Wholes and Parts of Objects

Introduction

Welcome to our lesson on exploring the wholes and parts of objects! In this lesson plan, we will guide learners through hands-on activities to deepen their understanding of wholes and parts and practice partitioning objects into parts.

Before beginning the lesson, your learner should be familiar with recognizing wholes and parts.

Key Concepts for Wholes and Parts of Objects

Here are some concepts that are helpful to know for the lesson:

• Partitioning: Partitioning refers to dividing objects or groups of objects into smaller parts or sections. Objects can be partitioned in various ways, resulting in parts of different sizes or uniform sizes.
• Part Sizes: The parts obtained from partitioning are always smaller than the whole object. The whole object is always larger than each of its parts.
• Recombining Parts: Partitioned parts can be combined back together to reconstruct the original whole object. This shows learners that the combined size of the parts is the same as the whole.

Teaching Plan

The following activities will help your learner understand wholes and parts of objects while they practice partitioning objects.

Examples and visuals to support the lesson:

1. Partitioning Objects into Two Parts

Once your learner has mastered identifying and describing "wholes" and "not wholes," it's time to introduce the concept of partitioning objects where a whole can be split into parts. For hands-on work, consider using bananas, which are easy for children to cut themselves, or pictures of a fruit/vegetable that can be cut in different ways using scissors.

Tasks and Questions:

• Can you cut your banana into two parts that don't look the same?
• Can you cut your banana into two parts that are about the same size?
• Can you cut your banana so that one part is a lot bigger than the other part?
• If you eat both parts, will you be eating the whole banana? (hinting at the concept that the parts can be combined to make the whole)
• How could you cut your banana to give you the biggest possible part? What do you notice about the other part? (drawing attention to the fact that if one part is large, the other part will be small)
• Can you cut your banana so that one part is bigger than the whole? Why not?

Encourage your learner to use the following generalized statements:

• A whole can be split into two parts in lots of different ways.
• A whole is always bigger than a part of the whole.
• A part is always smaller than its whole.

To promote deeper thinking, show a picture of the same object in a variety of orientations, split into two parts in a variety of ways, and ask your learner to identify a pair of images which show the whole being split in the same way.

Skill Check
I can split an object into two parts different ways. I know that the whole object is bigger than the parts and the parts are smaller than the whole.

2. Partitioning Objects into More Than Two Parts

Once your learner is secure in their understanding that a whole can be split into two parts, explore partitioning objects into more than two parts, reinforcing the key concepts from the first activity.

• Begin by providing a banana and asking, "Can you cut your banana into more than two parts?" Discuss the different ways that the banana can be cut.
• Use the following question to reinforce the concept that the parts, no matter how many there are, will combine to make the whole: If you ate all the parts of your banana, how much of the banana will you have eaten?
• Make your learner aware of the generalized statement: a whole can be split into more than two parts in lots of different ways. Have a discussion about whether it matters that the parts are different sizes or shapes to secure your learner's understanding of the concepts of wholes and parts.

Skill Check
I can split objects into more than two parts in different ways. I know that the parts can combine to make the whole.

3. Exploring Four Parts of an Object

Use this activity as an optional challenge for your learner. Provide them with a picture of an object such as a slice of cheese. Ask them, "Can you cut this picture of a slice of cheese into four parts so that one part is bigger than the other three? Can you do this in more than one way?"

Other similar tasks include cutting the slice into four parts so that:

• One part is a lot bigger than the other three.
• There are two large parts and two small parts.
• The parts are about the same size but look different.
• The parts all look the same.

After they complete a task, ask them, "Can you do it more than one way?" Tasks with more than one solution, such as these, encourage children to reason mathematically and creatively, and provide opportunities for them to reflect upon what's the same and what's different.

Skill Check
I can follow directions to split an object in a specific way.

Summary

By engaging in these activities, your learner will develop a deeper understanding of the relationships between wholes and parts. Understanding partitioning prepares your learner for many math skills, including fractions, ratios, and geometric shapes, where objects are divided and recombined to analyze their properties. Have fun exploring the concepts of splitting wholes into parts!

Teaching Plan adapted from NCETM under OGL license v3.