This lesson plan will introduce your learner to the commutative property of addition. We will explore the concept of writing addition equations in different ways using part-part-whole scenarios and first-then-now stories. By understanding that the sum remains the same even when the order of the addends is changed, your learner will grasp the concept of commutativity.
Here are a few concepts that are helpful to know for the lesson:
Commutative Property of Addition: The commutative property of addition states that the order of the addends can be changed without changing the sum. In other words, when we add two numbers, the result is the same regardless of the order in which we add them.
Maintaining Equivalence: It's important for learners to understand that the expressions are equivalent even when the addends are rearranged. For example, 3 + 2 is equivalent to 2 + 3 because they both have a sum of five. This can also be expressed as 3 + 2 = 2 + 3.
Commutativity for Other Operations: It's important to note that while the commutative property applies to addition and multiplication, it does not extend to subtraction or division. For subtraction and division, changing the order of numbers will generally result in different outcomes.
Teaching Plan
The following activities will help your learner become confident in understanding and applying the commutative property of addition.
Examples and visuals to support the lesson:
1. Commutative Property and Part-Part-Whole Stories
This activity will introduce your learner to the concept of commutativity using part-part-whole relationships.
Provide your learner with a part-part-whole scenario and have them write an addition equation that shows the relationship between the parts and the whole.
Using an example of two adult cats and four kittens, your learner may write the equation as 2 + 4 = 6 or 4 + 2 = 6. Discuss how the addends can be written in either order, but there are still six cats altogether.
Also, encourage your learner to vary the position of the equal sign. For example, the equation 2 + 4 = 6 can be written as 6 = 2 + 4.
Provide a variety of contexts and continue to have your learner write equations in different ways. Work towards the generalized statement: If we change the order of the addends, the sum remains the same.
Skill Check
I can write addition equations different ways.
2. Commutive Property and First-Then-Now Stories
In this activity, we'll see how the commutative property applies to first-then-now stories.
Note that the structure of first-then-now stories can make it more difficult to see that commutativity applies. For example, the same sum is given by each of the following sentences: At first, there is one child on the swings and then three more arrive. At first, there are three children on the swings and then one more arrives.
Incorporating concrete objects or pictures can help your learner understand how commutativity applies. Show your learner pictures for the first story problem and tell the story together. Then write the corresponding equation as 1 + 3 = 4.
Next, ask your learner to think about what the sum would be if the children arrived in the other order. Again, show the pictures and tell the story together. Then write the corresponding equation as 3 + 1 = 4.
Now discuss and compare the two sets of pictures and equations. Show your learner that the stories are equivalent by writing 1 + 3 = 3 + 1.
Skill Check
I know that the sum stays the same even if the order of the addends changes.
3. Defining the Commutative Property of Addition
Once your learner has explored different kinds of contexts, introduce the term "commutative."
Explain that the commutative property of addition means that we can change the order of the addends and the sum remains the same.
Emphasize that whatever the value of the addends, however big or small, we can change their order and the sum remains the same.
Continue to repeat and reinforce the generalized statement until your learner is able to express it on their own. ("If we change the order of the addends, the sum remains the same.")
Skill Check
I know that the commutative property means we can add numbers in any order and the sum stays the same.
4. Practice and Review
Next, provide your learner with opportunities to apply their understanding of the commutative property.
Review equations of the form a + b = b + a that your learner has seen during this lesson. For example, 3 + 1 = 1 + 3.
Emphasize that although the equation has more than one number on both sides, it is still an equation. Point out that each side of the equation is equivalent. Using the example of 3 + 1 = 1 + 3, each side of the equation has a sum of 4.
Provide your learner with tasks for them to practice completing equations such as 1 + 6 = ? + 1.
Skill Check
I can use the commutative property to solve addition problems.
Summary
Through part-part-whole scenarios and first-then-now stories, this lesson plan has introduced your learner to the commutative property of addition. This property allows us to change the order of addends in an addition equation without changing the sum. By recognizing and applying the commutative property, your learner can enhance their understanding of addition and strengthen their problem-solving skills. Continued practice with different contexts and equations will further solidify this important mathematical concept.
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Skill Check