In this lesson plan, your learner will be introduced to a powerful tool for understanding how groups of objects can be partitioned and represented visually. We will start by exploring partitioning groups of concrete objects and arranging them within part-part-whole cherry diagrams. As we progress, we will use numerals to represent the wholes and parts on the cherry diagrams.
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. Groups 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 group while the whole group is always larger than each of its parts.
Recombining Parts: Partitioned parts can be combined back together to reconstruct the original whole group. This shows learners that the combined size of the parts is the same as the whole.
Cherry Diagrams: Cherry diagrams serve as a tool to help learners visualize part-part-whole relationships. The cherry diagrams show one circle that represents the whole group extending to two or more circles that represent the parts of the group.
Teaching Plan
The following activities will help your learner become confident with using part-part-whole cherry diagrams.
Examples and visuals to support the lesson:
1. Moving Objects from Whole to Parts
The purpose of this activity is to familiarize your learner with part-part-whole cherry diagrams. Use a variety of contexts that demonstrate the partitioning of whole groups into two clearly identifiable parts. Encourage your learner to practice describing the wholes and parts in full sentences.
Provide your learner with a large part-part-whole diagram, along with concrete objects of cut-out pictures that can be physically arranged on the diagram. Next, demonstrate how to move objects from the whole section of the diagram into the parts section.
Ensure that objects are not shown in the whole and parts sections simultaneously. For instance, avoid displaying five objects in the whole section at the same time as showing five objects (as three and two, for example) in the parts sections. The resulting diagram would show a total of ten objects which may lead to confusion.
Skill Check
I can split a whole group of objects into two parts on a cherry diagram.
2. Moving Objects from Parts Back to Whole
Once your learner is comfortable moving objects from the whole section to the parts sections, demonstrate moving them from the parts sections back to the whole.
Continue to move the objects back and forth to represent splitting them into parts (partitioning) and recombining the parts. This will help your learner recognize that the whole and the two parts are equivalent quantities.
Emphasize the concept of conservation of number and the equivalence between the parts and the whole. For example, ask your learner "Do we still have five?" after splitting into parts.
Incorporate a range of contexts and variations, such as:
Changing the orientation of the diagram (with the whole section on the left instead of the top) will help your learner realize that the orientation doesn't affect the relationships of the quantities.
Including examples where the two parts contain the same number of items.
Using groups composed of objects of different sizes and shapes.
Partitioning a given whole in several different ways.
Skill Check
I can combine the parts of group together to make a whole group on a cherry diagram.
3. Representing Whole and Parts with Numerals
Next, we'll move on to representing the whole and parts with numerals.
Moving completely into the abstract representation can be a difficult step for children, so it helps to link the numerals to a real context. For example, show a picture of 3 umbrellas where 2 are open and 1 is closed. This will provide your learner with a clear way of partitioning and numbering the groups.
Provide a cherry diagram with the pictures along with one with the numerals. Have your learner describe in full sentences what each numeral represents. For example, the 3 represents the whole group of umbrellas. The 1 represents the closed umbrella. The 2 represents the open umbrellas.
Continue to use the picture and numeral models together so that your learner can make connections between the concrete, pictorial, and abstract representations.
Skill Check
I can use numbers on a cherry diagram to show the whole group and parts of the group.
4. Partitioning Different Ways
In the previous activity, the context prompted your learner to partition the group in a particular way (for example, open umbrellas and closed umbrellas). Now they will physically partition groups of objects in a variety of ways.
Provide your learner with a large cherry diagram and a group of identical manipulatives such as counters or cubes. Using identical objects will help them to see how the group can be split into parts regardless of features like color or size. Encourage your learner to explore the different ways that these objects can be partitioned.
Initially, provide prompts to guide your learner. For example, tell them "Show me five cubes in the whole group. Five is the whole." Make sure they put the correct number of objects in the whole section. Then tell them "Three is a part and two is a part." Have them move the cubes into the parts sections. Have them repeat after you, "Three is a part. Two is a part. Five is the whole."
Next, have your learner combine the parts into the whole section again, reinforcing the idea that the parts can be recombined to make the whole and that the starting quantity is conserved. Repeat the partitioning and recombining process in different ways.
When they are ready, guide your learner in transitioning to pictorial representations by drawing the cubes on printed cherry diagrams (one diagram showing the objects in the whole section and another diagram showing the objects in the parts sections). Finally, support the transition from pictorial to abstract by having them write the numerals on a diagram.
Skill Check
I can split a group into parts in different ways and combine them back together into a whole group.
5. Discussion Questions
Throughout the activities, ask your learner the following questions to reinforce key points:
"What do you notice about the size of the parts and the size of the whole?" Draw attention to the fact that neither part is larger than the whole; each part is smaller than the whole.
"What happens when you put the two parts back together?" Draw attention to the fact that the two parts together have to equal the number of the whole group (conservation of number).
"How many different ways can you split the whole group into two parts?" Encourage your learner to use the stem sentence "___ is the whole; ___ is a part and ___ is a part." Emphasize that the context can be described by beginning with the whole or by beginning with the parts. For example: "Dan has 5 pennies. There are three pennies in one pocket and two pennies in the other." Or "Dan has three pennies in one pocket and two pennies in the other. He has five pennies altogether."
To provide challenge, ask questions such as "Liam says he has 5 cupcakes and that he can put three cupcakes on one plate and three cupcakes on another plate. Is he right?" This example explores the concept that the two parts cannot total more than the whole.
Skill Check
I can use cherry diagrams to answer math questions about wholes and parts of groups.
6. Challenge Activities
Have your learner explore partitioning a group of identical objects into three parts. Provide contexts that challenge them to split them as many ways as possible. To provide additional challenge, you could extend it to more than three parts. You could also have them tell their own story that represents partitioning into three or more parts. For example, tell them to tell a story about sharing cookies with friends and draw a cherry diagram to represent it.
Summary
This lesson plan has introduced your learner to the concept of part-part-whole cherry diagrams as a method to represent and explore partitioning groups of objects. We began by using concrete objects to physically arrange and visualize partitions and progressed to writing numerals on the cherry diagrams. These skills will pave the way for deeper explorations into math concepts involving grouping, distribution, and relationships between numbers.
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Skill Check