##
* *Reflection: Diverse Entry Points
One digit by two digit Multiplication - Section 3: Concept development

As seen in my reflection video, I need to make adjustments to the flow of this unit. I had anticipated being able to move onto estimating products after this lesson, but it became very apparent that I need to slow down and give students more time to practice this concept. Some students were able to make sense of the model and use the model to find products. For most of my students, this lesson was difficult.

In examining students work and through my questioning, I think there are several reasons why this lesson was difficult for students. As seen in this second student video, the model wasn't quite making sense to her, and it became a bit of a guessing game in trying to figure out where numbers go and which numbers go where. This was a common error among many of my students. This student simply knew there were three digits that needed to go on the area model somewhere. She wasn't connecting that the 70 + 3 came from the 73.

Another confusing point for many of my students was that they were not connecting their previous work with multiplying by multiples of tens to the area model. I need to create another lesson and provide more scaffolds for them in order to develop this concept and help students see **patterns **in multiplying by multiples of ten and the relationship to the area model when separating the tens and ones.

See this next lesson in which students can practice multiplying numbers by multiples of ten as a great example of informal formative assessment and adjusting my instruction as necessary based on students' needs.

*Adjustments needed*

*Diverse Entry Points: Adjustments needed*

# One digit by two digit Multiplication

Lesson 5 of 22

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

*61 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.

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#### Warm Up

*7 min*

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.

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#### Concept development

*40 min*

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.

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#### Student debrief - Wrap up

*10 min*

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.

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- UNIT 1: Getting to Know You- First Days of School
- UNIT 2: Multiplication with Whole Numbers
- UNIT 3: Place Value
- UNIT 4: Understanding Division and Remainders
- UNIT 5: Operations with Fractions
- UNIT 6: Fraction Equivalents and Ordering Fractions
- UNIT 7: Division with Whole Numbers
- UNIT 8: Place value
- UNIT 9: Geometry
- UNIT 10: Measurment
- UNIT 11: Fractions and Decimals

- LESSON 1: Multiplicative Comparison Problems
- LESSON 2: Finding Factors and Prime Numbers
- LESSON 3: Multiplication arrays
- LESSON 4: Mental Math and Multiplication with Tens
- LESSON 5: One digit by two digit Multiplication
- LESSON 6: Multiplying multiples of ten - Not your Daily Grind
- LESSON 7: Multiplying one digit by two digits using the AREA MODEL
- LESSON 8: Methods of One-Digit by Two-Digit Multiplication
- LESSON 9: Compare methods of one digit by double digit multiplication
- LESSON 10: Practice Makes Perfect
- LESSON 11: Two-Digit by Two-Digit Multiplication
- LESSON 12: Looking at Different Multiplication Methods
- LESSON 13: Multplication Application with Food Service Staff
- LESSON 14: Multiplication Methods using COMPUTERS!
- LESSON 15: Multiplication and First Quarter Assessment
- LESSON 16: Using Games to practice multi-digit multiplication
- LESSON 17: Multiplication Bingo - Game Day 2
- LESSON 18: Estimate Products
- LESSON 19: Multiplication and Problem Solving to Make Bracelets Day 1
- LESSON 20: Multiplication and Problem Solving to Make Bracelets Day 2
- LESSON 21: Bracelet Wrap Up
- LESSON 22: Multiplication Card Game and Factorial Fun