Welcome to our lesson on finding part-part-whole relationships! Understanding how numbers can be broken down into smaller parts is a fundamental skill in mathematics. In this lesson plan, we will introduce a systematic process for finding combinations of part-part-whole relationships. Providing learners with a structured approach ensures that they can identify every combination while deepening their understanding of numbers.
One key concept in part-part-whole relationships is realizing that a systematic process can be used for finding combinations.
One strategy involves starting with the total number paired with 0 and then decreasing the first number by one while increasing the second number by one until reaching 0 paired with the total number.
For example, when exploring combinations of five, the process begins with 5 paired with 0, then progresses to 4 paired with 1, and so on. This step-by-step approach ensures that all possible combinations are considered.
It's important to note that learners may not immediately catch on to this process, but encourage them to study the results to identify any patterns or relationships between the numbers.
Teaching Plan
Here are some strategies that can help your learner become confident in finding part-part-whole relationships. Be sure to reinforce the concepts with ongoing practice, activities, and games.
Examples and visuals to support the lesson:
1. Representing Part-Part-Whole Relationships
For this activity, your learner will need double-sided counters with distinguishable sides, such as different colors on each side. You can also use game tokens or coins with stickers.
Begin by providing your learner with five counters and ask them to arrange the counters in any way they prefer, deciding how many to show as one color and how many as another.
Next, create a drawing of the arranged counters in a line and then draw a corresponding part-part-whole model, such as a cherry diagram. The diagram should have the number 5 at the top to represent the total number of counters, with the number of each color counter represented in the bottom circles.
Work through different combinations of counters in no particular order, emphasizing that it's not necessary for the learner to find every combination at this stage. The goal is to familiarize them with the process of representing part-part-whole relationships.
If your learner arranges all counters as one color, draw the cherry model with 0 as one of the parts to indicate that there are none of the other color.
Also, note that while finding combinations of colors, the order matters. For example, three red and two blue is different from three blue and two red, although they can be represented by the same cherry diagram. This works because the cherry diagram only considers the numbers, not the colors.
To facilitate language and communication, use stem sentences to help your learner explain which number represents each color. For instance, "The five represents all the counters. The ___ represents the blue counters. The ___ represents the red counters." This structured approach encourages clear communication and understanding of the part-part-whole relationships.
Skill Check
I can use math tools like counters to find part-part-whole combinations.
2. Using a Strategy for Finding Part-Part-Whole Combinations
In this activity, we'll introduce a step-by-step process to ensure that we find all possible combinations of part-part-whole relationships.
Begin by asking your learner, "How can we be sure that we have all the possible combinations?" Give them time to brainstorm different ideas. If they haven't already discovered it, introduce the idea of following a systematic process to ensure comprehensive coverage.
Line up five double-sided counters with the same color. Then systematically flip one counter at a time, giving your learner time to verbalize the color combinations they observe. Record each combination in a table or with cherry models to visually represent the part-part-whole relationships.
After working through each example together, review the table or cherry models with your learner to reinforce understanding and ensure that all possible combinations have been identified.
Skill Check
I can use a strategy to find every part-part-whole combination.
3. Ongoing Reinforcement
To wrap up the lesson, summarize by identifying the three different number pairs that make five. These pairs include 5&0, 4&1, and 3&2.
Have your learner create a poster featuring the three cherry representations of these pairs so that they can refer to them in upcoming lessons and activities. Becoming fluent in these pairs will provide them with a strong foundation for addition and subtraction skills, as they will intuitively understand the relationship between numbers.
Provide opportunities for ongoing practice with these pairs. For instance, your learner can play a game like "snap" with number cards ranging from 0 to 5. Each player flips a card, and they say "snap" when a pair comes up that totals five. They can refer to their part-part-whole posters to check that their pairs indeed total five.
Summary
In this lesson, we have explored the concept of part-part-whole relationships and introduced a systematic process for finding combinations of these relationships. Following a step-by-step strategy helps learners develop fluency in finding number pairs and provides a strong foundation for addition and subtraction skills.
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Skill Check