# One digit by two digit Multiplication

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## Objective

SWBAT represent one-digit by two-digit multiplication, using area models.

#### Big Idea

Students compute one-digit by two digit multiplication in a movement activity.

## Number Hook - Magic Trick

4 minutes

This number trick is called Give Me 5.

I ask students to think of a number. Then they add the next consecutive number to it. Then they will add 9 to that number and then divide by two. Then they subtract their original number.  The answer is 5.

I choose this number trick for one purpose only.  It became apparent that my students didn't know what the word consecutive was.  I chose this engagement tactic solely to reinforce the concept and word consecutive.  After this trick and by repeating the word consecutive, I am confident my students now know what consecutive means.

## Warm Up

7 minutes

This warm up is called Finger Flash Match. This will be the first time my students do this so I take a little bit longer to explain the directions.  I write five equations in which a multiplication is followed by an unknown addition. When I point to the equation with my pointer, students flash the number, using their fingers, to solve for the unknown.  I display:

82 = 8 x 10 + d  (students should hold up 2 fingers)

9 x 4 + n = 42

37 = 6 x 6 + s

96 = 10 x 9 + h

6 x 9 + b = 58

When students work to figure out the unknown in the above equations, it is generally quiet to allow for think time.  This is a quick activity and I move quickly through it.

This is an important skill for students to master.  CCSS 4.OA.2 states that students will use a symbol to represent the unknown number in a problem. While this is not a comprehensive lesson or assessment of that task, it does get students thinking about unknowns and used to seeing symbols or letters to represent numbers.

## Concept development

40 minutes

I begin this lesson by modeling the area model for multiplication. I show this by decomposing a 2-digit number into tens and ones, and then model area representations  and partial product arrays. This lesson provides conceptual understanding of what occurs in a 2-digit by one-digit multiplication problem. Partial product models serve as transitions to understanding the standard multiplication algorithm.

After I show the area model, we do several together.  Students build the area models on  personal whiteboards that have dots on one side. They can then build the rectangles, using the correct amount of dots to visually see thew square units. I find this step to be necessary before using a paper and pencil model.

Then I have students participate in an activity I call "Walk the Room."  Students will use clipboards as they walk around the room to solve the problems that are posted. All of the problems posted are written horizontally. I purposely chose to have problems written horizontally to dissuade students from using the shortcut or standard algorithm they may have learned from parents or others. I have many two-digit by one-digit multiplication number sentences hanging around the room for students to solve. They do not need to solve all of them, there are a lot. I tell students that I would like theme to solve between 6 and 10 problems. Students can wander to a problem that is not being completed by another student.

The area model is the easiest method for students to use.  By teaching it first, I am able to build conceptual understanding for all students and provide a method that any student can use. For students that struggle with the area model, I pull them out during my re-teach time and present other alternatives, such as using base ten blocks.  Students would build a number like 26 and then do that 4 times to model 4 x 26.  I then make connections between the base ten block method and the area model method by rearranging the base ten blocks to show the two columns of tens together in four rows and the  six columns of ones together in four rows.

This video shows what my classroom look like before students enter and "walk the room."

This video shows what the the area model for multiplication looks like. This is not my showme video, but is similar to how I present this model to students.

If the video does not play click here

## Student debrief - Wrap up

10 minutes

I wanted students to find the product of both of these numbers sentences 2 x 30 and 2 x 37.

I ended up helping, observing, and listening to many students, and ran out of time.  It also became glaringly apparent during the course of this lesson that the material was difficult for my students and confusing. See the Reflection section in this lesson for more information and my ideas on what I will do next.