Recognizing Wholes and Parts

Introduction

At this foundational stage, children begin to grasp how things can be broken down into smaller components (parts) that together make up a larger unit (whole). This skill prepares them for understanding many mathematical concepts. In this lesson plan, we will explore the concept of wholes and parts using familiar objects.

The Importance of Learning Wholes and Parts

Understanding wholes and parts provides learners with a foundation for understanding part-whole relationships. This concept applies to several math concepts. Here are a few examples:

• Addition: Recognizing that combining parts makes a whole prepares children for addition. For example, understanding that 2 and 3 together make 5 sets the stage for basic addition facts.
• Subtraction: Knowing that a whole can be broken into parts helps in understanding subtraction. For instance, knowing that 5 (whole) - 3 (part) = 2 (remaining part) introduces the concept of subtraction.
• Geometry: Recognizing wholes and parts helps in understanding basic geometric shapes and their compositions. For instance, realizing that a square can be made of smaller triangles or rectangles highlights the relationship between parts and wholes.
• Measurement: Understanding wholes and parts is crucial for measurement concepts. For example, realizing that two halves make a whole helps in grasping basic units of measurement like halves and quarters.

Common Mistakes and Misconceptions

Keep these common mistakes in mind during the lesson:

• Confusing Whole and Hole: Young learners may confuse the words "whole" and "hole." Provide visual representations such as drawings or physical objects to demonstrate the difference between a whole (complete object) and a hole (an opening or gap). During the lesson, emphasize the spelling of "whole" and have your learner practice writing and spelling the word.
• Equating Size with Being a Part: Children might think that something is considered a part just because it is smaller in size compared to another similar object. For example, believing that a whole apple is only a part of an apple if it is smaller than a different apple. Show different-sized objects (e.g., large and small apples) and explain that both can be considered wholes (complete objects).

Teaching Plan

The following activities will introduce your learner to the concept of wholes and parts.

Examples and visuals to support the lesson:

1. Introducing the Concept of Wholes

To begin, let's introduce the idea of a whole using familiar objects. It's important to use objects that remain recognizable when split into parts. For example, we'll avoid using objects like a length of ribbon, as it can be challenging for children to recognize it as a whole object once it's cut up.

• Start by using objects like a whole carrot, apple, etc., as they can easily be cut or broken up.
• Introduce the term "whole" by asking what makes an object a whole and give your learner a moment to come up with their own response.
• Explain that "whole" means having all of the item and show a variety of objects such as a whole banana, a whole sandwich, etc.
• Encourage deeper thinking by asking questions like "Is this a whole apple? Why is it a whole apple? Can you see anything else that is a whole?"
• Build towards using the stem sentence: "This is a whole ___ because I have all of it."

Skill Check
I can recognize things that are whole.

2. Different Sizes of Wholes

Once your learner is able to identify whole objects, let's introduce the concept of wholes that can be different sizes. Use different-sized examples of a given object to draw attention to the essential feature of a whole as being a complete object, regardless of its size.

• Ask questions like "What do you notice? What's the same? What's different?"
• Prompt your learner to compare different-sized examples of objects and ask questions like "Is the small carrot a whole carrot? How do we know?"
• Include a range of familiar objects of different shapes and sizes to reinforce the concept.

Skill Check
I know that whole objects can be different sizes.

3. Parts of a Whole

Now, let's move on to the concept of "not whole" by showing part of a whole object. This will help clarify the essential feature of a whole: that it represents the entire object.

• Show half of a carrot and ask your learner "Is this a whole carrot?" and prompt them to explain their answer.
• Encourage the use of stem sentences like "This is not a whole ___ because I don't have all of it" or "This is not a whole ___ because I only have part of it."
• Encourage your learner to identify "wholes" and "not wholes" in a group of objects, using a variety of shapes and sizes.

Skill Check
I can recognize things that are not whole.

Summary

This lesson plan introduces your learner to the concept of wholes and parts using familiar objects. Through hands-on activities, they explore what makes an object a whole and learn to identify different-sized wholes. They also explore the idea of "not wholes" by examining parts of objects, reinforcing the understanding that a whole represents the entire object.

Teaching Plan adapted from NCETM under OGL license v3.