My students love to distribute mail around the building, so I think it will be fun to allow them to see how the distributive property can help them deliver smaller numbers to help them better understand multiplication. I want my students to gain understanding of how distributive property can help them break a one digit number multiplied by a two digit number down into an (one by one) multiplication problem.
Materials: colors, pencils, grid paper
Since we have been exploring how to multiply by multiples of ten, my students are ready explore how distributive property can help them break apart numbers to make them easier to multiply.
I take into consideration that my students need to be able to reason about their answers. I do not want them giving answers that are obviously wrong.
To do this, I ask a student to build 4 rows of 50 using base tens (make the connection with 4 x 5 by writing it on the board). Ask them how much 4 rows of 50 is and have them explain how they know.
Then I ask another student build 4 rows of 3 (put 4x3 on the board). Again, I ask a student for the product.
I model and explain how to show 4 rows of 53 (write on the board 4x53). Again, I ask students how much this is and how did they determine this method.
I put another problem on the board (say 3 x 34). I ask students if they can model (in pairs?) this problem, and find the product, using the base ten materials. When they are done, I discuss as a class.
Students Responses: Some students are able to explain; however, their responses are very vague. I will model how to explain mathematically through out the lesson to ensure students are able to explain fluently.
If students struggle to grasp this concept, I will continue to demonstrate and probe further until they are ready to move deeper into the lesson.
MP2-Reason abstractly and quantitatively.
I start by saying, "Mailers Get Ready!"
Because students learn differently, I want my students to experience different ways to solve problems. In this portion of the lesson I want to make sure that students understand how the distributive property can be used to help them solve multiplication problems. Hopefully while working students will find ways to use obvious patterns to reason about their answers.
I set them loose to work in pairs and record their answers on their worksheet. Students will continue practicing on the steps I modeled in the warm up section. I remind students to use base ten materials to create models that represent their problems. These models can be used to help them understand the value of the digit. As students are working, I will circle the room to check for understanding. Often students will need a little guidance through careful questioning to help them make connections. I take notes as I listen in on their conversation. I use those notes to correct any misconceptions when they are finished with the given task.
What will you do first here?
How do you know?
What is the product of both multiplication problems?
Since you have two products here, what do you need to do to combine them?
Can you explain what you did?
What did you notice about the value of the digits when you added your products?
MP8-Look for and express regularity in repeated reasoning.
After students are finished working I will invite 1-2 students to share out what they noticed.
Some students are able to illustrate their answers, and some students are able to uncover what they illustrate by identifying the underlying function of the problem.
I start by saying, “Are you guys to place the stamp on this lesson?"
In this section I want my students to have an opportunity to break numbers apart using the distributive property which greatly assists the mental math process. I encourage students to build models using the base-ten blocks to help them better understand the value of a digit. Students need to experience different ways to solve problems mathematically. To help assist struggling students I will leave the mathematical model used in the warm up as a guide.
Students will be given 15 minutes or so to express and solve the given problems using distributive property. As students are working, I will circle the room to check for understanding.
How does this process make it easier for you to multiply?
After you break down the problem, how do you find your answer? Explain?
Can you represent this problem if you had a different sum? Why/How?
Identify the number of rows you have?
What if you only circled groups of tens, how many ones will be left over?
Having students to explain the process, help them connect to the repeated strategies performed. I hope for them to use illustration and prior knowledge to be able to reason and explain better. Seemly students are able to use both concepts to express their problem solving decisions. MP2,8
I tell students it is time to show me what you know. Who is ready to show me how to deliver numbers in smaller pieces so it can help you understand the process of multiplying?
Students will use their math journal to create their own math problem to break down and explain using the skills they have learned. I will use their notes to asses students readiness.