Welcome to our lesson plan on understanding wholes and parts of groups! In this lesson, your learner will engage in hands-on activities to deepen their understanding of how groups of objects can be defined as wholes, and how they can be split into parts.
Here are some concepts that are helpful to know for the lesson:
Defining a Whole Group: A group of objects is defined as a whole based on the context of the situation or the information provided in a problem. For example, a collection of eggs is considered a group based on the carton they are in. The objects within a group can be identical or different from each other.
Identifying "Not Whole" Groups: A part of a group, which learners may refer to as a "not whole" group, is identified when one or more objects are missing from the original group.
Partitioning into Smaller Groups: Groups of objects can be partitioned in various ways, where the original group is divided into smaller groups based on specific criteria or conditions. This partitioning allows for different arrangements and combinations of the objects within the group.
Teaching Plan
The following activities will help your learner understand wholes and parts of groups while they practice partitioning objects.
Examples and visuals to support the lesson:
1. Introducing Whole Groups
Begin by using concrete representations to introduce the concept that a "whole" can refer to a full group of discrete objects. For example, a full tray of six cupcakes. Use boxes or trays with spaces for the objects to fit in so that your learner can easily see if any are missing.
Tasks and Questions:
Help your learner identify a "whole tray of cupcakes" vs "not a whole tray of cupcakes."
Show different representations of the whole and ask questions like, how do we know this is the whole group of cupcakes?
Encourage your learner to apply what they learned about partitioning one object into parts to explain that if the tray is full of cupcakes, they have the whole group of cupcakes and none are missing.
Use the stem sentence: "This is a whole group of ___ because I have all of them and none are missing."
Skill Check
I can recognize a group of objects as a whole group.
2. Variation in Whole Groups
In this activity, we will explore variation within groups.
Show your learner whole groups containing non-identical objects, such as different colored eggs in a tray full of eggs, or different colored chocolates in a full box of chocolates. Ask questions to explore whether it is still a whole group if the objects are no longer identical.
Encourage deeper thinking by providing examples where part of the whole is covered and ask whether the group is still whole. Encourage your learner to discuss and explain their reasoning.
Skill Check
I know that a group of objects is still a whole group even if the objects are different.
3. Exploring Parts of Groups
Once your learner can identify a group of objects as a whole, move on to the concept of "not whole" by exploring parts of groups.
Show part of a whole group of objects and ask your learner whether it is the whole. Have them explain why they know that it is not a whole group.
Encourage your learner to use the stem sentence: "This is not a whole group of ___ because we don't have all of them, some of them are missing."
Skill Check
I know that a group is not whole if some of the objects are missing.
4. Extending the Concept of Whole Groups
In the first three activities, the groups were clearly defined by the container that the objects were in. This activity extends to contexts where the whole group is defined as a given number of objects.
Begin with an example using concrete objects. For example, "I have 4 toy cars." Show your learner the four toy cars. Ask them if this is the whole group of cars. Encourage them to explain how they know.
Next, provide variation by showing a different number of objects. For example by saying, "You have 6 toy cars, show me your whole group of cars." Ensure that your learner understands that whole can refer to groups of different quantities.
Encourage them to use the stem sentence: "This is the whole group of ___, I have all of them."
Skill Check
I can tell if a group of objects is whole based on the number of objects that should be in the group.
5. Identifying Parts of Groups
Once your learner understands the concept of a whole group of discrete objects, begin to identify a part of the whole group.
Provide your learner with a picture of a group of objects. Guide them in identifying the whole and a part of the group. For example, "There are 4 pencils in the whole group. There are three pencils in the part of the group that is circled."
Include problems where your learner is asked to create or draw the whole group of objects and must identify a part of the group.
To encourage deeper thinking, ask questions such as: What is the smallest number of toy cars you could have in your part? What is the largest number of toy cars you could have in your part?
As they learn to identify the whole and part of a group, encourage them to use a stem sentence such as: "There are (number) ___ in the whole group. There are (number) ___ in this part of the group."
Skill Check
I can use numbers to describe the wholes and parts of groups.
6. Partitioning Groups in Different Ways
Provide a task where you define the number of objects in the whole group and challenge your learner to find how many different ways they can split the group into parts. At this stage, it is not necessary to take commutativity into account. For now, it is okay to consider "three and one " as being different from "one and three" even though the objects are identical.
Skill Check
I can split a group into smaller parts in different ways.
Summary
By engaging in these activities, your learner developed a deeper understanding of wholes and parts of groups. They learned that groups of objects can be defined as wholes and practiced partitioning groups into parts. Partitioning groups helps learners solve problems involving distribution, sharing, or rearrangement of objects within a set. This skill will prepare your learner for many math skills including addition, subtraction, multiplication, and fractions.
With over 12 years of experience as a classroom teacher, tutor, and homeschool parent, my specialty is easing math anxiety for students of all ages. I'm committed to empowering parents to confidently support their children in math!
Skill Check