Partitioning Numbers to 5

Introduction

Welcome to partitioning numbers! Partitioning is a crucial skill in mathematics that allows learners to break down whole numbers into smaller parts, enhancing their understanding of numerical relationships. In this lesson plan, we will explore key concepts behind partitioning numbers to 5, provide strategies for representing partitioning, and offer practical activities to help learners master this fundamental mathematical skill.

Before beginning the lesson, your learner should be comfortable counting sets up to 5.

Key Concepts for Partitioning Numbers to 5

One key concept behind partitioning numbers is the recognition that a number can be split in various ways, leading to different part-whole relationships.

To represent partitioning, learners can use various diagrams and models. Common representations include part-part-whole models such as cherry diagrams and bar models.

• Part-Part-Whole Models: Part-part-whole models depict the relationship between the whole number and its constituent parts.
• Cherry Diagrams: Cherry diagrams (also called number bonds) are a type of part-part-whole model that represents partitioning using a circle (cherry) at the top connecting to two circles underneath.
• Bar Models: Bar models are another kind of part-part-whole model showing bars whose lengths correspond to the whole number and its parts.

These visual tools help learners visualize the relationship between the whole number and its parts, facilitating comprehension and problem-solving. This lesson will focus on using cherry diagrams.

Teaching Plan

The following activities will help your learner become confident in partitioning numbers. While the ultimate goal is fluency in partitioning up to 10, focus on developing their fluency with numbers up to five at this stage. Go through each activity using the number 5, then proceed to 4, 3, 2, and 1.

Examples and visuals to support the lesson:

1. Recognizing Parts of a Group

To help your learner grasp the concept of partitioning numbers up to five, begin by providing both concrete and picture representations of five items.

• Choose items that can be quickly subitized, allowing your learner to recognize the number of items without counting each one. Take the time to ensure they are comfortable counting and subitizing to 5.
• Include groups where the items can be easily classified into two distinct groups. For example, you could use cupcakes with and without cherries, a group of children where some are sitting and some standing, or a collection of triangles of different colors.
• To draw your learner's attention to the smaller quantities within the group, ask questions such as "what numbers can you see?" Encourage them to describe what they observe using full sentences, incorporating numbers that represent the parts and the whole. For instance, they might say they see five triangles, with four being green and one being red.
• As your learner describes what they see, use drawings or diagrams to visually represent the part-part-whole relationship. Cherry diagrams and bar models are effective tools for illustrating this relationship. These diagrams typically show the quantity of the whole written at the top, with the quantities of the parts displayed underneath.

Skill Check
I can see how a group of objects is made of smaller groups.

2. Making Part-Part-Whole Diagrams

Once your learner has grasped the concept of part-part-whole diagrams through the examples provided, have them create their own diagrams based on verbal descriptions and pictures.

• Provide groups of items with different contexts that can be easily partitioned based on color, size, or other obvious distinctions.
• Incorporate both pictures and descriptions to aid understanding. For instance, you could say, "There are five sheep. Four sheep are black, and one sheep is white. Draw this on a part-part-whole diagram."
• Introduce examples where the items are partitioned into more than two parts. For example, present a bunch of flowers with three different colors or describe a scenario like, "I have one spoon, two forks, and two knives. I have five pieces of cutlery."

Skill Check
I can draw pictures to show how a number is made of smaller numbers.

3. Partitioning a Number in Different Ways

In this activity, your learner will have the opportunity to independently discover part-part-whole relationships and create corresponding diagrams.

• Present them with scenarios that allow for exploration of different ways to partition a set of items. Emphasize the flexibility of partitioning, highlighting that a number can be divided in various ways.
• Draw attention to cases where one of the parts is zero. For instance, all five flowers being red. Encouraging your learner to include zero in their diagrams will broaden their understanding of partitioning.
• Allow your learner time to practice completing part-whole diagrams for each solution they find. At this stage, there's no need for them to follow a systematic method or find a pattern in creating their diagrams, although they may discover one on their own. It's okay if there's repetition in their answers; use these instances as teaching opportunities. For example, point out repetitions by saying, "Look, we've got a three and a two again."

Skill Check
I can find different ways to split a number into two smaller numbers.

4. Challenge Activity

After your learner has demonstrated a solid understanding of partitioning numbers up to five and creating part-part-whole diagrams, challenge them with a more complex task to assess their comprehension and encourage critical thinking.

• Present a scenario such as: "There are two plant pots and five seeds. The gardener puts more seeds in Pot A than Pot B. How many seeds might be in each pot? How many seeds cannot be in Pot A?"
• This task prompts your learner to think critically about how to partition the number 5 effectively and consider different possibilities for distributing the seeds between the two pots.
• Encourage them to use drawings or concrete objects to work through the problem. Have them explain their thoughts process and discuss any challenges they encounter.

Skill Check
I can use what I know about parts of numbers to solve problems.

Once your learner has shown proficiency in partitioning the number 5, gradually introduce the numbers 4, 3, 2, and 1 in a similar manner. Each step builds upon their understanding and fluency in creating part-part-whole diagrams, ultimately strengthening their overall grasp of numerical concepts.

Additional Resources

Use these resources to support your learner's journey in partitioning numbers to 5:

• Part-Whole Cherry Models (mathsbot.com)

Summary

In this lesson plan, we explored the concept of partitioning numbers to 5, a fundamental skill in mathematics. By breaking down whole numbers into smaller parts, learners gain a deeper understanding of numerical relationships and develop problem-solving skills. We discussed key concepts behind partitioning, explored various ways to represent partitioning using diagrams and models, and provided practical activities to help learners build fluency in part-part-whole relationships.

Teaching Plan adapted from NCETM under OGL license v3.