In this unit plan, we will explore different strategies and tools to teach part-whole relationships. By the end of this unit, your learner will be able to recognize and describe part-whole relationships for numbers up to 10, decompose and compose quantities in multiple ways, and use visual tools to represent these relationships.
Key Concepts
Let's cover a few key concepts for understanding part-whole relationships and how to help your learner develop fluency with them.
Part-Whole Fluency: Part-whole fluency is the ability to recognize and describe the relationships between numbers. It involves understanding how numbers can be composed (built) and decomposed (broken down) in multiple ways. By developing part-whole fluency, children gain a solid foundation for addition and subtraction, as well as a deeper understanding of number sense.
Composing and Decomposing Numbers: Composing involves combining smaller numbers to build a larger one. For example, we can combine 3 and 4 to form 7. On the other hand, decomposing involves partitioning a larger number into smaller parts. For example, we can decompose 6 into 2 and 4. These concepts lay the foundation for addition and subtraction skills, as children learn to manipulate numbers flexibly and understand their composition and structure.
Make 5 and Make 10: Make 5 and Make 10 involve composing 5 and 10, respectively. In Make 5, children recognize pairs of numbers that can be combined to form five such as 2 and 3. Similarly, in Make 10, they identify pairs of numbers that combine to 10, such as 6 and 4. These strategies lay the groundwork for mental math enabling students to quickly recall addition facts and build confidence in their math abilities.
Unit Plan for Exploring Part-Whole Relationships
Begin with smaller numbers up to 5, and gradually increase to 10 as your learner is ready. These skills should be worked on gradually and consistently throughout the school year, allowing your learner to fully grasp the concepts before moving on to larger numbers.
Learning Goals
The activities in this unit plan will help your learner develop fluency in the following skills:
Explore wholes and parts for objects and groups of objects.
Use objects, drawings, and numbers to decompose (partition) and compose (combine) quantities up to 10 in different ways.
Use visual tools such as part-part-whole cherry diagrams and bar models to represent part-part-whole relationships up to 10.
Find all possible combinations for decomposing quantities up to 10 into two parts.
Find missing parts of part-part-whole combinations up to 10.
Before beginning the lessons, your learner should be able to count groups of up to 10 items. It is also beneficial if they can subitize up to 5.
1. Understanding Wholes and Parts
Introduce the concept of wholes and parts to your learner using concrete objects and pictures.
Provide your learner with objects or pictures that can easily be cut or broken into parts such as a banana or piece of paper. Discuss the concept of a whole and how the object can be divided into parts. Encourage your learner to identify different ways to cut the object into parts.
Provide a collection of objects such as toys or blocks. Ask your learner to count the number of objects in the collection. Explain that the total number represents the whole group of objects and that it can be split into parts. Encourage your learner to identify different parts of the collection, such as groups of two or three objects.
2. Decomposing and Composing Quantities
Use objects, pictures, and numbers to decompose and compose quantities up to 10.
Give your learner a set of cubes. Ask them to build a train using a specific number of cubes, such as 5.
Have your learner take apart the train and rearrange the cubes into groups to create different combinations.
Discuss the different ways the cubes can be partitioned and how the parts relate to the whole group of cubes.
Provide a variety of objects and pictures for your learner to practice partitioning up to five and gradually increase to 10.
3. Part-Part-Whole Diagrams
Introduce your learner to visual tools such as cherry diagrams and bar models for modeling relationships between wholes and parts.
Using a cherry diagram as a mat, show your learner how to partition a group of objects into parts. Start by placing objects in the circle that represents the "whole" and move them to the circles that represent the "parts."
Explain that instead of using the objects, we can write numbers on the cherry model to show the quantity of the whole and the quantities of the parts.
Choose a number, such as 5, and ask your learner to represent a group of 5 objects using the cherry diagram. Have them represent the group with objects, then with numbers.
Repeat with different numbers, gradually increasing the complexity up to 10.
4. Finding Combinations of Parts
Once your learner is comfortable partitioning groups using objects, pictures, and models, challenge them to find all the possible ways that a number can be decomposed.
Give your learner a number such as 5 and have them find all the ways it can be decomposed into two parts. Provide objects such as coins or two-colored counters that can be flipped to show combinations of heads and tails, or red and yellow, for example.
Encourage your learner to look for patterns and use their knowledge of part-whole relationships to find all possible combinations.
Repeat with different numbers, gradually increasing to 10.
5. Finding Missing Parts
Next, your learner can demonstrate their fluency in part-whole relationships by finding missing values. Begin with finding missing parts up to five, then gradually up to 10.
Provide your learner with part-part-whole diagrams that have a missing quantity. Have them use reasoning skills, drawings, or objects to find the missing value.
For example, show them a bar model that has 3 and 4 written for the parts and ask your learner to find the value of the whole. They can reason that 3 and 4 combine to make 7, so the whole has to be 7.
You can also show them a model that has the whole and one part, and ask your learner to find the other part. For example, you can write 6 for the whole and 1 for a part. Your learner can reason that the other part has to be 5.
By incorporating activities and visual tools like bar models, cherry diagrams, and cube trains, you can effectively teach your learner about part-whole relationships. These strategies will provide your learner with a solid foundation for understanding numbers and developing their critical thinking skills. Remember to work at a pace that is comfortable for your learner and provide plenty of opportunities for practice and exploration.
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