Partitioning with objects and pictures is an engaging and effective way to introduce young learners to foundational concepts in mathematics. In this lesson plan, your learner will explore partitioning numbers 6 to 10 into two distinct parts. We'll begin with partitioning groups of objects and pictures, then represent the numbers with part-part-whole models.
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.
When first learning to find combinations, students often begin by randomly arranging a set of objects into two groups. However, following a strategy ensures that all combinations are found while helping learners discover relationships between numbers.
One strategy for finding combinations 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 six, the process begins with 6 paired with 0, then progresses to 5 paired with 1, and so on. This step-by-step approach ensures that all possible combinations are considered.
Teaching Plan
The following activities will help your learner become confident in partitioning numbers 6 to 10. Begin with number 6 and work up to 10. Spend several days reinforcing each number before progressing to the next number.
Examples and visuals to support the lesson:
1. Partitioning with Objects and Pictures
In this activity, your learner will explore the different ways to partition six into two parts.
Begin with concrete or picture representations where the context suggests a particular way of partitioning. For example, you can show your learner a picture of flags with two different patterns.
Have your learner represent the partitioning on part-part-whole diagrams. Encourage them to describe the meaning of the numbers. For example: "Six is the whole. Four is a part and two is a part."
Next, provide contexts where the items are identical, or where there is more than one way of partitioning. Once again, have your learner represent the contexts with various part-pat-whole diagrams and describe the meanings of the numbers.
Remember to include cases where one of the parts is zero. You can also challenge your learner to partition the six objects into more than two groups.
Skill Check
I can use objects, pictures, and models to show how a number is made of smaller numbers.
2. Finding All Combinations
Once your learner is comfortable partitioning six objects or pictures into parts, progress to using.
Provide your learner with a set of six double-sided counters. With double-sided counters, each part can be represented with a different color. For example, partitioning six into 5 and 1 can be shown as 5 red counters and 1 blue counter.
Encourage your learner to use the counters to systematically find all possible ways to partition six into two parts.
To begin, line up six 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. Refer to our lesson on Finding Part-Part-Whole Combinations for more details.
Record each combination using a part-part-whole model (cherry or bar model) to visually represent the part-part-whole relationships.
After working through each combination, review the part-part-whole 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. Building Connections
As you work through each number, take advantage of opportunities to build connections with other concepts. Here are a few examples:
For combinations where 5 is a part, encourage your learner to describe the whole number as "five and some more." For example, using counters or a part-part-whole model that partitions eight into five and three, have your learner say, "Eight is five and three more."
For combinations where both parts are the same number, tell your learner that they are called doubles. Encourage your learner to point out doubles whenever they occur. Recognizing doubles will come in handy as your learner works on addition.
Place extra emphasis on ways to partition ten as this will prepare your learner for addition and subtraction fluency. For instance, your learner can play a game like "snap" with number cards ranging from 0 to 10. Each player flips a card and says "snap" when a pair comes up that totals ten.
After your learner has shown proficiency in partitioning the number 6, repeat the activities for numbers 7, 8, 9, and 10 in a similar manner. Keep in mind that larger numbers have more combinations so the activities may take more time.
Summary
In this lesson plan, we explored the concept of partitioning numbers 6 to 10, a fundamental skill in mathematics. We started with objects and pictures and then created part-part-whole models to show different ways that each number can be partitioned. By breaking down whole numbers into smaller parts, learners gain a deeper understanding of numerical relationships preparing them for other skills such as addition and subtraction.
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Skill Check