Note to the Teacher:
The concepts taught in this lesson-the commutative property and the relationship between addition and subtraction-are multi-layered and complex. In this lesson, students are introduced to the idea that addition and subtraction are related for the first time. Expect this to be a process! At this point, I want students to be able to notice that the the two operations are related in some way, even if they aren't able to explain how they are opposite yet.
Review:
We have been investigating the relationship between addition problems that have the same two addends. We saw that it didn’t matter what order you put the numbers in, they equal the same sum. Today we are going to look at how addition and subtraction can be related. We are going to look at two problems-one is an addition problem, one is a subtraction problem. I want us to see if we can figure out how these two problems are the same and how they are different.
Connect:
Addition and subtraction are opposites. In addition we get more. In subtraction we take away. But they are related. When we figure out how they are related, it will help us solve problems in our head.
Objective: How are the addition and subtraction facts related?
I'll quickly read one of the cookie problems and share a student's answer from the Flip Flop plan. Go here to see this plan!
I have 5 cookies. I get 3 more cookies. How many cookies do I have now?
Today we are going to figure out a different story. In this story, you are going to get some cookies, but then you are going to eat those cookies right away!
Now you have 8 cookies. You eat the 3 new cookies! How many cookies do you have now?
Guiding Questions:
What is happening in this problem?
How is this problem similar to the problem we just read and solved?
Partner talk: Solve this problem with a partner. How many cookies do you have now?
How are the number sentences the same?
How are they different?
Why does the subtraction sentence start with 8? Let’s look at both of these stories with 2 different colors of cubes. I’ll act out the problem with a student.
Think Aloud: We had 5, we put 3 with it and then we had 8. When we took the 3 away, it was the opposite of getting more cookies, we took them right away! And now we only have 5 left.
During this part of the lesson, I'll give each student or each pair of students 10 cubes to model the problem. I'll have one student to also model the action on the class number line. The Common Core standards ask students to be able to model problems in a variety of ways, this portion of the lesson exposes students to at least 2 ways to solve.
Focus Question: How are these story problems the same and different?
Present problem:
I have 5 cookies. My mom gives me 4 more cookies. How many cookies do I have now?
Students model with cubes and then watch as we model what they did on the number line.
I have 9 cookies. I eat my 4 of the cookies. How many cookies do I have now?
Students model with cubes and then watch as we model what they did on the number line.
Debrief questions:
On the number line-where were the 6 new cookies? I'll focus on how they were the jumps that we made.
What happened when we took the cookies away on the number line? Why did we go back to where we started?
Write number sentences for both. How are these number sentences the same? How are they different?
See video for how I differentiate student work, particularly with scaffolded questioning.
The attached document is the master copy of the independent practice. I left the numbers out so you can write numbers in to the problem that match your students' needs. They also provide space for students to write about their strategy, which is aligned to the CCSS emphasis on writing across the curriculum.
We will close the lesson with all students back together on the carpet.
I’ll choose related facts that a student had and ask:
-What is the answer to the addition sentence?
-How can the addition sentence help you with this subtraction sentence?