbers combine and separate.

Activities to Reinforce Learning

Activity: How Many Now?

• Task: Create a train of 6 cubes to offer a visual learning experience.

  1. Add one more cube and record the total.

  2. Add another cube and record the new total.

  3. Remove one cube and record the resultant total.

  4. Remove two cubes and record the final total.

Towers, Towers, Towers

1. Part 1: Building Towers: Participants construct towers using cubes (4-10) for comparative analysis, ensuring consistent starting points for stacks.

2. Part 2: Child Analysis:

   • Observe how children with and without hierarchical inclusion perceive quantities in towers:

     • Without Hierarchical Inclusion: Count each block individually.

     • With Hierarchical Inclusion: Identify relationships between quantities to simplify counting.

Nearby Numbers Board Game

• Instructions:

  1. Shuffle numeral cards and place face down in a stack.

  2. Take turns revealing cards and placing them in the correct sequence on the board.

  3. Engage in an explanation of sequences as a group to foster mutual understanding.

Treasure Hunt Activity

• Setup Instructions:

  1. Create a deck of index cards representing number sequences, ensuring to include treasure cards.

  2. Establish rows with color-coded dot cards and fill with numeral and treasure cards, modifying based on the interaction of players.

Show One More/One Less Activities

• Materials Required: Ten frames, counters, and numeral cards.

• Activity Steps:

  1. Work in pairs to demonstrate one more or one less using ten frames, matching to numeral cards.

  2. Analyze the differences in quantities shown on each frame.

Count On Two More Activity

• Materials Required: Count On Two More board and numeral cards.

• Steps:

  1. Flip a numeral card; represent it using counters.

  2. Count on two more and record the subsequent total.

Importance of Number Relationships

Recognizing 'one more' and 'one less' enhances:

• Counting Fluency: Developing a natural and quick ability to count.

• Understanding Cardinality: Grasping the concept that the last number counted represents the total amount.

• Foundations for Addition and Subtraction Skills: Establishing a solid groundwork for future mathematical operations.

Anchoring to 5 and 10 Concepts

• Highlight the significance of understanding number relationships in foundational math practices.

• Engage in discussions regarding anchoring numbers to 5 and 10 during collaborative activities to solidify conceptual understanding.

Part-Part-Whole Relationships

Defining the Concept

• Focus on how quantities can be divided and understood in parts, which is critical for shaping a deeper number sense.

Activities

• Implement hands-on tasks that explore combinations of numbers through the use of counters and number cards, promoting interactive learning.

Homework Check-in

• Review materials from the session and discuss the relevance of part-whole relationships as illustrated in the readings.

Midterm Exam Preparation

• Midterm Scheduled: For the week of March 24-28, 2025.

• Structure: Includes a mix of question types: multiple choice and short essay.

• Encourage students to organize their notes efficiently in preparation for the exam to ensure success in assessment.